-/* Decimal Number module for the decNumber C Library
- Copyright (C) 2005 Free Software Foundation, Inc.
+/* Decimal number arithmetic module for the decNumber C Library.
+ Copyright (C) 2005, 2007, 2009 Free Software Foundation, Inc.
Contributed by IBM Corporation. Author Mike Cowlishaw.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
- Software Foundation; either version 2, or (at your option) any later
+ Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
- You should have received a copy of the GNU General Public License
- along with GCC; see the file COPYING. If not, write to the Free
- Software Foundation, 59 Temple Place - Suite 330, Boston, MA
- 02111-1307, USA. */
-
-/* ------------------------------------------------------------------ */
-/* This module comprises the routines for Standard Decimal Arithmetic */
-/* as defined in the specification which may be found on the */
-/* http://www2.hursley.ibm.com/decimal web pages. It implements both */
-/* the full ('extended') arithmetic and the simpler ('subset') */
-/* arithmetic. */
-/* */
-/* Usage notes: */
-/* */
-/* 1. This code is ANSI C89 except: */
-/* */
-/* a) Line comments (double forward slash) are used. (Most C */
-/* compilers accept these. If yours does not, a simple script */
-/* can be used to convert them to ANSI C comments.) */
-/* */
+Under Section 7 of GPL version 3, you are granted additional
+permissions described in the GCC Runtime Library Exception, version
+3.1, as published by the Free Software Foundation.
+
+You should have received a copy of the GNU General Public License and
+a copy of the GCC Runtime Library Exception along with this program;
+see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
+<http://www.gnu.org/licenses/>. */
+
+/* ------------------------------------------------------------------ */
+/* Decimal Number arithmetic module */
+/* ------------------------------------------------------------------ */
+/* This module comprises the routines for arbitrary-precision General */
+/* Decimal Arithmetic as defined in the specification which may be */
+/* found on the General Decimal Arithmetic pages. It implements both */
+/* the full ('extended') arithmetic and the simpler ('subset') */
+/* arithmetic. */
+/* */
+/* Usage notes: */
+/* */
+/* 1. This code is ANSI C89 except: */
+/* */
+/* a) C99 line comments (double forward slash) are used. (Most C */
+/* compilers accept these. If yours does not, a simple script */
+/* can be used to convert them to ANSI C comments.) */
+/* */
/* b) Types from C99 stdint.h are used. If you do not have this */
-/* header file, see the User's Guide section of the decNumber */
-/* documentation; this lists the necessary definitions. */
-/* */
-/* c) If DECDPUN>4, non-ANSI 64-bit 'long long' types are used. */
-/* To avoid these, set DECDPUN <= 4 (see documentation). */
-/* */
+/* header file, see the User's Guide section of the decNumber */
+/* documentation; this lists the necessary definitions. */
+/* */
+/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */
+/* uint64_t types may be used. To avoid these, set DECUSE64=0 */
+/* and DECDPUN<=4 (see documentation). */
+/* */
+/* The code also conforms to C99 restrictions; in particular, */
+/* strict aliasing rules are observed. */
+/* */
/* 2. The decNumber format which this library uses is optimized for */
/* efficient processing of relatively short numbers; in particular */
/* it allows the use of fixed sized structures and minimizes copy */
/* and move operations. It does, however, support arbitrary */
/* precision (up to 999,999,999 digits) and arbitrary exponent */
/* range (Emax in the range 0 through 999,999,999 and Emin in the */
-/* range -999,999,999 through 0). */
-/* */
-/* 3. Operands to operator functions are never modified unless they */
+/* range -999,999,999 through 0). Mathematical functions (for */
+/* example decNumberExp) as identified below are restricted more */
+/* tightly: digits, emax, and -emin in the context must be <= */
+/* DEC_MAX_MATH (999999), and their operand(s) must be within */
+/* these bounds. */
+/* */
+/* 3. Logical functions are further restricted; their operands must */
+/* be finite, positive, have an exponent of zero, and all digits */
+/* must be either 0 or 1. The result will only contain digits */
+/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */
+/* */
+/* 4. Operands to operator functions are never modified unless they */
/* are also specified to be the result number (which is always */
-/* permitted). Other than that case, operands may not overlap. */
-/* */
-/* 4. Error handling: the type of the error is ORed into the status */
+/* permitted). Other than that case, operands must not overlap. */
+/* */
+/* 5. Error handling: the type of the error is ORed into the status */
/* flags in the current context (decContext structure). The */
/* SIGFPE signal is then raised if the corresponding trap-enabler */
-/* flag in the decContext is set (is 1). */
-/* */
+/* flag in the decContext is set (is 1). */
+/* */
/* It is the responsibility of the caller to clear the status */
-/* flags as required. */
-/* */
+/* flags as required. */
+/* */
/* The result of any routine which returns a number will always */
/* be a valid number (which may be a special value, such as an */
-/* Infinity or NaN). */
-/* */
-/* 5. The decNumber format is not an exchangeable concrete */
+/* Infinity or NaN). */
+/* */
+/* 6. The decNumber format is not an exchangeable concrete */
/* representation as it comprises fields which may be machine- */
-/* dependent (big-endian or little-endian, for example). */
+/* dependent (packed or unpacked, or special length, for example). */
/* Canonical conversions to and from strings are provided; other */
-/* conversions are available in separate modules. */
-/* */
-/* 6. Normally, input operands are assumed to be valid. Set DECCHECK */
+/* conversions are available in separate modules. */
+/* */
+/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */
/* to 1 for extended operand checking (including NULL operands). */
/* Results are undefined if a badly-formed structure (or a NULL */
-/* NULL pointer to a structure) is provided, though with DECCHECK */
+/* pointer to a structure) is provided, though with DECCHECK */
/* enabled the operator routines are protected against exceptions. */
/* (Except if the result pointer is NULL, which is unrecoverable.) */
-/* */
+/* */
/* However, the routines will never cause exceptions if they are */
/* given well-formed operands, even if the value of the operands */
/* is inappropriate for the operation and DECCHECK is not set. */
-/* */
-/* 7. Subset arithmetic is available only if DECSUBSET is set to 1. */
+/* (Except for SIGFPE, as and where documented.) */
+/* */
+/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */
/* ------------------------------------------------------------------ */
-/* Implementation notes for maintenance of this module: */
-/* */
-/* 1. Storage leak protection: Routines which use malloc are not */
+/* Implementation notes for maintenance of this module: */
+/* */
+/* 1. Storage leak protection: Routines which use malloc are not */
/* permitted to use return for fastpath or error exits (i.e., */
-/* they follow strict structured programming conventions). */
+/* they follow strict structured programming conventions). */
/* Instead they have a do{}while(0); construct surrounding the */
-/* code which is protected -- break may be used from this. */
-/* Other routines are allowed to use the return statement inline. */
-/* */
-/* Storage leak accounting can be enabled using DECALLOC. */
-/* */
-/* 2. All loops use the for(;;) construct. Any do construct is for */
-/* protection as just described. */
-/* */
+/* code which is protected -- break may be used to exit this. */
+/* Other routines can safely use the return statement inline. */
+/* */
+/* Storage leak accounting can be enabled using DECALLOC. */
+/* */
+/* 2. All loops use the for(;;) construct. Any do construct does */
+/* not loop; it is for allocation protection as just described. */
+/* */
/* 3. Setting status in the context must always be the very last */
/* action in a routine, as non-0 status may raise a trap and hence */
/* the call to set status may not return (if the handler uses long */
/* jump). Therefore all cleanup must be done first. In general, */
-/* to achieve this we accumulate status and only finally apply it */
-/* by calling decContextSetStatus (via decStatus). */
-/* */
-/* Routines which allocate storage cannot, therefore, use the */
-/* 'top level' routines which could cause a non-returning */
+/* to achieve this status is accumulated and is only applied just */
+/* before return by calling decContextSetStatus (via decStatus). */
+/* */
+/* Routines which allocate storage cannot, in general, use the */
+/* 'top level' routines which could cause a non-returning */
/* transfer of control. The decXxxxOp routines are safe (do not */
/* call decStatus even if traps are set in the context) and should */
-/* be used instead (they are also a little faster). */
-/* */
+/* be used instead (they are also a little faster). */
+/* */
/* 4. Exponent checking is minimized by allowing the exponent to */
/* grow outside its limits during calculations, provided that */
/* the decFinalize function is called later. Multiplication and */
/* require more careful checks because of the risk of 31-bit */
/* overflow (the most negative valid exponent is -1999999997, for */
/* a 999999999-digit number with adjusted exponent of -999999999). */
-/* */
+/* */
/* 5. Rounding is deferred until finalization of results, with any */
/* 'off to the right' data being represented as a single digit */
/* residue (in the range -1 through 9). This avoids any double- */
-/* rounding when more than one shortening takes place (for */
-/* example, when a result is subnormal). */
-/* */
+/* rounding when more than one shortening takes place (for */
+/* example, when a result is subnormal). */
+/* */
/* 6. The digits count is allowed to rise to a multiple of DECDPUN */
/* during many operations, so whole Units are handled and exact */
/* accounting of digits is not needed. The correct digits value */
/* is found by decGetDigits, which accounts for leading zeros. */
/* This must be called before any rounding if the number of digits */
-/* is not known exactly. */
-/* */
-/* 7. We use the multiply-by-reciprocal 'trick' for partitioning */
+/* is not known exactly. */
+/* */
+/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */
/* numbers up to four digits, using appropriate constants. This */
/* is not useful for longer numbers because overflow of 32 bits */
/* would lead to 4 multiplies, which is almost as expensive as */
-/* a divide (unless we assumed floating-point multiply available). */
-/* */
-/* 8. Unusual abbreviations possibly used in the commentary: */
-/* lhs -- left hand side (operand, of an operation) */
-/* lsd -- least significant digit (of coefficient) */
-/* lsu -- least significant Unit (of coefficient) */
-/* msd -- most significant digit (of coefficient) */
-/* msu -- most significant Unit (of coefficient) */
-/* rhs -- right hand side (operand, of an operation) */
-/* +ve -- positive */
-/* -ve -- negative */
-/* ------------------------------------------------------------------ */
-
-#include <stdlib.h> /* for malloc, free, etc. */
-#include <stdio.h> /* for printf [if needed] */
-#include <string.h> /* for strcpy */
-#include <ctype.h> /* for lower */
-#include "decNumber.h" /* base number library */
-#include "decNumberLocal.h" /* decNumber local types, etc. */
+/* a divide (unless a floating-point or 64-bit multiply is */
+/* assumed to be available). */
+/* */
+/* 8. Unusual abbreviations that may be used in the commentary: */
+/* lhs -- left hand side (operand, of an operation) */
+/* lsd -- least significant digit (of coefficient) */
+/* lsu -- least significant Unit (of coefficient) */
+/* msd -- most significant digit (of coefficient) */
+/* msi -- most significant item (in an array) */
+/* msu -- most significant Unit (of coefficient) */
+/* rhs -- right hand side (operand, of an operation) */
+/* +ve -- positive */
+/* -ve -- negative */
+/* ** -- raise to the power */
+/* ------------------------------------------------------------------ */
+
+#include <stdlib.h> /* for malloc, free, etc. */
+#include <stdio.h> /* for printf [if needed] */
+#include <string.h> /* for strcpy */
+#include <ctype.h> /* for lower */
+#include "dconfig.h" /* for GCC definitions */
+#include "decNumber.h" /* base number library */
+#include "decNumberLocal.h" /* decNumber local types, etc. */
/* Constants */
-/* Public constant array: powers of ten (powers[n]==10**n) */
-const uInt powers[] = { 1, 10, 100, 1000, 10000, 100000, 1000000,
- 10000000, 100000000, 1000000000
-};
+/* Public lookup table used by the D2U macro */
+const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
-/* Local constants */
-#define DIVIDE 0x80 /* Divide operators */
-#define REMAINDER 0x40 /* .. */
-#define DIVIDEINT 0x20 /* .. */
-#define REMNEAR 0x10 /* .. */
-#define COMPARE 0x01 /* Compare operators */
-#define COMPMAX 0x02 /* .. */
-#define COMPMIN 0x03 /* .. */
-#define COMPNAN 0x04 /* .. [NaN processing] */
-
-#define DEC_sNaN 0x40000000 /* local status: sNaN signal */
-#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */
+#define DECVERB 1 /* set to 1 for verbose DECCHECK */
+#define powers DECPOWERS /* old internal name */
-static Unit one[] = { 1 }; /* Unit array of 1, used for incrementing */
+/* Local constants */
+#define DIVIDE 0x80 /* Divide operators */
+#define REMAINDER 0x40 /* .. */
+#define DIVIDEINT 0x20 /* .. */
+#define REMNEAR 0x10 /* .. */
+#define COMPARE 0x01 /* Compare operators */
+#define COMPMAX 0x02 /* .. */
+#define COMPMIN 0x03 /* .. */
+#define COMPTOTAL 0x04 /* .. */
+#define COMPNAN 0x05 /* .. [NaN processing] */
+#define COMPSIG 0x06 /* .. [signaling COMPARE] */
+#define COMPMAXMAG 0x07 /* .. */
+#define COMPMINMAG 0x08 /* .. */
+
+#define DEC_sNaN 0x40000000 /* local status: sNaN signal */
+#define BADINT (Int)0x80000000 /* most-negative Int; error indicator */
+/* Next two indicate an integer >= 10**6, and its parity (bottom bit) */
+#define BIGEVEN (Int)0x80000002
+#define BIGODD (Int)0x80000003
+
+static Unit uarrone[1]={1}; /* Unit array of 1, used for incrementing */
/* Granularity-dependent code */
#if DECDPUN<=4
-#define eInt Int /* extended integer */
-#define ueInt uInt /* unsigned extended integer */
+ #define eInt Int /* extended integer */
+ #define ueInt uInt /* unsigned extended integer */
/* Constant multipliers for divide-by-power-of five using reciprocal */
/* multiply, after removing powers of 2 by shifting, and final shift */
/* of 17 [we only need up to **4] */
-static const uInt multies[] = { 131073, 26215, 5243, 1049, 210 };
-
+ static const uInt multies[]={131073, 26215, 5243, 1049, 210};
/* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
-#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
+ #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
#else
- /* For DECDPUN>4 we currently use non-ANSI 64-bit types. These could */
- /* be replaced by subroutine calls later. */
-#ifdef long
-#undef long
-#endif
-typedef signed long long Long;
-typedef unsigned long long uLong;
-#define eInt Long /* extended integer */
-#define ueInt uLong /* unsigned extended integer */
+ /* For DECDPUN>4 non-ANSI-89 64-bit types are needed. */
+ #if !DECUSE64
+ #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
+ #endif
+ #define eInt Long /* extended integer */
+ #define ueInt uLong /* unsigned extended integer */
#endif
/* Local routines */
-static decNumber *decAddOp (decNumber *, decNumber *, decNumber *,
- decContext *, uByte, uInt *);
-static void decApplyRound (decNumber *, decContext *, Int, uInt *);
-static Int decCompare (decNumber * lhs, decNumber * rhs);
-static decNumber *decCompareOp (decNumber *, decNumber *, decNumber *,
- decContext *, Flag, uInt *);
-static void decCopyFit (decNumber *, decNumber *, decContext *,
- Int *, uInt *);
-static decNumber *decDivideOp (decNumber *, decNumber *, decNumber *,
- decContext *, Flag, uInt *);
-static void decFinalize (decNumber *, decContext *, Int *, uInt *);
-static Int decGetDigits (Unit *, Int);
-#if DECSUBSET
-static Int decGetInt (decNumber *, decContext *);
-#else
-static Int decGetInt (decNumber *);
-#endif
-static decNumber *decMultiplyOp (decNumber *, decNumber *, decNumber *,
- decContext *, uInt *);
-static decNumber *decNaNs (decNumber *, decNumber *, decNumber *, uInt *);
-static decNumber *decQuantizeOp (decNumber *, decNumber *, decNumber *,
- decContext *, Flag, uInt *);
-static void decSetCoeff (decNumber *, decContext *, Unit *,
- Int, Int *, uInt *);
-static void decSetOverflow (decNumber *, decContext *, uInt *);
-static void decSetSubnormal (decNumber *, decContext *, Int *, uInt *);
-static Int decShiftToLeast (Unit *, Int, Int);
-static Int decShiftToMost (Unit *, Int, Int);
-static void decStatus (decNumber *, uInt, decContext *);
-static Flag decStrEq (const char *, const char *);
-static void decToString (decNumber *, char[], Flag);
-static decNumber *decTrim (decNumber *, Flag, Int *);
-static Int decUnitAddSub (Unit *, Int, Unit *, Int, Int, Unit *, Int);
-static Int decUnitCompare (Unit *, Int, Unit *, Int, Int);
+static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
+ decContext *, uByte, uInt *);
+static Flag decBiStr(const char *, const char *, const char *);
+static uInt decCheckMath(const decNumber *, decContext *, uInt *);
+static void decApplyRound(decNumber *, decContext *, Int, uInt *);
+static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
+static decNumber * decCompareOp(decNumber *, const decNumber *,
+ const decNumber *, decContext *,
+ Flag, uInt *);
+static void decCopyFit(decNumber *, const decNumber *, decContext *,
+ Int *, uInt *);
+static decNumber * decDecap(decNumber *, Int);
+static decNumber * decDivideOp(decNumber *, const decNumber *,
+ const decNumber *, decContext *, Flag, uInt *);
+static decNumber * decExpOp(decNumber *, const decNumber *,
+ decContext *, uInt *);
+static void decFinalize(decNumber *, decContext *, Int *, uInt *);
+static Int decGetDigits(Unit *, Int);
+static Int decGetInt(const decNumber *);
+static decNumber * decLnOp(decNumber *, const decNumber *,
+ decContext *, uInt *);
+static decNumber * decMultiplyOp(decNumber *, const decNumber *,
+ const decNumber *, decContext *,
+ uInt *);
+static decNumber * decNaNs(decNumber *, const decNumber *,
+ const decNumber *, decContext *, uInt *);
+static decNumber * decQuantizeOp(decNumber *, const decNumber *,
+ const decNumber *, decContext *, Flag,
+ uInt *);
+static void decReverse(Unit *, Unit *);
+static void decSetCoeff(decNumber *, decContext *, const Unit *,
+ Int, Int *, uInt *);
+static void decSetMaxValue(decNumber *, decContext *);
+static void decSetOverflow(decNumber *, decContext *, uInt *);
+static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
+static Int decShiftToLeast(Unit *, Int, Int);
+static Int decShiftToMost(Unit *, Int, Int);
+static void decStatus(decNumber *, uInt, decContext *);
+static void decToString(const decNumber *, char[], Flag);
+static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
+static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
+ Unit *, Int);
+static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
#if !DECSUBSET
/* decFinish == decFinalize when no subset arithmetic needed */
#define decFinish(a,b,c,d) decFinalize(a,b,c,d)
#else
-static void decFinish (decNumber *, decContext *, Int *, uInt *);
-static decNumber *decRoundOperand (decNumber *, decContext *, uInt *);
+static void decFinish(decNumber *, decContext *, Int *, uInt *);
+static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
#endif
+/* Local macros */
+/* masked special-values bits */
+#define SPECIALARG (rhs->bits & DECSPECIAL)
+#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
+
/* Diagnostic macros, etc. */
#if DECALLOC
/* Handle malloc/free accounting. If enabled, our accountable routines */
/* and free routines. */
#define malloc(a) decMalloc(a)
#define free(a) decFree(a)
-#define DECFENCE 0x5a /* corruption detector */
+#define DECFENCE 0x5a /* corruption detector */
/* 'Our' malloc and free: */
-static void *decMalloc (size_t);
-static void decFree (void *);
-uInt decAllocBytes = 0; /* count of bytes allocated */
+static void *decMalloc(size_t);
+static void decFree(void *);
+uInt decAllocBytes=0; /* count of bytes allocated */
/* Note that DECALLOC code only checks for storage buffer overflow. */
-/* To check for memory leaks, the decAllocBytes variable should be */
+/* To check for memory leaks, the decAllocBytes variable must be */
/* checked to be 0 at appropriate times (e.g., after the test */
/* harness completes a set of tests). This checking may be unreliable */
/* if the testing is done in a multi-thread environment. */
#endif
#if DECCHECK
-/* Optional operand checking routines. Enabling these means that */
-/* decNumber and decContext operands to operator routines are checked */
-/* for correctness. This roughly doubles the execution time of the */
+/* Optional checking routines. Enabling these means that decNumber */
+/* and decContext operands to operator routines are checked for */
+/* correctness. This roughly doubles the execution time of the */
/* fastest routines (and adds 600+ bytes), so should not normally be */
/* used in 'production'. */
-#define DECUNUSED (void *)(0xffffffff)
-static Flag decCheckOperands (decNumber *, decNumber *, decNumber *,
- decContext *);
-static Flag decCheckNumber (decNumber *, decContext *);
+/* decCheckInexact is used to check that inexact results have a full */
+/* complement of digits (where appropriate -- this is not the case */
+/* for Quantize, for example) */
+#define DECUNRESU ((decNumber *)(void *)0xffffffff)
+#define DECUNUSED ((const decNumber *)(void *)0xffffffff)
+#define DECUNCONT ((decContext *)(void *)(0xffffffff))
+static Flag decCheckOperands(decNumber *, const decNumber *,
+ const decNumber *, decContext *);
+static Flag decCheckNumber(const decNumber *);
+static void decCheckInexact(const decNumber *, decContext *);
#endif
#if DECTRACE || DECCHECK
-/* Optional trace/debugging routines. */
-void decNumberShow (decNumber *); /* displays the components of a number */
-static void decDumpAr (char, Unit *, Int);
+/* Optional trace/debugging routines (may or may not be used) */
+void decNumberShow(const decNumber *); /* displays the components of a number */
+static void decDumpAr(char, const Unit *, Int);
#endif
/* ================================================================== */
-/* Conversions */
+/* Conversions */
/* ================================================================== */
/* ------------------------------------------------------------------ */
-/* to-scientific-string -- conversion to numeric string */
-/* to-engineering-string -- conversion to numeric string */
-/* */
-/* decNumberToString(dn, string); */
-/* decNumberToEngString(dn, string); */
-/* */
-/* dn is the decNumber to convert */
-/* string is the string where the result will be laid out */
-/* */
-/* string must be at least dn->digits+14 characters long */
-/* */
-/* No error is possible, and no status can be set. */
-/* ------------------------------------------------------------------ */
-char *
-decNumberToString (decNumber * dn, char *string)
-{
- decToString (dn, string, 0);
+/* from-int32 -- conversion from Int or uInt */
+/* */
+/* dn is the decNumber to receive the integer */
+/* in or uin is the integer to be converted */
+/* returns dn */
+/* */
+/* No error is possible. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberFromInt32(decNumber *dn, Int in) {
+ uInt unsig;
+ if (in>=0) unsig=in;
+ else { /* negative (possibly BADINT) */
+ if (in==BADINT) unsig=(uInt)1073741824*2; /* special case */
+ else unsig=-in; /* invert */
+ }
+ /* in is now positive */
+ decNumberFromUInt32(dn, unsig);
+ if (in<0) dn->bits=DECNEG; /* sign needed */
+ return dn;
+ } /* decNumberFromInt32 */
+
+decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
+ Unit *up; /* work pointer */
+ decNumberZero(dn); /* clean */
+ if (uin==0) return dn; /* [or decGetDigits bad call] */
+ for (up=dn->lsu; uin>0; up++) {
+ *up=(Unit)(uin%(DECDPUNMAX+1));
+ uin=uin/(DECDPUNMAX+1);
+ }
+ dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
+ return dn;
+ } /* decNumberFromUInt32 */
+
+/* ------------------------------------------------------------------ */
+/* to-int32 -- conversion to Int or uInt */
+/* */
+/* dn is the decNumber to convert */
+/* set is the context for reporting errors */
+/* returns the converted decNumber, or 0 if Invalid is set */
+/* */
+/* Invalid is set if the decNumber does not have exponent==0 or if */
+/* it is a NaN, Infinite, or out-of-range. */
+/* ------------------------------------------------------------------ */
+Int decNumberToInt32(const decNumber *dn, decContext *set) {
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
+ #endif
+
+ /* special or too many digits, or bad exponent */
+ if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; /* bad */
+ else { /* is a finite integer with 10 or fewer digits */
+ Int d; /* work */
+ const Unit *up; /* .. */
+ uInt hi=0, lo; /* .. */
+ up=dn->lsu; /* -> lsu */
+ lo=*up; /* get 1 to 9 digits */
+ #if DECDPUN>1 /* split to higher */
+ hi=lo/10;
+ lo=lo%10;
+ #endif
+ up++;
+ /* collect remaining Units, if any, into hi */
+ for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
+ /* now low has the lsd, hi the remainder */
+ if (hi>214748364 || (hi==214748364 && lo>7)) { /* out of range? */
+ /* most-negative is a reprieve */
+ if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
+ /* bad -- drop through */
+ }
+ else { /* in-range always */
+ Int i=X10(hi)+lo;
+ if (dn->bits&DECNEG) return -i;
+ return i;
+ }
+ } /* integer */
+ decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
+ return 0;
+ } /* decNumberToInt32 */
+
+uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
+ #endif
+ /* special or too many digits, or bad exponent, or negative (<0) */
+ if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
+ || (dn->bits&DECNEG && !ISZERO(dn))); /* bad */
+ else { /* is a finite integer with 10 or fewer digits */
+ Int d; /* work */
+ const Unit *up; /* .. */
+ uInt hi=0, lo; /* .. */
+ up=dn->lsu; /* -> lsu */
+ lo=*up; /* get 1 to 9 digits */
+ #if DECDPUN>1 /* split to higher */
+ hi=lo/10;
+ lo=lo%10;
+ #endif
+ up++;
+ /* collect remaining Units, if any, into hi */
+ for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
+
+ /* now low has the lsd, hi the remainder */
+ if (hi>429496729 || (hi==429496729 && lo>5)) ; /* no reprieve possible */
+ else return X10(hi)+lo;
+ } /* integer */
+ decContextSetStatus(set, DEC_Invalid_operation); /* [may not return] */
+ return 0;
+ } /* decNumberToUInt32 */
+
+/* ------------------------------------------------------------------ */
+/* to-scientific-string -- conversion to numeric string */
+/* to-engineering-string -- conversion to numeric string */
+/* */
+/* decNumberToString(dn, string); */
+/* decNumberToEngString(dn, string); */
+/* */
+/* dn is the decNumber to convert */
+/* string is the string where the result will be laid out */
+/* */
+/* string must be at least dn->digits+14 characters long */
+/* */
+/* No error is possible, and no status can be set. */
+/* ------------------------------------------------------------------ */
+char * decNumberToString(const decNumber *dn, char *string){
+ decToString(dn, string, 0);
return string;
-}
+ } /* DecNumberToString */
-char *
-decNumberToEngString (decNumber * dn, char *string)
-{
- decToString (dn, string, 1);
+char * decNumberToEngString(const decNumber *dn, char *string){
+ decToString(dn, string, 1);
return string;
-}
-
-/* ------------------------------------------------------------------ */
-/* to-number -- conversion from numeric string */
-/* */
-/* decNumberFromString -- convert string to decNumber */
-/* dn -- the number structure to fill */
-/* chars[] -- the string to convert ('\0' terminated) */
-/* set -- the context used for processing any error, */
-/* determining the maximum precision available */
-/* (set.digits), determining the maximum and minimum */
-/* exponent (set.emax and set.emin), determining if */
-/* extended values are allowed, and checking the */
-/* rounding mode if overflow occurs or rounding is */
-/* needed. */
-/* */
+ } /* DecNumberToEngString */
+
+/* ------------------------------------------------------------------ */
+/* to-number -- conversion from numeric string */
+/* */
+/* decNumberFromString -- convert string to decNumber */
+/* dn -- the number structure to fill */
+/* chars[] -- the string to convert ('\0' terminated) */
+/* set -- the context used for processing any error, */
+/* determining the maximum precision available */
+/* (set.digits), determining the maximum and minimum */
+/* exponent (set.emax and set.emin), determining if */
+/* extended values are allowed, and checking the */
+/* rounding mode if overflow occurs or rounding is */
+/* needed. */
+/* */
/* The length of the coefficient and the size of the exponent are */
-/* checked by this routine, so the correct error (Underflow or */
+/* checked by this routine, so the correct error (Underflow or */
/* Overflow) can be reported or rounding applied, as necessary. */
-/* */
-/* If bad syntax is detected, the result will be a quiet NaN. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberFromString (decNumber * dn, char chars[], decContext * set)
-{
- Int exponent = 0; /* working exponent [assume 0] */
- uByte bits = 0; /* working flags [assume +ve] */
- Unit *res; /* where result will be built */
- Unit resbuff[D2U (DECBUFFER + 1)]; /* local buffer in case need temporary */
- Unit *allocres = NULL; /* -> allocated result, iff allocated */
- Int need; /* units needed for result */
- Int d = 0; /* count of digits found in decimal part */
- char *dotchar = NULL; /* where dot was found */
- char *cfirst; /* -> first character of decimal part */
- char *last = NULL; /* -> last digit of decimal part */
- char *firstexp; /* -> first significant exponent digit */
- char *c; /* work */
- Unit *up; /* .. */
-#if DECDPUN>1
- Int i; /* .. */
-#endif
- Int residue = 0; /* rounding residue */
- uInt status = 0; /* error code */
-
-#if DECCHECK
- if (decCheckOperands (DECUNUSED, DECUNUSED, DECUNUSED, set))
- return decNumberZero (dn);
-#endif
-
- do
- { /* status & malloc protection */
- c = chars; /* -> input character */
- if (*c == '-')
- { /* handle leading '-' */
- bits = DECNEG;
- c++;
+/* */
+/* If bad syntax is detected, the result will be a quiet NaN. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberFromString(decNumber *dn, const char chars[],
+ decContext *set) {
+ Int exponent=0; /* working exponent [assume 0] */
+ uByte bits=0; /* working flags [assume +ve] */
+ Unit *res; /* where result will be built */
+ Unit resbuff[SD2U(DECBUFFER+9)];/* local buffer in case need temporary */
+ /* [+9 allows for ln() constants] */
+ Unit *allocres=NULL; /* -> allocated result, iff allocated */
+ Int d=0; /* count of digits found in decimal part */
+ const char *dotchar=NULL; /* where dot was found */
+ const char *cfirst=chars; /* -> first character of decimal part */
+ const char *last=NULL; /* -> last digit of decimal part */
+ const char *c; /* work */
+ Unit *up; /* .. */
+ #if DECDPUN>1
+ Int cut, out; /* .. */
+ #endif
+ Int residue; /* rounding residue */
+ uInt status=0; /* error code */
+
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
+ return decNumberZero(dn);
+ #endif
+
+ do { /* status & malloc protection */
+ for (c=chars;; c++) { /* -> input character */
+ if (*c>='0' && *c<='9') { /* test for Arabic digit */
+ last=c;
+ d++; /* count of real digits */
+ continue; /* still in decimal part */
}
- else if (*c == '+')
- c++; /* step over leading '+' */
- /* We're at the start of the number [we think] */
- cfirst = c; /* save */
- for (;; c++)
- {
- if (*c >= '0' && *c <= '9')
- { /* test for Arabic digit */
- last = c;
- d++; /* count of real digits */
- continue; /* still in decimal part */
- }
- if (*c != '.')
- break; /* done with decimal part */
- /* dot: record, check, and ignore */
- if (dotchar != NULL)
- { /* two dots */
- last = NULL; /* indicate bad */
- break;
- } /* .. and go report */
- dotchar = c; /* offset into decimal part */
- } /* c */
-
- if (last == NULL)
- { /* no decimal digits, or >1 . */
-#if DECSUBSET
- /* If subset then infinities and NaNs are not allowed */
- if (!set->extended)
- {
- status = DEC_Conversion_syntax;
- break; /* all done */
- }
- else
- {
-#endif
- /* Infinities and NaNs are possible, here */
- decNumberZero (dn); /* be optimistic */
- if (decStrEq (c, "Infinity") || decStrEq (c, "Inf"))
- {
- dn->bits = bits | DECINF;
- break; /* all done */
- }
- else
- { /* a NaN expected */
- /* 2003.09.10 NaNs are now permitted to have a sign */
- status = DEC_Conversion_syntax; /* assume the worst */
- dn->bits = bits | DECNAN; /* assume simple NaN */
- if (*c == 's' || *c == 'S')
- { /* looks like an` sNaN */
- c++;
- dn->bits = bits | DECSNAN;
- }
- if (*c != 'n' && *c != 'N')
- break; /* check caseless "NaN" */
- c++;
- if (*c != 'a' && *c != 'A')
- break; /* .. */
- c++;
- if (*c != 'n' && *c != 'N')
- break; /* .. */
- c++;
- /* now nothing, or nnnn, expected */
- /* -> start of integer and skip leading 0s [including plain 0] */
- for (cfirst = c; *cfirst == '0';)
- cfirst++;
- if (*cfirst == '\0')
- { /* "NaN" or "sNaN", maybe with all 0s */
- status = 0; /* it's good */
- break; /* .. */
- }
- /* something other than 0s; setup last and d as usual [no dots] */
- for (c = cfirst;; c++, d++)
- {
- if (*c < '0' || *c > '9')
- break; /* test for Arabic digit */
- last = c;
- }
- if (*c != '\0')
- break; /* not all digits */
- if (d > set->digits)
- break; /* too many digits */
- /* good; drop through and convert the integer */
- status = 0;
- bits = dn->bits; /* for copy-back */
- } /* NaN expected */
-#if DECSUBSET
- }
-#endif
- } /* last==NULL */
-
- if (*c != '\0')
- { /* more there; exponent expected... */
- Flag nege = 0; /* 1=negative exponent */
- if (*c != 'e' && *c != 'E')
- {
- status = DEC_Conversion_syntax;
- break;
- }
-
- /* Found 'e' or 'E' -- now process explicit exponent */
- /* 1998.07.11: sign no longer required */
- c++; /* to (expected) sign */
- if (*c == '-')
- {
- nege = 1;
- c++;
- }
- else if (*c == '+')
- c++;
- if (*c == '\0')
- {
- status = DEC_Conversion_syntax;
- break;
- }
-
- for (; *c == '0' && *(c + 1) != '\0';)
- c++; /* strip insignificant zeros */
- firstexp = c; /* save exponent digit place */
- for (;; c++)
- {
- if (*c < '0' || *c > '9')
- break; /* not a digit */
- exponent = X10 (exponent) + (Int) * c - (Int) '0';
- } /* c */
- /* if we didn't end on '\0' must not be a digit */
- if (*c != '\0')
- {
- status = DEC_Conversion_syntax;
- break;
- }
-
- /* (this next test must be after the syntax check) */
- /* if it was too long the exponent may have wrapped, so check */
- /* carefully and set it to a certain overflow if wrap possible */
- if (c >= firstexp + 9 + 1)
- {
- if (c > firstexp + 9 + 1 || *firstexp > '1')
- exponent = DECNUMMAXE * 2;
- /* [up to 1999999999 is OK, for example 1E-1000000998] */
- }
- if (nege)
- exponent = -exponent; /* was negative */
- } /* had exponent */
- /* Here when all inspected; syntax is good */
-
- /* Handle decimal point... */
- if (dotchar != NULL && dotchar < last) /* embedded . found, so */
- exponent = exponent - (last - dotchar); /* .. adjust exponent */
- /* [we can now ignore the .] */
-
- /* strip leading zeros/dot (leave final if all 0's) */
- for (c = cfirst; c < last; c++)
- {
- if (*c == '0')
- d--; /* 0 stripped */
- else if (*c != '.')
- break;
- cfirst++; /* step past leader */
- } /* c */
-
-#if DECSUBSET
- /* We can now make a rapid exit for zeros if !extended */
- if (*cfirst == '0' && !set->extended)
- {
- decNumberZero (dn); /* clean result */
- break; /* [could be return] */
+ if (*c=='.' && dotchar==NULL) { /* first '.' */
+ dotchar=c; /* record offset into decimal part */
+ if (c==cfirst) cfirst++; /* first digit must follow */
+ continue;}
+ if (c==chars) { /* first in string... */
+ if (*c=='-') { /* valid - sign */
+ cfirst++;
+ bits=DECNEG;
+ continue;}
+ if (*c=='+') { /* valid + sign */
+ cfirst++;
+ continue;}
}
-#endif
-
- /* OK, the digits string is good. Copy to the decNumber, or to
- a temporary decNumber if rounding is needed */
- if (d <= set->digits)
- res = dn->lsu; /* fits into given decNumber */
- else
- { /* rounding needed */
- need = D2U (d); /* units needed */
- res = resbuff; /* assume use local buffer */
- if (need * sizeof (Unit) > sizeof (resbuff))
- { /* too big for local */
- allocres = (Unit *) malloc (need * sizeof (Unit));
- if (allocres == NULL)
- {
- status |= DEC_Insufficient_storage;
- break;
- }
- res = allocres;
- }
+ /* *c is not a digit, or a valid +, -, or '.' */
+ break;
+ } /* c */
+
+ if (last==NULL) { /* no digits yet */
+ status=DEC_Conversion_syntax;/* assume the worst */
+ if (*c=='\0') break; /* and no more to come... */
+ #if DECSUBSET
+ /* if subset then infinities and NaNs are not allowed */
+ if (!set->extended) break; /* hopeless */
+ #endif
+ /* Infinities and NaNs are possible, here */
+ if (dotchar!=NULL) break; /* .. unless had a dot */
+ decNumberZero(dn); /* be optimistic */
+ if (decBiStr(c, "infinity", "INFINITY")
+ || decBiStr(c, "inf", "INF")) {
+ dn->bits=bits | DECINF;
+ status=0; /* is OK */
+ break; /* all done */
}
- /* res now -> number lsu, buffer, or allocated storage for Unit array */
-
- /* Place the coefficient into the selected Unit array */
-#if DECDPUN>1
- i = d % DECDPUN; /* digits in top unit */
- if (i == 0)
- i = DECDPUN;
- up = res + D2U (d) - 1; /* -> msu */
- *up = 0;
- for (c = cfirst;; c++)
- { /* along the digits */
- if (*c == '.')
- { /* ignore . [don't decrement i] */
- if (c != last)
- continue;
- break;
- }
- *up = (Unit) (X10 (*up) + (Int) * c - (Int) '0');
- i--;
- if (i > 0)
- continue; /* more for this unit */
- if (up == res)
- break; /* just filled the last unit */
- i = DECDPUN;
- up--;
- *up = 0;
- } /* c */
-#else
- /* DECDPUN==1 */
- up = res; /* -> lsu */
- for (c = last; c >= cfirst; c--)
- { /* over each character, from least */
- if (*c == '.')
- continue; /* ignore . [don't step b] */
- *up = (Unit) ((Int) * c - (Int) '0');
- up++;
- } /* c */
-#endif
-
- dn->bits = bits;
- dn->exponent = exponent;
- dn->digits = d;
-
- /* if not in number (too long) shorten into the number */
- if (d > set->digits)
- decSetCoeff (dn, set, res, d, &residue, &status);
-
- /* Finally check for overflow or subnormal and round as needed */
- decFinalize (dn, set, &residue, &status);
- /* decNumberShow(dn); */
- }
- while (0); /* [for break] */
+ /* a NaN expected */
+ /* 2003.09.10 NaNs are now permitted to have a sign */
+ dn->bits=bits | DECNAN; /* assume simple NaN */
+ if (*c=='s' || *c=='S') { /* looks like an sNaN */
+ c++;
+ dn->bits=bits | DECSNAN;
+ }
+ if (*c!='n' && *c!='N') break; /* check caseless "NaN" */
+ c++;
+ if (*c!='a' && *c!='A') break; /* .. */
+ c++;
+ if (*c!='n' && *c!='N') break; /* .. */
+ c++;
+ /* now either nothing, or nnnn payload, expected */
+ /* -> start of integer and skip leading 0s [including plain 0] */
+ for (cfirst=c; *cfirst=='0';) cfirst++;
+ if (*cfirst=='\0') { /* "NaN" or "sNaN", maybe with all 0s */
+ status=0; /* it's good */
+ break; /* .. */
+ }
+ /* something other than 0s; setup last and d as usual [no dots] */
+ for (c=cfirst;; c++, d++) {
+ if (*c<'0' || *c>'9') break; /* test for Arabic digit */
+ last=c;
+ }
+ if (*c!='\0') break; /* not all digits */
+ if (d>set->digits-1) {
+ /* [NB: payload in a decNumber can be full length unless */
+ /* clamped, in which case can only be digits-1] */
+ if (set->clamp) break;
+ if (d>set->digits) break;
+ } /* too many digits? */
+ /* good; drop through to convert the integer to coefficient */
+ status=0; /* syntax is OK */
+ bits=dn->bits; /* for copy-back */
+ } /* last==NULL */
+
+ else if (*c!='\0') { /* more to process... */
+ /* had some digits; exponent is only valid sequence now */
+ Flag nege; /* 1=negative exponent */
+ const char *firstexp; /* -> first significant exponent digit */
+ status=DEC_Conversion_syntax;/* assume the worst */
+ if (*c!='e' && *c!='E') break;
+ /* Found 'e' or 'E' -- now process explicit exponent */
+ /* 1998.07.11: sign no longer required */
+ nege=0;
+ c++; /* to (possible) sign */
+ if (*c=='-') {nege=1; c++;}
+ else if (*c=='+') c++;
+ if (*c=='\0') break;
+
+ for (; *c=='0' && *(c+1)!='\0';) c++; /* strip insignificant zeros */
+ firstexp=c; /* save exponent digit place */
+ for (; ;c++) {
+ if (*c<'0' || *c>'9') break; /* not a digit */
+ exponent=X10(exponent)+(Int)*c-(Int)'0';
+ } /* c */
+ /* if not now on a '\0', *c must not be a digit */
+ if (*c!='\0') break;
+
+ /* (this next test must be after the syntax checks) */
+ /* if it was too long the exponent may have wrapped, so check */
+ /* carefully and set it to a certain overflow if wrap possible */
+ if (c>=firstexp+9+1) {
+ if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
+ /* [up to 1999999999 is OK, for example 1E-1000000998] */
+ }
+ if (nege) exponent=-exponent; /* was negative */
+ status=0; /* is OK */
+ } /* stuff after digits */
+
+ /* Here when whole string has been inspected; syntax is good */
+ /* cfirst->first digit (never dot), last->last digit (ditto) */
+
+ /* strip leading zeros/dot [leave final 0 if all 0's] */
+ if (*cfirst=='0') { /* [cfirst has stepped over .] */
+ for (c=cfirst; c<last; c++, cfirst++) {
+ if (*c=='.') continue; /* ignore dots */
+ if (*c!='0') break; /* non-zero found */
+ d--; /* 0 stripped */
+ } /* c */
+ #if DECSUBSET
+ /* make a rapid exit for easy zeros if !extended */
+ if (*cfirst=='0' && !set->extended) {
+ decNumberZero(dn); /* clean result */
+ break; /* [could be return] */
+ }
+ #endif
+ } /* at least one leading 0 */
+
+ /* Handle decimal point... */
+ if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */
+ exponent-=(last-dotchar); /* adjust exponent */
+ /* [we can now ignore the .] */
+
+ /* OK, the digits string is good. Assemble in the decNumber, or in */
+ /* a temporary units array if rounding is needed */
+ if (d<=set->digits) res=dn->lsu; /* fits into supplied decNumber */
+ else { /* rounding needed */
+ Int needbytes=D2U(d)*sizeof(Unit);/* bytes needed */
+ res=resbuff; /* assume use local buffer */
+ if (needbytes>(Int)sizeof(resbuff)) { /* too big for local */
+ allocres=(Unit *)malloc(needbytes);
+ if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
+ res=allocres;
+ }
+ }
+ /* res now -> number lsu, buffer, or allocated storage for Unit array */
+
+ /* Place the coefficient into the selected Unit array */
+ /* [this is often 70% of the cost of this function when DECDPUN>1] */
+ #if DECDPUN>1
+ out=0; /* accumulator */
+ up=res+D2U(d)-1; /* -> msu */
+ cut=d-(up-res)*DECDPUN; /* digits in top unit */
+ for (c=cfirst;; c++) { /* along the digits */
+ if (*c=='.') continue; /* ignore '.' [don't decrement cut] */
+ out=X10(out)+(Int)*c-(Int)'0';
+ if (c==last) break; /* done [never get to trailing '.'] */
+ cut--;
+ if (cut>0) continue; /* more for this unit */
+ *up=(Unit)out; /* write unit */
+ up--; /* prepare for unit below.. */
+ cut=DECDPUN; /* .. */
+ out=0; /* .. */
+ } /* c */
+ *up=(Unit)out; /* write lsu */
+
+ #else
+ /* DECDPUN==1 */
+ up=res; /* -> lsu */
+ for (c=last; c>=cfirst; c--) { /* over each character, from least */
+ if (*c=='.') continue; /* ignore . [don't step up] */
+ *up=(Unit)((Int)*c-(Int)'0');
+ up++;
+ } /* c */
+ #endif
+
+ dn->bits=bits;
+ dn->exponent=exponent;
+ dn->digits=d;
+
+ /* if not in number (too long) shorten into the number */
+ if (d>set->digits) {
+ residue=0;
+ decSetCoeff(dn, set, res, d, &residue, &status);
+ /* always check for overflow or subnormal and round as needed */
+ decFinalize(dn, set, &residue, &status);
+ }
+ else { /* no rounding, but may still have overflow or subnormal */
+ /* [these tests are just for performance; finalize repeats them] */
+ if ((dn->exponent-1<set->emin-dn->digits)
+ || (dn->exponent-1>set->emax-set->digits)) {
+ residue=0;
+ decFinalize(dn, set, &residue, &status);
+ }
+ }
+ /* decNumberShow(dn); */
+ } while(0); /* [for break] */
- if (allocres != NULL)
- free (allocres); /* drop any storage we used */
- if (status != 0)
- decStatus (dn, status, set);
+ if (allocres!=NULL) free(allocres); /* drop any storage used */
+ if (status!=0) decStatus(dn, status, set);
return dn;
-}
+ } /* decNumberFromString */
/* ================================================================== */
-/* Operators */
+/* Operators */
/* ================================================================== */
/* ------------------------------------------------------------------ */
-/* decNumberAbs -- absolute value operator */
-/* */
-/* This computes C = abs(A) */
-/* */
-/* res is C, the result. C may be A */
-/* rhs is A */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
+/* decNumberAbs -- absolute value operator */
+/* */
+/* This computes C = abs(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* See also decNumberCopyAbs for a quiet bitwise version of this. */
+/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* This has the same effect as decNumberPlus unless A is negative, */
-/* in which case it has the same effect as decNumberMinus. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberAbs (decNumber * res, decNumber * rhs, decContext * set)
-{
- decNumber dzero; /* for 0 */
- uInt status = 0; /* accumulator */
-
-#if DECCHECK
- if (decCheckOperands (res, DECUNUSED, rhs, set))
+/* in which case it has the same effect as decNumberMinus. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dzero; /* for 0 */
+ uInt status=0; /* accumulator */
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ decNumberZero(&dzero); /* set 0 */
+ dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
+ decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberAbs */
+
+/* ------------------------------------------------------------------ */
+/* decNumberAdd -- add two Numbers */
+/* */
+/* This computes C = A + B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+/* This just calls the routine shared with Subtract */
+decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decAddOp(res, lhs, rhs, set, 0, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberAdd */
+
+/* ------------------------------------------------------------------ */
+/* decNumberAnd -- AND two Numbers, digitwise */
+/* */
+/* This computes C = A & B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X&X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context (used for result length and error report) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Logical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ const Unit *ua, *ub; /* -> operands */
+ const Unit *msua, *msub; /* -> operand msus */
+ Unit *uc, *msuc; /* -> result and its msu */
+ Int msudigs; /* digits in res msu */
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
+ decStatus(res, DEC_Invalid_operation, set);
return res;
-#endif
+ }
- decNumberZero (&dzero); /* set 0 */
- dzero.exponent = rhs->exponent; /* [no coefficient expansion] */
- decAddOp (res, &dzero, rhs, set, (uByte) (rhs->bits & DECNEG), &status);
- if (status != 0)
- decStatus (res, status, set);
+ /* operands are valid */
+ ua=lhs->lsu; /* bottom-up */
+ ub=rhs->lsu; /* .. */
+ uc=res->lsu; /* .. */
+ msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
+ msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
+ msuc=uc+D2U(set->digits)-1; /* -> msu of result */
+ msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
+ for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
+ Unit a, b; /* extract units */
+ if (ua>msua) a=0;
+ else a=*ua;
+ if (ub>msub) b=0;
+ else b=*ub;
+ *uc=0; /* can now write back */
+ if (a|b) { /* maybe 1 bits to examine */
+ Int i, j;
+ *uc=0; /* can now write back */
+ /* This loop could be unrolled and/or use BIN2BCD tables */
+ for (i=0; i<DECDPUN; i++) {
+ if (a&b&1) *uc=*uc+(Unit)powers[i]; /* effect AND */
+ j=a%10;
+ a=a/10;
+ j|=b%10;
+ b=b/10;
+ if (j>1) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ if (uc==msuc && i==msudigs-1) break; /* just did final digit */
+ } /* each digit */
+ } /* both OK */
+ } /* each unit */
+ /* [here uc-1 is the msu of the result] */
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);
+ res->exponent=0; /* integer */
+ res->bits=0; /* sign=0 */
+ return res; /* [no status to set] */
+ } /* decNumberAnd */
+
+/* ------------------------------------------------------------------ */
+/* decNumberCompare -- compare two Numbers */
+/* */
+/* This computes C = A ? B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for one digit (or NaN). */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decCompareOp(res, lhs, rhs, set, COMPARE, &status);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } /* decNumberCompare */
+
+/* ------------------------------------------------------------------ */
+/* decNumberCompareSignal -- compare, signalling on all NaNs */
+/* */
+/* This computes C = A ? B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for one digit (or NaN). */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
+ if (status!=0) decStatus(res, status, set);
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberAdd -- add two Numbers */
-/* */
-/* This computes C = A + B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-/* This just calls the routine shared with Subtract */
-decNumber *
-decNumberAdd (decNumber * res, decNumber * lhs, decNumber * rhs,
- decContext * set)
-{
- uInt status = 0; /* accumulator */
- decAddOp (res, lhs, rhs, set, 0, &status);
- if (status != 0)
- decStatus (res, status, set);
+ } /* decNumberCompareSignal */
+
+/* ------------------------------------------------------------------ */
+/* decNumberCompareTotal -- compare two Numbers, using total ordering */
+/* */
+/* This computes C = A ? B, under total ordering */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for one digit; the result will always be one of */
+/* -1, 0, or 1. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
+ if (status!=0) decStatus(res, status, set);
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberCompare -- compare two Numbers */
-/* */
-/* This computes C = A ? B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for one digit. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberCompare (decNumber * res, decNumber * lhs, decNumber * rhs,
- decContext * set)
-{
- uInt status = 0; /* accumulator */
- decCompareOp (res, lhs, rhs, set, COMPARE, &status);
- if (status != 0)
- decStatus (res, status, set);
+ } /* decNumberCompareTotal */
+
+/* ------------------------------------------------------------------ */
+/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */
+/* */
+/* This computes C = |A| ? |B|, under total ordering */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for one digit; the result will always be one of */
+/* -1, 0, or 1. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ uInt needbytes; /* for space calculations */
+ decNumber bufa[D2N(DECBUFFER+1)];/* +1 in case DECBUFFER=0 */
+ decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
+ decNumber bufb[D2N(DECBUFFER+1)];
+ decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
+ decNumber *a, *b; /* temporary pointers */
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ /* if either is negative, take a copy and absolute */
+ if (decNumberIsNegative(lhs)) { /* lhs<0 */
+ a=bufa;
+ needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { /* need malloc space */
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { /* hopeless -- abandon */
+ status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; /* use the allocated space */
+ }
+ decNumberCopy(a, lhs); /* copy content */
+ a->bits&=~DECNEG; /* .. and clear the sign */
+ lhs=a; /* use copy from here on */
+ }
+ if (decNumberIsNegative(rhs)) { /* rhs<0 */
+ b=bufb;
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufb)) { /* need malloc space */
+ allocbufb=(decNumber *)malloc(needbytes);
+ if (allocbufb==NULL) { /* hopeless -- abandon */
+ status|=DEC_Insufficient_storage;
+ break;}
+ b=allocbufb; /* use the allocated space */
+ }
+ decNumberCopy(b, rhs); /* copy content */
+ b->bits&=~DECNEG; /* .. and clear the sign */
+ rhs=b; /* use copy from here on */
+ }
+ decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
+ } while(0); /* end protected */
+
+ if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
+ if (allocbufb!=NULL) free(allocbufb); /* .. */
+ if (status!=0) decStatus(res, status, set);
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberDivide -- divide one number by another */
-/* */
-/* This computes C = A / B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberDivide (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- uInt status = 0; /* accumulator */
- decDivideOp (res, lhs, rhs, set, DIVIDE, &status);
- if (status != 0)
- decStatus (res, status, set);
+ } /* decNumberCompareTotalMag */
+
+/* ------------------------------------------------------------------ */
+/* decNumberDivide -- divide one number by another */
+/* */
+/* This computes C = A / B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
+ } /* decNumberDivide */
/* ------------------------------------------------------------------ */
/* decNumberDivideInteger -- divide and return integer quotient */
-/* */
+/* */
/* This computes C = A # B, where # is the integer divide operator */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X#X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberDivideInteger (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- uInt status = 0; /* accumulator */
- decDivideOp (res, lhs, rhs, set, DIVIDEINT, &status);
- if (status != 0)
- decStatus (res, status, set);
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X#X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
+ if (status!=0) decStatus(res, status, set);
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberMax -- compare two Numbers and return the maximum */
-/* */
-/* This computes C = A ? B, returning the maximum or A if equal */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberMax (decNumber * res, decNumber * lhs, decNumber * rhs,
- decContext * set)
-{
- uInt status = 0; /* accumulator */
- decCompareOp (res, lhs, rhs, set, COMPMAX, &status);
- if (status != 0)
- decStatus (res, status, set);
+ } /* decNumberDivideInteger */
+
+/* ------------------------------------------------------------------ */
+/* decNumberExp -- exponentiation */
+/* */
+/* This computes C = exp(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* Finite results will always be full precision and Inexact, except */
+/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
+/* */
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+/* This is a wrapper for decExpOp which can handle the slightly wider */
+/* (double) range needed by Ln (which has to be able to calculate */
+/* exp(-a) where a can be the tiniest number (Ntiny). */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ uInt status=0; /* accumulator */
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
+ #endif
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ /* Check restrictions; these restrictions ensure that if h=8 (see */
+ /* decExpOp) then the result will either overflow or underflow to 0. */
+ /* Other math functions restrict the input range, too, for inverses. */
+ /* If not violated then carry out the operation. */
+ if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operand and set lostDigits status, as needed */
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ decExpOp(res, rhs, set, &status);
+ } while(0); /* end protected */
+
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
+ #endif
+ /* apply significant status */
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberMin -- compare two Numbers and return the minimum */
-/* */
-/* This computes C = A ? B, returning the minimum or A if equal */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberMin (decNumber * res, decNumber * lhs, decNumber * rhs,
- decContext * set)
-{
- uInt status = 0; /* accumulator */
- decCompareOp (res, lhs, rhs, set, COMPMIN, &status);
- if (status != 0)
- decStatus (res, status, set);
+ } /* decNumberExp */
+
+/* ------------------------------------------------------------------ */
+/* decNumberFMA -- fused multiply add */
+/* */
+/* This computes D = (A * B) + C with only one rounding */
+/* */
+/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */
+/* lhs is A */
+/* rhs is B */
+/* fhs is C [far hand side] */
+/* set is the context */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, const decNumber *fhs,
+ decContext *set) {
+ uInt status=0; /* accumulator */
+ decContext dcmul; /* context for the multiplication */
+ uInt needbytes; /* for space calculations */
+ decNumber bufa[D2N(DECBUFFER*2+1)];
+ decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
+ decNumber *acc; /* accumulator pointer */
+ decNumber dzero; /* work */
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) { /* [undefined if subset] */
+ status|=DEC_Invalid_operation;
+ break;}
+ #endif
+ /* Check math restrictions [these ensure no overflow or underflow] */
+ if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
+ || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
+ || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
+ /* set up context for multiply */
+ dcmul=*set;
+ dcmul.digits=lhs->digits+rhs->digits; /* just enough */
+ /* [The above may be an over-estimate for subset arithmetic, but that's OK] */
+ dcmul.emax=DEC_MAX_EMAX; /* effectively unbounded .. */
+ dcmul.emin=DEC_MIN_EMIN; /* [thanks to Math restrictions] */
+ /* set up decNumber space to receive the result of the multiply */
+ acc=bufa; /* may fit */
+ needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { /* need malloc space */
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { /* hopeless -- abandon */
+ status|=DEC_Insufficient_storage;
+ break;}
+ acc=allocbufa; /* use the allocated space */
+ }
+ /* multiply with extended range and necessary precision */
+ /*printf("emin=%ld\n", dcmul.emin); */
+ decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
+ /* Only Invalid operation (from sNaN or Inf * 0) is possible in */
+ /* status; if either is seen than ignore fhs (in case it is */
+ /* another sNaN) and set acc to NaN unless we had an sNaN */
+ /* [decMultiplyOp leaves that to caller] */
+ /* Note sNaN has to go through addOp to shorten payload if */
+ /* necessary */
+ if ((status&DEC_Invalid_operation)!=0) {
+ if (!(status&DEC_sNaN)) { /* but be true invalid */
+ decNumberZero(res); /* acc not yet set */
+ res->bits=DECNAN;
+ break;
+ }
+ decNumberZero(&dzero); /* make 0 (any non-NaN would do) */
+ fhs=&dzero; /* use that */
+ }
+ #if DECCHECK
+ else { /* multiply was OK */
+ if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
+ }
+ #endif
+ /* add the third operand and result -> res, and all is done */
+ decAddOp(res, acc, fhs, set, 0, &status);
+ } while(0); /* end protected */
+
+ if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberMinus -- prefix minus operator */
-/* */
-/* This computes C = 0 - A */
-/* */
-/* res is C, the result. C may be A */
-/* rhs is A */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-/* We simply use AddOp for the subtract, which will do the necessary. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberMinus (decNumber * res, decNumber * rhs, decContext * set)
-{
- decNumber dzero;
- uInt status = 0; /* accumulator */
-
-#if DECCHECK
- if (decCheckOperands (res, DECUNUSED, rhs, set))
+ } /* decNumberFMA */
+
+/* ------------------------------------------------------------------ */
+/* decNumberInvert -- invert a Number, digitwise */
+/* */
+/* This computes C = ~A */
+/* */
+/* res is C, the result. C may be A (e.g., X=~X) */
+/* rhs is A */
+/* set is the context (used for result length and error report) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Logical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ const Unit *ua, *msua; /* -> operand and its msu */
+ Unit *uc, *msuc; /* -> result and its msu */
+ Int msudigs; /* digits in res msu */
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
+ decStatus(res, DEC_Invalid_operation, set);
return res;
-#endif
+ }
+ /* operand is valid */
+ ua=rhs->lsu; /* bottom-up */
+ uc=res->lsu; /* .. */
+ msua=ua+D2U(rhs->digits)-1; /* -> msu of rhs */
+ msuc=uc+D2U(set->digits)-1; /* -> msu of result */
+ msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
+ for (; uc<=msuc; ua++, uc++) { /* Unit loop */
+ Unit a; /* extract unit */
+ Int i, j; /* work */
+ if (ua>msua) a=0;
+ else a=*ua;
+ *uc=0; /* can now write back */
+ /* always need to examine all bits in rhs */
+ /* This loop could be unrolled and/or use BIN2BCD tables */
+ for (i=0; i<DECDPUN; i++) {
+ if ((~a)&1) *uc=*uc+(Unit)powers[i]; /* effect INVERT */
+ j=a%10;
+ a=a/10;
+ if (j>1) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ if (uc==msuc && i==msudigs-1) break; /* just did final digit */
+ } /* each digit */
+ } /* each unit */
+ /* [here uc-1 is the msu of the result] */
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);
+ res->exponent=0; /* integer */
+ res->bits=0; /* sign=0 */
+ return res; /* [no status to set] */
+ } /* decNumberInvert */
+
+/* ------------------------------------------------------------------ */
+/* decNumberLn -- natural logarithm */
+/* */
+/* This computes C = ln(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Notable cases: */
+/* A<0 -> Invalid */
+/* A=0 -> -Infinity (Exact) */
+/* A=+Infinity -> +Infinity (Exact) */
+/* A=1 exactly -> 0 (Exact) */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+/* This is a wrapper for decLnOp which can handle the slightly wider */
+/* (+11) range needed by Ln, Log10, etc. (which may have to be able */
+/* to calculate at p+e+2). */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ uInt status=0; /* accumulator */
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
+ #endif
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ /* Check restrictions; this is a math function; if not violated */
+ /* then carry out the operation. */
+ if (!decCheckMath(rhs, set, &status)) do { /* protect allocation */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operand and set lostDigits status, as needed */
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ /* special check in subset for rhs=0 */
+ if (ISZERO(rhs)) { /* +/- zeros -> error */
+ status|=DEC_Invalid_operation;
+ break;}
+ } /* extended=0 */
+ #endif
+ decLnOp(res, rhs, set, &status);
+ } while(0); /* end protected */
+
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
+ #endif
+ /* apply significant status */
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberLn */
+
+/* ------------------------------------------------------------------ */
+/* decNumberLogB - get adjusted exponent, by 754 rules */
+/* */
+/* This computes C = adjustedexponent(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context, used only for digits and status */
+/* */
+/* C must have space for 10 digits (A might have 10**9 digits and */
+/* an exponent of +999999999, or one digit and an exponent of */
+/* -1999999999). */
+/* */
+/* This returns the adjusted exponent of A after (in theory) padding */
+/* with zeros on the right to set->digits digits while keeping the */
+/* same value. The exponent is not limited by emin/emax. */
+/* */
+/* Notable cases: */
+/* A<0 -> Use |A| */
+/* A=0 -> -Infinity (Division by zero) */
+/* A=Infinite -> +Infinity (Exact) */
+/* A=1 exactly -> 0 (Exact) */
+/* NaNs are propagated as usual */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ uInt status=0; /* accumulator */
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ /* NaNs as usual; Infinities return +Infinity; 0->oops */
+ if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
+ else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
+ else if (decNumberIsZero(rhs)) {
+ decNumberZero(res); /* prepare for Infinity */
+ res->bits=DECNEG|DECINF; /* -Infinity */
+ status|=DEC_Division_by_zero; /* as per 754 */
+ }
+ else { /* finite non-zero */
+ Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
+ decNumberFromInt32(res, ae); /* lay it out */
+ }
- decNumberZero (&dzero); /* make 0 */
- dzero.exponent = rhs->exponent; /* [no coefficient expansion] */
- decAddOp (res, &dzero, rhs, set, DECNEG, &status);
- if (status != 0)
- decStatus (res, status, set);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } /* decNumberLogB */
+
+/* ------------------------------------------------------------------ */
+/* decNumberLog10 -- logarithm in base 10 */
+/* */
+/* This computes C = log10(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Notable cases: */
+/* A<0 -> Invalid */
+/* A=0 -> -Infinity (Exact) */
+/* A=+Infinity -> +Infinity (Exact) */
+/* A=10**n (if n is an integer) -> n (Exact) */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+/* This calculates ln(A)/ln(10) using appropriate precision. For */
+/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */
+/* requested digits and t is the number of digits in the exponent */
+/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */
+/* fastpath in decLnOp. The final division is done to the requested */
+/* precision. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ uInt status=0, ignore=0; /* status accumulators */
+ uInt needbytes; /* for space calculations */
+ Int p; /* working precision */
+ Int t; /* digits in exponent of A */
+
+ /* buffers for a and b working decimals */
+ /* (adjustment calculator, same size) */
+ decNumber bufa[D2N(DECBUFFER+2)];
+ decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
+ decNumber *a=bufa; /* temporary a */
+ decNumber bufb[D2N(DECBUFFER+2)];
+ decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
+ decNumber *b=bufb; /* temporary b */
+ decNumber bufw[D2N(10)]; /* working 2-10 digit number */
+ decNumber *w=bufw; /* .. */
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
+ #endif
+
+ decContext aset; /* working context */
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ /* Check restrictions; this is a math function; if not violated */
+ /* then carry out the operation. */
+ if (!decCheckMath(rhs, set, &status)) do { /* protect malloc */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operand and set lostDigits status, as needed */
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ /* special check in subset for rhs=0 */
+ if (ISZERO(rhs)) { /* +/- zeros -> error */
+ status|=DEC_Invalid_operation;
+ break;}
+ } /* extended=0 */
+ #endif
+
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
+
+ /* handle exact powers of 10; only check if +ve finite */
+ if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
+ Int residue=0; /* (no residue) */
+ uInt copystat=0; /* clean status */
+
+ /* round to a single digit... */
+ aset.digits=1;
+ decCopyFit(w, rhs, &aset, &residue, ©stat); /* copy & shorten */
+ /* if exact and the digit is 1, rhs is a power of 10 */
+ if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
+ /* the exponent, conveniently, is the power of 10; making */
+ /* this the result needs a little care as it might not fit, */
+ /* so first convert it into the working number, and then move */
+ /* to res */
+ decNumberFromInt32(w, w->exponent);
+ residue=0;
+ decCopyFit(res, w, set, &residue, &status); /* copy & round */
+ decFinish(res, set, &residue, &status); /* cleanup/set flags */
+ break;
+ } /* not a power of 10 */
+ } /* not a candidate for exact */
+
+ /* simplify the information-content calculation to use 'total */
+ /* number of digits in a, including exponent' as compared to the */
+ /* requested digits, as increasing this will only rarely cost an */
+ /* iteration in ln(a) anyway */
+ t=6; /* it can never be >6 */
+
+ /* allocate space when needed... */
+ p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
+ needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { /* need malloc space */
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { /* hopeless -- abandon */
+ status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; /* use the allocated space */
+ }
+ aset.digits=p; /* as calculated */
+ aset.emax=DEC_MAX_MATH; /* usual bounds */
+ aset.emin=-DEC_MAX_MATH; /* .. */
+ aset.clamp=0; /* and no concrete format */
+ decLnOp(a, rhs, &aset, &status); /* a=ln(rhs) */
+
+ /* skip the division if the result so far is infinite, NaN, or */
+ /* zero, or there was an error; note NaN from sNaN needs copy */
+ if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
+ if (a->bits&DECSPECIAL || ISZERO(a)) {
+ decNumberCopy(res, a); /* [will fit] */
+ break;}
+
+ /* for ln(10) an extra 3 digits of precision are needed */
+ p=set->digits+3;
+ needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufb)) { /* need malloc space */
+ allocbufb=(decNumber *)malloc(needbytes);
+ if (allocbufb==NULL) { /* hopeless -- abandon */
+ status|=DEC_Insufficient_storage;
+ break;}
+ b=allocbufb; /* use the allocated space */
+ }
+ decNumberZero(w); /* set up 10... */
+ #if DECDPUN==1
+ w->lsu[1]=1; w->lsu[0]=0; /* .. */
+ #else
+ w->lsu[0]=10; /* .. */
+ #endif
+ w->digits=2; /* .. */
+
+ aset.digits=p;
+ decLnOp(b, w, &aset, &ignore); /* b=ln(10) */
+
+ aset.digits=set->digits; /* for final divide */
+ decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */
+ } while(0); /* [for break] */
+
+ if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
+ if (allocbufb!=NULL) free(allocbufb); /* .. */
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); /* .. */
+ #endif
+ /* apply significant status */
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberLog10 */
+
+/* ------------------------------------------------------------------ */
+/* decNumberMax -- compare two Numbers and return the maximum */
+/* */
+/* This computes C = A ? B, returning the maximum by 754 rules */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberMax */
+
+/* ------------------------------------------------------------------ */
+/* decNumberMaxMag -- compare and return the maximum by magnitude */
+/* */
+/* This computes C = A ? B, returning the maximum by 754 rules */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberMaxMag */
+
+/* ------------------------------------------------------------------ */
+/* decNumberMin -- compare two Numbers and return the minimum */
+/* */
+/* This computes C = A ? B, returning the minimum by 754 rules */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
+ } /* decNumberMin */
+
+/* ------------------------------------------------------------------ */
+/* decNumberMinMag -- compare and return the minimum by magnitude */
+/* */
+/* This computes C = A ? B, returning the minimum by 754 rules */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberMinMag */
/* ------------------------------------------------------------------ */
-/* decNumberPlus -- prefix plus operator */
-/* */
-/* This computes C = 0 + A */
-/* */
-/* res is C, the result. C may be A */
-/* rhs is A */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
+/* decNumberMinus -- prefix minus operator */
+/* */
+/* This computes C = 0 - A */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* See also decNumberCopyNegate for a quiet bitwise version of this. */
+/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
-/* We simply use AddOp; Add will take fast path after preparing A. */
-/* Performance is a concern here, as this routine is often used to */
-/* check operands and apply rounding and overflow/underflow testing. */
+/* Simply use AddOp for the subtract, which will do the necessary. */
/* ------------------------------------------------------------------ */
-decNumber *
-decNumberPlus (decNumber * res, decNumber * rhs, decContext * set)
-{
+decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
+ decContext *set) {
decNumber dzero;
- uInt status = 0; /* accumulator */
-
-#if DECCHECK
- if (decCheckOperands (res, DECUNUSED, rhs, set))
- return res;
-#endif
-
- decNumberZero (&dzero); /* make 0 */
- dzero.exponent = rhs->exponent; /* [no coefficient expansion] */
- decAddOp (res, &dzero, rhs, set, 0, &status);
- if (status != 0)
- decStatus (res, status, set);
+ uInt status=0; /* accumulator */
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ decNumberZero(&dzero); /* make 0 */
+ dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
+ decAddOp(res, &dzero, rhs, set, DECNEG, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberMultiply -- multiply two Numbers */
-/* */
-/* This computes C = A x B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberMultiply (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- uInt status = 0; /* accumulator */
- decMultiplyOp (res, lhs, rhs, set, &status);
- if (status != 0)
- decStatus (res, status, set);
+ } /* decNumberMinus */
+
+/* ------------------------------------------------------------------ */
+/* decNumberNextMinus -- next towards -Infinity */
+/* */
+/* This computes C = A - infinitesimal, rounded towards -Infinity */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* This is a generalization of 754 NextDown. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dtiny; /* constant */
+ decContext workset=*set; /* work */
+ uInt status=0; /* accumulator */
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ /* +Infinity is the special case */
+ if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
+ decSetMaxValue(res, set); /* is +ve */
+ /* there is no status to set */
+ return res;
+ }
+ decNumberZero(&dtiny); /* start with 0 */
+ dtiny.lsu[0]=1; /* make number that is .. */
+ dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
+ workset.round=DEC_ROUND_FLOOR;
+ decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
+ status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */
+ if (status!=0) decStatus(res, status, set);
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberNormalize -- remove trailing zeros */
-/* */
-/* This computes C = 0 + A, and normalizes the result */
-/* */
-/* res is C, the result. C may be A */
-/* rhs is A */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberNormalize (decNumber * res, decNumber * rhs, decContext * set)
-{
- decNumber *allocrhs = NULL; /* non-NULL if rounded rhs allocated */
- uInt status = 0; /* as usual */
- Int residue = 0; /* as usual */
- Int dropped; /* work */
-
-#if DECCHECK
- if (decCheckOperands (res, DECUNUSED, rhs, set))
+ } /* decNumberNextMinus */
+
+/* ------------------------------------------------------------------ */
+/* decNumberNextPlus -- next towards +Infinity */
+/* */
+/* This computes C = A + infinitesimal, rounded towards +Infinity */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* This is a generalization of 754 NextUp. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dtiny; /* constant */
+ decContext workset=*set; /* work */
+ uInt status=0; /* accumulator */
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ /* -Infinity is the special case */
+ if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
+ decSetMaxValue(res, set);
+ res->bits=DECNEG; /* negative */
+ /* there is no status to set */
return res;
-#endif
-
- do
- { /* protect allocated storage */
-#if DECSUBSET
- if (!set->extended)
- {
- /* reduce operand and set lostDigits status, as needed */
- if (rhs->digits > set->digits)
- {
- allocrhs = decRoundOperand (rhs, set, &status);
- if (allocrhs == NULL)
- break;
- rhs = allocrhs;
+ }
+ decNumberZero(&dtiny); /* start with 0 */
+ dtiny.lsu[0]=1; /* make number that is .. */
+ dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
+ workset.round=DEC_ROUND_CEILING;
+ decAddOp(res, rhs, &dtiny, &workset, 0, &status);
+ status&=DEC_Invalid_operation|DEC_sNaN; /* only sNaN Invalid please */
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } /* decNumberNextPlus */
+
+/* ------------------------------------------------------------------ */
+/* decNumberNextToward -- next towards rhs */
+/* */
+/* This computes C = A +/- infinitesimal, rounded towards */
+/* +/-Infinity in the direction of B, as per 754-1985 nextafter */
+/* modified during revision but dropped from 754-2008. */
+/* */
+/* res is C, the result. C may be A or B. */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* This is a generalization of 754-1985 NextAfter. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ decNumber dtiny; /* constant */
+ decContext workset=*set; /* work */
+ Int result; /* .. */
+ uInt status=0; /* accumulator */
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
+ decNaNs(res, lhs, rhs, set, &status);
+ }
+ else { /* Is numeric, so no chance of sNaN Invalid, etc. */
+ result=decCompare(lhs, rhs, 0); /* sign matters */
+ if (result==BADINT) status|=DEC_Insufficient_storage; /* rare */
+ else { /* valid compare */
+ if (result==0) decNumberCopySign(res, lhs, rhs); /* easy */
+ else { /* differ: need NextPlus or NextMinus */
+ uByte sub; /* add or subtract */
+ if (result<0) { /* lhs<rhs, do nextplus */
+ /* -Infinity is the special case */
+ if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
+ decSetMaxValue(res, set);
+ res->bits=DECNEG; /* negative */
+ return res; /* there is no status to set */
}
- }
-#endif
- /* [following code does not require input rounding] */
-
- /* specials copy through, except NaNs need care */
- if (decNumberIsNaN (rhs))
- {
- decNaNs (res, rhs, NULL, &status);
- break;
- }
-
- /* reduce result to the requested length and copy to result */
- decCopyFit (res, rhs, set, &residue, &status); /* copy & round */
- decFinish (res, set, &residue, &status); /* cleanup/set flags */
- decTrim (res, 1, &dropped); /* normalize in place */
+ workset.round=DEC_ROUND_CEILING;
+ sub=0; /* add, please */
+ } /* plus */
+ else { /* lhs>rhs, do nextminus */
+ /* +Infinity is the special case */
+ if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
+ decSetMaxValue(res, set);
+ return res; /* there is no status to set */
+ }
+ workset.round=DEC_ROUND_FLOOR;
+ sub=DECNEG; /* subtract, please */
+ } /* minus */
+ decNumberZero(&dtiny); /* start with 0 */
+ dtiny.lsu[0]=1; /* make number that is .. */
+ dtiny.exponent=DEC_MIN_EMIN-1; /* .. smaller than tiniest */
+ decAddOp(res, lhs, &dtiny, &workset, sub, &status); /* + or - */
+ /* turn off exceptions if the result is a normal number */
+ /* (including Nmin), otherwise let all status through */
+ if (decNumberIsNormal(res, set)) status=0;
+ } /* unequal */
+ } /* compare OK */
+ } /* numeric */
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } /* decNumberNextToward */
+
+/* ------------------------------------------------------------------ */
+/* decNumberOr -- OR two Numbers, digitwise */
+/* */
+/* This computes C = A | B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X|X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context (used for result length and error report) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Logical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ const Unit *ua, *ub; /* -> operands */
+ const Unit *msua, *msub; /* -> operand msus */
+ Unit *uc, *msuc; /* -> result and its msu */
+ Int msudigs; /* digits in res msu */
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
}
- while (0); /* end protected */
-
- if (allocrhs != NULL)
- free (allocrhs); /* .. */
- if (status != 0)
- decStatus (res, status, set); /* then report status */
+ /* operands are valid */
+ ua=lhs->lsu; /* bottom-up */
+ ub=rhs->lsu; /* .. */
+ uc=res->lsu; /* .. */
+ msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
+ msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
+ msuc=uc+D2U(set->digits)-1; /* -> msu of result */
+ msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
+ for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
+ Unit a, b; /* extract units */
+ if (ua>msua) a=0;
+ else a=*ua;
+ if (ub>msub) b=0;
+ else b=*ub;
+ *uc=0; /* can now write back */
+ if (a|b) { /* maybe 1 bits to examine */
+ Int i, j;
+ /* This loop could be unrolled and/or use BIN2BCD tables */
+ for (i=0; i<DECDPUN; i++) {
+ if ((a|b)&1) *uc=*uc+(Unit)powers[i]; /* effect OR */
+ j=a%10;
+ a=a/10;
+ j|=b%10;
+ b=b/10;
+ if (j>1) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ if (uc==msuc && i==msudigs-1) break; /* just did final digit */
+ } /* each digit */
+ } /* non-zero */
+ } /* each unit */
+ /* [here uc-1 is the msu of the result] */
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);
+ res->exponent=0; /* integer */
+ res->bits=0; /* sign=0 */
+ return res; /* [no status to set] */
+ } /* decNumberOr */
+
+/* ------------------------------------------------------------------ */
+/* decNumberPlus -- prefix plus operator */
+/* */
+/* This computes C = 0 + A */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* See also decNumberCopy for a quiet bitwise version of this. */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+/* This simply uses AddOp; Add will take fast path after preparing A. */
+/* Performance is a concern here, as this routine is often used to */
+/* check operands and apply rounding and overflow/underflow testing. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decNumber dzero;
+ uInt status=0; /* accumulator */
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ decNumberZero(&dzero); /* make 0 */
+ dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
+ decAddOp(res, &dzero, rhs, set, 0, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberPower -- raise a number to an integer power */
-/* */
-/* This computes C = A ** B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X**X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* */
-/* Specification restriction: abs(n) must be <=999999999 */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberPower (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
- decNumber *allocrhs = NULL; /* .., rhs */
- decNumber *allocdac = NULL; /* -> allocated acc buffer, iff used */
- decNumber *inrhs = rhs; /* save original rhs */
- Int reqdigits = set->digits; /* requested DIGITS */
- Int n; /* RHS in binary */
- Int i; /* work */
-#if DECSUBSET
- Int dropped; /* .. */
-#endif
- uInt needbytes; /* buffer size needed */
- Flag seenbit; /* seen a bit while powering */
- Int residue = 0; /* rounding residue */
- uInt status = 0; /* accumulator */
- uByte bits = 0; /* result sign if errors */
- decContext workset; /* working context */
- decNumber dnOne; /* work value 1... */
+ } /* decNumberPlus */
+
+/* ------------------------------------------------------------------ */
+/* decNumberMultiply -- multiply two Numbers */
+/* */
+/* This computes C = A x B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decMultiplyOp(res, lhs, rhs, set, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberMultiply */
+
+/* ------------------------------------------------------------------ */
+/* decNumberPower -- raise a number to a power */
+/* */
+/* This computes C = A ** B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X**X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Mathematical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* */
+/* However, if 1999999997<=B<=999999999 and B is an integer then the */
+/* restrictions on A and the context are relaxed to the usual bounds, */
+/* for compatibility with the earlier (integer power only) version */
+/* of this function. */
+/* */
+/* When B is an integer, the result may be exact, even if rounded. */
+/* */
+/* The final result is rounded according to the context; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
+ decNumber *allocrhs=NULL; /* .., rhs */
+ #endif
+ decNumber *allocdac=NULL; /* -> allocated acc buffer, iff used */
+ decNumber *allocinv=NULL; /* -> allocated 1/x buffer, iff used */
+ Int reqdigits=set->digits; /* requested DIGITS */
+ Int n; /* rhs in binary */
+ Flag rhsint=0; /* 1 if rhs is an integer */
+ Flag useint=0; /* 1 if can use integer calculation */
+ Flag isoddint=0; /* 1 if rhs is an integer and odd */
+ Int i; /* work */
+ #if DECSUBSET
+ Int dropped; /* .. */
+ #endif
+ uInt needbytes; /* buffer size needed */
+ Flag seenbit; /* seen a bit while powering */
+ Int residue=0; /* rounding residue */
+ uInt status=0; /* accumulators */
+ uByte bits=0; /* result sign if errors */
+ decContext aset; /* working context */
+ decNumber dnOne; /* work value 1... */
/* local accumulator buffer [a decNumber, with digits+elength+1 digits] */
- uByte dacbuff[sizeof (decNumber) + D2U (DECBUFFER + 9) * sizeof (Unit)];
+ decNumber dacbuff[D2N(DECBUFFER+9)];
+ decNumber *dac=dacbuff; /* -> result accumulator */
/* same again for possible 1/lhs calculation */
- uByte lhsbuff[sizeof (decNumber) + D2U (DECBUFFER + 9) * sizeof (Unit)];
- decNumber *dac = (decNumber *) dacbuff; /* -> result accumulator */
-
-#if DECCHECK
- if (decCheckOperands (res, lhs, rhs, set))
- return res;
-#endif
-
- do
- { /* protect allocated storage */
-#if DECSUBSET
- if (!set->extended)
- {
- /* reduce operands and set lostDigits status, as needed */
- if (lhs->digits > reqdigits)
- {
- alloclhs = decRoundOperand (lhs, set, &status);
- if (alloclhs == NULL)
- break;
- lhs = alloclhs;
- }
- /* rounding won't affect the result, but we might signal lostDigits */
- /* as well as the error for non-integer [x**y would need this too] */
- if (rhs->digits > reqdigits)
- {
- allocrhs = decRoundOperand (rhs, set, &status);
- if (allocrhs == NULL)
- break;
- rhs = allocrhs;
- }
+ decNumber invbuff[D2N(DECBUFFER+9)];
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) { /* reduce operands and set status, as needed */
+ if (lhs->digits>reqdigits) {
+ alloclhs=decRoundOperand(lhs, set, &status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
}
-#endif
- /* [following code does not require input rounding] */
-
- /* handle rhs Infinity */
- if (decNumberIsInfinite (rhs))
- {
- status |= DEC_Invalid_operation; /* bad */
- break;
- }
- /* handle NaNs */
- if ((lhs->bits | rhs->bits) & (DECNAN | DECSNAN))
- {
- decNaNs (res, lhs, rhs, &status);
- break;
+ if (rhs->digits>reqdigits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
}
+ }
+ #endif
+ /* [following code does not require input rounding] */
+
+ /* handle NaNs and rhs Infinity (lhs infinity is harder) */
+ if (SPECIALARGS) {
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { /* NaNs */
+ decNaNs(res, lhs, rhs, set, &status);
+ break;}
+ if (decNumberIsInfinite(rhs)) { /* rhs Infinity */
+ Flag rhsneg=rhs->bits&DECNEG; /* save rhs sign */
+ if (decNumberIsNegative(lhs) /* lhs<0 */
+ && !decNumberIsZero(lhs)) /* .. */
+ status|=DEC_Invalid_operation;
+ else { /* lhs >=0 */
+ decNumberZero(&dnOne); /* set up 1 */
+ dnOne.lsu[0]=1;
+ decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */
+ decNumberZero(res); /* prepare for 0/1/Infinity */
+ if (decNumberIsNegative(dac)) { /* lhs<1 */
+ if (rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */
+ }
+ else if (dac->lsu[0]==0) { /* lhs=1 */
+ /* 1**Infinity is inexact, so return fully-padded 1.0000 */
+ Int shift=set->digits-1;
+ *res->lsu=1; /* was 0, make int 1 */
+ res->digits=decShiftToMost(res->lsu, 1, shift);
+ res->exponent=-shift; /* make 1.0000... */
+ status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
+ }
+ else { /* lhs>1 */
+ if (!rhsneg) res->bits|=DECINF; /* +Infinity [else is +0] */
+ }
+ } /* lhs>=0 */
+ break;}
+ /* [lhs infinity drops through] */
+ } /* specials */
+
+ /* Original rhs may be an integer that fits and is in range */
+ n=decGetInt(rhs);
+ if (n!=BADINT) { /* it is an integer */
+ rhsint=1; /* record the fact for 1**n */
+ isoddint=(Flag)n&1; /* [works even if big] */
+ if (n!=BIGEVEN && n!=BIGODD) /* can use integer path? */
+ useint=1; /* looks good */
+ }
- /* Original rhs must be an integer that fits and is in range */
-#if DECSUBSET
- n = decGetInt (inrhs, set);
-#else
- n = decGetInt (inrhs);
-#endif
- if (n == BADINT || n > 999999999 || n < -999999999)
- {
- status |= DEC_Invalid_operation;
- break;
+ if (decNumberIsNegative(lhs) /* -x .. */
+ && isoddint) bits=DECNEG; /* .. to an odd power */
+
+ /* handle LHS infinity */
+ if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */
+ uByte rbits=rhs->bits; /* save */
+ decNumberZero(res); /* prepare */
+ if (n==0) *res->lsu=1; /* [-]Inf**0 => 1 */
+ else {
+ /* -Inf**nonint -> error */
+ if (!rhsint && decNumberIsNegative(lhs)) {
+ status|=DEC_Invalid_operation; /* -Inf**nonint is error */
+ break;}
+ if (!(rbits & DECNEG)) bits|=DECINF; /* was not a **-n */
+ /* [otherwise will be 0 or -0] */
+ res->bits=bits;
}
- if (n < 0)
- { /* negative */
- n = -n; /* use the absolute value */
+ break;}
+
+ /* similarly handle LHS zero */
+ if (decNumberIsZero(lhs)) {
+ if (n==0) { /* 0**0 => Error */
+ #if DECSUBSET
+ if (!set->extended) { /* [unless subset] */
+ decNumberZero(res);
+ *res->lsu=1; /* return 1 */
+ break;}
+ #endif
+ status|=DEC_Invalid_operation;
}
- if (decNumberIsNegative (lhs) /* -x .. */
- && (n & 0x00000001))
- bits = DECNEG; /* .. to an odd power */
-
- /* handle LHS infinity */
- if (decNumberIsInfinite (lhs))
- { /* [NaNs already handled] */
- uByte rbits = rhs->bits; /* save */
- decNumberZero (res);
- if (n == 0)
- *res->lsu = 1; /* [-]Inf**0 => 1 */
- else
- {
- if (!(rbits & DECNEG))
- bits |= DECINF; /* was not a **-n */
- /* [otherwise will be 0 or -0] */
- res->bits = bits;
- }
- break;
+ else { /* 0**x */
+ uByte rbits=rhs->bits; /* save */
+ if (rbits & DECNEG) { /* was a 0**(-n) */
+ #if DECSUBSET
+ if (!set->extended) { /* [bad if subset] */
+ status|=DEC_Invalid_operation;
+ break;}
+ #endif
+ bits|=DECINF;
+ }
+ decNumberZero(res); /* prepare */
+ /* [otherwise will be 0 or -0] */
+ res->bits=bits;
}
-
- /* clone the context */
- workset = *set; /* copy all fields */
+ break;}
+
+ /* here both lhs and rhs are finite; rhs==0 is handled in the */
+ /* integer path. Next handle the non-integer cases */
+ if (!useint) { /* non-integral rhs */
+ /* any -ve lhs is bad, as is either operand or context out of */
+ /* bounds */
+ if (decNumberIsNegative(lhs)) {
+ status|=DEC_Invalid_operation;
+ break;}
+ if (decCheckMath(lhs, set, &status)
+ || decCheckMath(rhs, set, &status)) break; /* variable status */
+
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); /* clean context */
+ aset.emax=DEC_MAX_MATH; /* usual bounds */
+ aset.emin=-DEC_MAX_MATH; /* .. */
+ aset.clamp=0; /* and no concrete format */
+
+ /* calculate the result using exp(ln(lhs)*rhs), which can */
+ /* all be done into the accumulator, dac. The precision needed */
+ /* is enough to contain the full information in the lhs (which */
+ /* is the total digits, including exponent), or the requested */
+ /* precision, if larger, + 4; 6 is used for the exponent */
+ /* maximum length, and this is also used when it is shorter */
+ /* than the requested digits as it greatly reduces the >0.5 ulp */
+ /* cases at little cost (because Ln doubles digits each */
+ /* iteration so a few extra digits rarely causes an extra */
+ /* iteration) */
+ aset.digits=MAXI(lhs->digits, set->digits)+6+4;
+ } /* non-integer rhs */
+
+ else { /* rhs is in-range integer */
+ if (n==0) { /* x**0 = 1 */
+ /* (0**0 was handled above) */
+ decNumberZero(res); /* result=1 */
+ *res->lsu=1; /* .. */
+ break;}
+ /* rhs is a non-zero integer */
+ if (n<0) n=-n; /* use abs(n) */
+
+ aset=*set; /* clone the context */
+ aset.round=DEC_ROUND_HALF_EVEN; /* internally use balanced */
/* calculate the working DIGITS */
- workset.digits = reqdigits + (inrhs->digits + inrhs->exponent) + 1;
- /* it's an error if this is more than we can handle */
- if (workset.digits > DECNUMMAXP)
- {
- status |= DEC_Invalid_operation;
- break;
- }
-
- /* workset.digits is the count of digits for the accumulator we need */
- /* if accumulator is too long for local storage, then allocate */
- needbytes =
- sizeof (decNumber) + (D2U (workset.digits) - 1) * sizeof (Unit);
- /* [needbytes also used below if 1/lhs needed] */
- if (needbytes > sizeof (dacbuff))
- {
- allocdac = (decNumber *) malloc (needbytes);
- if (allocdac == NULL)
- { /* hopeless -- abandon */
- status |= DEC_Insufficient_storage;
- break;
- }
- dac = allocdac; /* use the allocated space */
+ aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
+ #if DECSUBSET
+ if (!set->extended) aset.digits--; /* use classic precision */
+ #endif
+ /* it's an error if this is more than can be handled */
+ if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
+ } /* integer path */
+
+ /* aset.digits is the count of digits for the accumulator needed */
+ /* if accumulator is too long for local storage, then allocate */
+ needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
+ /* [needbytes also used below if 1/lhs needed] */
+ if (needbytes>sizeof(dacbuff)) {
+ allocdac=(decNumber *)malloc(needbytes);
+ if (allocdac==NULL) { /* hopeless -- abandon */
+ status|=DEC_Insufficient_storage;
+ break;}
+ dac=allocdac; /* use the allocated space */
+ }
+ /* here, aset is set up and accumulator is ready for use */
+
+ if (!useint) { /* non-integral rhs */
+ /* x ** y; special-case x=1 here as it will otherwise always */
+ /* reduce to integer 1; decLnOp has a fastpath which detects */
+ /* the case of x=1 */
+ decLnOp(dac, lhs, &aset, &status); /* dac=ln(lhs) */
+ /* [no error possible, as lhs 0 already handled] */
+ if (ISZERO(dac)) { /* x==1, 1.0, etc. */
+ /* need to return fully-padded 1.0000 etc., but rhsint->1 */
+ *dac->lsu=1; /* was 0, make int 1 */
+ if (!rhsint) { /* add padding */
+ Int shift=set->digits-1;
+ dac->digits=decShiftToMost(dac->lsu, 1, shift);
+ dac->exponent=-shift; /* make 1.0000... */
+ status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
+ }
}
- decNumberZero (dac); /* acc=1 */
- *dac->lsu = 1; /* .. */
-
- if (n == 0)
- { /* x**0 is usually 1 */
- /* 0**0 is bad unless subset, when it becomes 1 */
- if (ISZERO (lhs)
-#if DECSUBSET
- && set->extended
-#endif
- )
- status |= DEC_Invalid_operation;
- else
- decNumberCopy (res, dac); /* copy the 1 */
- break;
+ else {
+ decMultiplyOp(dac, dac, rhs, &aset, &status); /* dac=dac*rhs */
+ decExpOp(dac, dac, &aset, &status); /* dac=exp(dac) */
}
-
- /* if a negative power we'll need the constant 1, and if not subset */
- /* we'll invert the lhs now rather than inverting the result later */
- if (decNumberIsNegative (rhs))
- { /* was a **-n [hence digits>0] */
- decNumberCopy (&dnOne, dac); /* dnOne=1; [needed now or later] */
-#if DECSUBSET
- if (set->extended)
- { /* need to calculate 1/lhs */
-#endif
- /* divide lhs into 1, putting result in dac [dac=1/dac] */
- decDivideOp (dac, &dnOne, lhs, &workset, DIVIDE, &status);
- if (alloclhs != NULL)
- {
- free (alloclhs); /* done with intermediate */
- alloclhs = NULL; /* indicate freed */
- }
- /* now locate or allocate space for the inverted lhs */
- if (needbytes > sizeof (lhsbuff))
- {
- alloclhs = (decNumber *) malloc (needbytes);
- if (alloclhs == NULL)
- { /* hopeless -- abandon */
- status |= DEC_Insufficient_storage;
- break;
- }
- lhs = alloclhs; /* use the allocated space */
- }
- else
- lhs = (decNumber *) lhsbuff; /* use stack storage */
- /* [lhs now points to buffer or allocated storage] */
- decNumberCopy (lhs, dac); /* copy the 1/lhs */
- decNumberCopy (dac, &dnOne); /* restore acc=1 */
-#if DECSUBSET
+ /* and drop through for final rounding */
+ } /* non-integer rhs */
+
+ else { /* carry on with integer */
+ decNumberZero(dac); /* acc=1 */
+ *dac->lsu=1; /* .. */
+
+ /* if a negative power the constant 1 is needed, and if not subset */
+ /* invert the lhs now rather than inverting the result later */
+ if (decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */
+ decNumber *inv=invbuff; /* asssume use fixed buffer */
+ decNumberCopy(&dnOne, dac); /* dnOne=1; [needed now or later] */
+ #if DECSUBSET
+ if (set->extended) { /* need to calculate 1/lhs */
+ #endif
+ /* divide lhs into 1, putting result in dac [dac=1/dac] */
+ decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
+ /* now locate or allocate space for the inverted lhs */
+ if (needbytes>sizeof(invbuff)) {
+ allocinv=(decNumber *)malloc(needbytes);
+ if (allocinv==NULL) { /* hopeless -- abandon */
+ status|=DEC_Insufficient_storage;
+ break;}
+ inv=allocinv; /* use the allocated space */
}
-#endif
+ /* [inv now points to big-enough buffer or allocated storage] */
+ decNumberCopy(inv, dac); /* copy the 1/lhs */
+ decNumberCopy(dac, &dnOne); /* restore acc=1 */
+ lhs=inv; /* .. and go forward with new lhs */
+ #if DECSUBSET
+ }
+ #endif
}
/* Raise-to-the-power loop... */
- seenbit = 0; /* set once we've seen a 1-bit */
- for (i = 1;; i++)
- { /* for each bit [top bit ignored] */
- /* abandon if we have had overflow or terminal underflow */
- if (status & (DEC_Overflow | DEC_Underflow))
- { /* interesting? */
- if (status & DEC_Overflow || ISZERO (dac))
- break;
- }
- /* [the following two lines revealed an optimizer bug in a C++ */
- /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
- n = n << 1; /* move next bit to testable position */
- if (n < 0)
- { /* top bit is set */
- seenbit = 1; /* OK, we're off */
- decMultiplyOp (dac, dac, lhs, &workset, &status); /* dac=dac*x */
- }
- if (i == 31)
- break; /* that was the last bit */
- if (!seenbit)
- continue; /* we don't have to square 1 */
- decMultiplyOp (dac, dac, dac, &workset, &status); /* dac=dac*dac [square] */
- } /*i *//* 32 bits */
+ seenbit=0; /* set once a 1-bit is encountered */
+ for (i=1;;i++){ /* for each bit [top bit ignored] */
+ /* abandon if had overflow or terminal underflow */
+ if (status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
+ if (status&DEC_Overflow || ISZERO(dac)) break;
+ }
+ /* [the following two lines revealed an optimizer bug in a C++ */
+ /* compiler, with symptom: 5**3 -> 25, when n=n+n was used] */
+ n=n<<1; /* move next bit to testable position */
+ if (n<0) { /* top bit is set */
+ seenbit=1; /* OK, significant bit seen */
+ decMultiplyOp(dac, dac, lhs, &aset, &status); /* dac=dac*x */
+ }
+ if (i==31) break; /* that was the last bit */
+ if (!seenbit) continue; /* no need to square 1 */
+ decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */
+ } /*i*/ /* 32 bits */
/* complete internal overflow or underflow processing */
- if (status & (DEC_Overflow | DEC_Subnormal))
- {
-#if DECSUBSET
- /* If subset, and power was negative, reverse the kind of -erflow */
- /* [1/x not yet done] */
- if (!set->extended && decNumberIsNegative (rhs))
- {
- if (status & DEC_Overflow)
- status ^= DEC_Overflow | DEC_Underflow | DEC_Subnormal;
- else
- { /* trickier -- Underflow may or may not be set */
- status &= ~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
- status |= DEC_Overflow;
- }
+ if (status & (DEC_Overflow|DEC_Underflow)) {
+ #if DECSUBSET
+ /* If subset, and power was negative, reverse the kind of -erflow */
+ /* [1/x not yet done] */
+ if (!set->extended && decNumberIsNegative(rhs)) {
+ if (status & DEC_Overflow)
+ status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
+ else { /* trickier -- Underflow may or may not be set */
+ status&=~(DEC_Underflow | DEC_Subnormal); /* [one or both] */
+ status|=DEC_Overflow;
}
-#endif
- dac->bits = (dac->bits & ~DECNEG) | bits; /* force correct sign */
- /* round subnormals [to set.digits rather than workset.digits] */
- /* or set overflow result similarly as required */
- decFinalize (dac, set, &residue, &status);
- decNumberCopy (res, dac); /* copy to result (is now OK length) */
- break;
+ }
+ #endif
+ dac->bits=(dac->bits & ~DECNEG) | bits; /* force correct sign */
+ /* round subnormals [to set.digits rather than aset.digits] */
+ /* or set overflow result similarly as required */
+ decFinalize(dac, set, &residue, &status);
+ decNumberCopy(res, dac); /* copy to result (is now OK length) */
+ break;
}
-#if DECSUBSET
- if (!set->extended && /* subset math */
- decNumberIsNegative (rhs))
- { /* was a **-n [hence digits>0] */
- /* so divide result into 1 [dac=1/dac] */
- decDivideOp (dac, &dnOne, dac, &workset, DIVIDE, &status);
+ #if DECSUBSET
+ if (!set->extended && /* subset math */
+ decNumberIsNegative(rhs)) { /* was a **-n [hence digits>0] */
+ /* so divide result into 1 [dac=1/dac] */
+ decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
}
-#endif
-
- /* reduce result to the requested length and copy to result */
- decCopyFit (res, dac, set, &residue, &status);
- decFinish (res, set, &residue, &status); /* final cleanup */
-#if DECSUBSET
- if (!set->extended)
- decTrim (res, 0, &dropped); /* trailing zeros */
-#endif
- }
- while (0); /* end protected */
-
- if (allocdac != NULL)
- free (allocdac); /* drop any storage we used */
- if (allocrhs != NULL)
- free (allocrhs); /* .. */
- if (alloclhs != NULL)
- free (alloclhs); /* .. */
- if (status != 0)
- decStatus (res, status, set);
+ #endif
+ } /* rhs integer path */
+
+ /* reduce result to the requested length and copy to result */
+ decCopyFit(res, dac, set, &residue, &status);
+ decFinish(res, set, &residue, &status); /* final cleanup */
+ #if DECSUBSET
+ if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */
+ #endif
+ } while(0); /* end protected */
+
+ if (allocdac!=NULL) free(allocdac); /* drop any storage used */
+ if (allocinv!=NULL) free(allocinv); /* .. */
+ #if DECSUBSET
+ if (alloclhs!=NULL) free(alloclhs); /* .. */
+ if (allocrhs!=NULL) free(allocrhs); /* .. */
+ #endif
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
+ } /* decNumberPower */
/* ------------------------------------------------------------------ */
-/* decNumberQuantize -- force exponent to requested value */
-/* */
+/* decNumberQuantize -- force exponent to requested value */
+/* */
/* This computes C = op(A, B), where op adjusts the coefficient */
/* of C (by rounding or shifting) such that the exponent (-scale) */
/* of C has exponent of B. The numerical value of C will equal A, */
-/* except for the effects of any rounding that occurred. */
-/* */
-/* res is C, the result. C may be A or B */
-/* lhs is A, the number to adjust */
-/* rhs is B, the number with exponent to match */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* */
+/* except for the effects of any rounding that occurred. */
+/* */
+/* res is C, the result. C may be A or B */
+/* lhs is A, the number to adjust */
+/* rhs is B, the number with exponent to match */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* */
/* Unless there is an error or the result is infinite, the exponent */
-/* after the operation is guaranteed to be equal to that of B. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberQuantize (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- uInt status = 0; /* accumulator */
- decQuantizeOp (res, lhs, rhs, set, 1, &status);
- if (status != 0)
- decStatus (res, status, set);
+/* after the operation is guaranteed to be equal to that of B. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decQuantizeOp(res, lhs, rhs, set, 1, &status);
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } /* decNumberQuantize */
+
+/* ------------------------------------------------------------------ */
+/* decNumberReduce -- remove trailing zeros */
+/* */
+/* This computes C = 0 + A, and normalizes the result */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+/* Previously known as Normalize */
+decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ return decNumberReduce(res, rhs, set);
+ } /* decNumberNormalize */
+
+decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
+ #endif
+ uInt status=0; /* as usual */
+ Int residue=0; /* as usual */
+ Int dropped; /* work */
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operand and set lostDigits status, as needed */
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ /* [following code does not require input rounding] */
+
+ /* Infinities copy through; NaNs need usual treatment */
+ if (decNumberIsNaN(rhs)) {
+ decNaNs(res, rhs, NULL, set, &status);
+ break;
+ }
+
+ /* reduce result to the requested length and copy to result */
+ decCopyFit(res, rhs, set, &residue, &status); /* copy & round */
+ decFinish(res, set, &residue, &status); /* cleanup/set flags */
+ decTrim(res, set, 1, 0, &dropped); /* normalize in place */
+ /* [may clamp] */
+ } while(0); /* end protected */
+
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); /* .. */
+ #endif
+ if (status!=0) decStatus(res, status, set);/* then report status */
return res;
-}
+ } /* decNumberReduce */
/* ------------------------------------------------------------------ */
-/* decNumberRescale -- force exponent to requested value */
-/* */
+/* decNumberRescale -- force exponent to requested value */
+/* */
/* This computes C = op(A, B), where op adjusts the coefficient */
/* of C (by rounding or shifting) such that the exponent (-scale) */
/* of C has the value B. The numerical value of C will equal A, */
-/* except for the effects of any rounding that occurred. */
-/* */
-/* res is C, the result. C may be A or B */
-/* lhs is A, the number to adjust */
-/* rhs is B, the requested exponent */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* */
+/* except for the effects of any rounding that occurred. */
+/* */
+/* res is C, the result. C may be A or B */
+/* lhs is A, the number to adjust */
+/* rhs is B, the requested exponent */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* */
/* Unless there is an error or the result is infinite, the exponent */
-/* after the operation is guaranteed to be equal to B. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberRescale (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- uInt status = 0; /* accumulator */
- decQuantizeOp (res, lhs, rhs, set, 0, &status);
- if (status != 0)
- decStatus (res, status, set);
+/* after the operation is guaranteed to be equal to B. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decQuantizeOp(res, lhs, rhs, set, 0, &status);
+ if (status!=0) decStatus(res, status, set);
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberRemainder -- divide and return remainder */
-/* */
-/* This computes C = A % B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberRemainder (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- uInt status = 0; /* accumulator */
- decDivideOp (res, lhs, rhs, set, REMAINDER, &status);
- if (status != 0)
- decStatus (res, status, set);
+ } /* decNumberRescale */
+
+/* ------------------------------------------------------------------ */
+/* decNumberRemainder -- divide and return remainder */
+/* */
+/* This computes C = A % B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
+ } /* decNumberRemainder */
/* ------------------------------------------------------------------ */
/* decNumberRemainderNear -- divide and return remainder from nearest */
-/* */
+/* */
/* This computes C = A % B, where % is the IEEE remainder operator */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberRemainderNear (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- uInt status = 0; /* accumulator */
- decDivideOp (res, lhs, rhs, set, REMNEAR, &status);
- if (status != 0)
- decStatus (res, status, set);
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
+ return res;
+ } /* decNumberRemainderNear */
+
+/* ------------------------------------------------------------------ */
+/* decNumberRotate -- rotate the coefficient of a Number left/right */
+/* */
+/* This computes C = A rot B (in base ten and rotating set->digits */
+/* digits). */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */
+/* lhs is A */
+/* rhs is B, the number of digits to rotate (-ve to right) */
+/* set is the context */
+/* */
+/* The digits of the coefficient of A are rotated to the left (if B */
+/* is positive) or to the right (if B is negative) without adjusting */
+/* the exponent or the sign of A. If lhs->digits is less than */
+/* set->digits the coefficient is padded with zeros on the left */
+/* before the rotate. Any leading zeros in the result are removed */
+/* as usual. */
+/* */
+/* B must be an integer (q=0) and in the range -set->digits through */
+/* +set->digits. */
+/* C must have space for set->digits digits. */
+/* NaNs are propagated as usual. Infinities are unaffected (but */
+/* B must be valid). No status is set unless B is invalid or an */
+/* operand is an sNaN. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ Int rotate; /* rhs as an Int */
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ /* NaNs propagate as normal */
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
+ decNaNs(res, lhs, rhs, set, &status);
+ /* rhs must be an integer */
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
+ status=DEC_Invalid_operation;
+ else { /* both numeric, rhs is an integer */
+ rotate=decGetInt(rhs); /* [cannot fail] */
+ if (rotate==BADINT /* something bad .. */
+ || rotate==BIGODD || rotate==BIGEVEN /* .. very big .. */
+ || abs(rotate)>set->digits) /* .. or out of range */
+ status=DEC_Invalid_operation;
+ else { /* rhs is OK */
+ decNumberCopy(res, lhs);
+ /* convert -ve rotate to equivalent positive rotation */
+ if (rotate<0) rotate=set->digits+rotate;
+ if (rotate!=0 && rotate!=set->digits /* zero or full rotation */
+ && !decNumberIsInfinite(res)) { /* lhs was infinite */
+ /* left-rotate to do; 0 < rotate < set->digits */
+ uInt units, shift; /* work */
+ uInt msudigits; /* digits in result msu */
+ Unit *msu=res->lsu+D2U(res->digits)-1; /* current msu */
+ Unit *msumax=res->lsu+D2U(set->digits)-1; /* rotation msu */
+ for (msu++; msu<=msumax; msu++) *msu=0; /* ensure high units=0 */
+ res->digits=set->digits; /* now full-length */
+ msudigits=MSUDIGITS(res->digits); /* actual digits in msu */
+
+ /* rotation here is done in-place, in three steps */
+ /* 1. shift all to least up to one unit to unit-align final */
+ /* lsd [any digits shifted out are rotated to the left, */
+ /* abutted to the original msd (which may require split)] */
+ /* */
+ /* [if there are no whole units left to rotate, the */
+ /* rotation is now complete] */
+ /* */
+ /* 2. shift to least, from below the split point only, so that */
+ /* the final msd is in the right place in its Unit [any */
+ /* digits shifted out will fit exactly in the current msu, */
+ /* left aligned, no split required] */
+ /* */
+ /* 3. rotate all the units by reversing left part, right */
+ /* part, and then whole */
+ /* */
+ /* example: rotate right 8 digits (2 units + 2), DECDPUN=3. */
+ /* */
+ /* start: 00a bcd efg hij klm npq */
+ /* */
+ /* 1a 000 0ab cde fgh|ijk lmn [pq saved] */
+ /* 1b 00p qab cde fgh|ijk lmn */
+ /* */
+ /* 2a 00p qab cde fgh|00i jkl [mn saved] */
+ /* 2b mnp qab cde fgh|00i jkl */
+ /* */
+ /* 3a fgh cde qab mnp|00i jkl */
+ /* 3b fgh cde qab mnp|jkl 00i */
+ /* 3c 00i jkl mnp qab cde fgh */
+
+ /* Step 1: amount to shift is the partial right-rotate count */
+ rotate=set->digits-rotate; /* make it right-rotate */
+ units=rotate/DECDPUN; /* whole units to rotate */
+ shift=rotate%DECDPUN; /* left-over digits count */
+ if (shift>0) { /* not an exact number of units */
+ uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */
+ decShiftToLeast(res->lsu, D2U(res->digits), shift);
+ if (shift>msudigits) { /* msumax-1 needs >0 digits */
+ uInt rem=save%powers[shift-msudigits];/* split save */
+ *msumax=(Unit)(save/powers[shift-msudigits]); /* and insert */
+ *(msumax-1)=*(msumax-1)
+ +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); /* .. */
+ }
+ else { /* all fits in msumax */
+ *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); /* [maybe *1] */
+ }
+ } /* digits shift needed */
+
+ /* If whole units to rotate... */
+ if (units>0) { /* some to do */
+ /* Step 2: the units to touch are the whole ones in rotate, */
+ /* if any, and the shift is DECDPUN-msudigits (which may be */
+ /* 0, again) */
+ shift=DECDPUN-msudigits;
+ if (shift>0) { /* not an exact number of units */
+ uInt save=res->lsu[0]%powers[shift]; /* save low digit(s) */
+ decShiftToLeast(res->lsu, units, shift);
+ *msumax=*msumax+(Unit)(save*powers[msudigits]);
+ } /* partial shift needed */
+
+ /* Step 3: rotate the units array using triple reverse */
+ /* (reversing is easy and fast) */
+ decReverse(res->lsu+units, msumax); /* left part */
+ decReverse(res->lsu, res->lsu+units-1); /* right part */
+ decReverse(res->lsu, msumax); /* whole */
+ } /* whole units to rotate */
+ /* the rotation may have left an undetermined number of zeros */
+ /* on the left, so true length needs to be calculated */
+ res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
+ } /* rotate needed */
+ } /* rhs OK */
+ } /* numerics */
+ if (status!=0) decStatus(res, status, set);
return res;
-}
+ } /* decNumberRotate */
/* ------------------------------------------------------------------ */
-/* decNumberSameQuantum -- test for equal exponents */
-/* */
+/* decNumberSameQuantum -- test for equal exponents */
+/* */
/* res is the result number, which will contain either 0 or 1 */
-/* lhs is a number to test */
-/* rhs is the second (usually a pattern) */
-/* */
-/* No errors are possible and no context is needed. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberSameQuantum (decNumber * res, decNumber * lhs, decNumber * rhs)
-{
- uByte merged; /* merged flags */
- Unit ret = 0; /* return value */
-
-#if DECCHECK
- if (decCheckOperands (res, lhs, rhs, DECUNUSED))
- return res;
-#endif
-
- merged = (lhs->bits | rhs->bits) & DECSPECIAL;
- if (merged)
- {
- if (decNumberIsNaN (lhs) && decNumberIsNaN (rhs))
- ret = 1;
- else if (decNumberIsInfinite (lhs) && decNumberIsInfinite (rhs))
- ret = 1;
- /* [anything else with a special gives 0] */
+/* lhs is a number to test */
+/* rhs is the second (usually a pattern) */
+/* */
+/* No errors are possible and no context is needed. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs) {
+ Unit ret=0; /* return value */
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
+ #endif
+
+ if (SPECIALARGS) {
+ if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
+ else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
+ /* [anything else with a special gives 0] */
}
- else if (lhs->exponent == rhs->exponent)
- ret = 1;
+ else if (lhs->exponent==rhs->exponent) ret=1;
- decNumberZero (res); /* OK to overwrite an operand */
- *res->lsu = ret;
+ decNumberZero(res); /* OK to overwrite an operand now */
+ *res->lsu=ret;
+ return res;
+ } /* decNumberSameQuantum */
+
+/* ------------------------------------------------------------------ */
+/* decNumberScaleB -- multiply by a power of 10 */
+/* */
+/* This computes C = A x 10**B where B is an integer (q=0) with */
+/* maximum magnitude 2*(emax+digits) */
+/* */
+/* res is C, the result. C may be A or B */
+/* lhs is A, the number to adjust */
+/* rhs is B, the requested power of ten to use */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* The result may underflow or overflow. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ Int reqexp; /* requested exponent change [B] */
+ uInt status=0; /* accumulator */
+ Int residue; /* work */
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ /* Handle special values except lhs infinite */
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
+ decNaNs(res, lhs, rhs, set, &status);
+ /* rhs must be an integer */
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
+ status=DEC_Invalid_operation;
+ else {
+ /* lhs is a number; rhs is a finite with q==0 */
+ reqexp=decGetInt(rhs); /* [cannot fail] */
+ if (reqexp==BADINT /* something bad .. */
+ || reqexp==BIGODD || reqexp==BIGEVEN /* .. very big .. */
+ || abs(reqexp)>(2*(set->digits+set->emax))) /* .. or out of range */
+ status=DEC_Invalid_operation;
+ else { /* rhs is OK */
+ decNumberCopy(res, lhs); /* all done if infinite lhs */
+ if (!decNumberIsInfinite(res)) { /* prepare to scale */
+ res->exponent+=reqexp; /* adjust the exponent */
+ residue=0;
+ decFinalize(res, set, &residue, &status); /* .. and check */
+ } /* finite LHS */
+ } /* rhs OK */
+ } /* rhs finite */
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } /* decNumberScaleB */
+
+/* ------------------------------------------------------------------ */
+/* decNumberShift -- shift the coefficient of a Number left or right */
+/* */
+/* This computes C = A << B or C = A >> -B (in base ten). */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */
+/* lhs is A */
+/* rhs is B, the number of digits to shift (-ve to right) */
+/* set is the context */
+/* */
+/* The digits of the coefficient of A are shifted to the left (if B */
+/* is positive) or to the right (if B is negative) without adjusting */
+/* the exponent or the sign of A. */
+/* */
+/* B must be an integer (q=0) and in the range -set->digits through */
+/* +set->digits. */
+/* C must have space for set->digits digits. */
+/* NaNs are propagated as usual. Infinities are unaffected (but */
+/* B must be valid). No status is set unless B is invalid or an */
+/* operand is an sNaN. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+ Int shift; /* rhs as an Int */
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ /* NaNs propagate as normal */
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
+ decNaNs(res, lhs, rhs, set, &status);
+ /* rhs must be an integer */
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
+ status=DEC_Invalid_operation;
+ else { /* both numeric, rhs is an integer */
+ shift=decGetInt(rhs); /* [cannot fail] */
+ if (shift==BADINT /* something bad .. */
+ || shift==BIGODD || shift==BIGEVEN /* .. very big .. */
+ || abs(shift)>set->digits) /* .. or out of range */
+ status=DEC_Invalid_operation;
+ else { /* rhs is OK */
+ decNumberCopy(res, lhs);
+ if (shift!=0 && !decNumberIsInfinite(res)) { /* something to do */
+ if (shift>0) { /* to left */
+ if (shift==set->digits) { /* removing all */
+ *res->lsu=0; /* so place 0 */
+ res->digits=1; /* .. */
+ }
+ else { /* */
+ /* first remove leading digits if necessary */
+ if (res->digits+shift>set->digits) {
+ decDecap(res, res->digits+shift-set->digits);
+ /* that updated res->digits; may have gone to 1 (for a */
+ /* single digit or for zero */
+ }
+ if (res->digits>1 || *res->lsu) /* if non-zero.. */
+ res->digits=decShiftToMost(res->lsu, res->digits, shift);
+ } /* partial left */
+ } /* left */
+ else { /* to right */
+ if (-shift>=res->digits) { /* discarding all */
+ *res->lsu=0; /* so place 0 */
+ res->digits=1; /* .. */
+ }
+ else {
+ decShiftToLeast(res->lsu, D2U(res->digits), -shift);
+ res->digits-=(-shift);
+ }
+ } /* to right */
+ } /* non-0 non-Inf shift */
+ } /* rhs OK */
+ } /* numerics */
+ if (status!=0) decStatus(res, status, set);
return res;
-}
+ } /* decNumberShift */
/* ------------------------------------------------------------------ */
-/* decNumberSquareRoot -- square root operator */
-/* */
-/* This computes C = squareroot(A) */
-/* */
-/* res is C, the result. C may be A */
-/* rhs is A */
-/* set is the context; note that rounding mode has no effect */
-/* */
-/* C must have space for set->digits digits. */
+/* decNumberSquareRoot -- square root operator */
+/* */
+/* This computes C = squareroot(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
-/* This uses the following varying-precision algorithm in: */
-/* */
+/* This uses the following varying-precision algorithm in: */
+/* */
/* Properly Rounded Variable Precision Square Root, T. E. Hull and */
/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
-/* pp229-237, ACM, September 1985. */
-/* */
+/* pp229-237, ACM, September 1985. */
+/* */
+/* The square-root is calculated using Newton's method, after which */
+/* a check is made to ensure the result is correctly rounded. */
+/* */
/* % [Reformatted original Numerical Turing source code follows.] */
-/* function sqrt(x : real) : real */
+/* function sqrt(x : real) : real */
/* % sqrt(x) returns the properly rounded approximation to the square */
/* % root of x, in the precision of the calling environment, or it */
-/* % fails if x < 0. */
-/* % t e hull and a abrham, august, 1984 */
-/* if x <= 0 then */
-/* if x < 0 then */
-/* assert false */
-/* else */
-/* result 0 */
-/* end if */
-/* end if */
-/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
-/* var e := getexp(x) % exponent part of x */
-/* var approx : real */
-/* if e mod 2 = 0 then */
-/* approx := .259 + .819 * f % approx to root of f */
-/* else */
-/* f := f/l0 % adjustments */
-/* e := e + 1 % for odd */
-/* approx := .0819 + 2.59 * f % exponent */
-/* end if */
-/* */
-/* var p:= 3 */
-/* const maxp := currentprecision + 2 */
-/* loop */
-/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
-/* precision p */
-/* approx := .5 * (approx + f/approx) */
-/* exit when p = maxp */
-/* end loop */
-/* */
+/* % fails if x < 0. */
+/* % t e hull and a abrham, august, 1984 */
+/* if x <= 0 then */
+/* if x < 0 then */
+/* assert false */
+/* else */
+/* result 0 */
+/* end if */
+/* end if */
+/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
+/* var e := getexp(x) % exponent part of x */
+/* var approx : real */
+/* if e mod 2 = 0 then */
+/* approx := .259 + .819 * f % approx to root of f */
+/* else */
+/* f := f/l0 % adjustments */
+/* e := e + 1 % for odd */
+/* approx := .0819 + 2.59 * f % exponent */
+/* end if */
+/* */
+/* var p:= 3 */
+/* const maxp := currentprecision + 2 */
+/* loop */
+/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
+/* precision p */
+/* approx := .5 * (approx + f/approx) */
+/* exit when p = maxp */
+/* end loop */
+/* */
/* % approx is now within 1 ulp of the properly rounded square root */
/* % of f; to ensure proper rounding, compare squares of (approx - */
-/* % l/2 ulp) and (approx + l/2 ulp) with f. */
-/* p := currentprecision */
-/* begin */
-/* precision p + 2 */
-/* const approxsubhalf := approx - setexp(.5, -p) */
-/* if mulru(approxsubhalf, approxsubhalf) > f then */
-/* approx := approx - setexp(.l, -p + 1) */
-/* else */
-/* const approxaddhalf := approx + setexp(.5, -p) */
-/* if mulrd(approxaddhalf, approxaddhalf) < f then */
-/* approx := approx + setexp(.l, -p + 1) */
-/* end if */
-/* end if */
-/* end */
-/* result setexp(approx, e div 2) % fix exponent */
-/* end sqrt */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberSquareRoot (decNumber * res, decNumber * rhs, decContext * set)
-{
- decContext workset, approxset; /* work contexts */
- decNumber dzero; /* used for constant zero */
- Int maxp = set->digits + 2; /* largest working precision */
- Int residue = 0; /* rounding residue */
- uInt status = 0, ignore = 0; /* status accumulators */
- Int exp; /* working exponent */
- Int ideal; /* ideal (preferred) exponent */
- uInt needbytes; /* work */
- Int dropped; /* .. */
-
- decNumber *allocrhs = NULL; /* non-NULL if rounded rhs allocated */
+/* % l/2 ulp) and (approx + l/2 ulp) with f. */
+/* p := currentprecision */
+/* begin */
+/* precision p + 2 */
+/* const approxsubhalf := approx - setexp(.5, -p) */
+/* if mulru(approxsubhalf, approxsubhalf) > f then */
+/* approx := approx - setexp(.l, -p + 1) */
+/* else */
+/* const approxaddhalf := approx + setexp(.5, -p) */
+/* if mulrd(approxaddhalf, approxaddhalf) < f then */
+/* approx := approx + setexp(.l, -p + 1) */
+/* end if */
+/* end if */
+/* end */
+/* result setexp(approx, e div 2) % fix exponent */
+/* end sqrt */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decContext workset, approxset; /* work contexts */
+ decNumber dzero; /* used for constant zero */
+ Int maxp; /* largest working precision */
+ Int workp; /* working precision */
+ Int residue=0; /* rounding residue */
+ uInt status=0, ignore=0; /* status accumulators */
+ uInt rstatus; /* .. */
+ Int exp; /* working exponent */
+ Int ideal; /* ideal (preferred) exponent */
+ Int needbytes; /* work */
+ Int dropped; /* .. */
+
+ #if DECSUBSET
+ decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
+ #endif
/* buffer for f [needs +1 in case DECBUFFER 0] */
- uByte buff[sizeof (decNumber) + (D2U (DECBUFFER + 1) - 1) * sizeof (Unit)];
- /* buffer for a [needs +2 to match maxp] */
- uByte bufa[sizeof (decNumber) + (D2U (DECBUFFER + 2) - 1) * sizeof (Unit)];
+ decNumber buff[D2N(DECBUFFER+1)];
+ /* buffer for a [needs +2 to match likely maxp] */
+ decNumber bufa[D2N(DECBUFFER+2)];
/* buffer for temporary, b [must be same size as a] */
- uByte bufb[sizeof (decNumber) + (D2U (DECBUFFER + 2) - 1) * sizeof (Unit)];
- decNumber *allocbuff = NULL; /* -> allocated buff, iff allocated */
- decNumber *allocbufa = NULL; /* -> allocated bufa, iff allocated */
- decNumber *allocbufb = NULL; /* -> allocated bufb, iff allocated */
- decNumber *f = (decNumber *) buff; /* reduced fraction */
- decNumber *a = (decNumber *) bufa; /* approximation to result */
- decNumber *b = (decNumber *) bufb; /* intermediate result */
+ decNumber bufb[D2N(DECBUFFER+2)];
+ decNumber *allocbuff=NULL; /* -> allocated buff, iff allocated */
+ decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
+ decNumber *allocbufb=NULL; /* -> allocated bufb, iff allocated */
+ decNumber *f=buff; /* reduced fraction */
+ decNumber *a=bufa; /* approximation to result */
+ decNumber *b=bufb; /* intermediate result */
/* buffer for temporary variable, up to 3 digits */
- uByte buft[sizeof (decNumber) + (D2U (3) - 1) * sizeof (Unit)];
- decNumber *t = (decNumber *) buft; /* up-to-3-digit constant or work */
-
-#if DECCHECK
- if (decCheckOperands (res, DECUNUSED, rhs, set))
- return res;
-#endif
-
- do
- { /* protect allocated storage */
-#if DECSUBSET
- if (!set->extended)
- {
- /* reduce operand and set lostDigits status, as needed */
- if (rhs->digits > set->digits)
- {
- allocrhs = decRoundOperand (rhs, set, &status);
- if (allocrhs == NULL)
- break;
- /* [Note: 'f' allocation below could reuse this buffer if */
- /* used, but as this is rare we keep them separate for clarity.] */
- rhs = allocrhs;
- }
+ decNumber buft[D2N(3)];
+ decNumber *t=buft; /* up-to-3-digit constant or work */
+
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operand and set lostDigits status, as needed */
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, &status);
+ if (allocrhs==NULL) break;
+ /* [Note: 'f' allocation below could reuse this buffer if */
+ /* used, but as this is rare they are kept separate for clarity.] */
+ rhs=allocrhs;
}
-#endif
- /* [following code does not require input rounding] */
-
- /* handle infinities and NaNs */
- if (rhs->bits & DECSPECIAL)
- {
- if (decNumberIsInfinite (rhs))
- { /* an infinity */
- if (decNumberIsNegative (rhs))
- status |= DEC_Invalid_operation;
- else
- decNumberCopy (res, rhs); /* +Infinity */
- }
- else
- decNaNs (res, rhs, NULL, &status); /* a NaN */
- break;
+ }
+ #endif
+ /* [following code does not require input rounding] */
+
+ /* handle infinities and NaNs */
+ if (SPECIALARG) {
+ if (decNumberIsInfinite(rhs)) { /* an infinity */
+ if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
+ else decNumberCopy(res, rhs); /* +Infinity */
}
+ else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
+ break;
+ }
- /* calculate the ideal (preferred) exponent [floor(exp/2)] */
- /* [We would like to write: ideal=rhs->exponent>>1, but this */
- /* generates a compiler warning. Generated code is the same.] */
- ideal = (rhs->exponent & ~1) / 2; /* target */
+ /* calculate the ideal (preferred) exponent [floor(exp/2)] */
+ /* [It would be nicer to write: ideal=rhs->exponent>>1, but this */
+ /* generates a compiler warning. Generated code is the same.] */
+ ideal=(rhs->exponent&~1)/2; /* target */
+
+ /* handle zeros */
+ if (ISZERO(rhs)) {
+ decNumberCopy(res, rhs); /* could be 0 or -0 */
+ res->exponent=ideal; /* use the ideal [safe] */
+ /* use decFinish to clamp any out-of-range exponent, etc. */
+ decFinish(res, set, &residue, &status);
+ break;
+ }
- /* handle zeros */
- if (ISZERO (rhs))
- {
- decNumberCopy (res, rhs); /* could be 0 or -0 */
- res->exponent = ideal; /* use the ideal [safe] */
- break;
- }
+ /* any other -x is an oops */
+ if (decNumberIsNegative(rhs)) {
+ status|=DEC_Invalid_operation;
+ break;
+ }
- /* any other -x is an oops */
- if (decNumberIsNegative (rhs))
- {
- status |= DEC_Invalid_operation;
- break;
- }
+ /* space is needed for three working variables */
+ /* f -- the same precision as the RHS, reduced to 0.01->0.99... */
+ /* a -- Hull's approximation -- precision, when assigned, is */
+ /* currentprecision+1 or the input argument precision, */
+ /* whichever is larger (+2 for use as temporary) */
+ /* b -- intermediate temporary result (same size as a) */
+ /* if any is too long for local storage, then allocate */
+ workp=MAXI(set->digits+1, rhs->digits); /* actual rounding precision */
+ workp=MAXI(workp, 7); /* at least 7 for low cases */
+ maxp=workp+2; /* largest working precision */
+
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
+ if (needbytes>(Int)sizeof(buff)) {
+ allocbuff=(decNumber *)malloc(needbytes);
+ if (allocbuff==NULL) { /* hopeless -- abandon */
+ status|=DEC_Insufficient_storage;
+ break;}
+ f=allocbuff; /* use the allocated space */
+ }
+ /* a and b both need to be able to hold a maxp-length number */
+ needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
+ if (needbytes>(Int)sizeof(bufa)) { /* [same applies to b] */
+ allocbufa=(decNumber *)malloc(needbytes);
+ allocbufb=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */
+ status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; /* use the allocated spaces */
+ b=allocbufb; /* .. */
+ }
- /* we need space for three working variables */
- /* f -- the same precision as the RHS, reduced to 0.01->0.99... */
- /* a -- Hull's approx -- precision, when assigned, is */
- /* currentprecision (we allow +2 for use as temporary) */
- /* b -- intermediate temporary result */
- /* if any is too long for local storage, then allocate */
- needbytes =
- sizeof (decNumber) + (D2U (rhs->digits) - 1) * sizeof (Unit);
- if (needbytes > sizeof (buff))
- {
- allocbuff = (decNumber *) malloc (needbytes);
- if (allocbuff == NULL)
- { /* hopeless -- abandon */
- status |= DEC_Insufficient_storage;
- break;
- }
- f = allocbuff; /* use the allocated space */
- }
- /* a and b both need to be able to hold a maxp-length number */
- needbytes = sizeof (decNumber) + (D2U (maxp) - 1) * sizeof (Unit);
- if (needbytes > sizeof (bufa))
- { /* [same applies to b] */
- allocbufa = (decNumber *) malloc (needbytes);
- allocbufb = (decNumber *) malloc (needbytes);
- if (allocbufa == NULL || allocbufb == NULL)
- { /* hopeless */
- status |= DEC_Insufficient_storage;
- break;
- }
- a = allocbufa; /* use the allocated space */
- b = allocbufb; /* .. */
- }
+ /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
+ decNumberCopy(f, rhs);
+ exp=f->exponent+f->digits; /* adjusted to Hull rules */
+ f->exponent=-(f->digits); /* to range */
+
+ /* set up working context */
+ decContextDefault(&workset, DEC_INIT_DECIMAL64);
+ workset.emax=DEC_MAX_EMAX;
+ workset.emin=DEC_MIN_EMIN;
+
+ /* [Until further notice, no error is possible and status bits */
+ /* (Rounded, etc.) should be ignored, not accumulated.] */
+
+ /* Calculate initial approximation, and allow for odd exponent */
+ workset.digits=workp; /* p for initial calculation */
+ t->bits=0; t->digits=3;
+ a->bits=0; a->digits=3;
+ if ((exp & 1)==0) { /* even exponent */
+ /* Set t=0.259, a=0.819 */
+ t->exponent=-3;
+ a->exponent=-3;
+ #if DECDPUN>=3
+ t->lsu[0]=259;
+ a->lsu[0]=819;
+ #elif DECDPUN==2
+ t->lsu[0]=59; t->lsu[1]=2;
+ a->lsu[0]=19; a->lsu[1]=8;
+ #else
+ t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
+ a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
+ #endif
+ }
+ else { /* odd exponent */
+ /* Set t=0.0819, a=2.59 */
+ f->exponent--; /* f=f/10 */
+ exp++; /* e=e+1 */
+ t->exponent=-4;
+ a->exponent=-2;
+ #if DECDPUN>=3
+ t->lsu[0]=819;
+ a->lsu[0]=259;
+ #elif DECDPUN==2
+ t->lsu[0]=19; t->lsu[1]=8;
+ a->lsu[0]=59; a->lsu[1]=2;
+ #else
+ t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
+ a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
+ #endif
+ }
- /* copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 */
- decNumberCopy (f, rhs);
- exp = f->exponent + f->digits; /* adjusted to Hull rules */
- f->exponent = -(f->digits); /* to range */
-
- /* set up working contexts (the second is used for Numerical */
- /* Turing assignment) */
- decContextDefault (&workset, DEC_INIT_DECIMAL64);
- decContextDefault (&approxset, DEC_INIT_DECIMAL64);
- approxset.digits = set->digits; /* approx's length */
-
- /* [Until further notice, no error is possible and status bits */
- /* (Rounded, etc.) should be ignored, not accumulated.] */
-
- /* Calculate initial approximation, and allow for odd exponent */
- workset.digits = set->digits; /* p for initial calculation */
- t->bits = 0;
- t->digits = 3;
- a->bits = 0;
- a->digits = 3;
- if ((exp & 1) == 0)
- { /* even exponent */
- /* Set t=0.259, a=0.819 */
- t->exponent = -3;
- a->exponent = -3;
-#if DECDPUN>=3
- t->lsu[0] = 259;
- a->lsu[0] = 819;
-#elif DECDPUN==2
- t->lsu[0] = 59;
- t->lsu[1] = 2;
- a->lsu[0] = 19;
- a->lsu[1] = 8;
-#else
- t->lsu[0] = 9;
- t->lsu[1] = 5;
- t->lsu[2] = 2;
- a->lsu[0] = 9;
- a->lsu[1] = 1;
- a->lsu[2] = 8;
-#endif
- }
- else
- { /* odd exponent */
- /* Set t=0.0819, a=2.59 */
- f->exponent--; /* f=f/10 */
- exp++; /* e=e+1 */
- t->exponent = -4;
- a->exponent = -2;
-#if DECDPUN>=3
- t->lsu[0] = 819;
- a->lsu[0] = 259;
-#elif DECDPUN==2
- t->lsu[0] = 19;
- t->lsu[1] = 8;
- a->lsu[0] = 59;
- a->lsu[1] = 2;
-#else
- t->lsu[0] = 9;
- t->lsu[1] = 1;
- t->lsu[2] = 8;
- a->lsu[0] = 9;
- a->lsu[1] = 5;
- a->lsu[2] = 2;
-#endif
- }
- decMultiplyOp (a, a, f, &workset, &ignore); /* a=a*f */
- decAddOp (a, a, t, &workset, 0, &ignore); /* ..+t */
- /* [a is now the initial approximation for sqrt(f), calculated with */
- /* currentprecision, which is also a's precision.] */
-
- /* the main calculation loop */
- decNumberZero (&dzero); /* make 0 */
- decNumberZero (t); /* set t = 0.5 */
- t->lsu[0] = 5; /* .. */
- t->exponent = -1; /* .. */
- workset.digits = 3; /* initial p */
- for (;;)
- {
- /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */
- workset.digits = workset.digits * 2 - 2;
- if (workset.digits > maxp)
- workset.digits = maxp;
- /* a = 0.5 * (a + f/a) */
- /* [calculated at p then rounded to currentprecision] */
- decDivideOp (b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
- decAddOp (b, b, a, &workset, 0, &ignore); /* b=b+a */
- decMultiplyOp (a, b, t, &workset, &ignore); /* a=b*0.5 */
- /* assign to approx [round to length] */
- decAddOp (a, &dzero, a, &approxset, 0, &ignore);
- if (workset.digits == maxp)
- break; /* just did final */
- } /* loop */
-
- /* a is now at currentprecision and within 1 ulp of the properly */
- /* rounded square root of f; to ensure proper rounding, compare */
- /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
- /* Here workset.digits=maxp and t=0.5 */
- workset.digits--; /* maxp-1 is OK now */
- t->exponent = -set->digits - 1; /* make 0.5 ulp */
- decNumberCopy (b, a);
- decAddOp (b, b, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
- workset.round = DEC_ROUND_UP;
- decMultiplyOp (b, b, b, &workset, &ignore); /* b = mulru(b, b) */
- decCompareOp (b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
- if (decNumberIsNegative (b))
- { /* f < b [i.e., b > f] */
- /* this is the more common adjustment, though both are rare */
- t->exponent++; /* make 1.0 ulp */
- t->lsu[0] = 1; /* .. */
- decAddOp (a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
- /* assign to approx [round to length] */
- decAddOp (a, &dzero, a, &approxset, 0, &ignore);
- }
- else
- {
- decNumberCopy (b, a);
- decAddOp (b, b, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */
- workset.round = DEC_ROUND_DOWN;
- decMultiplyOp (b, b, b, &workset, &ignore); /* b = mulrd(b, b) */
- decCompareOp (b, b, f, &workset, COMPARE, &ignore); /* b ? f */
- if (decNumberIsNegative (b))
- { /* b < f */
- t->exponent++; /* make 1.0 ulp */
- t->lsu[0] = 1; /* .. */
- decAddOp (a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */
- /* assign to approx [round to length] */
- decAddOp (a, &dzero, a, &approxset, 0, &ignore);
- }
+ decMultiplyOp(a, a, f, &workset, &ignore); /* a=a*f */
+ decAddOp(a, a, t, &workset, 0, &ignore); /* ..+t */
+ /* [a is now the initial approximation for sqrt(f), calculated with */
+ /* currentprecision, which is also a's precision.] */
+
+ /* the main calculation loop */
+ decNumberZero(&dzero); /* make 0 */
+ decNumberZero(t); /* set t = 0.5 */
+ t->lsu[0]=5; /* .. */
+ t->exponent=-1; /* .. */
+ workset.digits=3; /* initial p */
+ for (; workset.digits<maxp;) {
+ /* set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp] */
+ workset.digits=MINI(workset.digits*2-2, maxp);
+ /* a = 0.5 * (a + f/a) */
+ /* [calculated at p then rounded to currentprecision] */
+ decDivideOp(b, f, a, &workset, DIVIDE, &ignore); /* b=f/a */
+ decAddOp(b, b, a, &workset, 0, &ignore); /* b=b+a */
+ decMultiplyOp(a, b, t, &workset, &ignore); /* a=b*0.5 */
+ } /* loop */
+
+ /* Here, 0.1 <= a < 1 [Hull], and a has maxp digits */
+ /* now reduce to length, etc.; this needs to be done with a */
+ /* having the correct exponent so as to handle subnormals */
+ /* correctly */
+ approxset=*set; /* get emin, emax, etc. */
+ approxset.round=DEC_ROUND_HALF_EVEN;
+ a->exponent+=exp/2; /* set correct exponent */
+ rstatus=0; /* clear status */
+ residue=0; /* .. and accumulator */
+ decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */
+ decFinish(a, &approxset, &residue, &rstatus); /* clean and finalize */
+
+ /* Overflow was possible if the input exponent was out-of-range, */
+ /* in which case quit */
+ if (rstatus&DEC_Overflow) {
+ status=rstatus; /* use the status as-is */
+ decNumberCopy(res, a); /* copy to result */
+ break;
+ }
+
+ /* Preserve status except Inexact/Rounded */
+ status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
+
+ /* Carry out the Hull correction */
+ a->exponent-=exp/2; /* back to 0.1->1 */
+
+ /* a is now at final precision and within 1 ulp of the properly */
+ /* rounded square root of f; to ensure proper rounding, compare */
+ /* squares of (a - l/2 ulp) and (a + l/2 ulp) with f. */
+ /* Here workset.digits=maxp and t=0.5, and a->digits determines */
+ /* the ulp */
+ workset.digits--; /* maxp-1 is OK now */
+ t->exponent=-a->digits-1; /* make 0.5 ulp */
+ decAddOp(b, a, t, &workset, DECNEG, &ignore); /* b = a - 0.5 ulp */
+ workset.round=DEC_ROUND_UP;
+ decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulru(b, b) */
+ decCompareOp(b, f, b, &workset, COMPARE, &ignore); /* b ? f, reversed */
+ if (decNumberIsNegative(b)) { /* f < b [i.e., b > f] */
+ /* this is the more common adjustment, though both are rare */
+ t->exponent++; /* make 1.0 ulp */
+ t->lsu[0]=1; /* .. */
+ decAddOp(a, a, t, &workset, DECNEG, &ignore); /* a = a - 1 ulp */
+ /* assign to approx [round to length] */
+ approxset.emin-=exp/2; /* adjust to match a */
+ approxset.emax-=exp/2;
+ decAddOp(a, &dzero, a, &approxset, 0, &ignore);
+ }
+ else {
+ decAddOp(b, a, t, &workset, 0, &ignore); /* b = a + 0.5 ulp */
+ workset.round=DEC_ROUND_DOWN;
+ decMultiplyOp(b, b, b, &workset, &ignore); /* b = mulrd(b, b) */
+ decCompareOp(b, b, f, &workset, COMPARE, &ignore); /* b ? f */
+ if (decNumberIsNegative(b)) { /* b < f */
+ t->exponent++; /* make 1.0 ulp */
+ t->lsu[0]=1; /* .. */
+ decAddOp(a, a, t, &workset, 0, &ignore); /* a = a + 1 ulp */
+ /* assign to approx [round to length] */
+ approxset.emin-=exp/2; /* adjust to match a */
+ approxset.emax-=exp/2;
+ decAddOp(a, &dzero, a, &approxset, 0, &ignore);
}
- /* [no errors are possible in the above, and rounding/inexact during */
- /* estimation are irrelevant, so status was not accumulated] */
-
- /* Here, 0.1 <= a < 1 [Hull] */
- a->exponent += exp / 2; /* set correct exponent */
-
- /* Process Subnormals */
- decFinalize (a, set, &residue, &status);
-
- /* count dropable zeros [after any subnormal rounding] */
- decNumberCopy (b, a);
- decTrim (b, 1, &dropped); /* [drops trailing zeros] */
-
- /* Finally set Inexact and Rounded. The answer can only be exact if */
- /* it is short enough so that squaring it could fit in set->digits, */
- /* so this is the only (relatively rare) time we have to check */
- /* carefully */
- if (b->digits * 2 - 1 > set->digits)
- { /* cannot fit */
- status |= DEC_Inexact | DEC_Rounded;
+ }
+ /* [no errors are possible in the above, and rounding/inexact during */
+ /* estimation are irrelevant, so status was not accumulated] */
+
+ /* Here, 0.1 <= a < 1 (still), so adjust back */
+ a->exponent+=exp/2; /* set correct exponent */
+
+ /* count droppable zeros [after any subnormal rounding] by */
+ /* trimming a copy */
+ decNumberCopy(b, a);
+ decTrim(b, set, 1, 1, &dropped); /* [drops trailing zeros] */
+
+ /* Set Inexact and Rounded. The answer can only be exact if */
+ /* it is short enough so that squaring it could fit in workp */
+ /* digits, so this is the only (relatively rare) condition that */
+ /* a careful check is needed */
+ if (b->digits*2-1 > workp) { /* cannot fit */
+ status|=DEC_Inexact|DEC_Rounded;
+ }
+ else { /* could be exact/unrounded */
+ uInt mstatus=0; /* local status */
+ decMultiplyOp(b, b, b, &workset, &mstatus); /* try the multiply */
+ if (mstatus&DEC_Overflow) { /* result just won't fit */
+ status|=DEC_Inexact|DEC_Rounded;
}
- else
- { /* could be exact/unrounded */
- uInt mstatus = 0; /* local status */
- decMultiplyOp (b, b, b, &workset, &mstatus); /* try the multiply */
- if (mstatus != 0)
- { /* result won't fit */
- status |= DEC_Inexact | DEC_Rounded;
- }
- else
- { /* plausible */
- decCompareOp (t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
- if (!ISZERO (t))
- {
- status |= DEC_Inexact | DEC_Rounded;
- }
- else
- { /* is Exact */
- /* here, dropped is the count of trailing zeros in 'a' */
- /* use closest exponent to ideal... */
- Int todrop = ideal - a->exponent; /* most we can drop */
-
- if (todrop < 0)
- { /* ideally would add 0s */
- status |= DEC_Rounded;
- }
- else
- { /* unrounded */
- if (dropped < todrop)
- todrop = dropped; /* clamp to those available */
- if (todrop > 0)
- { /* OK, some to drop */
- decShiftToLeast (a->lsu, D2U (a->digits), todrop);
- a->exponent += todrop; /* maintain numerical value */
- a->digits -= todrop; /* new length */
- }
- }
- }
+ else { /* plausible */
+ decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
+ if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */
+ else { /* is Exact */
+ /* here, dropped is the count of trailing zeros in 'a' */
+ /* use closest exponent to ideal... */
+ Int todrop=ideal-a->exponent; /* most that can be dropped */
+ if (todrop<0) status|=DEC_Rounded; /* ideally would add 0s */
+ else { /* unrounded */
+ /* there are some to drop, but emax may not allow all */
+ Int maxexp=set->emax-set->digits+1;
+ Int maxdrop=maxexp-a->exponent;
+ if (todrop>maxdrop && set->clamp) { /* apply clamping */
+ todrop=maxdrop;
+ status|=DEC_Clamped;
+ }
+ if (dropped<todrop) { /* clamp to those available */
+ todrop=dropped;
+ status|=DEC_Clamped;
+ }
+ if (todrop>0) { /* have some to drop */
+ decShiftToLeast(a->lsu, D2U(a->digits), todrop);
+ a->exponent+=todrop; /* maintain numerical value */
+ a->digits-=todrop; /* new length */
+ }
}
+ }
}
- decNumberCopy (res, a); /* assume this is the result */
- }
- while (0); /* end protected */
-
- if (allocbuff != NULL)
- free (allocbuff); /* drop any storage we used */
- if (allocbufa != NULL)
- free (allocbufa); /* .. */
- if (allocbufb != NULL)
- free (allocbufb); /* .. */
- if (allocrhs != NULL)
- free (allocrhs); /* .. */
- if (status != 0)
- decStatus (res, status, set); /* then report status */
+ }
+
+ /* double-check Underflow, as perhaps the result could not have */
+ /* been subnormal (initial argument too big), or it is now Exact */
+ if (status&DEC_Underflow) {
+ Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
+ /* check if truly subnormal */
+ #if DECEXTFLAG /* DEC_Subnormal too */
+ if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
+ #else
+ if (ae>=set->emin*2) status&=~DEC_Underflow;
+ #endif
+ /* check if truly inexact */
+ if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
+ }
+
+ decNumberCopy(res, a); /* a is now the result */
+ } while(0); /* end protected */
+
+ if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */
+ if (allocbufa!=NULL) free(allocbufa); /* .. */
+ if (allocbufb!=NULL) free(allocbufb); /* .. */
+ #if DECSUBSET
+ if (allocrhs !=NULL) free(allocrhs); /* .. */
+ #endif
+ if (status!=0) decStatus(res, status, set);/* then report status */
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberSubtract -- subtract two Numbers */
-/* */
-/* This computes C = A - B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X-X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decNumberSubtract (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- uInt status = 0; /* accumulator */
-
- decAddOp (res, lhs, rhs, set, DECNEG, &status);
- if (status != 0)
- decStatus (res, status, set);
+ } /* decNumberSquareRoot */
+
+/* ------------------------------------------------------------------ */
+/* decNumberSubtract -- subtract two Numbers */
+/* */
+/* This computes C = A - B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X-X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* */
+/* C must have space for set->digits digits. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ uInt status=0; /* accumulator */
+
+ decAddOp(res, lhs, rhs, set, DECNEG, &status);
+ if (status!=0) decStatus(res, status, set);
+ #if DECCHECK
+ decCheckInexact(res, set);
+ #endif
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNumberToIntegralValue -- round-to-integral-value */
-/* */
-/* res is the result */
-/* rhs is input number */
-/* set is the context */
-/* */
-/* res must have space for any value of rhs. */
-/* */
-/* This implements the IEEE special operator and therefore treats */
-/* special values as valid, and also never sets Inexact. For finite */
-/* numbers it returns rescale(rhs, 0) if rhs->exponent is <0. */
-/* Otherwise the result is rhs (so no error is possible). */
-/* */
+ } /* decNumberSubtract */
+
+/* ------------------------------------------------------------------ */
+/* decNumberToIntegralExact -- round-to-integral-value with InExact */
+/* decNumberToIntegralValue -- round-to-integral-value */
+/* */
+/* res is the result */
+/* rhs is input number */
+/* set is the context */
+/* */
+/* res must have space for any value of rhs. */
+/* */
+/* This implements the IEEE special operators and therefore treats */
+/* special values as valid. For finite numbers it returns */
+/* rescale(rhs, 0) if rhs->exponent is <0. */
+/* Otherwise the result is rhs (so no error is possible, except for */
+/* sNaN). */
+/* */
/* The context is used for rounding mode and status after sNaN, but */
-/* the digits setting is ignored. */
+/* the digits setting is ignored. The Exact version will signal */
+/* Inexact if the result differs numerically from rhs; the other */
+/* never signals Inexact. */
/* ------------------------------------------------------------------ */
-decNumber *
-decNumberToIntegralValue (decNumber * res, decNumber * rhs, decContext * set)
-{
+decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
+ decContext *set) {
decNumber dn;
- decContext workset; /* working context */
+ decContext workset; /* working context */
+ uInt status=0; /* accumulator */
-#if DECCHECK
- if (decCheckOperands (res, DECUNUSED, rhs, set))
- return res;
-#endif
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
/* handle infinities and NaNs */
- if (rhs->bits & DECSPECIAL)
- {
- uInt status = 0;
- if (decNumberIsInfinite (rhs))
- decNumberCopy (res, rhs); /* an Infinity */
- else
- decNaNs (res, rhs, NULL, &status); /* a NaN */
- if (status != 0)
- decStatus (res, status, set);
- return res;
+ if (SPECIALARG) {
+ if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); /* an Infinity */
+ else decNaNs(res, rhs, NULL, set, &status); /* a NaN */
}
+ else { /* finite */
+ /* have a finite number; no error possible (res must be big enough) */
+ if (rhs->exponent>=0) return decNumberCopy(res, rhs);
+ /* that was easy, but if negative exponent there is work to do... */
+ workset=*set; /* clone rounding, etc. */
+ workset.digits=rhs->digits; /* no length rounding */
+ workset.traps=0; /* no traps */
+ decNumberZero(&dn); /* make a number with exponent 0 */
+ decNumberQuantize(res, rhs, &dn, &workset);
+ status|=workset.status;
+ }
+ if (status!=0) decStatus(res, status, set);
+ return res;
+ } /* decNumberToIntegralExact */
+
+decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
+ decContext *set) {
+ decContext workset=*set; /* working context */
+ workset.traps=0; /* no traps */
+ decNumberToIntegralExact(res, rhs, &workset);
+ /* this never affects set, except for sNaNs; NaN will have been set */
+ /* or propagated already, so no need to call decStatus */
+ set->status|=workset.status&DEC_Invalid_operation;
+ return res;
+ } /* decNumberToIntegralValue */
+
+/* ------------------------------------------------------------------ */
+/* decNumberXor -- XOR two Numbers, digitwise */
+/* */
+/* This computes C = A ^ B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X^X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context (used for result length and error report) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Logical function restrictions apply (see above); a NaN is */
+/* returned with Invalid_operation if a restriction is violated. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ const Unit *ua, *ub; /* -> operands */
+ const Unit *msua, *msub; /* -> operand msus */
+ Unit *uc, *msuc; /* -> result and its msu */
+ Int msudigs; /* digits in res msu */
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ /* operands are valid */
+ ua=lhs->lsu; /* bottom-up */
+ ub=rhs->lsu; /* .. */
+ uc=res->lsu; /* .. */
+ msua=ua+D2U(lhs->digits)-1; /* -> msu of lhs */
+ msub=ub+D2U(rhs->digits)-1; /* -> msu of rhs */
+ msuc=uc+D2U(set->digits)-1; /* -> msu of result */
+ msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
+ for (; uc<=msuc; ua++, ub++, uc++) { /* Unit loop */
+ Unit a, b; /* extract units */
+ if (ua>msua) a=0;
+ else a=*ua;
+ if (ub>msub) b=0;
+ else b=*ub;
+ *uc=0; /* can now write back */
+ if (a|b) { /* maybe 1 bits to examine */
+ Int i, j;
+ /* This loop could be unrolled and/or use BIN2BCD tables */
+ for (i=0; i<DECDPUN; i++) {
+ if ((a^b)&1) *uc=*uc+(Unit)powers[i]; /* effect XOR */
+ j=a%10;
+ a=a/10;
+ j|=b%10;
+ b=b/10;
+ if (j>1) {
+ decStatus(res, DEC_Invalid_operation, set);
+ return res;
+ }
+ if (uc==msuc && i==msudigs-1) break; /* just did final digit */
+ } /* each digit */
+ } /* non-zero */
+ } /* each unit */
+ /* [here uc-1 is the msu of the result] */
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);
+ res->exponent=0; /* integer */
+ res->bits=0; /* sign=0 */
+ return res; /* [no status to set] */
+ } /* decNumberXor */
- /* we have a finite number; no error possible */
- if (rhs->exponent >= 0)
- return decNumberCopy (res, rhs);
- /* that was easy, but if negative exponent we have work to do... */
- workset = *set; /* clone rounding, etc. */
- workset.digits = rhs->digits; /* no length rounding */
- workset.traps = 0; /* no traps */
- decNumberZero (&dn); /* make a number with exponent 0 */
- return decNumberQuantize (res, rhs, &dn, &workset);
-}
/* ================================================================== */
-/* Utility routines */
+/* Utility routines */
/* ================================================================== */
/* ------------------------------------------------------------------ */
-/* decNumberCopy -- copy a number */
-/* */
-/* dest is the target decNumber */
-/* src is the source decNumber */
-/* returns dest */
-/* */
-/* (dest==src is allowed and is a no-op) */
-/* All fields are updated as required. This is a utility operation, */
-/* so special values are unchanged and no error is possible. */
+/* decNumberClass -- return the decClass of a decNumber */
+/* dn -- the decNumber to test */
+/* set -- the context to use for Emin */
+/* returns the decClass enum */
/* ------------------------------------------------------------------ */
-decNumber *
-decNumberCopy (decNumber * dest, decNumber * src)
-{
-
-#if DECCHECK
- if (src == NULL)
- return decNumberZero (dest);
-#endif
-
- if (dest == src)
- return dest; /* no copy required */
-
- /* We use explicit assignments here as structure assignment can copy */
+enum decClass decNumberClass(const decNumber *dn, decContext *set) {
+ if (decNumberIsSpecial(dn)) {
+ if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
+ if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
+ /* must be an infinity */
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
+ return DEC_CLASS_POS_INF;
+ }
+ /* is finite */
+ if (decNumberIsNormal(dn, set)) { /* most common */
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
+ return DEC_CLASS_POS_NORMAL;
+ }
+ /* is subnormal or zero */
+ if (decNumberIsZero(dn)) { /* most common */
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
+ return DEC_CLASS_POS_ZERO;
+ }
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
+ return DEC_CLASS_POS_SUBNORMAL;
+ } /* decNumberClass */
+
+/* ------------------------------------------------------------------ */
+/* decNumberClassToString -- convert decClass to a string */
+/* */
+/* eclass is a valid decClass */
+/* returns a constant string describing the class (max 13+1 chars) */
+/* ------------------------------------------------------------------ */
+const char *decNumberClassToString(enum decClass eclass) {
+ if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
+ if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
+ if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
+ if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
+ if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
+ if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
+ if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
+ if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
+ if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
+ if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
+ return DEC_ClassString_UN; /* Unknown */
+ } /* decNumberClassToString */
+
+/* ------------------------------------------------------------------ */
+/* decNumberCopy -- copy a number */
+/* */
+/* dest is the target decNumber */
+/* src is the source decNumber */
+/* returns dest */
+/* */
+/* (dest==src is allowed and is a no-op) */
+/* All fields are updated as required. This is a utility operation, */
+/* so special values are unchanged and no error is possible. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {
+
+ #if DECCHECK
+ if (src==NULL) return decNumberZero(dest);
+ #endif
+
+ if (dest==src) return dest; /* no copy required */
+
+ /* Use explicit assignments here as structure assignment could copy */
/* more than just the lsu (for small DECDPUN). This would not affect */
- /* the value of the results, but would disturb test harness spill */
+ /* the value of the results, but could disturb test harness spill */
/* checking. */
- dest->bits = src->bits;
- dest->exponent = src->exponent;
- dest->digits = src->digits;
- dest->lsu[0] = src->lsu[0];
- if (src->digits > DECDPUN)
- { /* more Units to come */
- Unit *s, *d, *smsup; /* work */
- /* memcpy for the remaining Units would be safe as they cannot */
- /* overlap. However, this explicit loop is faster in short cases. */
- d = dest->lsu + 1; /* -> first destination */
- smsup = src->lsu + D2U (src->digits); /* -> source msu+1 */
- for (s = src->lsu + 1; s < smsup; s++, d++)
- *d = *s;
+ dest->bits=src->bits;
+ dest->exponent=src->exponent;
+ dest->digits=src->digits;
+ dest->lsu[0]=src->lsu[0];
+ if (src->digits>DECDPUN) { /* more Units to come */
+ const Unit *smsup, *s; /* work */
+ Unit *d; /* .. */
+ /* memcpy for the remaining Units would be safe as they cannot */
+ /* overlap. However, this explicit loop is faster in short cases. */
+ d=dest->lsu+1; /* -> first destination */
+ smsup=src->lsu+D2U(src->digits); /* -> source msu+1 */
+ for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
}
return dest;
-}
+ } /* decNumberCopy */
+
+/* ------------------------------------------------------------------ */
+/* decNumberCopyAbs -- quiet absolute value operator */
+/* */
+/* This sets C = abs(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* */
+/* C must have space for set->digits digits. */
+/* No exception or error can occur; this is a quiet bitwise operation.*/
+/* See also decNumberAbs for a checking version of this. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
+ #endif
+ decNumberCopy(res, rhs);
+ res->bits&=~DECNEG; /* turn off sign */
+ return res;
+ } /* decNumberCopyAbs */
+
+/* ------------------------------------------------------------------ */
+/* decNumberCopyNegate -- quiet negate value operator */
+/* */
+/* This sets C = negate(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* */
+/* C must have space for set->digits digits. */
+/* No exception or error can occur; this is a quiet bitwise operation.*/
+/* See also decNumberMinus for a checking version of this. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
+ #endif
+ decNumberCopy(res, rhs);
+ res->bits^=DECNEG; /* invert the sign */
+ return res;
+ } /* decNumberCopyNegate */
+
+/* ------------------------------------------------------------------ */
+/* decNumberCopySign -- quiet copy and set sign operator */
+/* */
+/* This sets C = A with the sign of B */
+/* */
+/* res is C, the result. C may be A */
+/* lhs is A */
+/* rhs is B */
+/* */
+/* C must have space for set->digits digits. */
+/* No exception or error can occur; this is a quiet bitwise operation.*/
+/* ------------------------------------------------------------------ */
+decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs) {
+ uByte sign; /* rhs sign */
+ #if DECCHECK
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
+ #endif
+ sign=rhs->bits & DECNEG; /* save sign bit */
+ decNumberCopy(res, lhs);
+ res->bits&=~DECNEG; /* clear the sign */
+ res->bits|=sign; /* set from rhs */
+ return res;
+ } /* decNumberCopySign */
+
+/* ------------------------------------------------------------------ */
+/* decNumberGetBCD -- get the coefficient in BCD8 */
+/* dn is the source decNumber */
+/* bcd is the uInt array that will receive dn->digits BCD bytes, */
+/* most-significant at offset 0 */
+/* returns bcd */
+/* */
+/* bcd must have at least dn->digits bytes. No error is possible; if */
+/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */
+/* ------------------------------------------------------------------ */
+uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) {
+ uByte *ub=bcd+dn->digits-1; /* -> lsd */
+ const Unit *up=dn->lsu; /* Unit pointer, -> lsu */
+
+ #if DECDPUN==1 /* trivial simple copy */
+ for (; ub>=bcd; ub--, up++) *ub=*up;
+ #else /* chopping needed */
+ uInt u=*up; /* work */
+ uInt cut=DECDPUN; /* downcounter through unit */
+ for (; ub>=bcd; ub--) {
+ *ub=(uByte)(u%10); /* [*6554 trick inhibits, here] */
+ u=u/10;
+ cut--;
+ if (cut>0) continue; /* more in this unit */
+ up++;
+ u=*up;
+ cut=DECDPUN;
+ }
+ #endif
+ return bcd;
+ } /* decNumberGetBCD */
+
+/* ------------------------------------------------------------------ */
+/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */
+/* dn is the target decNumber */
+/* bcd is the uInt array that will source n BCD bytes, most- */
+/* significant at offset 0 */
+/* n is the number of digits in the source BCD array (bcd) */
+/* returns dn */
+/* */
+/* dn must have space for at least n digits. No error is possible; */
+/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */
+/* and bcd[0] zero. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
+ Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [target pointer] */
+ const uByte *ub=bcd; /* -> source msd */
+
+ #if DECDPUN==1 /* trivial simple copy */
+ for (; ub<bcd+n; ub++, up--) *up=*ub;
+ #else /* some assembly needed */
+ /* calculate how many digits in msu, and hence first cut */
+ Int cut=MSUDIGITS(n); /* [faster than remainder] */
+ for (;up>=dn->lsu; up--) { /* each Unit from msu */
+ *up=0; /* will take <=DECDPUN digits */
+ for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
+ cut=DECDPUN; /* next Unit has all digits */
+ }
+ #endif
+ dn->digits=n; /* set digit count */
+ return dn;
+ } /* decNumberSetBCD */
/* ------------------------------------------------------------------ */
-/* decNumberTrim -- remove insignificant zeros */
-/* */
-/* dn is the number to trim */
-/* returns dn */
-/* */
-/* All fields are updated as required. This is a utility operation, */
-/* so special values are unchanged and no error is possible. */
+/* decNumberIsNormal -- test normality of a decNumber */
+/* dn is the decNumber to test */
+/* set is the context to use for Emin */
+/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */
/* ------------------------------------------------------------------ */
-decNumber *
-decNumberTrim (decNumber * dn)
-{
- Int dropped; /* work */
- return decTrim (dn, 0, &dropped);
-}
+Int decNumberIsNormal(const decNumber *dn, decContext *set) {
+ Int ae; /* adjusted exponent */
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
+ #endif
+
+ if (decNumberIsSpecial(dn)) return 0; /* not finite */
+ if (decNumberIsZero(dn)) return 0; /* not non-zero */
+
+ ae=dn->exponent+dn->digits-1; /* adjusted exponent */
+ if (ae<set->emin) return 0; /* is subnormal */
+ return 1;
+ } /* decNumberIsNormal */
+
+/* ------------------------------------------------------------------ */
+/* decNumberIsSubnormal -- test subnormality of a decNumber */
+/* dn is the decNumber to test */
+/* set is the context to use for Emin */
+/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */
+/* ------------------------------------------------------------------ */
+Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
+ Int ae; /* adjusted exponent */
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
+ #endif
+
+ if (decNumberIsSpecial(dn)) return 0; /* not finite */
+ if (decNumberIsZero(dn)) return 0; /* not non-zero */
+
+ ae=dn->exponent+dn->digits-1; /* adjusted exponent */
+ if (ae<set->emin) return 1; /* is subnormal */
+ return 0;
+ } /* decNumberIsSubnormal */
+
+/* ------------------------------------------------------------------ */
+/* decNumberTrim -- remove insignificant zeros */
+/* */
+/* dn is the number to trim */
+/* returns dn */
+/* */
+/* All fields are updated as required. This is a utility operation, */
+/* so special values are unchanged and no error is possible. The */
+/* zeros are removed unconditionally. */
+/* ------------------------------------------------------------------ */
+decNumber * decNumberTrim(decNumber *dn) {
+ Int dropped; /* work */
+ decContext set; /* .. */
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
+ #endif
+ decContextDefault(&set, DEC_INIT_BASE); /* clamp=0 */
+ return decTrim(dn, &set, 0, 1, &dropped);
+ } /* decNumberTrim */
/* ------------------------------------------------------------------ */
/* decNumberVersion -- return the name and version of this module */
-/* */
-/* No error is possible. */
+/* */
+/* No error is possible. */
/* ------------------------------------------------------------------ */
-const char *
-decNumberVersion (void)
-{
+const char * decNumberVersion(void) {
return DECVERSION;
-}
+ } /* decNumberVersion */
/* ------------------------------------------------------------------ */
-/* decNumberZero -- set a number to 0 */
-/* */
-/* dn is the number to set, with space for one digit */
-/* returns dn */
-/* */
-/* No error is possible. */
+/* decNumberZero -- set a number to 0 */
+/* */
+/* dn is the number to set, with space for one digit */
+/* returns dn */
+/* */
+/* No error is possible. */
/* ------------------------------------------------------------------ */
/* Memset is not used as it is much slower in some environments. */
-decNumber *
-decNumberZero (decNumber * dn)
-{
+decNumber * decNumberZero(decNumber *dn) {
-#if DECCHECK
- if (decCheckOperands (dn, DECUNUSED, DECUNUSED, DECUNUSED))
- return dn;
-#endif
+ #if DECCHECK
+ if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
+ #endif
- dn->bits = 0;
- dn->exponent = 0;
- dn->digits = 1;
- dn->lsu[0] = 0;
+ dn->bits=0;
+ dn->exponent=0;
+ dn->digits=1;
+ dn->lsu[0]=0;
return dn;
-}
+ } /* decNumberZero */
/* ================================================================== */
-/* Local routines */
+/* Local routines */
/* ================================================================== */
/* ------------------------------------------------------------------ */
-/* decToString -- lay out a number into a string */
-/* */
-/* dn is the number to lay out */
-/* string is where to lay out the number */
-/* eng is 1 if Engineering, 0 if Scientific */
-/* */
-/* str must be at least dn->digits+14 characters long */
-/* No error is possible. */
-/* */
+/* decToString -- lay out a number into a string */
+/* */
+/* dn is the number to lay out */
+/* string is where to lay out the number */
+/* eng is 1 if Engineering, 0 if Scientific */
+/* */
+/* string must be at least dn->digits+14 characters long */
+/* No error is possible. */
+/* */
/* Note that this routine can generate a -0 or 0.000. These are */
/* never generated in subset to-number or arithmetic, but can occur */
-/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
+/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
/* ------------------------------------------------------------------ */
/* If DECCHECK is enabled the string "?" is returned if a number is */
/* invalid. */
-
-/* TODIGIT -- macro to remove the leading digit from the unsigned */
-/* integer u at column cut (counting from the right, LSD=0) and place */
-/* it as an ASCII character into the character pointed to by c. Note */
-/* that cut must be <= 9, and the maximum value for u is 2,000,000,000 */
-/* (as is needed for negative exponents of subnormals). The unsigned */
-/* integer pow is used as a temporary variable. */
-#define TODIGIT(u, cut, c) { \
- *(c)='0'; \
- pow=powers[cut]*2; \
- if ((u)>pow) { \
- pow*=4; \
- if ((u)>=pow) {(u)-=pow; *(c)+=8;} \
- pow/=2; \
- if ((u)>=pow) {(u)-=pow; *(c)+=4;} \
- pow/=2; \
- } \
- if ((u)>=pow) {(u)-=pow; *(c)+=2;} \
- pow/=2; \
- if ((u)>=pow) {(u)-=pow; *(c)+=1;} \
- }
-
-static void
-decToString (decNumber * dn, char *string, Flag eng)
-{
- Int exp = dn->exponent; /* local copy */
- Int e; /* E-part value */
- Int pre; /* digits before the '.' */
- Int cut; /* for counting digits in a Unit */
- char *c = string; /* work [output pointer] */
- Unit *up = dn->lsu + D2U (dn->digits) - 1; /* -> msu [input pointer] */
- uInt u, pow; /* work */
-
-#if DECCHECK
- if (decCheckOperands (DECUNUSED, dn, DECUNUSED, DECUNUSED))
- {
- strcpy (string, "?");
- return;
+static void decToString(const decNumber *dn, char *string, Flag eng) {
+ Int exp=dn->exponent; /* local copy */
+ Int e; /* E-part value */
+ Int pre; /* digits before the '.' */
+ Int cut; /* for counting digits in a Unit */
+ char *c=string; /* work [output pointer] */
+ const Unit *up=dn->lsu+D2U(dn->digits)-1; /* -> msu [input pointer] */
+ uInt u, pow; /* work */
+
+ #if DECCHECK
+ if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
+ strcpy(string, "?");
+ return;}
+ #endif
+
+ if (decNumberIsNegative(dn)) { /* Negatives get a minus */
+ *c='-';
+ c++;
}
-#endif
-
- if (decNumberIsNegative (dn))
- { /* Negatives get a minus (except */
- *c = '-'; /* NaNs, which remove the '-' below) */
+ if (dn->bits&DECSPECIAL) { /* Is a special value */
+ if (decNumberIsInfinite(dn)) {
+ strcpy(c, "Inf");
+ strcpy(c+3, "inity");
+ return;}
+ /* a NaN */
+ if (dn->bits&DECSNAN) { /* signalling NaN */
+ *c='s';
c++;
- }
- if (dn->bits & DECSPECIAL)
- { /* Is a special value */
- if (decNumberIsInfinite (dn))
- {
- strcpy (c, "Infinity");
- return;
- }
- /* a NaN */
- if (dn->bits & DECSNAN)
- { /* signalling NaN */
- *c = 's';
- c++;
- }
- strcpy (c, "NaN");
- c += 3; /* step past */
- /* if not a clean non-zero coefficient, that's all we have in a */
- /* NaN string */
- if (exp != 0 || (*dn->lsu == 0 && dn->digits == 1))
- return;
- /* [drop through to add integer] */
+ }
+ strcpy(c, "NaN");
+ c+=3; /* step past */
+ /* if not a clean non-zero coefficient, that's all there is in a */
+ /* NaN string */
+ if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
+ /* [drop through to add integer] */
}
/* calculate how many digits in msu, and hence first cut */
- cut = dn->digits % DECDPUN;
- if (cut == 0)
- cut = DECDPUN; /* msu is full */
- cut--; /* power of ten for digit */
-
- if (exp == 0)
- { /* simple integer [common fastpath, */
- /* used for NaNs, too] */
- for (; up >= dn->lsu; up--)
- { /* each Unit from msu */
- u = *up; /* contains DECDPUN digits to lay out */
- for (; cut >= 0; c++, cut--)
- TODIGIT (u, cut, c);
- cut = DECDPUN - 1; /* next Unit has all digits */
- }
- *c = '\0'; /* terminate the string */
- return;
- }
+ cut=MSUDIGITS(dn->digits); /* [faster than remainder] */
+ cut--; /* power of ten for digit */
+
+ if (exp==0) { /* simple integer [common fastpath] */
+ for (;up>=dn->lsu; up--) { /* each Unit from msu */
+ u=*up; /* contains DECDPUN digits to lay out */
+ for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
+ cut=DECDPUN-1; /* next Unit has all digits */
+ }
+ *c='\0'; /* terminate the string */
+ return;}
/* non-0 exponent -- assume plain form */
- pre = dn->digits + exp; /* digits before '.' */
- e = 0; /* no E */
- if ((exp > 0) || (pre < -5))
- { /* need exponential form */
- e = exp + dn->digits - 1; /* calculate E value */
- pre = 1; /* assume one digit before '.' */
- if (eng && (e != 0))
- { /* may need to adjust */
- Int adj; /* adjustment */
- /* The C remainder operator is undefined for negative numbers, so */
- /* we must use positive remainder calculation here */
- if (e < 0)
- {
- adj = (-e) % 3;
- if (adj != 0)
- adj = 3 - adj;
- }
- else
- { /* e>0 */
- adj = e % 3;
- }
- e = e - adj;
- /* if we are dealing with zero we will use exponent which is a */
- /* multiple of three, as expected, but there will only be the */
- /* one zero before the E, still. Otherwise note the padding. */
- if (!ISZERO (dn))
- pre += adj;
- else
- { /* is zero */
- if (adj != 0)
- { /* 0.00Esnn needed */
- e = e + 3;
- pre = -(2 - adj);
- }
- } /* zero */
- } /* eng */
- }
+ pre=dn->digits+exp; /* digits before '.' */
+ e=0; /* no E */
+ if ((exp>0) || (pre<-5)) { /* need exponential form */
+ e=exp+dn->digits-1; /* calculate E value */
+ pre=1; /* assume one digit before '.' */
+ if (eng && (e!=0)) { /* engineering: may need to adjust */
+ Int adj; /* adjustment */
+ /* The C remainder operator is undefined for negative numbers, so */
+ /* a positive remainder calculation must be used here */
+ if (e<0) {
+ adj=(-e)%3;
+ if (adj!=0) adj=3-adj;
+ }
+ else { /* e>0 */
+ adj=e%3;
+ }
+ e=e-adj;
+ /* if dealing with zero still produce an exponent which is a */
+ /* multiple of three, as expected, but there will only be the */
+ /* one zero before the E, still. Otherwise note the padding. */
+ if (!ISZERO(dn)) pre+=adj;
+ else { /* is zero */
+ if (adj!=0) { /* 0.00Esnn needed */
+ e=e+3;
+ pre=-(2-adj);
+ }
+ } /* zero */
+ } /* eng */
+ } /* need exponent */
/* lay out the digits of the coefficient, adding 0s and . as needed */
- u = *up;
- if (pre > 0)
- { /* xxx.xxx or xx00 (engineering) form */
- for (; pre > 0; pre--, c++, cut--)
- {
- if (cut < 0)
- { /* need new Unit */
- if (up == dn->lsu)
- break; /* out of input digits (pre>digits) */
- up--;
- cut = DECDPUN - 1;
- u = *up;
- }
- TODIGIT (u, cut, c);
+ u=*up;
+ if (pre>0) { /* xxx.xxx or xx00 (engineering) form */
+ Int n=pre;
+ for (; pre>0; pre--, c++, cut--) {
+ if (cut<0) { /* need new Unit */
+ if (up==dn->lsu) break; /* out of input digits (pre>digits) */
+ up--;
+ cut=DECDPUN-1;
+ u=*up;
}
- if (up > dn->lsu || (up == dn->lsu && cut >= 0))
- { /* more to come, after '.' */
- *c = '.';
- c++;
- for (;; c++, cut--)
- {
- if (cut < 0)
- { /* need new Unit */
- if (up == dn->lsu)
- break; /* out of input digits */
- up--;
- cut = DECDPUN - 1;
- u = *up;
- }
- TODIGIT (u, cut, c);
- }
+ TODIGIT(u, cut, c, pow);
+ }
+ if (n<dn->digits) { /* more to come, after '.' */
+ *c='.'; c++;
+ for (;; c++, cut--) {
+ if (cut<0) { /* need new Unit */
+ if (up==dn->lsu) break; /* out of input digits */
+ up--;
+ cut=DECDPUN-1;
+ u=*up;
+ }
+ TODIGIT(u, cut, c, pow);
}
- else
- for (; pre > 0; pre--, c++)
- *c = '0'; /* 0 padding (for engineering) needed */
+ }
+ else for (; pre>0; pre--, c++) *c='0'; /* 0 padding (for engineering) needed */
}
- else
- { /* 0.xxx or 0.000xxx form */
- *c = '0';
- c++;
- *c = '.';
- c++;
- for (; pre < 0; pre++, c++)
- *c = '0'; /* add any 0's after '.' */
- for (;; c++, cut--)
- {
- if (cut < 0)
- { /* need new Unit */
- if (up == dn->lsu)
- break; /* out of input digits */
- up--;
- cut = DECDPUN - 1;
- u = *up;
- }
- TODIGIT (u, cut, c);
+ else { /* 0.xxx or 0.000xxx form */
+ *c='0'; c++;
+ *c='.'; c++;
+ for (; pre<0; pre++, c++) *c='0'; /* add any 0's after '.' */
+ for (; ; c++, cut--) {
+ if (cut<0) { /* need new Unit */
+ if (up==dn->lsu) break; /* out of input digits */
+ up--;
+ cut=DECDPUN-1;
+ u=*up;
}
+ TODIGIT(u, cut, c, pow);
+ }
}
/* Finally add the E-part, if needed. It will never be 0, has a
base maximum and minimum of +999999999 through -999999999, but
- could range down to -1999999998 for subnormal numbers */
- if (e != 0)
- {
- Flag had = 0; /* 1=had non-zero */
- *c = 'E';
- c++;
- *c = '+';
- c++; /* assume positive */
- u = e; /* .. */
- if (e < 0)
- {
- *(c - 1) = '-'; /* oops, need - */
- u = -e; /* uInt, please */
- }
- /* layout the exponent (_itoa is not ANSI C) */
- for (cut = 9; cut >= 0; cut--)
- {
- TODIGIT (u, cut, c);
- if (*c == '0' && !had)
- continue; /* skip leading zeros */
- had = 1; /* had non-0 */
- c++; /* step for next */
- } /* cut */
+ could range down to -1999999998 for anormal numbers */
+ if (e!=0) {
+ Flag had=0; /* 1=had non-zero */
+ *c='E'; c++;
+ *c='+'; c++; /* assume positive */
+ u=e; /* .. */
+ if (e<0) {
+ *(c-1)='-'; /* oops, need - */
+ u=-e; /* uInt, please */
+ }
+ /* lay out the exponent [_itoa or equivalent is not ANSI C] */
+ for (cut=9; cut>=0; cut--) {
+ TODIGIT(u, cut, c, pow);
+ if (*c=='0' && !had) continue; /* skip leading zeros */
+ had=1; /* had non-0 */
+ c++; /* step for next */
+ } /* cut */
}
- *c = '\0'; /* terminate the string (all paths) */
+ *c='\0'; /* terminate the string (all paths) */
return;
-}
-
-/* ------------------------------------------------------------------ */
-/* decAddOp -- add/subtract operation */
-/* */
-/* This computes C = A + B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* negate is DECNEG if rhs should be negated, or 0 otherwise */
-/* status accumulates status for the caller */
-/* */
-/* C must have space for set->digits digits. */
-/* ------------------------------------------------------------------ */
-/* If possible, we calculate the coefficient directly into C. */
-/* However, if: */
-/* -- we need a digits+1 calculation because numbers are unaligned */
-/* and span more than set->digits digits */
-/* -- a carry to digits+1 digits looks possible */
+ } /* decToString */
+
+/* ------------------------------------------------------------------ */
+/* decAddOp -- add/subtract operation */
+/* */
+/* This computes C = A + B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* negate is DECNEG if rhs should be negated, or 0 otherwise */
+/* status accumulates status for the caller */
+/* */
+/* C must have space for set->digits digits. */
+/* Inexact in status must be 0 for correct Exact zero sign in result */
+/* ------------------------------------------------------------------ */
+/* If possible, the coefficient is calculated directly into C. */
+/* However, if: */
+/* -- a digits+1 calculation is needed because the numbers are */
+/* unaligned and span more than set->digits digits */
+/* -- a carry to digits+1 digits looks possible */
/* -- C is the same as A or B, and the result would destructively */
-/* overlap the A or B coefficient */
-/* then we must calculate into a temporary buffer. In this latter */
-/* case we use the local (stack) buffer if possible, and only if too */
-/* long for that do we resort to malloc. */
-/* */
-/* Misalignment is handled as follows: */
+/* overlap the A or B coefficient */
+/* then the result must be calculated into a temporary buffer. In */
+/* this case a local (stack) buffer is used if possible, and only if */
+/* too long for that does malloc become the final resort. */
+/* */
+/* Misalignment is handled as follows: */
/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
/* BPad: Apply the padding by a combination of shifting (whole */
-/* units) and multiplication (part units). */
-/* */
-/* Addition, especially x=x+1, is speed-critical, so we take pains */
-/* to make returning as fast as possible, by flagging any allocation. */
-/* ------------------------------------------------------------------ */
-static decNumber *
-decAddOp (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set, uByte negate, uInt * status)
-{
- decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
- decNumber *allocrhs = NULL; /* .., rhs */
- Int rhsshift; /* working shift (in Units) */
- Int maxdigits; /* longest logical length */
- Int mult; /* multiplier */
- Int residue; /* rounding accumulator */
- uByte bits; /* result bits */
- Flag diffsign; /* non-0 if arguments have different sign */
- Unit *acc; /* accumulator for result */
- Unit accbuff[D2U (DECBUFFER + 1)]; /* local buffer [+1 is for possible */
- /* final carry digit or DECBUFFER=0] */
- Unit *allocacc = NULL; /* -> allocated acc buffer, iff allocated */
- Flag alloced = 0; /* set non-0 if any allocations */
- Int reqdigits = set->digits; /* local copy; requested DIGITS */
- uByte merged; /* merged flags */
- Int padding; /* work */
-
-#if DECCHECK
- if (decCheckOperands (res, lhs, rhs, set))
- return res;
-#endif
+/* units) and multiplication (part units). */
+/* */
+/* Addition, especially x=x+1, is speed-critical. */
+/* The static buffer is larger than might be expected to allow for */
+/* calls from higher-level funtions (notable exp). */
+/* ------------------------------------------------------------------ */
+static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ uByte negate, uInt *status) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
+ decNumber *allocrhs=NULL; /* .., rhs */
+ #endif
+ Int rhsshift; /* working shift (in Units) */
+ Int maxdigits; /* longest logical length */
+ Int mult; /* multiplier */
+ Int residue; /* rounding accumulator */
+ uByte bits; /* result bits */
+ Flag diffsign; /* non-0 if arguments have different sign */
+ Unit *acc; /* accumulator for result */
+ Unit accbuff[SD2U(DECBUFFER*2+20)]; /* local buffer [*2+20 reduces many */
+ /* allocations when called from */
+ /* other operations, notable exp] */
+ Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
+ Int reqdigits=set->digits; /* local copy; requested DIGITS */
+ Int padding; /* work */
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operands and set lostDigits status, as needed */
+ if (lhs->digits>reqdigits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
+ }
+ if (rhs->digits>reqdigits) {
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ /* [following code does not require input rounding] */
+
+ /* note whether signs differ [used all paths] */
+ diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
+
+ /* handle infinities and NaNs */
+ if (SPECIALARGS) { /* a special bit set */
+ if (SPECIALARGS & (DECSNAN | DECNAN)) /* a NaN */
+ decNaNs(res, lhs, rhs, set, status);
+ else { /* one or two infinities */
+ if (decNumberIsInfinite(lhs)) { /* LHS is infinity */
+ /* two infinities with different signs is invalid */
+ if (decNumberIsInfinite(rhs) && diffsign) {
+ *status|=DEC_Invalid_operation;
+ break;
+ }
+ bits=lhs->bits & DECNEG; /* get sign from LHS */
+ }
+ else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */
+ bits|=DECINF;
+ decNumberZero(res);
+ res->bits=bits; /* set +/- infinity */
+ } /* an infinity */
+ break;
+ }
- do
- { /* protect allocated storage */
-#if DECSUBSET
- if (!set->extended)
- {
- /* reduce operands and set lostDigits status, as needed */
- if (lhs->digits > reqdigits)
- {
- alloclhs = decRoundOperand (lhs, set, status);
- if (alloclhs == NULL)
- break;
- lhs = alloclhs;
- alloced = 1;
+ /* Quick exit for add 0s; return the non-0, modified as need be */
+ if (ISZERO(lhs)) {
+ Int adjust; /* work */
+ Int lexp=lhs->exponent; /* save in case LHS==RES */
+ bits=lhs->bits; /* .. */
+ residue=0; /* clear accumulator */
+ decCopyFit(res, rhs, set, &residue, status); /* copy (as needed) */
+ res->bits^=negate; /* flip if rhs was negated */
+ #if DECSUBSET
+ if (set->extended) { /* exponents on zeros count */
+ #endif
+ /* exponent will be the lower of the two */
+ adjust=lexp-res->exponent; /* adjustment needed [if -ve] */
+ if (ISZERO(res)) { /* both 0: special IEEE 754 rules */
+ if (adjust<0) res->exponent=lexp; /* set exponent */
+ /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
+ if (diffsign) {
+ if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
+ else res->bits=DECNEG; /* preserve 0 sign */
}
- if (rhs->digits > reqdigits)
- {
- allocrhs = decRoundOperand (rhs, set, status);
- if (allocrhs == NULL)
- break;
- rhs = allocrhs;
- alloced = 1;
+ }
+ else { /* non-0 res */
+ if (adjust<0) { /* 0-padding needed */
+ if ((res->digits-adjust)>set->digits) {
+ adjust=res->digits-set->digits; /* to fit exactly */
+ *status|=DEC_Rounded; /* [but exact] */
+ }
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
+ res->exponent+=adjust; /* set the exponent. */
}
- }
-#endif
- /* [following code does not require input rounding] */
-
- /* note whether signs differ */
- diffsign = (Flag) ((lhs->bits ^ rhs->bits ^ negate) & DECNEG);
-
- /* handle infinities and NaNs */
- merged = (lhs->bits | rhs->bits) & DECSPECIAL;
- if (merged)
- { /* a special bit set */
- if (merged & (DECSNAN | DECNAN)) /* a NaN */
- decNaNs (res, lhs, rhs, status);
- else
- { /* one or two infinities */
- if (decNumberIsInfinite (lhs))
- { /* LHS is infinity */
- /* two infinities with different signs is invalid */
- if (decNumberIsInfinite (rhs) && diffsign)
- {
- *status |= DEC_Invalid_operation;
- break;
- }
- bits = lhs->bits & DECNEG; /* get sign from LHS */
- }
- else
- bits = (rhs->bits ^ negate) & DECNEG; /* RHS must be Infinity */
- bits |= DECINF;
- decNumberZero (res);
- res->bits = bits; /* set +/- infinity */
- } /* an infinity */
+ } /* non-0 res */
+ #if DECSUBSET
+ } /* extended */
+ #endif
+ decFinish(res, set, &residue, status); /* clean and finalize */
+ break;}
+
+ if (ISZERO(rhs)) { /* [lhs is non-zero] */
+ Int adjust; /* work */
+ Int rexp=rhs->exponent; /* save in case RHS==RES */
+ bits=rhs->bits; /* be clean */
+ residue=0; /* clear accumulator */
+ decCopyFit(res, lhs, set, &residue, status); /* copy (as needed) */
+ #if DECSUBSET
+ if (set->extended) { /* exponents on zeros count */
+ #endif
+ /* exponent will be the lower of the two */
+ /* [0-0 case handled above] */
+ adjust=rexp-res->exponent; /* adjustment needed [if -ve] */
+ if (adjust<0) { /* 0-padding needed */
+ if ((res->digits-adjust)>set->digits) {
+ adjust=res->digits-set->digits; /* to fit exactly */
+ *status|=DEC_Rounded; /* [but exact] */
+ }
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
+ res->exponent+=adjust; /* set the exponent. */
+ }
+ #if DECSUBSET
+ } /* extended */
+ #endif
+ decFinish(res, set, &residue, status); /* clean and finalize */
+ break;}
+
+ /* [NB: both fastpath and mainpath code below assume these cases */
+ /* (notably 0-0) have already been handled] */
+
+ /* calculate the padding needed to align the operands */
+ padding=rhs->exponent-lhs->exponent;
+
+ /* Fastpath cases where the numbers are aligned and normal, the RHS */
+ /* is all in one unit, no operand rounding is needed, and no carry, */
+ /* lengthening, or borrow is needed */
+ if (padding==0
+ && rhs->digits<=DECDPUN
+ && rhs->exponent>=set->emin /* [some normals drop through] */
+ && rhs->exponent<=set->emax-set->digits+1 /* [could clamp] */
+ && rhs->digits<=reqdigits
+ && lhs->digits<=reqdigits) {
+ Int partial=*lhs->lsu;
+ if (!diffsign) { /* adding */
+ partial+=*rhs->lsu;
+ if ((partial<=DECDPUNMAX) /* result fits in unit */
+ && (lhs->digits>=DECDPUN || /* .. and no digits-count change */
+ partial<(Int)powers[lhs->digits])) { /* .. */
+ if (res!=lhs) decNumberCopy(res, lhs); /* not in place */
+ *res->lsu=(Unit)partial; /* [copy could have overwritten RHS] */
break;
+ }
+ /* else drop out for careful add */
}
-
- /* Quick exit for add 0s; return the non-0, modified as need be */
- if (ISZERO (lhs))
- {
- Int adjust; /* work */
- Int lexp = lhs->exponent; /* save in case LHS==RES */
- bits = lhs->bits; /* .. */
- residue = 0; /* clear accumulator */
- decCopyFit (res, rhs, set, &residue, status); /* copy (as needed) */
- res->bits ^= negate; /* flip if rhs was negated */
-#if DECSUBSET
- if (set->extended)
- { /* exponents on zeros count */
-#endif
- /* exponent will be the lower of the two */
- adjust = lexp - res->exponent; /* adjustment needed [if -ve] */
- if (ISZERO (res))
- { /* both 0: special IEEE 854 rules */
- if (adjust < 0)
- res->exponent = lexp; /* set exponent */
- /* 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 */
- if (diffsign)
- {
- if (set->round != DEC_ROUND_FLOOR)
- res->bits = 0;
- else
- res->bits = DECNEG; /* preserve 0 sign */
- }
- }
- else
- { /* non-0 res */
- if (adjust < 0)
- { /* 0-padding needed */
- if ((res->digits - adjust) > set->digits)
- {
- adjust = res->digits - set->digits; /* to fit exactly */
- *status |= DEC_Rounded; /* [but exact] */
- }
- res->digits =
- decShiftToMost (res->lsu, res->digits, -adjust);
- res->exponent += adjust; /* set the exponent. */
- }
- } /* non-0 res */
-#if DECSUBSET
- } /* extended */
-#endif
- decFinish (res, set, &residue, status); /* clean and finalize */
+ else { /* signs differ */
+ partial-=*rhs->lsu;
+ if (partial>0) { /* no borrow needed, and non-0 result */
+ if (res!=lhs) decNumberCopy(res, lhs); /* not in place */
+ *res->lsu=(Unit)partial;
+ /* this could have reduced digits [but result>0] */
+ res->digits=decGetDigits(res->lsu, D2U(res->digits));
break;
+ }
+ /* else drop out for careful subtract */
}
+ }
- if (ISZERO (rhs))
- { /* [lhs is non-zero] */
- Int adjust; /* work */
- Int rexp = rhs->exponent; /* save in case RHS==RES */
- bits = rhs->bits; /* be clean */
- residue = 0; /* clear accumulator */
- decCopyFit (res, lhs, set, &residue, status); /* copy (as needed) */
-#if DECSUBSET
- if (set->extended)
- { /* exponents on zeros count */
-#endif
- /* exponent will be the lower of the two */
- /* [0-0 case handled above] */
- adjust = rexp - res->exponent; /* adjustment needed [if -ve] */
- if (adjust < 0)
- { /* 0-padding needed */
- if ((res->digits - adjust) > set->digits)
- {
- adjust = res->digits - set->digits; /* to fit exactly */
- *status |= DEC_Rounded; /* [but exact] */
- }
- res->digits =
- decShiftToMost (res->lsu, res->digits, -adjust);
- res->exponent += adjust; /* set the exponent. */
- }
-#if DECSUBSET
- } /* extended */
-#endif
- decFinish (res, set, &residue, status); /* clean and finalize */
- break;
- }
- /* [both fastpath and mainpath code below assume these cases */
- /* (notably 0-0) have already been handled] */
-
- /* calculate the padding needed to align the operands */
- padding = rhs->exponent - lhs->exponent;
-
- /* Fastpath cases where the numbers are aligned and normal, the RHS */
- /* is all in one unit, no operand rounding is needed, and no carry, */
- /* lengthening, or borrow is needed */
- if (rhs->digits <= DECDPUN && padding == 0 && rhs->exponent >= set->emin /* [some normals drop through] */
- && rhs->digits <= reqdigits && lhs->digits <= reqdigits)
- {
- Int partial = *lhs->lsu;
- if (!diffsign)
- { /* adding */
- Int maxv = DECDPUNMAX; /* highest no-overflow */
- if (lhs->digits < DECDPUN)
- maxv = powers[lhs->digits] - 1;
- partial += *rhs->lsu;
- if (partial <= maxv)
- { /* no carry */
- if (res != lhs)
- decNumberCopy (res, lhs); /* not in place */
- *res->lsu = (Unit) partial; /* [copy could have overwritten RHS] */
- break;
- }
- /* else drop out for careful add */
- }
- else
- { /* signs differ */
- partial -= *rhs->lsu;
- if (partial > 0)
- { /* no borrow needed, and non-0 result */
- if (res != lhs)
- decNumberCopy (res, lhs); /* not in place */
- *res->lsu = (Unit) partial;
- /* this could have reduced digits [but result>0] */
- res->digits = decGetDigits (res->lsu, D2U (res->digits));
- break;
- }
- /* else drop out for careful subtract */
- }
+ /* Now align (pad) the lhs or rhs so they can be added or */
+ /* subtracted, as necessary. If one number is much larger than */
+ /* the other (that is, if in plain form there is a least one */
+ /* digit between the lowest digit of one and the highest of the */
+ /* other) padding with up to DIGITS-1 trailing zeros may be */
+ /* needed; then apply rounding (as exotic rounding modes may be */
+ /* affected by the residue). */
+ rhsshift=0; /* rhs shift to left (padding) in Units */
+ bits=lhs->bits; /* assume sign is that of LHS */
+ mult=1; /* likely multiplier */
+
+ /* [if padding==0 the operands are aligned; no padding is needed] */
+ if (padding!=0) {
+ /* some padding needed; always pad the RHS, as any required */
+ /* padding can then be effected by a simple combination of */
+ /* shifts and a multiply */
+ Flag swapped=0;
+ if (padding<0) { /* LHS needs the padding */
+ const decNumber *t;
+ padding=-padding; /* will be +ve */
+ bits=(uByte)(rhs->bits^negate); /* assumed sign is now that of RHS */
+ t=lhs; lhs=rhs; rhs=t;
+ swapped=1;
}
- /* Now align (pad) the lhs or rhs so we can add or subtract them, as
- necessary. If one number is much larger than the other (that is,
- if in plain form there is a least one digit between the lowest
- digit or one and the highest of the other) we need to pad with up
- to DIGITS-1 trailing zeros, and then apply rounding (as exotic
- rounding modes may be affected by the residue).
- */
- rhsshift = 0; /* rhs shift to left (padding) in Units */
- bits = lhs->bits; /* assume sign is that of LHS */
- mult = 1; /* likely multiplier */
-
- /* if padding==0 the operands are aligned; no padding needed */
- if (padding != 0)
- {
- /* some padding needed */
- /* We always pad the RHS, as we can then effect any required */
- /* padding by a combination of shifts and a multiply */
- Flag swapped = 0;
- if (padding < 0)
- { /* LHS needs the padding */
- decNumber *t;
- padding = -padding; /* will be +ve */
- bits = (uByte) (rhs->bits ^ negate); /* assumed sign is now that of RHS */
- t = lhs;
- lhs = rhs;
- rhs = t;
- swapped = 1;
- }
-
- /* If, after pad, rhs would be longer than lhs by digits+1 or */
- /* more then lhs cannot affect the answer, except as a residue, */
- /* so we only need to pad up to a length of DIGITS+1. */
- if (rhs->digits + padding > lhs->digits + reqdigits + 1)
- {
- /* The RHS is sufficient */
- /* for residue we use the relative sign indication... */
- Int shift = reqdigits - rhs->digits; /* left shift needed */
- residue = 1; /* residue for rounding */
- if (diffsign)
- residue = -residue; /* signs differ */
- /* copy, shortening if necessary */
- decCopyFit (res, rhs, set, &residue, status);
- /* if it was already shorter, then need to pad with zeros */
- if (shift > 0)
- {
- res->digits = decShiftToMost (res->lsu, res->digits, shift);
- res->exponent -= shift; /* adjust the exponent. */
- }
- /* flip the result sign if unswapped and rhs was negated */
- if (!swapped)
- res->bits ^= negate;
- decFinish (res, set, &residue, status); /* done */
- break;
- }
-
- /* LHS digits may affect result */
- rhsshift = D2U (padding + 1) - 1; /* this much by Unit shift .. */
- mult = powers[padding - (rhsshift * DECDPUN)]; /* .. this by multiplication */
- } /* padding needed */
-
- if (diffsign)
- mult = -mult; /* signs differ */
-
- /* determine the longer operand */
- maxdigits = rhs->digits + padding; /* virtual length of RHS */
- if (lhs->digits > maxdigits)
- maxdigits = lhs->digits;
-
- /* Decide on the result buffer to use; if possible place directly */
- /* into result. */
- acc = res->lsu; /* assume build direct */
- /* If destructive overlap, or the number is too long, or a carry or */
- /* borrow to DIGITS+1 might be possible we must use a buffer. */
- /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
- if ((maxdigits >= reqdigits) /* is, or could be, too large */
- || (res == rhs && rhsshift > 0))
- { /* destructive overlap */
- /* buffer needed; choose it */
- /* we'll need units for maxdigits digits, +1 Unit for carry or borrow */
- Int need = D2U (maxdigits) + 1;
- acc = accbuff; /* assume use local buffer */
- if (need * sizeof (Unit) > sizeof (accbuff))
- {
- allocacc = (Unit *) malloc (need * sizeof (Unit));
- if (allocacc == NULL)
- { /* hopeless -- abandon */
- *status |= DEC_Insufficient_storage;
- break;
- }
- acc = allocacc;
- alloced = 1;
- }
+ /* If, after pad, rhs would be longer than lhs by digits+1 or */
+ /* more then lhs cannot affect the answer, except as a residue, */
+ /* so only need to pad up to a length of DIGITS+1. */
+ if (rhs->digits+padding > lhs->digits+reqdigits+1) {
+ /* The RHS is sufficient */
+ /* for residue use the relative sign indication... */
+ Int shift=reqdigits-rhs->digits; /* left shift needed */
+ residue=1; /* residue for rounding */
+ if (diffsign) residue=-residue; /* signs differ */
+ /* copy, shortening if necessary */
+ decCopyFit(res, rhs, set, &residue, status);
+ /* if it was already shorter, then need to pad with zeros */
+ if (shift>0) {
+ res->digits=decShiftToMost(res->lsu, res->digits, shift);
+ res->exponent-=shift; /* adjust the exponent. */
+ }
+ /* flip the result sign if unswapped and rhs was negated */
+ if (!swapped) res->bits^=negate;
+ decFinish(res, set, &residue, status); /* done */
+ break;}
+
+ /* LHS digits may affect result */
+ rhsshift=D2U(padding+1)-1; /* this much by Unit shift .. */
+ mult=powers[padding-(rhsshift*DECDPUN)]; /* .. this by multiplication */
+ } /* padding needed */
+
+ if (diffsign) mult=-mult; /* signs differ */
+
+ /* determine the longer operand */
+ maxdigits=rhs->digits+padding; /* virtual length of RHS */
+ if (lhs->digits>maxdigits) maxdigits=lhs->digits;
+
+ /* Decide on the result buffer to use; if possible place directly */
+ /* into result. */
+ acc=res->lsu; /* assume add direct to result */
+ /* If destructive overlap, or the number is too long, or a carry or */
+ /* borrow to DIGITS+1 might be possible, a buffer must be used. */
+ /* [Might be worth more sophisticated tests when maxdigits==reqdigits] */
+ if ((maxdigits>=reqdigits) /* is, or could be, too large */
+ || (res==rhs && rhsshift>0)) { /* destructive overlap */
+ /* buffer needed, choose it; units for maxdigits digits will be */
+ /* needed, +1 Unit for carry or borrow */
+ Int need=D2U(maxdigits)+1;
+ acc=accbuff; /* assume use local buffer */
+ if (need*sizeof(Unit)>sizeof(accbuff)) {
+ /* printf("malloc add %ld %ld\n", need, sizeof(accbuff)); */
+ allocacc=(Unit *)malloc(need*sizeof(Unit));
+ if (allocacc==NULL) { /* hopeless -- abandon */
+ *status|=DEC_Insufficient_storage;
+ break;}
+ acc=allocacc;
}
+ }
- res->bits = (uByte) (bits & DECNEG); /* it's now safe to overwrite.. */
- res->exponent = lhs->exponent; /* .. operands (even if aliased) */
-
-#if DECTRACE
- decDumpAr ('A', lhs->lsu, D2U (lhs->digits));
- decDumpAr ('B', rhs->lsu, D2U (rhs->digits));
- printf (" :h: %d %d\n", rhsshift, mult);
-#endif
-
- /* add [A+B*m] or subtract [A+B*(-m)] */
- res->digits = decUnitAddSub (lhs->lsu, D2U (lhs->digits), rhs->lsu, D2U (rhs->digits), rhsshift, acc, mult) * DECDPUN; /* [units -> digits] */
- if (res->digits < 0)
- { /* we borrowed */
- res->digits = -res->digits;
- res->bits ^= DECNEG; /* flip the sign */
+ res->bits=(uByte)(bits&DECNEG); /* it's now safe to overwrite.. */
+ res->exponent=lhs->exponent; /* .. operands (even if aliased) */
+
+ #if DECTRACE
+ decDumpAr('A', lhs->lsu, D2U(lhs->digits));
+ decDumpAr('B', rhs->lsu, D2U(rhs->digits));
+ printf(" :h: %ld %ld\n", rhsshift, mult);
+ #endif
+
+ /* add [A+B*m] or subtract [A+B*(-m)] */
+ res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
+ rhs->lsu, D2U(rhs->digits),
+ rhsshift, acc, mult)
+ *DECDPUN; /* [units -> digits] */
+ if (res->digits<0) { /* borrowed... */
+ res->digits=-res->digits;
+ res->bits^=DECNEG; /* flip the sign */
+ }
+ #if DECTRACE
+ decDumpAr('+', acc, D2U(res->digits));
+ #endif
+
+ /* If a buffer was used the result must be copied back, possibly */
+ /* shortening. (If no buffer was used then the result must have */
+ /* fit, so can't need rounding and residue must be 0.) */
+ residue=0; /* clear accumulator */
+ if (acc!=res->lsu) {
+ #if DECSUBSET
+ if (set->extended) { /* round from first significant digit */
+ #endif
+ /* remove leading zeros that were added due to rounding up to */
+ /* integral Units -- before the test for rounding. */
+ if (res->digits>reqdigits)
+ res->digits=decGetDigits(acc, D2U(res->digits));
+ decSetCoeff(res, set, acc, res->digits, &residue, status);
+ #if DECSUBSET
}
-#if DECTRACE
- decDumpAr ('+', acc, D2U (res->digits));
-#endif
-
- /* If we used a buffer we need to copy back, possibly shortening */
- /* (If we didn't use buffer it must have fit, so can't need rounding */
- /* and residue must be 0.) */
- residue = 0; /* clear accumulator */
- if (acc != res->lsu)
- {
-#if DECSUBSET
- if (set->extended)
- { /* round from first significant digit */
-#endif
- /* remove leading zeros that we added due to rounding up to */
- /* integral Units -- before the test for rounding. */
- if (res->digits > reqdigits)
- res->digits = decGetDigits (acc, D2U (res->digits));
- decSetCoeff (res, set, acc, res->digits, &residue, status);
-#if DECSUBSET
+ else { /* subset arithmetic rounds from original significant digit */
+ /* May have an underestimate. This only occurs when both */
+ /* numbers fit in DECDPUN digits and are padding with a */
+ /* negative multiple (-10, -100...) and the top digit(s) become */
+ /* 0. (This only matters when using X3.274 rules where the */
+ /* leading zero could be included in the rounding.) */
+ if (res->digits<maxdigits) {
+ *(acc+D2U(res->digits))=0; /* ensure leading 0 is there */
+ res->digits=maxdigits;
+ }
+ else {
+ /* remove leading zeros that added due to rounding up to */
+ /* integral Units (but only those in excess of the original */
+ /* maxdigits length, unless extended) before test for rounding. */
+ if (res->digits>reqdigits) {
+ res->digits=decGetDigits(acc, D2U(res->digits));
+ if (res->digits<maxdigits) res->digits=maxdigits;
}
- else
- { /* subset arithmetic rounds from original significant digit */
- /* We may have an underestimate. This only occurs when both */
- /* numbers fit in DECDPUN digits and we are padding with a */
- /* negative multiple (-10, -100...) and the top digit(s) become */
- /* 0. (This only matters if we are using X3.274 rules where the */
- /* leading zero could be included in the rounding.) */
- if (res->digits < maxdigits)
- {
- *(acc + D2U (res->digits)) = 0; /* ensure leading 0 is there */
- res->digits = maxdigits;
- }
- else
- {
- /* remove leading zeros that we added due to rounding up to */
- /* integral Units (but only those in excess of the original */
- /* maxdigits length, unless extended) before test for rounding. */
- if (res->digits > reqdigits)
- {
- res->digits = decGetDigits (acc, D2U (res->digits));
- if (res->digits < maxdigits)
- res->digits = maxdigits;
- }
- }
- decSetCoeff (res, set, acc, res->digits, &residue, status);
- /* Now apply rounding if needed before removing leading zeros. */
- /* This is safe because subnormals are not a possibility */
- if (residue != 0)
- {
- decApplyRound (res, set, residue, status);
- residue = 0; /* we did what we had to do */
- }
- } /* subset */
-#endif
- } /* used buffer */
-
- /* strip leading zeros [these were left on in case of subset subtract] */
- res->digits = decGetDigits (res->lsu, D2U (res->digits));
-
- /* apply checks and rounding */
- decFinish (res, set, &residue, status);
+ }
+ decSetCoeff(res, set, acc, res->digits, &residue, status);
+ /* Now apply rounding if needed before removing leading zeros. */
+ /* This is safe because subnormals are not a possibility */
+ if (residue!=0) {
+ decApplyRound(res, set, residue, status);
+ residue=0; /* did what needed to be done */
+ }
+ } /* subset */
+ #endif
+ } /* used buffer */
+
+ /* strip leading zeros [these were left on in case of subset subtract] */
+ res->digits=decGetDigits(res->lsu, D2U(res->digits));
+
+ /* apply checks and rounding */
+ decFinish(res, set, &residue, status);
+
+ /* "When the sum of two operands with opposite signs is exactly */
+ /* zero, the sign of that sum shall be '+' in all rounding modes */
+ /* except round toward -Infinity, in which mode that sign shall be */
+ /* '-'." [Subset zeros also never have '-', set by decFinish.] */
+ if (ISZERO(res) && diffsign
+ #if DECSUBSET
+ && set->extended
+ #endif
+ && (*status&DEC_Inexact)==0) {
+ if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */
+ else res->bits&=~DECNEG; /* sign + */
+ }
+ } while(0); /* end protected */
- /* "When the sum of two operands with opposite signs is exactly */
- /* zero, the sign of that sum shall be '+' in all rounding modes */
- /* except round toward -Infinity, in which mode that sign shall be */
- /* '-'." [Subset zeros also never have '-', set by decFinish.] */
- if (ISZERO (res) && diffsign
-#if DECSUBSET
- && set->extended
-#endif
- && (*status & DEC_Inexact) == 0)
- {
- if (set->round == DEC_ROUND_FLOOR)
- res->bits |= DECNEG; /* sign - */
- else
- res->bits &= ~DECNEG; /* sign + */
- }
- }
- while (0); /* end protected */
-
- if (alloced)
- {
- if (allocacc != NULL)
- free (allocacc); /* drop any storage we used */
- if (allocrhs != NULL)
- free (allocrhs); /* .. */
- if (alloclhs != NULL)
- free (alloclhs); /* .. */
- }
+ if (allocacc!=NULL) free(allocacc); /* drop any storage used */
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); /* .. */
+ if (alloclhs!=NULL) free(alloclhs); /* .. */
+ #endif
return res;
-}
+ } /* decAddOp */
/* ------------------------------------------------------------------ */
-/* decDivideOp -- division operation */
-/* */
+/* decDivideOp -- division operation */
+/* */
/* This routine performs the calculations for all four division */
/* operators (divide, divideInteger, remainder, remainderNear). */
-/* */
-/* C=A op B */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
+/* */
+/* C=A op B */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
-/* status is the usual accumulator */
-/* */
-/* C must have space for set->digits digits. */
-/* */
+/* status is the usual accumulator */
+/* */
+/* C must have space for set->digits digits. */
+/* */
/* ------------------------------------------------------------------ */
/* The underlying algorithm of this routine is the same as in the */
/* 1981 S/370 implementation, that is, non-restoring long division */
/* with bi-unit (rather than bi-digit) estimation for each unit */
/* multiplier. In this pseudocode overview, complications for the */
/* Remainder operators and division residues for exact rounding are */
-/* omitted for clarity. */
-/* */
-/* Prepare operands and handle special values */
-/* Test for x/0 and then 0/x */
-/* Exp =Exp1 - Exp2 */
-/* Exp =Exp +len(var1) -len(var2) */
-/* Sign=Sign1 * Sign2 */
-/* Pad accumulator (Var1) to double-length with 0's (pad1) */
-/* Pad Var2 to same length as Var1 */
+/* omitted for clarity. */
+/* */
+/* Prepare operands and handle special values */
+/* Test for x/0 and then 0/x */
+/* Exp =Exp1 - Exp2 */
+/* Exp =Exp +len(var1) -len(var2) */
+/* Sign=Sign1 * Sign2 */
+/* Pad accumulator (Var1) to double-length with 0's (pad1) */
+/* Pad Var2 to same length as Var1 */
/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
-/* have=0 */
-/* Do until (have=digits+1 OR residue=0) */
-/* if exp<0 then if integer divide/residue then leave */
-/* this_unit=0 */
-/* Do forever */
-/* compare numbers */
-/* if <0 then leave inner_loop */
-/* if =0 then (* quick exit without subtract *) do */
-/* this_unit=this_unit+1; output this_unit */
-/* leave outer_loop; end */
-/* Compare lengths of numbers (mantissae): */
-/* If same then tops2=msu2pair -- {units 1&2 of var2} */
-/* else tops2=msu2plus -- {0, unit 1 of var2} */
-/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
-/* mult=tops1/tops2 -- Good and safe guess at divisor */
-/* if mult=0 then mult=1 */
-/* this_unit=this_unit+mult */
-/* subtract */
-/* end inner_loop */
-/* if have\=0 | this_unit\=0 then do */
-/* output this_unit */
-/* have=have+1; end */
-/* var2=var2/10 */
-/* exp=exp-1 */
-/* end outer_loop */
-/* exp=exp+1 -- set the proper exponent */
-/* if have=0 then generate answer=0 */
-/* Return (Result is defined by Var1) */
-/* */
-/* ------------------------------------------------------------------ */
-/* We need two working buffers during the long division; one (digits+ */
+/* have=0 */
+/* Do until (have=digits+1 OR residue=0) */
+/* if exp<0 then if integer divide/residue then leave */
+/* this_unit=0 */
+/* Do forever */
+/* compare numbers */
+/* if <0 then leave inner_loop */
+/* if =0 then (* quick exit without subtract *) do */
+/* this_unit=this_unit+1; output this_unit */
+/* leave outer_loop; end */
+/* Compare lengths of numbers (mantissae): */
+/* If same then tops2=msu2pair -- {units 1&2 of var2} */
+/* else tops2=msu2plus -- {0, unit 1 of var2} */
+/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
+/* mult=tops1/tops2 -- Good and safe guess at divisor */
+/* if mult=0 then mult=1 */
+/* this_unit=this_unit+mult */
+/* subtract */
+/* end inner_loop */
+/* if have\=0 | this_unit\=0 then do */
+/* output this_unit */
+/* have=have+1; end */
+/* var2=var2/10 */
+/* exp=exp-1 */
+/* end outer_loop */
+/* exp=exp+1 -- set the proper exponent */
+/* if have=0 then generate answer=0 */
+/* Return (Result is defined by Var1) */
+/* */
+/* ------------------------------------------------------------------ */
+/* Two working buffers are needed during the division; one (digits+ */
/* 1) to accumulate the result, and the other (up to 2*digits+1) for */
-/* long subtractions. These are acc and var1 respectively. */
+/* long subtractions. These are acc and var1 respectively. */
/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
-/* ------------------------------------------------------------------ */
-static decNumber *
-decDivideOp (decNumber * res,
- decNumber * lhs, decNumber * rhs,
- decContext * set, Flag op, uInt * status)
-{
- decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
- decNumber *allocrhs = NULL; /* .., rhs */
- Unit accbuff[D2U (DECBUFFER + DECDPUN)]; /* local buffer */
- Unit *acc = accbuff; /* -> accumulator array for result */
- Unit *allocacc = NULL; /* -> allocated buffer, iff allocated */
- Unit *accnext; /* -> where next digit will go */
- Int acclength; /* length of acc needed [Units] */
- Int accunits; /* count of units accumulated */
- Int accdigits; /* count of digits accumulated */
-
- Unit varbuff[D2U (DECBUFFER * 2 + DECDPUN) * sizeof (Unit)]; /* buffer for var1 */
- Unit *var1 = varbuff; /* -> var1 array for long subtraction */
- Unit *varalloc = NULL; /* -> allocated buffer, iff used */
-
- Unit *var2; /* -> var2 array */
-
- Int var1units, var2units; /* actual lengths */
- Int var2ulen; /* logical length (units) */
- Int var1initpad = 0; /* var1 initial padding (digits) */
- Unit *msu1, *msu2; /* -> msu of each var */
- Int msu2plus; /* msu2 plus one [does not vary] */
- eInt msu2pair; /* msu2 pair plus one [does not vary] */
- Int maxdigits; /* longest LHS or required acc length */
- Int mult; /* multiplier for subtraction */
- Unit thisunit; /* current unit being accumulated */
- Int residue; /* for rounding */
- Int reqdigits = set->digits; /* requested DIGITS */
- Int exponent; /* working exponent */
- Int maxexponent = 0; /* DIVIDE maximum exponent if unrounded */
- uByte bits; /* working sign */
- uByte merged; /* merged flags */
- Unit *target, *source; /* work */
- uInt const *pow; /* .. */
- Int shift, cut; /* .. */
-#if DECSUBSET
- Int dropped; /* work */
-#endif
+/* The static buffers may be larger than might be expected to allow */
+/* for calls from higher-level funtions (notable exp). */
+/* ------------------------------------------------------------------ */
+static decNumber * decDivideOp(decNumber *res,
+ const decNumber *lhs, const decNumber *rhs,
+ decContext *set, Flag op, uInt *status) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
+ decNumber *allocrhs=NULL; /* .., rhs */
+ #endif
+ Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */
+ Unit *acc=accbuff; /* -> accumulator array for result */
+ Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */
+ Unit *accnext; /* -> where next digit will go */
+ Int acclength; /* length of acc needed [Units] */
+ Int accunits; /* count of units accumulated */
+ Int accdigits; /* count of digits accumulated */
+
+ Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; /* buffer for var1 */
+ Unit *var1=varbuff; /* -> var1 array for long subtraction */
+ Unit *varalloc=NULL; /* -> allocated buffer, iff used */
+ Unit *msu1; /* -> msu of var1 */
+
+ const Unit *var2; /* -> var2 array */
+ const Unit *msu2; /* -> msu of var2 */
+ Int msu2plus; /* msu2 plus one [does not vary] */
+ eInt msu2pair; /* msu2 pair plus one [does not vary] */
+
+ Int var1units, var2units; /* actual lengths */
+ Int var2ulen; /* logical length (units) */
+ Int var1initpad=0; /* var1 initial padding (digits) */
+ Int maxdigits; /* longest LHS or required acc length */
+ Int mult; /* multiplier for subtraction */
+ Unit thisunit; /* current unit being accumulated */
+ Int residue; /* for rounding */
+ Int reqdigits=set->digits; /* requested DIGITS */
+ Int exponent; /* working exponent */
+ Int maxexponent=0; /* DIVIDE maximum exponent if unrounded */
+ uByte bits; /* working sign */
+ Unit *target; /* work */
+ const Unit *source; /* .. */
+ uInt const *pow; /* .. */
+ Int shift, cut; /* .. */
+ #if DECSUBSET
+ Int dropped; /* work */
+ #endif
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operands and set lostDigits status, as needed */
+ if (lhs->digits>reqdigits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
+ }
+ if (rhs->digits>reqdigits) {
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
+ }
+ }
+ #endif
+ /* [following code does not require input rounding] */
-#if DECCHECK
- if (decCheckOperands (res, lhs, rhs, set))
- return res;
-#endif
+ bits=(lhs->bits^rhs->bits)&DECNEG; /* assumed sign for divisions */
- do
- { /* protect allocated storage */
-#if DECSUBSET
- if (!set->extended)
- {
- /* reduce operands and set lostDigits status, as needed */
- if (lhs->digits > reqdigits)
- {
- alloclhs = decRoundOperand (lhs, set, status);
- if (alloclhs == NULL)
- break;
- lhs = alloclhs;
- }
- if (rhs->digits > reqdigits)
- {
- allocrhs = decRoundOperand (rhs, set, status);
- if (allocrhs == NULL)
- break;
- rhs = allocrhs;
- }
+ /* handle infinities and NaNs */
+ if (SPECIALARGS) { /* a special bit set */
+ if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
+ decNaNs(res, lhs, rhs, set, status);
+ break;
}
-#endif
- /* [following code does not require input rounding] */
-
- bits = (lhs->bits ^ rhs->bits) & DECNEG; /* assumed sign for divisions */
-
- /* handle infinities and NaNs */
- merged = (lhs->bits | rhs->bits) & DECSPECIAL;
- if (merged)
- { /* a special bit set */
- if (merged & (DECSNAN | DECNAN))
- { /* one or two NaNs */
- decNaNs (res, lhs, rhs, status);
- break;
- }
- /* one or two infinities */
- if (decNumberIsInfinite (lhs))
- { /* LHS (dividend) is infinite */
- if (decNumberIsInfinite (rhs) || /* two infinities are invalid .. */
- op & (REMAINDER | REMNEAR))
- { /* as is remainder of infinity */
- *status |= DEC_Invalid_operation;
- break;
- }
- /* [Note that infinity/0 raises no exceptions] */
- decNumberZero (res);
- res->bits = bits | DECINF; /* set +/- infinity */
- break;
- }
- else
- { /* RHS (divisor) is infinite */
- residue = 0;
- if (op & (REMAINDER | REMNEAR))
- {
- /* result is [finished clone of] lhs */
- decCopyFit (res, lhs, set, &residue, status);
- }
- else
- { /* a division */
- decNumberZero (res);
- res->bits = bits; /* set +/- zero */
- /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */
- /* is a 0 with infinitely negative exponent, clamped to minimum */
- if (op & DIVIDE)
- {
- res->exponent = set->emin - set->digits + 1;
- *status |= DEC_Clamped;
- }
- }
- decFinish (res, set, &residue, status);
- break;
- }
+ /* one or two infinities */
+ if (decNumberIsInfinite(lhs)) { /* LHS (dividend) is infinite */
+ if (decNumberIsInfinite(rhs) || /* two infinities are invalid .. */
+ op & (REMAINDER | REMNEAR)) { /* as is remainder of infinity */
+ *status|=DEC_Invalid_operation;
+ break;
+ }
+ /* [Note that infinity/0 raises no exceptions] */
+ decNumberZero(res);
+ res->bits=bits|DECINF; /* set +/- infinity */
+ break;
}
-
- /* handle 0 rhs (x/0) */
- if (ISZERO (rhs))
- { /* x/0 is always exceptional */
- if (ISZERO (lhs))
- {
- decNumberZero (res); /* [after lhs test] */
- *status |= DEC_Division_undefined; /* 0/0 will become NaN */
- }
- else
- {
- decNumberZero (res);
- if (op & (REMAINDER | REMNEAR))
- *status |= DEC_Invalid_operation;
- else
- {
- *status |= DEC_Division_by_zero; /* x/0 */
- res->bits = bits | DECINF; /* .. is +/- Infinity */
- }
+ else { /* RHS (divisor) is infinite */
+ residue=0;
+ if (op&(REMAINDER|REMNEAR)) {
+ /* result is [finished clone of] lhs */
+ decCopyFit(res, lhs, set, &residue, status);
+ }
+ else { /* a division */
+ decNumberZero(res);
+ res->bits=bits; /* set +/- zero */
+ /* for DIVIDEINT the exponent is always 0. For DIVIDE, result */
+ /* is a 0 with infinitely negative exponent, clamped to minimum */
+ if (op&DIVIDE) {
+ res->exponent=set->emin-set->digits+1;
+ *status|=DEC_Clamped;
}
- break;
+ }
+ decFinish(res, set, &residue, status);
+ break;
}
+ }
- /* handle 0 lhs (0/x) */
- if (ISZERO (lhs))
- { /* 0/x [x!=0] */
-#if DECSUBSET
- if (!set->extended)
- decNumberZero (res);
- else
- {
-#endif
- if (op & DIVIDE)
- {
- residue = 0;
- exponent = lhs->exponent - rhs->exponent; /* ideal exponent */
- decNumberCopy (res, lhs); /* [zeros always fit] */
- res->bits = bits; /* sign as computed */
- res->exponent = exponent; /* exponent, too */
- decFinalize (res, set, &residue, status); /* check exponent */
- }
- else if (op & DIVIDEINT)
- {
- decNumberZero (res); /* integer 0 */
- res->bits = bits; /* sign as computed */
- }
- else
- { /* a remainder */
- exponent = rhs->exponent; /* [save in case overwrite] */
- decNumberCopy (res, lhs); /* [zeros always fit] */
- if (exponent < res->exponent)
- res->exponent = exponent; /* use lower */
- }
-#if DECSUBSET
- }
-#endif
+ /* handle 0 rhs (x/0) */
+ if (ISZERO(rhs)) { /* x/0 is always exceptional */
+ if (ISZERO(lhs)) {
+ decNumberZero(res); /* [after lhs test] */
+ *status|=DEC_Division_undefined;/* 0/0 will become NaN */
+ }
+ else {
+ decNumberZero(res);
+ if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
+ else {
+ *status|=DEC_Division_by_zero; /* x/0 */
+ res->bits=bits|DECINF; /* .. is +/- Infinity */
+ }
+ }
+ break;}
+
+ /* handle 0 lhs (0/x) */
+ if (ISZERO(lhs)) { /* 0/x [x!=0] */
+ #if DECSUBSET
+ if (!set->extended) decNumberZero(res);
+ else {
+ #endif
+ if (op&DIVIDE) {
+ residue=0;
+ exponent=lhs->exponent-rhs->exponent; /* ideal exponent */
+ decNumberCopy(res, lhs); /* [zeros always fit] */
+ res->bits=bits; /* sign as computed */
+ res->exponent=exponent; /* exponent, too */
+ decFinalize(res, set, &residue, status); /* check exponent */
+ }
+ else if (op&DIVIDEINT) {
+ decNumberZero(res); /* integer 0 */
+ res->bits=bits; /* sign as computed */
+ }
+ else { /* a remainder */
+ exponent=rhs->exponent; /* [save in case overwrite] */
+ decNumberCopy(res, lhs); /* [zeros always fit] */
+ if (exponent<res->exponent) res->exponent=exponent; /* use lower */
+ }
+ #if DECSUBSET
+ }
+ #endif
+ break;}
+
+ /* Precalculate exponent. This starts off adjusted (and hence fits */
+ /* in 31 bits) and becomes the usual unadjusted exponent as the */
+ /* division proceeds. The order of evaluation is important, here, */
+ /* to avoid wrap. */
+ exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
+
+ /* If the working exponent is -ve, then some quick exits are */
+ /* possible because the quotient is known to be <1 */
+ /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
+ if (exponent<0 && !(op==DIVIDE)) {
+ if (op&DIVIDEINT) {
+ decNumberZero(res); /* integer part is 0 */
+ #if DECSUBSET
+ if (set->extended)
+ #endif
+ res->bits=bits; /* set +/- zero */
+ break;}
+ /* fastpath remainders so long as the lhs has the smaller */
+ /* (or equal) exponent */
+ if (lhs->exponent<=rhs->exponent) {
+ if (op&REMAINDER || exponent<-1) {
+ /* It is REMAINDER or safe REMNEAR; result is [finished */
+ /* clone of] lhs (r = x - 0*y) */
+ residue=0;
+ decCopyFit(res, lhs, set, &residue, status);
+ decFinish(res, set, &residue, status);
break;
+ }
+ /* [unsafe REMNEAR drops through] */
}
+ } /* fastpaths */
+
+ /* Long (slow) division is needed; roll up the sleeves... */
+
+ /* The accumulator will hold the quotient of the division. */
+ /* If it needs to be too long for stack storage, then allocate. */
+ acclength=D2U(reqdigits+DECDPUN); /* in Units */
+ if (acclength*sizeof(Unit)>sizeof(accbuff)) {
+ /* printf("malloc dvacc %ld units\n", acclength); */
+ allocacc=(Unit *)malloc(acclength*sizeof(Unit));
+ if (allocacc==NULL) { /* hopeless -- abandon */
+ *status|=DEC_Insufficient_storage;
+ break;}
+ acc=allocacc; /* use the allocated space */
+ }
- /* Precalculate exponent. This starts off adjusted (and hence fits */
- /* in 31 bits) and becomes the usual unadjusted exponent as the */
- /* division proceeds. The order of evaluation is important, here, */
- /* to avoid wrap. */
- exponent =
- (lhs->exponent + lhs->digits) - (rhs->exponent + rhs->digits);
-
- /* If the working exponent is -ve, then some quick exits are */
- /* possible because the quotient is known to be <1 */
- /* [for REMNEAR, it needs to be < -1, as -0.5 could need work] */
- if (exponent < 0 && !(op == DIVIDE))
- {
- if (op & DIVIDEINT)
- {
- decNumberZero (res); /* integer part is 0 */
-#if DECSUBSET
- if (set->extended)
-#endif
- res->bits = bits; /* set +/- zero */
- break;
- }
- /* we can fastpath remainders so long as the lhs has the */
- /* smaller (or equal) exponent */
- if (lhs->exponent <= rhs->exponent)
- {
- if (op & REMAINDER || exponent < -1)
- {
- /* It is REMAINDER or safe REMNEAR; result is [finished */
- /* clone of] lhs (r = x - 0*y) */
- residue = 0;
- decCopyFit (res, lhs, set, &residue, status);
- decFinish (res, set, &residue, status);
- break;
- }
- /* [unsafe REMNEAR drops through] */
- }
- } /* fastpaths */
-
- /* We need long (slow) division; roll up the sleeves... */
-
- /* The accumulator will hold the quotient of the division. */
- /* If it needs to be too long for stack storage, then allocate. */
- acclength = D2U (reqdigits + DECDPUN); /* in Units */
- if (acclength * sizeof (Unit) > sizeof (accbuff))
- {
- allocacc = (Unit *) malloc (acclength * sizeof (Unit));
- if (allocacc == NULL)
- { /* hopeless -- abandon */
- *status |= DEC_Insufficient_storage;
- break;
- }
- acc = allocacc; /* use the allocated space */
- }
+ /* var1 is the padded LHS ready for subtractions. */
+ /* If it needs to be too long for stack storage, then allocate. */
+ /* The maximum units needed for var1 (long subtraction) is: */
+ /* Enough for */
+ /* (rhs->digits+reqdigits-1) -- to allow full slide to right */
+ /* or (lhs->digits) -- to allow for long lhs */
+ /* whichever is larger */
+ /* +1 -- for rounding of slide to right */
+ /* +1 -- for leading 0s */
+ /* +1 -- for pre-adjust if a remainder or DIVIDEINT */
+ /* [Note: unused units do not participate in decUnitAddSub data] */
+ maxdigits=rhs->digits+reqdigits-1;
+ if (lhs->digits>maxdigits) maxdigits=lhs->digits;
+ var1units=D2U(maxdigits)+2;
+ /* allocate a guard unit above msu1 for REMAINDERNEAR */
+ if (!(op&DIVIDE)) var1units++;
+ if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
+ /* printf("malloc dvvar %ld units\n", var1units+1); */
+ varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
+ if (varalloc==NULL) { /* hopeless -- abandon */
+ *status|=DEC_Insufficient_storage;
+ break;}
+ var1=varalloc; /* use the allocated space */
+ }
- /* var1 is the padded LHS ready for subtractions. */
- /* If it needs to be too long for stack storage, then allocate. */
- /* The maximum units we need for var1 (long subtraction) is: */
- /* Enough for */
- /* (rhs->digits+reqdigits-1) -- to allow full slide to right */
- /* or (lhs->digits) -- to allow for long lhs */
- /* whichever is larger */
- /* +1 -- for rounding of slide to right */
- /* +1 -- for leading 0s */
- /* +1 -- for pre-adjust if a remainder or DIVIDEINT */
- /* [Note: unused units do not participate in decUnitAddSub data] */
- maxdigits = rhs->digits + reqdigits - 1;
- if (lhs->digits > maxdigits)
- maxdigits = lhs->digits;
- var1units = D2U (maxdigits) + 2;
- /* allocate a guard unit above msu1 for REMAINDERNEAR */
- if (!(op & DIVIDE))
- var1units++;
- if ((var1units + 1) * sizeof (Unit) > sizeof (varbuff))
- {
- varalloc = (Unit *) malloc ((var1units + 1) * sizeof (Unit));
- if (varalloc == NULL)
- { /* hopeless -- abandon */
- *status |= DEC_Insufficient_storage;
- break;
- }
- var1 = varalloc; /* use the allocated space */
- }
+ /* Extend the lhs and rhs to full long subtraction length. The lhs */
+ /* is truly extended into the var1 buffer, with 0 padding, so a */
+ /* subtract in place is always possible. The rhs (var2) has */
+ /* virtual padding (implemented by decUnitAddSub). */
+ /* One guard unit was allocated above msu1 for rem=rem+rem in */
+ /* REMAINDERNEAR. */
+ msu1=var1+var1units-1; /* msu of var1 */
+ source=lhs->lsu+D2U(lhs->digits)-1; /* msu of input array */
+ for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
+ for (; target>=var1; target--) *target=0;
+
+ /* rhs (var2) is left-aligned with var1 at the start */
+ var2ulen=var1units; /* rhs logical length (units) */
+ var2units=D2U(rhs->digits); /* rhs actual length (units) */
+ var2=rhs->lsu; /* -> rhs array */
+ msu2=var2+var2units-1; /* -> msu of var2 [never changes] */
+ /* now set up the variables which will be used for estimating the */
+ /* multiplication factor. If these variables are not exact, add */
+ /* 1 to make sure that the multiplier is never overestimated. */
+ msu2plus=*msu2; /* it's value .. */
+ if (var2units>1) msu2plus++; /* .. +1 if any more */
+ msu2pair=(eInt)*msu2*(DECDPUNMAX+1);/* top two pair .. */
+ if (var2units>1) { /* .. [else treat 2nd as 0] */
+ msu2pair+=*(msu2-1); /* .. */
+ if (var2units>2) msu2pair++; /* .. +1 if any more */
+ }
- /* Extend the lhs and rhs to full long subtraction length. The lhs */
- /* is truly extended into the var1 buffer, with 0 padding, so we can */
- /* subtract in place. The rhs (var2) has virtual padding */
- /* (implemented by decUnitAddSub). */
- /* We allocated one guard unit above msu1 for rem=rem+rem in REMAINDERNEAR */
- msu1 = var1 + var1units - 1; /* msu of var1 */
- source = lhs->lsu + D2U (lhs->digits) - 1; /* msu of input array */
- for (target = msu1; source >= lhs->lsu; source--, target--)
- *target = *source;
- for (; target >= var1; target--)
- *target = 0;
-
- /* rhs (var2) is left-aligned with var1 at the start */
- var2ulen = var1units; /* rhs logical length (units) */
- var2units = D2U (rhs->digits); /* rhs actual length (units) */
- var2 = rhs->lsu; /* -> rhs array */
- msu2 = var2 + var2units - 1; /* -> msu of var2 [never changes] */
- /* now set up the variables which we'll use for estimating the */
- /* multiplication factor. If these variables are not exact, we add */
- /* 1 to make sure that we never overestimate the multiplier. */
- msu2plus = *msu2; /* it's value .. */
- if (var2units > 1)
- msu2plus++; /* .. +1 if any more */
- msu2pair = (eInt) * msu2 * (DECDPUNMAX + 1); /* top two pair .. */
- if (var2units > 1)
- { /* .. [else treat 2nd as 0] */
- msu2pair += *(msu2 - 1); /* .. */
- if (var2units > 2)
- msu2pair++; /* .. +1 if any more */
+ /* The calculation is working in units, which may have leading zeros, */
+ /* but the exponent was calculated on the assumption that they are */
+ /* both left-aligned. Adjust the exponent to compensate: add the */
+ /* number of leading zeros in var1 msu and subtract those in var2 msu. */
+ /* [This is actually done by counting the digits and negating, as */
+ /* lead1=DECDPUN-digits1, and similarly for lead2.] */
+ for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
+ for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
+
+ /* Now, if doing an integer divide or remainder, ensure that */
+ /* the result will be Unit-aligned. To do this, shift the var1 */
+ /* accumulator towards least if need be. (It's much easier to */
+ /* do this now than to reassemble the residue afterwards, if */
+ /* doing a remainder.) Also ensure the exponent is not negative. */
+ if (!(op&DIVIDE)) {
+ Unit *u; /* work */
+ /* save the initial 'false' padding of var1, in digits */
+ var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
+ /* Determine the shift to do. */
+ if (exponent<0) cut=-exponent;
+ else cut=DECDPUN-exponent%DECDPUN;
+ decShiftToLeast(var1, var1units, cut);
+ exponent+=cut; /* maintain numerical value */
+ var1initpad-=cut; /* .. and reduce padding */
+ /* clean any most-significant units which were just emptied */
+ for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
+ } /* align */
+ else { /* is DIVIDE */
+ maxexponent=lhs->exponent-rhs->exponent; /* save */
+ /* optimization: if the first iteration will just produce 0, */
+ /* preadjust to skip it [valid for DIVIDE only] */
+ if (*msu1<*msu2) {
+ var2ulen--; /* shift down */
+ exponent-=DECDPUN; /* update the exponent */
}
+ }
- /* Since we are working in units, the units may have leading zeros, */
- /* but we calculated the exponent on the assumption that they are */
- /* both left-aligned. Adjust the exponent to compensate: add the */
- /* number of leading zeros in var1 msu and subtract those in var2 msu. */
- /* [We actually do this by counting the digits and negating, as */
- /* lead1=DECDPUN-digits1, and similarly for lead2.] */
- for (pow = &powers[1]; *msu1 >= *pow; pow++)
- exponent--;
- for (pow = &powers[1]; *msu2 >= *pow; pow++)
- exponent++;
-
- /* Now, if doing an integer divide or remainder, we want to ensure */
- /* that the result will be Unit-aligned. To do this, we shift the */
- /* var1 accumulator towards least if need be. (It's much easier to */
- /* do this now than to reassemble the residue afterwards, if we are */
- /* doing a remainder.) Also ensure the exponent is not negative. */
- if (!(op & DIVIDE))
- {
- Unit *u;
- /* save the initial 'false' padding of var1, in digits */
- var1initpad = (var1units - D2U (lhs->digits)) * DECDPUN;
- /* Determine the shift to do. */
- if (exponent < 0)
- cut = -exponent;
- else
- cut = DECDPUN - exponent % DECDPUN;
- decShiftToLeast (var1, var1units, cut);
- exponent += cut; /* maintain numerical value */
- var1initpad -= cut; /* .. and reduce padding */
- /* clean any most-significant units we just emptied */
- for (u = msu1; cut >= DECDPUN; cut -= DECDPUN, u--)
- *u = 0;
- } /* align */
- else
- { /* is DIVIDE */
- maxexponent = lhs->exponent - rhs->exponent; /* save */
- /* optimization: if the first iteration will just produce 0, */
- /* preadjust to skip it [valid for DIVIDE only] */
- if (*msu1 < *msu2)
- {
- var2ulen--; /* shift down */
- exponent -= DECDPUN; /* update the exponent */
+ /* ---- start the long-division loops ------------------------------ */
+ accunits=0; /* no units accumulated yet */
+ accdigits=0; /* .. or digits */
+ accnext=acc+acclength-1; /* -> msu of acc [NB: allows digits+1] */
+ for (;;) { /* outer forever loop */
+ thisunit=0; /* current unit assumed 0 */
+ /* find the next unit */
+ for (;;) { /* inner forever loop */
+ /* strip leading zero units [from either pre-adjust or from */
+ /* subtract last time around]. Leave at least one unit. */
+ for (; *msu1==0 && msu1>var1; msu1--) var1units--;
+
+ if (var1units<var2ulen) break; /* var1 too low for subtract */
+ if (var1units==var2ulen) { /* unit-by-unit compare needed */
+ /* compare the two numbers, from msu */
+ const Unit *pv1, *pv2;
+ Unit v2; /* units to compare */
+ pv2=msu2; /* -> msu */
+ for (pv1=msu1; ; pv1--, pv2--) {
+ /* v1=*pv1 -- always OK */
+ v2=0; /* assume in padding */
+ if (pv2>=var2) v2=*pv2; /* in range */
+ if (*pv1!=v2) break; /* no longer the same */
+ if (pv1==var1) break; /* done; leave pv1 as is */
}
+ /* here when all inspected or a difference seen */
+ if (*pv1<v2) break; /* var1 too low to subtract */
+ if (*pv1==v2) { /* var1 == var2 */
+ /* reach here if var1 and var2 are identical; subtraction */
+ /* would increase digit by one, and the residue will be 0 so */
+ /* the calculation is done; leave the loop with residue=0. */
+ thisunit++; /* as though subtracted */
+ *var1=0; /* set var1 to 0 */
+ var1units=1; /* .. */
+ break; /* from inner */
+ } /* var1 == var2 */
+ /* *pv1>v2. Prepare for real subtraction; the lengths are equal */
+ /* Estimate the multiplier (there's always a msu1-1)... */
+ /* Bring in two units of var2 to provide a good estimate. */
+ mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
+ } /* lengths the same */
+ else { /* var1units > var2ulen, so subtraction is safe */
+ /* The var2 msu is one unit towards the lsu of the var1 msu, */
+ /* so only one unit for var2 can be used. */
+ mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
+ }
+ if (mult==0) mult=1; /* must always be at least 1 */
+ /* subtraction needed; var1 is > var2 */
+ thisunit=(Unit)(thisunit+mult); /* accumulate */
+ /* subtract var1-var2, into var1; only the overlap needs */
+ /* processing, as this is an in-place calculation */
+ shift=var2ulen-var2units;
+ #if DECTRACE
+ decDumpAr('1', &var1[shift], var1units-shift);
+ decDumpAr('2', var2, var2units);
+ printf("m=%ld\n", -mult);
+ #endif
+ decUnitAddSub(&var1[shift], var1units-shift,
+ var2, var2units, 0,
+ &var1[shift], -mult);
+ #if DECTRACE
+ decDumpAr('#', &var1[shift], var1units-shift);
+ #endif
+ /* var1 now probably has leading zeros; these are removed at the */
+ /* top of the inner loop. */
+ } /* inner loop */
+
+ /* The next unit has been calculated in full; unless it's a */
+ /* leading zero, add to acc */
+ if (accunits!=0 || thisunit!=0) { /* is first or non-zero */
+ *accnext=thisunit; /* store in accumulator */
+ /* account exactly for the new digits */
+ if (accunits==0) {
+ accdigits++; /* at least one */
+ for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
+ }
+ else accdigits+=DECDPUN;
+ accunits++; /* update count */
+ accnext--; /* ready for next */
+ if (accdigits>reqdigits) break; /* have enough digits */
}
- /* ---- start the long-division loops ------------------------------ */
- accunits = 0; /* no units accumulated yet */
- accdigits = 0; /* .. or digits */
- accnext = acc + acclength - 1; /* -> msu of acc [NB: allows digits+1] */
- for (;;)
- { /* outer forever loop */
- thisunit = 0; /* current unit assumed 0 */
- /* find the next unit */
- for (;;)
- { /* inner forever loop */
- /* strip leading zero units [from either pre-adjust or from */
- /* subtract last time around]. Leave at least one unit. */
- for (; *msu1 == 0 && msu1 > var1; msu1--)
- var1units--;
-
- if (var1units < var2ulen)
- break; /* var1 too low for subtract */
- if (var1units == var2ulen)
- { /* unit-by-unit compare needed */
- /* compare the two numbers, from msu */
- Unit *pv1, *pv2, v2; /* units to compare */
- pv2 = msu2; /* -> msu */
- for (pv1 = msu1;; pv1--, pv2--)
- {
- /* v1=*pv1 -- always OK */
- v2 = 0; /* assume in padding */
- if (pv2 >= var2)
- v2 = *pv2; /* in range */
- if (*pv1 != v2)
- break; /* no longer the same */
- if (pv1 == var1)
- break; /* done; leave pv1 as is */
- }
- /* here when all inspected or a difference seen */
- if (*pv1 < v2)
- break; /* var1 too low to subtract */
- if (*pv1 == v2)
- { /* var1 == var2 */
- /* reach here if var1 and var2 are identical; subtraction */
- /* would increase digit by one, and the residue will be 0 so */
- /* we are done; leave the loop with residue set to 0. */
- thisunit++; /* as though subtracted */
- *var1 = 0; /* set var1 to 0 */
- var1units = 1; /* .. */
- break; /* from inner */
- } /* var1 == var2 */
- /* *pv1>v2. Prepare for real subtraction; the lengths are equal */
- /* Estimate the multiplier (there's always a msu1-1)... */
- /* Bring in two units of var2 to provide a good estimate. */
- mult =
- (Int) (((eInt) * msu1 * (DECDPUNMAX + 1) +
- *(msu1 - 1)) / msu2pair);
- } /* lengths the same */
- else
- { /* var1units > var2ulen, so subtraction is safe */
- /* The var2 msu is one unit towards the lsu of the var1 msu, */
- /* so we can only use one unit for var2. */
- mult =
- (Int) (((eInt) * msu1 * (DECDPUNMAX + 1) +
- *(msu1 - 1)) / msu2plus);
- }
- if (mult == 0)
- mult = 1; /* must always be at least 1 */
- /* subtraction needed; var1 is > var2 */
- thisunit = (Unit) (thisunit + mult); /* accumulate */
- /* subtract var1-var2, into var1; only the overlap needs */
- /* processing, as we are in place */
- shift = var2ulen - var2units;
-#if DECTRACE
- decDumpAr ('1', &var1[shift], var1units - shift);
- decDumpAr ('2', var2, var2units);
- printf ("m=%d\n", -mult);
-#endif
- decUnitAddSub (&var1[shift], var1units - shift,
- var2, var2units, 0, &var1[shift], -mult);
-#if DECTRACE
- decDumpAr ('#', &var1[shift], var1units - shift);
-#endif
- /* var1 now probably has leading zeros; these are removed at the */
- /* top of the inner loop. */
- } /* inner loop */
-
- /* We have the next unit; unless it's a leading zero, add to acc */
- if (accunits != 0 || thisunit != 0)
- { /* put the unit we got */
- *accnext = thisunit; /* store in accumulator */
- /* account exactly for the digits we got */
- if (accunits == 0)
- {
- accdigits++; /* at least one */
- for (pow = &powers[1]; thisunit >= *pow; pow++)
- accdigits++;
- }
- else
- accdigits += DECDPUN;
- accunits++; /* update count */
- accnext--; /* ready for next */
- if (accdigits > reqdigits)
- break; /* we have all we need */
+ /* if the residue is zero, the operation is done (unless divide */
+ /* or divideInteger and still not enough digits yet) */
+ if (*var1==0 && var1units==1) { /* residue is 0 */
+ if (op&(REMAINDER|REMNEAR)) break;
+ if ((op&DIVIDE) && (exponent<=maxexponent)) break;
+ /* [drop through if divideInteger] */
+ }
+ /* also done enough if calculating remainder or integer */
+ /* divide and just did the last ('units') unit */
+ if (exponent==0 && !(op&DIVIDE)) break;
+
+ /* to get here, var1 is less than var2, so divide var2 by the per- */
+ /* Unit power of ten and go for the next digit */
+ var2ulen--; /* shift down */
+ exponent-=DECDPUN; /* update the exponent */
+ } /* outer loop */
+
+ /* ---- division is complete --------------------------------------- */
+ /* here: acc has at least reqdigits+1 of good results (or fewer */
+ /* if early stop), starting at accnext+1 (its lsu) */
+ /* var1 has any residue at the stopping point */
+ /* accunits is the number of digits collected in acc */
+ if (accunits==0) { /* acc is 0 */
+ accunits=1; /* show have a unit .. */
+ accdigits=1; /* .. */
+ *accnext=0; /* .. whose value is 0 */
+ }
+ else accnext++; /* back to last placed */
+ /* accnext now -> lowest unit of result */
+
+ residue=0; /* assume no residue */
+ if (op&DIVIDE) {
+ /* record the presence of any residue, for rounding */
+ if (*var1!=0 || var1units>1) residue=1;
+ else { /* no residue */
+ /* Had an exact division; clean up spurious trailing 0s. */
+ /* There will be at most DECDPUN-1, from the final multiply, */
+ /* and then only if the result is non-0 (and even) and the */
+ /* exponent is 'loose'. */
+ #if DECDPUN>1
+ Unit lsu=*accnext;
+ if (!(lsu&0x01) && (lsu!=0)) {
+ /* count the trailing zeros */
+ Int drop=0;
+ for (;; drop++) { /* [will terminate because lsu!=0] */
+ if (exponent>=maxexponent) break; /* don't chop real 0s */
+ #if DECDPUN<=4
+ if ((lsu-QUOT10(lsu, drop+1)
+ *powers[drop+1])!=0) break; /* found non-0 digit */
+ #else
+ if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */
+ #endif
+ exponent++;
}
-
- /* if the residue is zero, we're done (unless divide or */
- /* divideInteger and we haven't got enough digits yet) */
- if (*var1 == 0 && var1units == 1)
- { /* residue is 0 */
- if (op & (REMAINDER | REMNEAR))
- break;
- if ((op & DIVIDE) && (exponent <= maxexponent))
- break;
- /* [drop through if divideInteger] */
+ if (drop>0) {
+ accunits=decShiftToLeast(accnext, accunits, drop);
+ accdigits=decGetDigits(accnext, accunits);
+ accunits=D2U(accdigits);
+ /* [exponent was adjusted in the loop] */
}
- /* we've also done enough if calculating remainder or integer */
- /* divide and we just did the last ('units') unit */
- if (exponent == 0 && !(op & DIVIDE))
- break;
-
- /* to get here, var1 is less than var2, so divide var2 by the per- */
- /* Unit power of ten and go for the next digit */
- var2ulen--; /* shift down */
- exponent -= DECDPUN; /* update the exponent */
- } /* outer loop */
-
- /* ---- division is complete --------------------------------------- */
- /* here: acc has at least reqdigits+1 of good results (or fewer */
- /* if early stop), starting at accnext+1 (its lsu) */
- /* var1 has any residue at the stopping point */
- /* accunits is the number of digits we collected in acc */
- if (accunits == 0)
- { /* acc is 0 */
- accunits = 1; /* show we have one .. */
- accdigits = 1; /* .. */
- *accnext = 0; /* .. whose value is 0 */
+ } /* neither odd nor 0 */
+ #endif
+ } /* exact divide */
+ } /* divide */
+ else /* op!=DIVIDE */ {
+ /* check for coefficient overflow */
+ if (accdigits+exponent>reqdigits) {
+ *status|=DEC_Division_impossible;
+ break;
}
- else
- accnext++; /* back to last placed */
- /* accnext now -> lowest unit of result */
-
- residue = 0; /* assume no residue */
- if (op & DIVIDE)
- {
- /* record the presence of any residue, for rounding */
- if (*var1 != 0 || var1units > 1)
- residue = 1;
- else
- { /* no residue */
- /* We had an exact division; clean up spurious trailing 0s. */
- /* There will be at most DECDPUN-1, from the final multiply, */
- /* and then only if the result is non-0 (and even) and the */
- /* exponent is 'loose'. */
-#if DECDPUN>1
- Unit lsu = *accnext;
- if (!(lsu & 0x01) && (lsu != 0))
- {
- /* count the trailing zeros */
- Int drop = 0;
- for (;; drop++)
- { /* [will terminate because lsu!=0] */
- if (exponent >= maxexponent)
- break; /* don't chop real 0s */
-#if DECDPUN<=4
- if ((lsu - QUOT10 (lsu, drop + 1)
- * powers[drop + 1]) != 0)
- break; /* found non-0 digit */
-#else
- if (lsu % powers[drop + 1] != 0)
- break; /* found non-0 digit */
-#endif
- exponent++;
- }
- if (drop > 0)
- {
- accunits = decShiftToLeast (accnext, accunits, drop);
- accdigits = decGetDigits (accnext, accunits);
- accunits = D2U (accdigits);
- /* [exponent was adjusted in the loop] */
- }
- } /* neither odd nor 0 */
-#endif
- } /* exact divide */
- } /* divide */
- else /* op!=DIVIDE */
- {
- /* check for coefficient overflow */
- if (accdigits + exponent > reqdigits)
- {
- *status |= DEC_Division_impossible;
- break;
+ if (op & (REMAINDER|REMNEAR)) {
+ /* [Here, the exponent will be 0, because var1 was adjusted */
+ /* appropriately.] */
+ Int postshift; /* work */
+ Flag wasodd=0; /* integer was odd */
+ Unit *quotlsu; /* for save */
+ Int quotdigits; /* .. */
+
+ bits=lhs->bits; /* remainder sign is always as lhs */
+
+ /* Fastpath when residue is truly 0 is worthwhile [and */
+ /* simplifies the code below] */
+ if (*var1==0 && var1units==1) { /* residue is 0 */
+ Int exp=lhs->exponent; /* save min(exponents) */
+ if (rhs->exponent<exp) exp=rhs->exponent;
+ decNumberZero(res); /* 0 coefficient */
+ #if DECSUBSET
+ if (set->extended)
+ #endif
+ res->exponent=exp; /* .. with proper exponent */
+ res->bits=(uByte)(bits&DECNEG); /* [cleaned] */
+ decFinish(res, set, &residue, status); /* might clamp */
+ break;
+ }
+ /* note if the quotient was odd */
+ if (*accnext & 0x01) wasodd=1; /* acc is odd */
+ quotlsu=accnext; /* save in case need to reinspect */
+ quotdigits=accdigits; /* .. */
+
+ /* treat the residue, in var1, as the value to return, via acc */
+ /* calculate the unused zero digits. This is the smaller of: */
+ /* var1 initial padding (saved above) */
+ /* var2 residual padding, which happens to be given by: */
+ postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
+ /* [the 'exponent' term accounts for the shifts during divide] */
+ if (var1initpad<postshift) postshift=var1initpad;
+
+ /* shift var1 the requested amount, and adjust its digits */
+ var1units=decShiftToLeast(var1, var1units, postshift);
+ accnext=var1;
+ accdigits=decGetDigits(var1, var1units);
+ accunits=D2U(accdigits);
+
+ exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */
+ if (rhs->exponent<exponent) exponent=rhs->exponent;
+
+ /* Now correct the result if doing remainderNear; if it */
+ /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
+ /* the integer was odd then the result should be rem-rhs. */
+ if (op&REMNEAR) {
+ Int compare, tarunits; /* work */
+ Unit *up; /* .. */
+ /* calculate remainder*2 into the var1 buffer (which has */
+ /* 'headroom' of an extra unit and hence enough space) */
+ /* [a dedicated 'double' loop would be faster, here] */
+ tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
+ 0, accnext, 1);
+ /* decDumpAr('r', accnext, tarunits); */
+
+ /* Here, accnext (var1) holds tarunits Units with twice the */
+ /* remainder's coefficient, which must now be compared to the */
+ /* RHS. The remainder's exponent may be smaller than the RHS's. */
+ compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
+ rhs->exponent-exponent);
+ if (compare==BADINT) { /* deep trouble */
+ *status|=DEC_Insufficient_storage;
+ break;}
+
+ /* now restore the remainder by dividing by two; the lsu */
+ /* is known to be even. */
+ for (up=accnext; up<accnext+tarunits; up++) {
+ Int half; /* half to add to lower unit */
+ half=*up & 0x01;
+ *up/=2; /* [shift] */
+ if (!half) continue;
+ *(up-1)+=(DECDPUNMAX+1)/2;
}
- if (op & (REMAINDER | REMNEAR))
- {
- /* [Here, the exponent will be 0, because we adjusted var1 */
- /* appropriately.] */
- Int postshift; /* work */
- Flag wasodd = 0; /* integer was odd */
- Unit *quotlsu; /* for save */
- Int quotdigits; /* .. */
-
- /* Fastpath when residue is truly 0 is worthwhile [and */
- /* simplifies the code below] */
- if (*var1 == 0 && var1units == 1)
- { /* residue is 0 */
- Int exp = lhs->exponent; /* save min(exponents) */
- if (rhs->exponent < exp)
- exp = rhs->exponent;
- decNumberZero (res); /* 0 coefficient */
-#if DECSUBSET
- if (set->extended)
-#endif
- res->exponent = exp; /* .. with proper exponent */
+ /* [accunits still describes the original remainder length] */
+
+ if (compare>0 || (compare==0 && wasodd)) { /* adjustment needed */
+ Int exp, expunits, exprem; /* work */
+ /* This is effectively causing round-up of the quotient, */
+ /* so if it was the rare case where it was full and all */
+ /* nines, it would overflow and hence division-impossible */
+ /* should be raised */
+ Flag allnines=0; /* 1 if quotient all nines */
+ if (quotdigits==reqdigits) { /* could be borderline */
+ for (up=quotlsu; ; up++) {
+ if (quotdigits>DECDPUN) {
+ if (*up!=DECDPUNMAX) break;/* non-nines */
+ }
+ else { /* this is the last Unit */
+ if (*up==powers[quotdigits]-1) allnines=1;
break;
- }
- /* note if the quotient was odd */
- if (*accnext & 0x01)
- wasodd = 1; /* acc is odd */
- quotlsu = accnext; /* save in case need to reinspect */
- quotdigits = accdigits; /* .. */
-
- /* treat the residue, in var1, as the value to return, via acc */
- /* calculate the unused zero digits. This is the smaller of: */
- /* var1 initial padding (saved above) */
- /* var2 residual padding, which happens to be given by: */
- postshift =
- var1initpad + exponent - lhs->exponent + rhs->exponent;
- /* [the 'exponent' term accounts for the shifts during divide] */
- if (var1initpad < postshift)
- postshift = var1initpad;
-
- /* shift var1 the requested amount, and adjust its digits */
- var1units = decShiftToLeast (var1, var1units, postshift);
- accnext = var1;
- accdigits = decGetDigits (var1, var1units);
- accunits = D2U (accdigits);
-
- exponent = lhs->exponent; /* exponent is smaller of lhs & rhs */
- if (rhs->exponent < exponent)
- exponent = rhs->exponent;
- bits = lhs->bits; /* remainder sign is always as lhs */
-
- /* Now correct the result if we are doing remainderNear; if it */
- /* (looking just at coefficients) is > rhs/2, or == rhs/2 and */
- /* the integer was odd then the result should be rem-rhs. */
- if (op & REMNEAR)
- {
- Int compare, tarunits; /* work */
- Unit *up; /* .. */
-
-
- /* calculate remainder*2 into the var1 buffer (which has */
- /* 'headroom' of an extra unit and hence enough space) */
- /* [a dedicated 'double' loop would be faster, here] */
- tarunits =
- decUnitAddSub (accnext, accunits, accnext, accunits, 0,
- accnext, 1);
- /* decDumpAr('r', accnext, tarunits); */
-
- /* Here, accnext (var1) holds tarunits Units with twice the */
- /* remainder's coefficient, which we must now compare to the */
- /* RHS. The remainder's exponent may be smaller than the RHS's. */
- compare =
- decUnitCompare (accnext, tarunits, rhs->lsu,
- D2U (rhs->digits),
- rhs->exponent - exponent);
- if (compare == BADINT)
- { /* deep trouble */
- *status |= DEC_Insufficient_storage;
- break;
- }
-
- /* now restore the remainder by dividing by two; we know the */
- /* lsu is even. */
- for (up = accnext; up < accnext + tarunits; up++)
- {
- Int half; /* half to add to lower unit */
- half = *up & 0x01;
- *up /= 2; /* [shift] */
- if (!half)
- continue;
- *(up - 1) += (DECDPUNMAX + 1) / 2;
- }
- /* [accunits still describes the original remainder length] */
-
- if (compare > 0 || (compare == 0 && wasodd))
- { /* adjustment needed */
- Int exp, expunits, exprem; /* work */
- /* This is effectively causing round-up of the quotient, */
- /* so if it was the rare case where it was full and all */
- /* nines, it would overflow and hence division-impossible */
- /* should be raised */
- Flag allnines = 0; /* 1 if quotient all nines */
- if (quotdigits == reqdigits)
- { /* could be borderline */
- for (up = quotlsu;; up++)
- {
- if (quotdigits > DECDPUN)
- {
- if (*up != DECDPUNMAX)
- break; /* non-nines */
- }
- else
- { /* this is the last Unit */
- if (*up == powers[quotdigits] - 1)
- allnines = 1;
- break;
- }
- quotdigits -= DECDPUN; /* checked those digits */
- } /* up */
- } /* borderline check */
- if (allnines)
- {
- *status |= DEC_Division_impossible;
- break;
- }
-
- /* we need rem-rhs; the sign will invert. Again we can */
- /* safely use var1 for the working Units array. */
- exp = rhs->exponent - exponent; /* RHS padding needed */
- /* Calculate units and remainder from exponent. */
- expunits = exp / DECDPUN;
- exprem = exp % DECDPUN;
- /* subtract [A+B*(-m)]; the result will always be negative */
- accunits = -decUnitAddSub (accnext, accunits,
- rhs->lsu, D2U (rhs->digits),
- expunits, accnext,
- -(Int) powers[exprem]);
- accdigits = decGetDigits (accnext, accunits); /* count digits exactly */
- accunits = D2U (accdigits); /* and recalculate the units for copy */
- /* [exponent is as for original remainder] */
- bits ^= DECNEG; /* flip the sign */
- }
- } /* REMNEAR */
- } /* REMAINDER or REMNEAR */
- } /* not DIVIDE */
-
- /* Set exponent and bits */
- res->exponent = exponent;
- res->bits = (uByte) (bits & DECNEG); /* [cleaned] */
-
- /* Now the coefficient. */
- decSetCoeff (res, set, accnext, accdigits, &residue, status);
-
- decFinish (res, set, &residue, status); /* final cleanup */
-
-#if DECSUBSET
- /* If a divide then strip trailing zeros if subset [after round] */
- if (!set->extended && (op == DIVIDE))
- decTrim (res, 0, &dropped);
-#endif
- }
- while (0); /* end protected */
-
- if (varalloc != NULL)
- free (varalloc); /* drop any storage we used */
- if (allocacc != NULL)
- free (allocacc); /* .. */
- if (allocrhs != NULL)
- free (allocrhs); /* .. */
- if (alloclhs != NULL)
- free (alloclhs); /* .. */
+ }
+ quotdigits-=DECDPUN; /* checked those digits */
+ } /* up */
+ } /* borderline check */
+ if (allnines) {
+ *status|=DEC_Division_impossible;
+ break;}
+
+ /* rem-rhs is needed; the sign will invert. Again, var1 */
+ /* can safely be used for the working Units array. */
+ exp=rhs->exponent-exponent; /* RHS padding needed */
+ /* Calculate units and remainder from exponent. */
+ expunits=exp/DECDPUN;
+ exprem=exp%DECDPUN;
+ /* subtract [A+B*(-m)]; the result will always be negative */
+ accunits=-decUnitAddSub(accnext, accunits,
+ rhs->lsu, D2U(rhs->digits),
+ expunits, accnext, -(Int)powers[exprem]);
+ accdigits=decGetDigits(accnext, accunits); /* count digits exactly */
+ accunits=D2U(accdigits); /* and recalculate the units for copy */
+ /* [exponent is as for original remainder] */
+ bits^=DECNEG; /* flip the sign */
+ }
+ } /* REMNEAR */
+ } /* REMAINDER or REMNEAR */
+ } /* not DIVIDE */
+
+ /* Set exponent and bits */
+ res->exponent=exponent;
+ res->bits=(uByte)(bits&DECNEG); /* [cleaned] */
+
+ /* Now the coefficient. */
+ decSetCoeff(res, set, accnext, accdigits, &residue, status);
+
+ decFinish(res, set, &residue, status); /* final cleanup */
+
+ #if DECSUBSET
+ /* If a divide then strip trailing zeros if subset [after round] */
+ if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
+ #endif
+ } while(0); /* end protected */
+
+ if (varalloc!=NULL) free(varalloc); /* drop any storage used */
+ if (allocacc!=NULL) free(allocacc); /* .. */
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); /* .. */
+ if (alloclhs!=NULL) free(alloclhs); /* .. */
+ #endif
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decMultiplyOp -- multiplication operation */
-/* */
-/* This routine performs the multiplication C=A x B. */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X*X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* status is the usual accumulator */
-/* */
-/* C must have space for set->digits digits. */
-/* */
-/* ------------------------------------------------------------------ */
-/* Note: We use 'long' multiplication rather than Karatsuba, as the */
+ } /* decDivideOp */
+
+/* ------------------------------------------------------------------ */
+/* decMultiplyOp -- multiplication operation */
+/* */
+/* This routine performs the multiplication C=A x B. */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X*X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* status is the usual accumulator */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* ------------------------------------------------------------------ */
+/* 'Classic' multiplication is used rather than Karatsuba, as the */
/* latter would give only a minor improvement for the short numbers */
-/* we expect to handle most (and uses much more memory). */
-/* */
-/* We always have to use a buffer for the accumulator. */
-/* ------------------------------------------------------------------ */
-static decNumber *
-decMultiplyOp (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set, uInt * status)
-{
- decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
- decNumber *allocrhs = NULL; /* .., rhs */
- Unit accbuff[D2U (DECBUFFER * 2 + 1)]; /* local buffer (+1 in case DECBUFFER==0) */
- Unit *acc = accbuff; /* -> accumulator array for exact result */
- Unit *allocacc = NULL; /* -> allocated buffer, iff allocated */
- Unit *mer, *mermsup; /* work */
- Int accunits; /* Units of accumulator in use */
- Int madlength; /* Units in multiplicand */
- Int shift; /* Units to shift multiplicand by */
- Int need; /* Accumulator units needed */
- Int exponent; /* work */
- Int residue = 0; /* rounding residue */
- uByte bits; /* result sign */
- uByte merged; /* merged flags */
+/* expected to be handled most (and uses much more memory). */
+/* */
+/* There are two major paths here: the general-purpose ('old code') */
+/* path which handles all DECDPUN values, and a fastpath version */
+/* which is used if 64-bit ints are available, DECDPUN<=4, and more */
+/* than two calls to decUnitAddSub would be made. */
+/* */
+/* The fastpath version lumps units together into 8-digit or 9-digit */
+/* chunks, and also uses a lazy carry strategy to minimise expensive */
+/* 64-bit divisions. The chunks are then broken apart again into */
+/* units for continuing processing. Despite this overhead, the */
+/* fastpath can speed up some 16-digit operations by 10x (and much */
+/* more for higher-precision calculations). */
+/* */
+/* A buffer always has to be used for the accumulator; in the */
+/* fastpath, buffers are also always needed for the chunked copies of */
+/* of the operand coefficients. */
+/* Static buffers are larger than needed just for multiply, to allow */
+/* for calls from other operations (notably exp). */
+/* ------------------------------------------------------------------ */
+#define FASTMUL (DECUSE64 && DECDPUN<5)
+static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ uInt *status) {
+ Int accunits; /* Units of accumulator in use */
+ Int exponent; /* work */
+ Int residue=0; /* rounding residue */
+ uByte bits; /* result sign */
+ Unit *acc; /* -> accumulator Unit array */
+ Int needbytes; /* size calculator */
+ void *allocacc=NULL; /* -> allocated accumulator, iff allocated */
+ Unit accbuff[SD2U(DECBUFFER*4+1)]; /* buffer (+1 for DECBUFFER==0, */
+ /* *4 for calls from other operations) */
+ const Unit *mer, *mermsup; /* work */
+ Int madlength; /* Units in multiplicand */
+ Int shift; /* Units to shift multiplicand by */
+
+ #if FASTMUL
+ /* if DECDPUN is 1 or 3 work in base 10**9, otherwise */
+ /* (DECDPUN is 2 or 4) then work in base 10**8 */
+ #if DECDPUN & 1 /* odd */
+ #define FASTBASE 1000000000 /* base */
+ #define FASTDIGS 9 /* digits in base */
+ #define FASTLAZY 18 /* carry resolution point [1->18] */
+ #else
+ #define FASTBASE 100000000
+ #define FASTDIGS 8
+ #define FASTLAZY 1844 /* carry resolution point [1->1844] */
+ #endif
+ /* three buffers are used, two for chunked copies of the operands */
+ /* (base 10**8 or base 10**9) and one base 2**64 accumulator with */
+ /* lazy carry evaluation */
+ uInt zlhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
+ uInt *zlhi=zlhibuff; /* -> lhs array */
+ uInt *alloclhi=NULL; /* -> allocated buffer, iff allocated */
+ uInt zrhibuff[(DECBUFFER*2+1)/8+1]; /* buffer (+1 for DECBUFFER==0) */
+ uInt *zrhi=zrhibuff; /* -> rhs array */
+ uInt *allocrhi=NULL; /* -> allocated buffer, iff allocated */
+ uLong zaccbuff[(DECBUFFER*2+1)/4+2]; /* buffer (+1 for DECBUFFER==0) */
+ /* [allocacc is shared for both paths, as only one will run] */
+ uLong *zacc=zaccbuff; /* -> accumulator array for exact result */
+ #if DECDPUN==1
+ Int zoff; /* accumulator offset */
+ #endif
+ uInt *lip, *rip; /* item pointers */
+ uInt *lmsi, *rmsi; /* most significant items */
+ Int ilhs, irhs, iacc; /* item counts in the arrays */
+ Int lazy; /* lazy carry counter */
+ uLong lcarry; /* uLong carry */
+ uInt carry; /* carry (NB not uLong) */
+ Int count; /* work */
+ const Unit *cup; /* .. */
+ Unit *up; /* .. */
+ uLong *lp; /* .. */
+ Int p; /* .. */
+ #endif
+
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; /* -> allocated buffer, iff allocated */
+ decNumber *allocrhs=NULL; /* -> allocated buffer, iff allocated */
+ #endif
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ /* precalculate result sign */
+ bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
-#if DECCHECK
- if (decCheckOperands (res, lhs, rhs, set))
- return res;
-#endif
+ /* handle infinities and NaNs */
+ if (SPECIALARGS) { /* a special bit set */
+ if (SPECIALARGS & (DECSNAN | DECNAN)) { /* one or two NaNs */
+ decNaNs(res, lhs, rhs, set, status);
+ return res;}
+ /* one or two infinities; Infinity * 0 is invalid */
+ if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
+ ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
+ *status|=DEC_Invalid_operation;
+ return res;}
+ decNumberZero(res);
+ res->bits=bits|DECINF; /* infinity */
+ return res;}
+
+ /* For best speed, as in DMSRCN [the original Rexx numerics */
+ /* module], use the shorter number as the multiplier (rhs) and */
+ /* the longer as the multiplicand (lhs) to minimise the number of */
+ /* adds (partial products) */
+ if (lhs->digits<rhs->digits) { /* swap... */
+ const decNumber *hold=lhs;
+ lhs=rhs;
+ rhs=hold;
+ }
- do
- { /* protect allocated storage */
-#if DECSUBSET
- if (!set->extended)
- {
- /* reduce operands and set lostDigits status, as needed */
- if (lhs->digits > set->digits)
- {
- alloclhs = decRoundOperand (lhs, set, status);
- if (alloclhs == NULL)
- break;
- lhs = alloclhs;
- }
- if (rhs->digits > set->digits)
- {
- allocrhs = decRoundOperand (rhs, set, status);
- if (allocrhs == NULL)
- break;
- rhs = allocrhs;
- }
- }
-#endif
- /* [following code does not require input rounding] */
-
- /* precalculate result sign */
- bits = (uByte) ((lhs->bits ^ rhs->bits) & DECNEG);
-
- /* handle infinities and NaNs */
- merged = (lhs->bits | rhs->bits) & DECSPECIAL;
- if (merged)
- { /* a special bit set */
- if (merged & (DECSNAN | DECNAN))
- { /* one or two NaNs */
- decNaNs (res, lhs, rhs, status);
- break;
- }
- /* one or two infinities. Infinity * 0 is invalid */
- if (((lhs->bits & DECSPECIAL) == 0 && ISZERO (lhs))
- || ((rhs->bits & DECSPECIAL) == 0 && ISZERO (rhs)))
- {
- *status |= DEC_Invalid_operation;
- break;
- }
- decNumberZero (res);
- res->bits = bits | DECINF; /* infinity */
- break;
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operands and set lostDigits status, as needed */
+ if (lhs->digits>set->digits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
}
-
- /* For best speed, as in DMSRCN, we use the shorter number as the */
- /* multiplier (rhs) and the longer as the multiplicand (lhs) */
- if (lhs->digits < rhs->digits)
- { /* swap... */
- decNumber *hold = lhs;
- lhs = rhs;
- rhs = hold;
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
}
-
- /* if accumulator is too long for local storage, then allocate */
- need = D2U (lhs->digits) + D2U (rhs->digits); /* maximum units in result */
- if (need * sizeof (Unit) > sizeof (accbuff))
- {
- allocacc = (Unit *) malloc (need * sizeof (Unit));
- if (allocacc == NULL)
- {
- *status |= DEC_Insufficient_storage;
- break;
+ }
+ #endif
+ /* [following code does not require input rounding] */
+
+ #if FASTMUL /* fastpath can be used */
+ /* use the fast path if there are enough digits in the shorter */
+ /* operand to make the setup and takedown worthwhile */
+ #define NEEDTWO (DECDPUN*2) /* within two decUnitAddSub calls */
+ if (rhs->digits>NEEDTWO) { /* use fastpath... */
+ /* calculate the number of elements in each array */
+ ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; /* [ceiling] */
+ irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; /* .. */
+ iacc=ilhs+irhs;
+
+ /* allocate buffers if required, as usual */
+ needbytes=ilhs*sizeof(uInt);
+ if (needbytes>(Int)sizeof(zlhibuff)) {
+ alloclhi=(uInt *)malloc(needbytes);
+ zlhi=alloclhi;}
+ needbytes=irhs*sizeof(uInt);
+ if (needbytes>(Int)sizeof(zrhibuff)) {
+ allocrhi=(uInt *)malloc(needbytes);
+ zrhi=allocrhi;}
+
+ /* Allocating the accumulator space needs a special case when */
+ /* DECDPUN=1 because when converting the accumulator to Units */
+ /* after the multiplication each 8-byte item becomes 9 1-byte */
+ /* units. Therefore iacc extra bytes are needed at the front */
+ /* (rounded up to a multiple of 8 bytes), and the uLong */
+ /* accumulator starts offset the appropriate number of units */
+ /* to the right to avoid overwrite during the unchunking. */
+ needbytes=iacc*sizeof(uLong);
+ #if DECDPUN==1
+ zoff=(iacc+7)/8; /* items to offset by */
+ needbytes+=zoff*8;
+ #endif
+ if (needbytes>(Int)sizeof(zaccbuff)) {
+ allocacc=(uLong *)malloc(needbytes);
+ zacc=(uLong *)allocacc;}
+ if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
+ *status|=DEC_Insufficient_storage;
+ break;}
+
+ acc=(Unit *)zacc; /* -> target Unit array */
+ #if DECDPUN==1
+ zacc+=zoff; /* start uLong accumulator to right */
+ #endif
+
+ /* assemble the chunked copies of the left and right sides */
+ for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
+ for (p=0, *lip=0; p<FASTDIGS && count>0;
+ p+=DECDPUN, cup++, count-=DECDPUN)
+ *lip+=*cup*powers[p];
+ lmsi=lip-1; /* save -> msi */
+ for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
+ for (p=0, *rip=0; p<FASTDIGS && count>0;
+ p+=DECDPUN, cup++, count-=DECDPUN)
+ *rip+=*cup*powers[p];
+ rmsi=rip-1; /* save -> msi */
+
+ /* zero the accumulator */
+ for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
+
+ /* Start the multiplication */
+ /* Resolving carries can dominate the cost of accumulating the */
+ /* partial products, so this is only done when necessary. */
+ /* Each uLong item in the accumulator can hold values up to */
+ /* 2**64-1, and each partial product can be as large as */
+ /* (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to */
+ /* itself 18.4 times in a uLong without overflowing, so during */
+ /* the main calculation resolution is carried out every 18th */
+ /* add -- every 162 digits. Similarly, when FASTDIGS=8, the */
+ /* partial products can be added to themselves 1844.6 times in */
+ /* a uLong without overflowing, so intermediate carry */
+ /* resolution occurs only every 14752 digits. Hence for common */
+ /* short numbers usually only the one final carry resolution */
+ /* occurs. */
+ /* (The count is set via FASTLAZY to simplify experiments to */
+ /* measure the value of this approach: a 35% improvement on a */
+ /* [34x34] multiply.) */
+ lazy=FASTLAZY; /* carry delay count */
+ for (rip=zrhi; rip<=rmsi; rip++) { /* over each item in rhs */
+ lp=zacc+(rip-zrhi); /* where to add the lhs */
+ for (lip=zlhi; lip<=lmsi; lip++, lp++) { /* over each item in lhs */
+ *lp+=(uLong)(*lip)*(*rip); /* [this should in-line] */
+ } /* lip loop */
+ lazy--;
+ if (lazy>0 && rip!=rmsi) continue;
+ lazy=FASTLAZY; /* reset delay count */
+ /* spin up the accumulator resolving overflows */
+ for (lp=zacc; lp<zacc+iacc; lp++) {
+ if (*lp<FASTBASE) continue; /* it fits */
+ lcarry=*lp/FASTBASE; /* top part [slow divide] */
+ /* lcarry can exceed 2**32-1, so check again; this check */
+ /* and occasional extra divide (slow) is well worth it, as */
+ /* it allows FASTLAZY to be increased to 18 rather than 4 */
+ /* in the FASTDIGS=9 case */
+ if (lcarry<FASTBASE) carry=(uInt)lcarry; /* [usual] */
+ else { /* two-place carry [fairly rare] */
+ uInt carry2=(uInt)(lcarry/FASTBASE); /* top top part */
+ *(lp+2)+=carry2; /* add to item+2 */
+ *lp-=((uLong)FASTBASE*FASTBASE*carry2); /* [slow] */
+ carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */
}
- acc = allocacc; /* use the allocated space */
+ *(lp+1)+=carry; /* add to item above [inline] */
+ *lp-=((uLong)FASTBASE*carry); /* [inline] */
+ } /* carry resolution */
+ } /* rip loop */
+
+ /* The multiplication is complete; time to convert back into */
+ /* units. This can be done in-place in the accumulator and in */
+ /* 32-bit operations, because carries were resolved after the */
+ /* final add. This needs N-1 divides and multiplies for */
+ /* each item in the accumulator (which will become up to N */
+ /* units, where 2<=N<=9). */
+ for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
+ uInt item=(uInt)*lp; /* decapitate to uInt */
+ for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
+ uInt part=item/(DECDPUNMAX+1);
+ *up=(Unit)(item-(part*(DECDPUNMAX+1)));
+ item=part;
+ } /* p */
+ *up=(Unit)item; up++; /* [final needs no division] */
+ } /* lp */
+ accunits=up-acc; /* count of units */
+ }
+ else { /* here to use units directly, without chunking ['old code'] */
+ #endif
+
+ /* if accumulator will be too long for local storage, then allocate */
+ acc=accbuff; /* -> assume buffer for accumulator */
+ needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
+ if (needbytes>(Int)sizeof(accbuff)) {
+ allocacc=(Unit *)malloc(needbytes);
+ if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
+ acc=(Unit *)allocacc; /* use the allocated space */
}
/* Now the main long multiplication loop */
/* Unlike the equivalent in the IBM Java implementation, there */
- /* is no advantage in calculating from msu to lsu. So we do it */
+ /* is no advantage in calculating from msu to lsu. So, do it */
/* by the book, as it were. */
/* Each iteration calculates ACC=ACC+MULTAND*MULT */
- accunits = 1; /* accumulator starts at '0' */
- *acc = 0; /* .. (lsu=0) */
- shift = 0; /* no multiplicand shift at first */
- madlength = D2U (lhs->digits); /* we know this won't change */
- mermsup = rhs->lsu + D2U (rhs->digits); /* -> msu+1 of multiplier */
-
- for (mer = rhs->lsu; mer < mermsup; mer++)
- {
- /* Here, *mer is the next Unit in the multiplier to use */
- /* If non-zero [optimization] add it... */
- if (*mer != 0)
- {
- accunits =
- decUnitAddSub (&acc[shift], accunits - shift, lhs->lsu,
- madlength, 0, &acc[shift], *mer) + shift;
- }
- else
- { /* extend acc with a 0; we'll use it shortly */
- /* [this avoids length of <=0 later] */
- *(acc + accunits) = 0;
- accunits++;
- }
- /* multiply multiplicand by 10**DECDPUN for next Unit to left */
- shift++; /* add this for 'logical length' */
- } /* n */
-#if DECTRACE
- /* Show exact result */
- decDumpAr ('*', acc, accunits);
-#endif
+ accunits=1; /* accumulator starts at '0' */
+ *acc=0; /* .. (lsu=0) */
+ shift=0; /* no multiplicand shift at first */
+ madlength=D2U(lhs->digits); /* this won't change */
+ mermsup=rhs->lsu+D2U(rhs->digits); /* -> msu+1 of multiplier */
+
+ for (mer=rhs->lsu; mer<mermsup; mer++) {
+ /* Here, *mer is the next Unit in the multiplier to use */
+ /* If non-zero [optimization] add it... */
+ if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
+ lhs->lsu, madlength, 0,
+ &acc[shift], *mer)
+ + shift;
+ else { /* extend acc with a 0; it will be used shortly */
+ *(acc+accunits)=0; /* [this avoids length of <=0 later] */
+ accunits++;
+ }
+ /* multiply multiplicand by 10**DECDPUN for next Unit to left */
+ shift++; /* add this for 'logical length' */
+ } /* n */
+ #if FASTMUL
+ } /* unchunked units */
+ #endif
+ /* common end-path */
+ #if DECTRACE
+ decDumpAr('*', acc, accunits); /* Show exact result */
+ #endif
+
+ /* acc now contains the exact result of the multiplication, */
+ /* possibly with a leading zero unit; build the decNumber from */
+ /* it, noting if any residue */
+ res->bits=bits; /* set sign */
+ res->digits=decGetDigits(acc, accunits); /* count digits exactly */
+
+ /* There can be a 31-bit wrap in calculating the exponent. */
+ /* This can only happen if both input exponents are negative and */
+ /* both their magnitudes are large. If there was a wrap, set a */
+ /* safe very negative exponent, from which decFinalize() will */
+ /* raise a hard underflow shortly. */
+ exponent=lhs->exponent+rhs->exponent; /* calculate exponent */
+ if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
+ exponent=-2*DECNUMMAXE; /* force underflow */
+ res->exponent=exponent; /* OK to overwrite now */
+
+
+ /* Set the coefficient. If any rounding, residue records */
+ decSetCoeff(res, set, acc, res->digits, &residue, status);
+ decFinish(res, set, &residue, status); /* final cleanup */
+ } while(0); /* end protected */
+
+ if (allocacc!=NULL) free(allocacc); /* drop any storage used */
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); /* .. */
+ if (alloclhs!=NULL) free(alloclhs); /* .. */
+ #endif
+ #if FASTMUL
+ if (allocrhi!=NULL) free(allocrhi); /* .. */
+ if (alloclhi!=NULL) free(alloclhi); /* .. */
+ #endif
+ return res;
+ } /* decMultiplyOp */
+
+/* ------------------------------------------------------------------ */
+/* decExpOp -- effect exponentiation */
+/* */
+/* This computes C = exp(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. status is updated but */
+/* not set. */
+/* */
+/* Restrictions: */
+/* */
+/* digits, emax, and -emin in the context must be less than */
+/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */
+/* bounds or a zero. This is an internal routine, so these */
+/* restrictions are contractual and not enforced. */
+/* */
+/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* */
+/* Finite results will always be full precision and Inexact, except */
+/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
+/* ------------------------------------------------------------------ */
+/* This approach used here is similar to the algorithm described in */
+/* */
+/* Variable Precision Exponential Function, T. E. Hull and */
+/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
+/* pp79-91, ACM, June 1986. */
+/* */
+/* with the main difference being that the iterations in the series */
+/* evaluation are terminated dynamically (which does not require the */
+/* extra variable-precision variables which are expensive in this */
+/* context). */
+/* */
+/* The error analysis in Hull & Abrham's paper applies except for the */
+/* round-off error accumulation during the series evaluation. This */
+/* code does not precalculate the number of iterations and so cannot */
+/* use Horner's scheme. Instead, the accumulation is done at double- */
+/* precision, which ensures that the additions of the terms are exact */
+/* and do not accumulate round-off (and any round-off errors in the */
+/* terms themselves move 'to the right' faster than they can */
+/* accumulate). This code also extends the calculation by allowing, */
+/* in the spirit of other decNumber operators, the input to be more */
+/* precise than the result (the precision used is based on the more */
+/* precise of the input or requested result). */
+/* */
+/* Implementation notes: */
+/* */
+/* 1. This is separated out as decExpOp so it can be called from */
+/* other Mathematical functions (notably Ln) with a wider range */
+/* than normal. In particular, it can handle the slightly wider */
+/* (double) range needed by Ln (which has to be able to calculate */
+/* exp(-x) where x can be the tiniest number (Ntiny). */
+/* */
+/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */
+/* iterations by appoximately a third with additional (although */
+/* diminishing) returns as the range is reduced to even smaller */
+/* fractions. However, h (the power of 10 used to correct the */
+/* result at the end, see below) must be kept <=8 as otherwise */
+/* the final result cannot be computed. Hence the leverage is a */
+/* sliding value (8-h), where potentially the range is reduced */
+/* more for smaller values. */
+/* */
+/* The leverage that can be applied in this way is severely */
+/* limited by the cost of the raise-to-the power at the end, */
+/* which dominates when the number of iterations is small (less */
+/* than ten) or when rhs is short. As an example, the adjustment */
+/* x**10,000,000 needs 31 multiplications, all but one full-width. */
+/* */
+/* 3. The restrictions (especially precision) could be raised with */
+/* care, but the full decNumber range seems very hard within the */
+/* 32-bit limits. */
+/* */
+/* 4. The working precisions for the static buffers are twice the */
+/* obvious size to allow for calls from decNumberPower. */
+/* ------------------------------------------------------------------ */
+decNumber * decExpOp(decNumber *res, const decNumber *rhs,
+ decContext *set, uInt *status) {
+ uInt ignore=0; /* working status */
+ Int h; /* adjusted exponent for 0.xxxx */
+ Int p; /* working precision */
+ Int residue; /* rounding residue */
+ uInt needbytes; /* for space calculations */
+ const decNumber *x=rhs; /* (may point to safe copy later) */
+ decContext aset, tset, dset; /* working contexts */
+ Int comp; /* work */
+
+ /* the argument is often copied to normalize it, so (unusually) it */
+ /* is treated like other buffers, using DECBUFFER, +1 in case */
+ /* DECBUFFER is 0 */
+ decNumber bufr[D2N(DECBUFFER*2+1)];
+ decNumber *allocrhs=NULL; /* non-NULL if rhs buffer allocated */
+
+ /* the working precision will be no more than set->digits+8+1 */
+ /* so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER */
+ /* is 0 (and twice that for the accumulator) */
+
+ /* buffer for t, term (working precision plus) */
+ decNumber buft[D2N(DECBUFFER*2+9+1)];
+ decNumber *allocbuft=NULL; /* -> allocated buft, iff allocated */
+ decNumber *t=buft; /* term */
+ /* buffer for a, accumulator (working precision * 2), at least 9 */
+ decNumber bufa[D2N(DECBUFFER*4+18+1)];
+ decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
+ decNumber *a=bufa; /* accumulator */
+ /* decNumber for the divisor term; this needs at most 9 digits */
+ /* and so can be fixed size [16 so can use standard context] */
+ decNumber bufd[D2N(16)];
+ decNumber *d=bufd; /* divisor */
+ decNumber numone; /* constant 1 */
+
+ #if DECCHECK
+ Int iterations=0; /* for later sanity check */
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ if (SPECIALARG) { /* handle infinities and NaNs */
+ if (decNumberIsInfinite(rhs)) { /* an infinity */
+ if (decNumberIsNegative(rhs)) /* -Infinity -> +0 */
+ decNumberZero(res);
+ else decNumberCopy(res, rhs); /* +Infinity -> self */
+ }
+ else decNaNs(res, rhs, NULL, set, status); /* a NaN */
+ break;}
+
+ if (ISZERO(rhs)) { /* zeros -> exact 1 */
+ decNumberZero(res); /* make clean 1 */
+ *res->lsu=1; /* .. */
+ break;} /* [no status to set] */
+
+ /* e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path */
+ /* positive and negative tiny cases which will result in inexact */
+ /* 1. This also allows the later add-accumulate to always be */
+ /* exact (because its length will never be more than twice the */
+ /* working precision). */
+ /* The comparator (tiny) needs just one digit, so use the */
+ /* decNumber d for it (reused as the divisor, etc., below); its */
+ /* exponent is such that if x is positive it will have */
+ /* set->digits-1 zeros between the decimal point and the digit, */
+ /* which is 4, and if x is negative one more zero there as the */
+ /* more precise result will be of the form 0.9999999 rather than */
+ /* 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 */
+ /* or 0.00000004 if digits=7 and x<0. If RHS not larger than */
+ /* this then the result will be 1.000000 */
+ decNumberZero(d); /* clean */
+ *d->lsu=4; /* set 4 .. */
+ d->exponent=-set->digits; /* * 10**(-d) */
+ if (decNumberIsNegative(rhs)) d->exponent--; /* negative case */
+ comp=decCompare(d, rhs, 1); /* signless compare */
+ if (comp==BADINT) {
+ *status|=DEC_Insufficient_storage;
+ break;}
+ if (comp>=0) { /* rhs < d */
+ Int shift=set->digits-1;
+ decNumberZero(res); /* set 1 */
+ *res->lsu=1; /* .. */
+ res->digits=decShiftToMost(res->lsu, 1, shift);
+ res->exponent=-shift; /* make 1.0000... */
+ *status|=DEC_Inexact | DEC_Rounded; /* .. inexactly */
+ break;} /* tiny */
+
+ /* set up the context to be used for calculating a, as this is */
+ /* used on both paths below */
+ decContextDefault(&aset, DEC_INIT_DECIMAL64);
+ /* accumulator bounds are as requested (could underflow) */
+ aset.emax=set->emax; /* usual bounds */
+ aset.emin=set->emin; /* .. */
+ aset.clamp=0; /* and no concrete format */
+
+ /* calculate the adjusted (Hull & Abrham) exponent (where the */
+ /* decimal point is just to the left of the coefficient msd) */
+ h=rhs->exponent+rhs->digits;
+ /* if h>8 then 10**h cannot be calculated safely; however, when */
+ /* h=8 then exp(|rhs|) will be at least exp(1E+7) which is at */
+ /* least 6.59E+4342944, so (due to the restriction on Emax/Emin) */
+ /* overflow (or underflow to 0) is guaranteed -- so this case can */
+ /* be handled by simply forcing the appropriate excess */
+ if (h>8) { /* overflow/underflow */
+ /* set up here so Power call below will over or underflow to */
+ /* zero; set accumulator to either 2 or 0.02 */
+ /* [stack buffer for a is always big enough for this] */
+ decNumberZero(a);
+ *a->lsu=2; /* not 1 but < exp(1) */
+ if (decNumberIsNegative(rhs)) a->exponent=-2; /* make 0.02 */
+ h=8; /* clamp so 10**h computable */
+ p=9; /* set a working precision */
+ }
+ else { /* h<=8 */
+ Int maxlever=(rhs->digits>8?1:0);
+ /* [could/should increase this for precisions >40 or so, too] */
+
+ /* if h is 8, cannot normalize to a lower upper limit because */
+ /* the final result will not be computable (see notes above), */
+ /* but leverage can be applied whenever h is less than 8. */
+ /* Apply as much as possible, up to a MAXLEVER digits, which */
+ /* sets the tradeoff against the cost of the later a**(10**h). */
+ /* As h is increased, the working precision below also */
+ /* increases to compensate for the "constant digits at the */
+ /* front" effect. */
+ Int lever=MINI(8-h, maxlever); /* leverage attainable */
+ Int use=-rhs->digits-lever; /* exponent to use for RHS */
+ h+=lever; /* apply leverage selected */
+ if (h<0) { /* clamp */
+ use+=h; /* [may end up subnormal] */
+ h=0;
+ }
+ /* Take a copy of RHS if it needs normalization (true whenever x>=1) */
+ if (rhs->exponent!=use) {
+ decNumber *newrhs=bufr; /* assume will fit on stack */
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufr)) { /* need malloc space */
+ allocrhs=(decNumber *)malloc(needbytes);
+ if (allocrhs==NULL) { /* hopeless -- abandon */
+ *status|=DEC_Insufficient_storage;
+ break;}
+ newrhs=allocrhs; /* use the allocated space */
+ }
+ decNumberCopy(newrhs, rhs); /* copy to safe space */
+ newrhs->exponent=use; /* normalize; now <1 */
+ x=newrhs; /* ready for use */
+ /* decNumberShow(x); */
+ }
- /* acc now contains the exact result of the multiplication */
- /* Build a decNumber from it, noting if any residue */
- res->bits = bits; /* set sign */
- res->digits = decGetDigits (acc, accunits); /* count digits exactly */
-
- /* We might have a 31-bit wrap in calculating the exponent. */
- /* This can only happen if both input exponents are negative and */
- /* both their magnitudes are large. If we did wrap, we set a safe */
- /* very negative exponent, from which decFinalize() will raise a */
- /* hard underflow. */
- exponent = lhs->exponent + rhs->exponent; /* calculate exponent */
- if (lhs->exponent < 0 && rhs->exponent < 0 && exponent > 0)
- exponent = -2 * DECNUMMAXE; /* force underflow */
- res->exponent = exponent; /* OK to overwrite now */
-
- /* Set the coefficient. If any rounding, residue records */
- decSetCoeff (res, set, acc, res->digits, &residue, status);
-
- decFinish (res, set, &residue, status); /* final cleanup */
- }
- while (0); /* end protected */
-
- if (allocacc != NULL)
- free (allocacc); /* drop any storage we used */
- if (allocrhs != NULL)
- free (allocrhs); /* .. */
- if (alloclhs != NULL)
- free (alloclhs); /* .. */
+ /* Now use the usual power series to evaluate exp(x). The */
+ /* series starts as 1 + x + x^2/2 ... so prime ready for the */
+ /* third term by setting the term variable t=x, the accumulator */
+ /* a=1, and the divisor d=2. */
+
+ /* First determine the working precision. From Hull & Abrham */
+ /* this is set->digits+h+2. However, if x is 'over-precise' we */
+ /* need to allow for all its digits to potentially participate */
+ /* (consider an x where all the excess digits are 9s) so in */
+ /* this case use x->digits+h+2 */
+ p=MAXI(x->digits, set->digits)+h+2; /* [h<=8] */
+
+ /* a and t are variable precision, and depend on p, so space */
+ /* must be allocated for them if necessary */
+
+ /* the accumulator needs to be able to hold 2p digits so that */
+ /* the additions on the second and subsequent iterations are */
+ /* sufficiently exact. */
+ needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { /* need malloc space */
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { /* hopeless -- abandon */
+ *status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; /* use the allocated space */
+ }
+ /* the term needs to be able to hold p digits (which is */
+ /* guaranteed to be larger than x->digits, so the initial copy */
+ /* is safe); it may also be used for the raise-to-power */
+ /* calculation below, which needs an extra two digits */
+ needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
+ if (needbytes>sizeof(buft)) { /* need malloc space */
+ allocbuft=(decNumber *)malloc(needbytes);
+ if (allocbuft==NULL) { /* hopeless -- abandon */
+ *status|=DEC_Insufficient_storage;
+ break;}
+ t=allocbuft; /* use the allocated space */
+ }
+
+ decNumberCopy(t, x); /* term=x */
+ decNumberZero(a); *a->lsu=1; /* accumulator=1 */
+ decNumberZero(d); *d->lsu=2; /* divisor=2 */
+ decNumberZero(&numone); *numone.lsu=1; /* constant 1 for increment */
+
+ /* set up the contexts for calculating a, t, and d */
+ decContextDefault(&tset, DEC_INIT_DECIMAL64);
+ dset=tset;
+ /* accumulator bounds are set above, set precision now */
+ aset.digits=p*2; /* double */
+ /* term bounds avoid any underflow or overflow */
+ tset.digits=p;
+ tset.emin=DEC_MIN_EMIN; /* [emax is plenty] */
+ /* [dset.digits=16, etc., are sufficient] */
+
+ /* finally ready to roll */
+ for (;;) {
+ #if DECCHECK
+ iterations++;
+ #endif
+ /* only the status from the accumulation is interesting */
+ /* [but it should remain unchanged after first add] */
+ decAddOp(a, a, t, &aset, 0, status); /* a=a+t */
+ decMultiplyOp(t, t, x, &tset, &ignore); /* t=t*x */
+ decDivideOp(t, t, d, &tset, DIVIDE, &ignore); /* t=t/d */
+ /* the iteration ends when the term cannot affect the result, */
+ /* if rounded to p digits, which is when its value is smaller */
+ /* than the accumulator by p+1 digits. There must also be */
+ /* full precision in a. */
+ if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
+ && (a->digits>=p)) break;
+ decAddOp(d, d, &numone, &dset, 0, &ignore); /* d=d+1 */
+ } /* iterate */
+
+ #if DECCHECK
+ /* just a sanity check; comment out test to show always */
+ if (iterations>p+3)
+ printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
+ (LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
+ #endif
+ } /* h<=8 */
+
+ /* apply postconditioning: a=a**(10**h) -- this is calculated */
+ /* at a slightly higher precision than Hull & Abrham suggest */
+ if (h>0) {
+ Int seenbit=0; /* set once a 1-bit is seen */
+ Int i; /* counter */
+ Int n=powers[h]; /* always positive */
+ aset.digits=p+2; /* sufficient precision */
+ /* avoid the overhead and many extra digits of decNumberPower */
+ /* as all that is needed is the short 'multipliers' loop; here */
+ /* accumulate the answer into t */
+ decNumberZero(t); *t->lsu=1; /* acc=1 */
+ for (i=1;;i++){ /* for each bit [top bit ignored] */
+ /* abandon if have had overflow or terminal underflow */
+ if (*status & (DEC_Overflow|DEC_Underflow)) { /* interesting? */
+ if (*status&DEC_Overflow || ISZERO(t)) break;}
+ n=n<<1; /* move next bit to testable position */
+ if (n<0) { /* top bit is set */
+ seenbit=1; /* OK, have a significant bit */
+ decMultiplyOp(t, t, a, &aset, status); /* acc=acc*x */
+ }
+ if (i==31) break; /* that was the last bit */
+ if (!seenbit) continue; /* no need to square 1 */
+ decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */
+ } /*i*/ /* 32 bits */
+ /* decNumberShow(t); */
+ a=t; /* and carry on using t instead of a */
+ }
+
+ /* Copy and round the result to res */
+ residue=1; /* indicate dirt to right .. */
+ if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */
+ aset.digits=set->digits; /* [use default rounding] */
+ decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
+ decFinish(res, set, &residue, status); /* cleanup/set flags */
+ } while(0); /* end protected */
+
+ if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
+ if (allocbufa!=NULL) free(allocbufa); /* .. */
+ if (allocbuft!=NULL) free(allocbuft); /* .. */
+ /* [status is handled by caller] */
+ return res;
+ } /* decExpOp */
+
+/* ------------------------------------------------------------------ */
+/* Initial-estimate natural logarithm table */
+/* */
+/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */
+/* The result is a 4-digit encode of the coefficient (c=the */
+/* top 14 bits encoding 0-9999) and a 2-digit encode of the */
+/* exponent (e=the bottom 2 bits encoding 0-3) */
+/* */
+/* The resulting value is given by: */
+/* */
+/* v = -c * 10**(-e-3) */
+/* */
+/* where e and c are extracted from entry k = LNnn[x-10] */
+/* where x is truncated (NB) into the range 10 through 99, */
+/* and then c = k>>2 and e = k&3. */
+/* ------------------------------------------------------------------ */
+const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208,
+ 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312,
+ 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032,
+ 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
+ 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
+ 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
+ 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
+ 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801,
+ 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
+ 10130, 6046, 20055};
+
+/* ------------------------------------------------------------------ */
+/* decLnOp -- effect natural logarithm */
+/* */
+/* This computes C = ln(A) */
+/* */
+/* res is C, the result. C may be A */
+/* rhs is A */
+/* set is the context; note that rounding mode has no effect */
+/* */
+/* C must have space for set->digits digits. */
+/* */
+/* Notable cases: */
+/* A<0 -> Invalid */
+/* A=0 -> -Infinity (Exact) */
+/* A=+Infinity -> +Infinity (Exact) */
+/* A=1 exactly -> 0 (Exact) */
+/* */
+/* Restrictions (as for Exp): */
+/* */
+/* digits, emax, and -emin in the context must be less than */
+/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */
+/* bounds or a zero. This is an internal routine, so these */
+/* restrictions are contractual and not enforced. */
+/* */
+/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
+/* almost always be correctly rounded, but may be up to 1 ulp in */
+/* error in rare cases. */
+/* ------------------------------------------------------------------ */
+/* The result is calculated using Newton's method, with each */
+/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */
+/* Epperson 1989. */
+/* */
+/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
+/* This has to be calculated at the sum of the precision of x and the */
+/* working precision. */
+/* */
+/* Implementation notes: */
+/* */
+/* 1. This is separated out as decLnOp so it can be called from */
+/* other Mathematical functions (e.g., Log 10) with a wider range */
+/* than normal. In particular, it can handle the slightly wider */
+/* (+9+2) range needed by a power function. */
+/* */
+/* 2. The speed of this function is about 10x slower than exp, as */
+/* it typically needs 4-6 iterations for short numbers, and the */
+/* extra precision needed adds a squaring effect, twice. */
+/* */
+/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */
+/* as these are common requests. ln(10) is used by log10(x). */
+/* */
+/* 4. An iteration might be saved by widening the LNnn table, and */
+/* would certainly save at least one if it were made ten times */
+/* bigger, too (for truncated fractions 0.100 through 0.999). */
+/* However, for most practical evaluations, at least four or five */
+/* iterations will be neede -- so this would only speed up by */
+/* 20-25% and that probably does not justify increasing the table */
+/* size. */
+/* */
+/* 5. The static buffers are larger than might be expected to allow */
+/* for calls from decNumberPower. */
+/* ------------------------------------------------------------------ */
+decNumber * decLnOp(decNumber *res, const decNumber *rhs,
+ decContext *set, uInt *status) {
+ uInt ignore=0; /* working status accumulator */
+ uInt needbytes; /* for space calculations */
+ Int residue; /* rounding residue */
+ Int r; /* rhs=f*10**r [see below] */
+ Int p; /* working precision */
+ Int pp; /* precision for iteration */
+ Int t; /* work */
+
+ /* buffers for a (accumulator, typically precision+2) and b */
+ /* (adjustment calculator, same size) */
+ decNumber bufa[D2N(DECBUFFER+12)];
+ decNumber *allocbufa=NULL; /* -> allocated bufa, iff allocated */
+ decNumber *a=bufa; /* accumulator/work */
+ decNumber bufb[D2N(DECBUFFER*2+2)];
+ decNumber *allocbufb=NULL; /* -> allocated bufa, iff allocated */
+ decNumber *b=bufb; /* adjustment/work */
+
+ decNumber numone; /* constant 1 */
+ decNumber cmp; /* work */
+ decContext aset, bset; /* working contexts */
+
+ #if DECCHECK
+ Int iterations=0; /* for later sanity check */
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ if (SPECIALARG) { /* handle infinities and NaNs */
+ if (decNumberIsInfinite(rhs)) { /* an infinity */
+ if (decNumberIsNegative(rhs)) /* -Infinity -> error */
+ *status|=DEC_Invalid_operation;
+ else decNumberCopy(res, rhs); /* +Infinity -> self */
+ }
+ else decNaNs(res, rhs, NULL, set, status); /* a NaN */
+ break;}
+
+ if (ISZERO(rhs)) { /* +/- zeros -> -Infinity */
+ decNumberZero(res); /* make clean */
+ res->bits=DECINF|DECNEG; /* set - infinity */
+ break;} /* [no status to set] */
+
+ /* Non-zero negatives are bad... */
+ if (decNumberIsNegative(rhs)) { /* -x -> error */
+ *status|=DEC_Invalid_operation;
+ break;}
+
+ /* Here, rhs is positive, finite, and in range */
+
+ /* lookaside fastpath code for ln(2) and ln(10) at common lengths */
+ if (rhs->exponent==0 && set->digits<=40) {
+ #if DECDPUN==1
+ if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { /* ln(10) */
+ #else
+ if (rhs->lsu[0]==10 && rhs->digits==2) { /* ln(10) */
+ #endif
+ aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
+ #define LN10 "2.302585092994045684017991454684364207601"
+ decNumberFromString(res, LN10, &aset);
+ *status|=(DEC_Inexact | DEC_Rounded); /* is inexact */
+ break;}
+ if (rhs->lsu[0]==2 && rhs->digits==1) { /* ln(2) */
+ aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
+ #define LN2 "0.6931471805599453094172321214581765680755"
+ decNumberFromString(res, LN2, &aset);
+ *status|=(DEC_Inexact | DEC_Rounded);
+ break;}
+ } /* integer and short */
+
+ /* Determine the working precision. This is normally the */
+ /* requested precision + 2, with a minimum of 9. However, if */
+ /* the rhs is 'over-precise' then allow for all its digits to */
+ /* potentially participate (consider an rhs where all the excess */
+ /* digits are 9s) so in this case use rhs->digits+2. */
+ p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
+
+ /* Allocate space for the accumulator and the high-precision */
+ /* adjustment calculator, if necessary. The accumulator must */
+ /* be able to hold p digits, and the adjustment up to */
+ /* rhs->digits+p digits. They are also made big enough for 16 */
+ /* digits so that they can be used for calculating the initial */
+ /* estimate. */
+ needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufa)) { /* need malloc space */
+ allocbufa=(decNumber *)malloc(needbytes);
+ if (allocbufa==NULL) { /* hopeless -- abandon */
+ *status|=DEC_Insufficient_storage;
+ break;}
+ a=allocbufa; /* use the allocated space */
+ }
+ pp=p+rhs->digits;
+ needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
+ if (needbytes>sizeof(bufb)) { /* need malloc space */
+ allocbufb=(decNumber *)malloc(needbytes);
+ if (allocbufb==NULL) { /* hopeless -- abandon */
+ *status|=DEC_Insufficient_storage;
+ break;}
+ b=allocbufb; /* use the allocated space */
+ }
+
+ /* Prepare an initial estimate in acc. Calculate this by */
+ /* considering the coefficient of x to be a normalized fraction, */
+ /* f, with the decimal point at far left and multiplied by */
+ /* 10**r. Then, rhs=f*10**r and 0.1<=f<1, and */
+ /* ln(x) = ln(f) + ln(10)*r */
+ /* Get the initial estimate for ln(f) from a small lookup */
+ /* table (see above) indexed by the first two digits of f, */
+ /* truncated. */
+
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); /* 16-digit extended */
+ r=rhs->exponent+rhs->digits; /* 'normalised' exponent */
+ decNumberFromInt32(a, r); /* a=r */
+ decNumberFromInt32(b, 2302585); /* b=ln(10) (2.302585) */
+ b->exponent=-6; /* .. */
+ decMultiplyOp(a, a, b, &aset, &ignore); /* a=a*b */
+ /* now get top two digits of rhs into b by simple truncate and */
+ /* force to integer */
+ residue=0; /* (no residue) */
+ aset.digits=2; aset.round=DEC_ROUND_DOWN;
+ decCopyFit(b, rhs, &aset, &residue, &ignore); /* copy & shorten */
+ b->exponent=0; /* make integer */
+ t=decGetInt(b); /* [cannot fail] */
+ if (t<10) t=X10(t); /* adjust single-digit b */
+ t=LNnn[t-10]; /* look up ln(b) */
+ decNumberFromInt32(b, t>>2); /* b=ln(b) coefficient */
+ b->exponent=-(t&3)-3; /* set exponent */
+ b->bits=DECNEG; /* ln(0.10)->ln(0.99) always -ve */
+ aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; /* restore */
+ decAddOp(a, a, b, &aset, 0, &ignore); /* acc=a+b */
+ /* the initial estimate is now in a, with up to 4 digits correct. */
+ /* When rhs is at or near Nmax the estimate will be low, so we */
+ /* will approach it from below, avoiding overflow when calling exp. */
+
+ decNumberZero(&numone); *numone.lsu=1; /* constant 1 for adjustment */
+
+ /* accumulator bounds are as requested (could underflow, but */
+ /* cannot overflow) */
+ aset.emax=set->emax;
+ aset.emin=set->emin;
+ aset.clamp=0; /* no concrete format */
+ /* set up a context to be used for the multiply and subtract */
+ bset=aset;
+ bset.emax=DEC_MAX_MATH*2; /* use double bounds for the */
+ bset.emin=-DEC_MAX_MATH*2; /* adjustment calculation */
+ /* [see decExpOp call below] */
+ /* for each iteration double the number of digits to calculate, */
+ /* up to a maximum of p */
+ pp=9; /* initial precision */
+ /* [initially 9 as then the sequence starts 7+2, 16+2, and */
+ /* 34+2, which is ideal for standard-sized numbers] */
+ aset.digits=pp; /* working context */
+ bset.digits=pp+rhs->digits; /* wider context */
+ for (;;) { /* iterate */
+ #if DECCHECK
+ iterations++;
+ if (iterations>24) break; /* consider 9 * 2**24 */
+ #endif
+ /* calculate the adjustment (exp(-a)*x-1) into b. This is a */
+ /* catastrophic subtraction but it really is the difference */
+ /* from 1 that is of interest. */
+ /* Use the internal entry point to Exp as it allows the double */
+ /* range for calculating exp(-a) when a is the tiniest subnormal. */
+ a->bits^=DECNEG; /* make -a */
+ decExpOp(b, a, &bset, &ignore); /* b=exp(-a) */
+ a->bits^=DECNEG; /* restore sign of a */
+ /* now multiply by rhs and subtract 1, at the wider precision */
+ decMultiplyOp(b, b, rhs, &bset, &ignore); /* b=b*rhs */
+ decAddOp(b, b, &numone, &bset, DECNEG, &ignore); /* b=b-1 */
+
+ /* the iteration ends when the adjustment cannot affect the */
+ /* result by >=0.5 ulp (at the requested digits), which */
+ /* is when its value is smaller than the accumulator by */
+ /* set->digits+1 digits (or it is zero) -- this is a looser */
+ /* requirement than for Exp because all that happens to the */
+ /* accumulator after this is the final rounding (but note that */
+ /* there must also be full precision in a, or a=0). */
+
+ if (decNumberIsZero(b) ||
+ (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
+ if (a->digits==p) break;
+ if (decNumberIsZero(a)) {
+ decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); /* rhs=1 ? */
+ if (cmp.lsu[0]==0) a->exponent=0; /* yes, exact 0 */
+ else *status|=(DEC_Inexact | DEC_Rounded); /* no, inexact */
+ break;
+ }
+ /* force padding if adjustment has gone to 0 before full length */
+ if (decNumberIsZero(b)) b->exponent=a->exponent-p;
+ }
+
+ /* not done yet ... */
+ decAddOp(a, a, b, &aset, 0, &ignore); /* a=a+b for next estimate */
+ if (pp==p) continue; /* precision is at maximum */
+ /* lengthen the next calculation */
+ pp=pp*2; /* double precision */
+ if (pp>p) pp=p; /* clamp to maximum */
+ aset.digits=pp; /* working context */
+ bset.digits=pp+rhs->digits; /* wider context */
+ } /* Newton's iteration */
+
+ #if DECCHECK
+ /* just a sanity check; remove the test to show always */
+ if (iterations>24)
+ printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
+ (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
+ #endif
+
+ /* Copy and round the result to res */
+ residue=1; /* indicate dirt to right */
+ if (ISZERO(a)) residue=0; /* .. unless underflowed to 0 */
+ aset.digits=set->digits; /* [use default rounding] */
+ decCopyFit(res, a, &aset, &residue, status); /* copy & shorten */
+ decFinish(res, set, &residue, status); /* cleanup/set flags */
+ } while(0); /* end protected */
+
+ if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
+ if (allocbufb!=NULL) free(allocbufb); /* .. */
+ /* [status is handled by caller] */
return res;
-}
+ } /* decLnOp */
/* ------------------------------------------------------------------ */
-/* decQuantizeOp -- force exponent to requested value */
-/* */
+/* decQuantizeOp -- force exponent to requested value */
+/* */
/* This computes C = op(A, B), where op adjusts the coefficient */
/* of C (by rounding or shifting) such that the exponent (-scale) */
-/* of C has the value B or matches the exponent of B. */
+/* of C has the value B or matches the exponent of B. */
/* The numerical value of C will equal A, except for the effects of */
-/* any rounding that occurred. */
-/* */
-/* res is C, the result. C may be A or B */
-/* lhs is A, the number to adjust */
-/* rhs is B, the requested exponent */
-/* set is the context */
-/* quant is 1 for quantize or 0 for rescale */
+/* any rounding that occurred. */
+/* */
+/* res is C, the result. C may be A or B */
+/* lhs is A, the number to adjust */
+/* rhs is B, the requested exponent */
+/* set is the context */
+/* quant is 1 for quantize or 0 for rescale */
/* status is the status accumulator (this can be called without */
-/* risk of control loss) */
-/* */
-/* C must have space for set->digits digits. */
-/* */
+/* risk of control loss) */
+/* */
+/* C must have space for set->digits digits. */
+/* */
/* Unless there is an error or the result is infinite, the exponent */
-/* after the operation is guaranteed to be that requested. */
-/* ------------------------------------------------------------------ */
-static decNumber *
-decQuantizeOp (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set, Flag quant, uInt * status)
-{
- decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
- decNumber *allocrhs = NULL; /* .., rhs */
- decNumber *inrhs = rhs; /* save original rhs */
- Int reqdigits = set->digits; /* requested DIGITS */
- Int reqexp; /* requested exponent [-scale] */
- Int residue = 0; /* rounding residue */
- uByte merged; /* merged flags */
- Int etiny = set->emin - (set->digits - 1);
-
-#if DECCHECK
- if (decCheckOperands (res, lhs, rhs, set))
- return res;
-#endif
-
- do
- { /* protect allocated storage */
-#if DECSUBSET
- if (!set->extended)
- {
- /* reduce operands and set lostDigits status, as needed */
- if (lhs->digits > reqdigits)
- {
- alloclhs = decRoundOperand (lhs, set, status);
- if (alloclhs == NULL)
- break;
- lhs = alloclhs;
- }
- if (rhs->digits > reqdigits)
- { /* [this only checks lostDigits] */
- allocrhs = decRoundOperand (rhs, set, status);
- if (allocrhs == NULL)
- break;
- rhs = allocrhs;
- }
- }
-#endif
- /* [following code does not require input rounding] */
-
- /* Handle special values */
- merged = (lhs->bits | rhs->bits) & DECSPECIAL;
- if ((lhs->bits | rhs->bits) & DECSPECIAL)
- {
- /* NaNs get usual processing */
- if (merged & (DECSNAN | DECNAN))
- decNaNs (res, lhs, rhs, status);
- /* one infinity but not both is bad */
- else if ((lhs->bits ^ rhs->bits) & DECINF)
- *status |= DEC_Invalid_operation;
- /* both infinity: return lhs */
- else
- decNumberCopy (res, lhs); /* [nop if in place] */
- break;
+/* after the operation is guaranteed to be that requested. */
+/* ------------------------------------------------------------------ */
+static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ Flag quant, uInt *status) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
+ decNumber *allocrhs=NULL; /* .., rhs */
+ #endif
+ const decNumber *inrhs=rhs; /* save original rhs */
+ Int reqdigits=set->digits; /* requested DIGITS */
+ Int reqexp; /* requested exponent [-scale] */
+ Int residue=0; /* rounding residue */
+ Int etiny=set->emin-(reqdigits-1);
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operands and set lostDigits status, as needed */
+ if (lhs->digits>reqdigits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) break;
+ lhs=alloclhs;
}
-
- /* set requested exponent */
- if (quant)
- reqexp = inrhs->exponent; /* quantize -- match exponents */
- else
- { /* rescale -- use value of rhs */
- /* Original rhs must be an integer that fits and is in range */
-#if DECSUBSET
- reqexp = decGetInt (inrhs, set);
-#else
- reqexp = decGetInt (inrhs);
-#endif
+ if (rhs->digits>reqdigits) { /* [this only checks lostDigits] */
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) break;
+ rhs=allocrhs;
}
+ }
+ #endif
+ /* [following code does not require input rounding] */
+
+ /* Handle special values */
+ if (SPECIALARGS) {
+ /* NaNs get usual processing */
+ if (SPECIALARGS & (DECSNAN | DECNAN))
+ decNaNs(res, lhs, rhs, set, status);
+ /* one infinity but not both is bad */
+ else if ((lhs->bits ^ rhs->bits) & DECINF)
+ *status|=DEC_Invalid_operation;
+ /* both infinity: return lhs */
+ else decNumberCopy(res, lhs); /* [nop if in place] */
+ break;
+ }
-#if DECSUBSET
- if (!set->extended)
- etiny = set->emin; /* no subnormals */
-#endif
+ /* set requested exponent */
+ if (quant) reqexp=inrhs->exponent; /* quantize -- match exponents */
+ else { /* rescale -- use value of rhs */
+ /* Original rhs must be an integer that fits and is in range, */
+ /* which could be from -1999999997 to +999999999, thanks to */
+ /* subnormals */
+ reqexp=decGetInt(inrhs); /* [cannot fail] */
+ }
- if (reqexp == BADINT /* bad (rescale only) or .. */
- || (reqexp < etiny) /* < lowest */
- || (reqexp > set->emax))
- { /* > Emax */
- *status |= DEC_Invalid_operation;
- break;
+ #if DECSUBSET
+ if (!set->extended) etiny=set->emin; /* no subnormals */
+ #endif
+
+ if (reqexp==BADINT /* bad (rescale only) or .. */
+ || reqexp==BIGODD || reqexp==BIGEVEN /* very big (ditto) or .. */
+ || (reqexp<etiny) /* < lowest */
+ || (reqexp>set->emax)) { /* > emax */
+ *status|=DEC_Invalid_operation;
+ break;}
+
+ /* the RHS has been processed, so it can be overwritten now if necessary */
+ if (ISZERO(lhs)) { /* zero coefficient unchanged */
+ decNumberCopy(res, lhs); /* [nop if in place] */
+ res->exponent=reqexp; /* .. just set exponent */
+ #if DECSUBSET
+ if (!set->extended) res->bits=0; /* subset specification; no -0 */
+ #endif
+ }
+ else { /* non-zero lhs */
+ Int adjust=reqexp-lhs->exponent; /* digit adjustment needed */
+ /* if adjusted coefficient will definitely not fit, give up now */
+ if ((lhs->digits-adjust)>reqdigits) {
+ *status|=DEC_Invalid_operation;
+ break;
}
- /* we've processed the RHS, so we can overwrite it now if necessary */
- if (ISZERO (lhs))
- { /* zero coefficient unchanged */
- decNumberCopy (res, lhs); /* [nop if in place] */
- res->exponent = reqexp; /* .. just set exponent */
-#if DECSUBSET
- if (!set->extended)
- res->bits = 0; /* subset specification; no -0 */
-#endif
- }
- else
- { /* non-zero lhs */
- Int adjust = reqexp - lhs->exponent; /* digit adjustment needed */
- /* if adjusted coefficient will not fit, give up now */
- if ((lhs->digits - adjust) > reqdigits)
- {
- *status |= DEC_Invalid_operation;
- break;
+ if (adjust>0) { /* increasing exponent */
+ /* this will decrease the length of the coefficient by adjust */
+ /* digits, and must round as it does so */
+ decContext workset; /* work */
+ workset=*set; /* clone rounding, etc. */
+ workset.digits=lhs->digits-adjust; /* set requested length */
+ /* [note that the latter can be <1, here] */
+ decCopyFit(res, lhs, &workset, &residue, status); /* fit to result */
+ decApplyRound(res, &workset, residue, status); /* .. and round */
+ residue=0; /* [used] */
+ /* If just rounded a 999s case, exponent will be off by one; */
+ /* adjust back (after checking space), if so. */
+ if (res->exponent>reqexp) {
+ /* re-check needed, e.g., for quantize(0.9999, 0.001) under */
+ /* set->digits==3 */
+ if (res->digits==reqdigits) { /* cannot shift by 1 */
+ *status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */
+ *status|=DEC_Invalid_operation;
+ break;
}
+ res->digits=decShiftToMost(res->lsu, res->digits, 1); /* shift */
+ res->exponent--; /* (re)adjust the exponent. */
+ }
+ #if DECSUBSET
+ if (ISZERO(res) && !set->extended) res->bits=0; /* subset; no -0 */
+ #endif
+ } /* increase */
+ else /* adjust<=0 */ { /* decreasing or = exponent */
+ /* this will increase the length of the coefficient by -adjust */
+ /* digits, by adding zero or more trailing zeros; this is */
+ /* already checked for fit, above */
+ decNumberCopy(res, lhs); /* [it will fit] */
+ /* if padding needed (adjust<0), add it now... */
+ if (adjust<0) {
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
+ res->exponent+=adjust; /* adjust the exponent */
+ }
+ } /* decrease */
+ } /* non-zero */
- if (adjust > 0)
- { /* increasing exponent */
- /* this will decrease the length of the coefficient by adjust */
- /* digits, and must round as it does so */
- decContext workset; /* work */
- workset = *set; /* clone rounding, etc. */
- workset.digits = lhs->digits - adjust; /* set requested length */
- /* [note that the latter can be <1, here] */
- decCopyFit (res, lhs, &workset, &residue, status); /* fit to result */
- decApplyRound (res, &workset, residue, status); /* .. and round */
- residue = 0; /* [used] */
- /* If we rounded a 999s case, exponent will be off by one; */
- /* adjust back if so. */
- if (res->exponent > reqexp)
- {
- res->digits = decShiftToMost (res->lsu, res->digits, 1); /* shift */
- res->exponent--; /* (re)adjust the exponent. */
- }
-#if DECSUBSET
- if (ISZERO (res) && !set->extended)
- res->bits = 0; /* subset; no -0 */
-#endif
- } /* increase */
- else /* adjust<=0 */
- { /* decreasing or = exponent */
- /* this will increase the length of the coefficient by -adjust */
- /* digits, by adding trailing zeros. */
- decNumberCopy (res, lhs); /* [it will fit] */
- /* if padding needed (adjust<0), add it now... */
- if (adjust < 0)
- {
- res->digits =
- decShiftToMost (res->lsu, res->digits, -adjust);
- res->exponent += adjust; /* adjust the exponent */
- }
- } /* decrease */
- } /* non-zero */
-
- /* Check for overflow [do not use Finalize in this case, as an */
- /* overflow here is a "don't fit" situation] */
- if (res->exponent > set->emax - res->digits + 1)
- { /* too big */
- *status |= DEC_Invalid_operation;
- break;
- }
- else
- {
- decFinalize (res, set, &residue, status); /* set subnormal flags */
- *status &= ~DEC_Underflow; /* suppress Underflow [754r] */
- }
- }
- while (0); /* end protected */
+ /* Check for overflow [do not use Finalize in this case, as an */
+ /* overflow here is a "don't fit" situation] */
+ if (res->exponent>set->emax-res->digits+1) { /* too big */
+ *status|=DEC_Invalid_operation;
+ break;
+ }
+ else {
+ decFinalize(res, set, &residue, status); /* set subnormal flags */
+ *status&=~DEC_Underflow; /* suppress Underflow [as per 754] */
+ }
+ } while(0); /* end protected */
- if (allocrhs != NULL)
- free (allocrhs); /* drop any storage we used */
- if (alloclhs != NULL)
- free (alloclhs); /* .. */
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */
+ if (alloclhs!=NULL) free(alloclhs); /* .. */
+ #endif
return res;
-}
-
-/* ------------------------------------------------------------------ */
-/* decCompareOp -- compare, min, or max two Numbers */
-/* */
-/* This computes C = A ? B and returns the signum (as a Number) */
-/* for COMPARE or the maximum or minimum (for COMPMAX and COMPMIN). */
-/* */
-/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
-/* lhs is A */
-/* rhs is B */
-/* set is the context */
-/* op is the operation flag */
-/* status is the usual accumulator */
-/* */
+ } /* decQuantizeOp */
+
+/* ------------------------------------------------------------------ */
+/* decCompareOp -- compare, min, or max two Numbers */
+/* */
+/* This computes C = A ? B and carries out one of four operations: */
+/* COMPARE -- returns the signum (as a number) giving the */
+/* result of a comparison unless one or both */
+/* operands is a NaN (in which case a NaN results) */
+/* COMPSIG -- as COMPARE except that a quiet NaN raises */
+/* Invalid operation. */
+/* COMPMAX -- returns the larger of the operands, using the */
+/* 754 maxnum operation */
+/* COMPMAXMAG -- ditto, comparing absolute values */
+/* COMPMIN -- the 754 minnum operation */
+/* COMPMINMAG -- ditto, comparing absolute values */
+/* COMTOTAL -- returns the signum (as a number) giving the */
+/* result of a comparison using 754 total ordering */
+/* */
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
+/* lhs is A */
+/* rhs is B */
+/* set is the context */
+/* op is the operation flag */
+/* status is the usual accumulator */
+/* */
/* C must have space for one digit for COMPARE or set->digits for */
-/* COMPMAX and COMPMIN. */
+/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
/* ------------------------------------------------------------------ */
/* The emphasis here is on speed for common cases, and avoiding */
-/* coefficient comparison if possible. */
-/* ------------------------------------------------------------------ */
-decNumber *
-decCompareOp (decNumber * res, decNumber * lhs, decNumber * rhs,
- decContext * set, Flag op, uInt * status)
-{
- decNumber *alloclhs = NULL; /* non-NULL if rounded lhs allocated */
- decNumber *allocrhs = NULL; /* .., rhs */
- Int result = 0; /* default result value */
- uByte merged; /* merged flags */
- uByte bits = 0; /* non-0 for NaN */
-
-#if DECCHECK
- if (decCheckOperands (res, lhs, rhs, set))
- return res;
-#endif
-
- do
- { /* protect allocated storage */
-#if DECSUBSET
- if (!set->extended)
- {
- /* reduce operands and set lostDigits status, as needed */
- if (lhs->digits > set->digits)
- {
- alloclhs = decRoundOperand (lhs, set, status);
- if (alloclhs == NULL)
- {
- result = BADINT;
- break;
- }
- lhs = alloclhs;
- }
- if (rhs->digits > set->digits)
- {
- allocrhs = decRoundOperand (rhs, set, status);
- if (allocrhs == NULL)
- {
- result = BADINT;
- break;
- }
- rhs = allocrhs;
- }
+/* coefficient comparison if possible. */
+/* ------------------------------------------------------------------ */
+decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ Flag op, uInt *status) {
+ #if DECSUBSET
+ decNumber *alloclhs=NULL; /* non-NULL if rounded lhs allocated */
+ decNumber *allocrhs=NULL; /* .., rhs */
+ #endif
+ Int result=0; /* default result value */
+ uByte merged; /* work */
+
+ #if DECCHECK
+ if (decCheckOperands(res, lhs, rhs, set)) return res;
+ #endif
+
+ do { /* protect allocated storage */
+ #if DECSUBSET
+ if (!set->extended) {
+ /* reduce operands and set lostDigits status, as needed */
+ if (lhs->digits>set->digits) {
+ alloclhs=decRoundOperand(lhs, set, status);
+ if (alloclhs==NULL) {result=BADINT; break;}
+ lhs=alloclhs;
}
-#endif
- /* [following code does not require input rounding] */
-
- /* handle NaNs now; let infinities drop through */
- /* +++ review sNaN handling with 754r, for now assumes sNaN */
- /* (even just one) leads to NaN. */
- merged = (lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
- if (merged)
- { /* a NaN bit set */
- if (op == COMPARE);
- else if (merged & DECSNAN);
- else
- { /* 754r rules for MIN and MAX ignore single NaN */
- /* here if MIN or MAX, and one or two quiet NaNs */
- if (lhs->bits & rhs->bits & DECNAN);
- else
- { /* just one quiet NaN */
- /* force choice to be the non-NaN operand */
- op = COMPMAX;
- if (lhs->bits & DECNAN)
- result = -1; /* pick rhs */
- else
- result = +1; /* pick lhs */
- break;
- }
- }
- op = COMPNAN; /* use special path */
- decNaNs (res, lhs, rhs, status);
- break;
+ if (rhs->digits>set->digits) {
+ allocrhs=decRoundOperand(rhs, set, status);
+ if (allocrhs==NULL) {result=BADINT; break;}
+ rhs=allocrhs;
}
+ }
+ #endif
+ /* [following code does not require input rounding] */
- result = decCompare (lhs, rhs); /* we have numbers */
- }
- while (0); /* end protected */
-
- if (result == BADINT)
- *status |= DEC_Insufficient_storage; /* rare */
- else
- {
- if (op == COMPARE)
- { /* return signum */
- decNumberZero (res); /* [always a valid result] */
- if (result == 0)
- res->bits = bits; /* (maybe qNaN) */
- else
- {
- *res->lsu = 1;
- if (result < 0)
- res->bits = DECNEG;
- }
+ /* If total ordering then handle differing signs 'up front' */
+ if (op==COMPTOTAL) { /* total ordering */
+ if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {
+ result=-1;
+ break;
}
- else if (op == COMPNAN); /* special, drop through */
- else
- { /* MAX or MIN, non-NaN result */
- Int residue = 0; /* rounding accumulator */
- /* choose the operand for the result */
- decNumber *choice;
- if (result == 0)
- { /* operands are numerically equal */
- /* choose according to sign then exponent (see 754r) */
- uByte slhs = (lhs->bits & DECNEG);
- uByte srhs = (rhs->bits & DECNEG);
-#if DECSUBSET
- if (!set->extended)
- { /* subset: force left-hand */
- op = COMPMAX;
- result = +1;
- }
- else
-#endif
- if (slhs != srhs)
- { /* signs differ */
- if (slhs)
- result = -1; /* rhs is max */
- else
- result = +1; /* lhs is max */
- }
- else if (slhs && srhs)
- { /* both negative */
- if (lhs->exponent < rhs->exponent)
- result = +1;
- else
- result = -1;
- /* [if equal, we use lhs, technically identical] */
- }
- else
- { /* both positive */
- if (lhs->exponent > rhs->exponent)
- result = +1;
- else
- result = -1;
- /* [ditto] */
- }
- } /* numerically equal */
- /* here result will be non-0 */
- if (op == COMPMIN)
- result = -result; /* reverse if looking for MIN */
- choice = (result > 0 ? lhs : rhs); /* choose */
- /* copy chosen to result, rounding if need be */
- decCopyFit (res, choice, set, &residue, status);
- decFinish (res, set, &residue, status);
+ if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {
+ result=+1;
+ break;
+ }
+ }
+
+ /* handle NaNs specially; let infinities drop through */
+ /* This assumes sNaN (even just one) leads to NaN. */
+ merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
+ if (merged) { /* a NaN bit set */
+ if (op==COMPARE); /* result will be NaN */
+ else if (op==COMPSIG) /* treat qNaN as sNaN */
+ *status|=DEC_Invalid_operation | DEC_sNaN;
+ else if (op==COMPTOTAL) { /* total ordering, always finite */
+ /* signs are known to be the same; compute the ordering here */
+ /* as if the signs are both positive, then invert for negatives */
+ if (!decNumberIsNaN(lhs)) result=-1;
+ else if (!decNumberIsNaN(rhs)) result=+1;
+ /* here if both NaNs */
+ else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
+ else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
+ else { /* both NaN or both sNaN */
+ /* now it just depends on the payload */
+ result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
+ rhs->lsu, D2U(rhs->digits), 0);
+ /* [Error not possible, as these are 'aligned'] */
+ } /* both same NaNs */
+ if (decNumberIsNegative(lhs)) result=-result;
+ break;
+ } /* total order */
+
+ else if (merged & DECSNAN); /* sNaN -> qNaN */
+ else { /* here if MIN or MAX and one or two quiet NaNs */
+ /* min or max -- 754 rules ignore single NaN */
+ if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
+ /* just one NaN; force choice to be the non-NaN operand */
+ op=COMPMAX;
+ if (lhs->bits & DECNAN) result=-1; /* pick rhs */
+ else result=+1; /* pick lhs */
+ break;
+ }
+ } /* max or min */
+ op=COMPNAN; /* use special path */
+ decNaNs(res, lhs, rhs, set, status); /* propagate NaN */
+ break;
+ }
+ /* have numbers */
+ if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
+ else result=decCompare(lhs, rhs, 0); /* sign matters */
+ } while(0); /* end protected */
+
+ if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */
+ else {
+ if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { /* returning signum */
+ if (op==COMPTOTAL && result==0) {
+ /* operands are numerically equal or same NaN (and same sign, */
+ /* tested first); if identical, leave result 0 */
+ if (lhs->exponent!=rhs->exponent) {
+ if (lhs->exponent<rhs->exponent) result=-1;
+ else result=+1;
+ if (decNumberIsNegative(lhs)) result=-result;
+ } /* lexp!=rexp */
+ } /* total-order by exponent */
+ decNumberZero(res); /* [always a valid result] */
+ if (result!=0) { /* must be -1 or +1 */
+ *res->lsu=1;
+ if (result<0) res->bits=DECNEG;
}
+ }
+ else if (op==COMPNAN); /* special, drop through */
+ else { /* MAX or MIN, non-NaN result */
+ Int residue=0; /* rounding accumulator */
+ /* choose the operand for the result */
+ const decNumber *choice;
+ if (result==0) { /* operands are numerically equal */
+ /* choose according to sign then exponent (see 754) */
+ uByte slhs=(lhs->bits & DECNEG);
+ uByte srhs=(rhs->bits & DECNEG);
+ #if DECSUBSET
+ if (!set->extended) { /* subset: force left-hand */
+ op=COMPMAX;
+ result=+1;
+ }
+ else
+ #endif
+ if (slhs!=srhs) { /* signs differ */
+ if (slhs) result=-1; /* rhs is max */
+ else result=+1; /* lhs is max */
+ }
+ else if (slhs && srhs) { /* both negative */
+ if (lhs->exponent<rhs->exponent) result=+1;
+ else result=-1;
+ /* [if equal, use lhs, technically identical] */
+ }
+ else { /* both positive */
+ if (lhs->exponent>rhs->exponent) result=+1;
+ else result=-1;
+ /* [ditto] */
+ }
+ } /* numerically equal */
+ /* here result will be non-0; reverse if looking for MIN */
+ if (op==COMPMIN || op==COMPMINMAG) result=-result;
+ choice=(result>0 ? lhs : rhs); /* choose */
+ /* copy chosen to result, rounding if need be */
+ decCopyFit(res, choice, set, &residue, status);
+ decFinish(res, set, &residue, status);
+ }
}
- if (allocrhs != NULL)
- free (allocrhs); /* free any storage we used */
- if (alloclhs != NULL)
- free (alloclhs); /* .. */
+ #if DECSUBSET
+ if (allocrhs!=NULL) free(allocrhs); /* free any storage used */
+ if (alloclhs!=NULL) free(alloclhs); /* .. */
+ #endif
return res;
-}
+ } /* decCompareOp */
/* ------------------------------------------------------------------ */
-/* decCompare -- compare two decNumbers by numerical value */
-/* */
-/* This routine compares A ? B without altering them. */
-/* */
-/* Arg1 is A, a decNumber which is not a NaN */
-/* Arg2 is B, a decNumber which is not a NaN */
-/* */
+/* decCompare -- compare two decNumbers by numerical value */
+/* */
+/* This routine compares A ? B without altering them. */
+/* */
+/* Arg1 is A, a decNumber which is not a NaN */
+/* Arg2 is B, a decNumber which is not a NaN */
+/* Arg3 is 1 for a sign-independent compare, 0 otherwise */
+/* */
/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
-/* (the only possible failure is an allocation error) */
-/* ------------------------------------------------------------------ */
-/* This could be merged into decCompareOp */
-static Int
-decCompare (decNumber * lhs, decNumber * rhs)
-{
- Int result; /* result value */
- Int sigr; /* rhs signum */
- Int compare; /* work */
- result = 1; /* assume signum(lhs) */
- if (ISZERO (lhs))
- result = 0;
- else if (decNumberIsNegative (lhs))
- result = -1;
- sigr = 1; /* compute signum(rhs) */
- if (ISZERO (rhs))
- sigr = 0;
- else if (decNumberIsNegative (rhs))
- sigr = -1;
- if (result > sigr)
- return +1; /* L > R, return 1 */
- if (result < sigr)
- return -1; /* R < L, return -1 */
-
- /* signums are the same */
- if (result == 0)
- return 0; /* both 0 */
- /* Both non-zero */
- if ((lhs->bits | rhs->bits) & DECINF)
- { /* one or more infinities */
- if (lhs->bits == rhs->bits)
- result = 0; /* both the same */
- else if (decNumberIsInfinite (rhs))
- result = -result;
- return result;
+/* (the only possible failure is an allocation error) */
+/* ------------------------------------------------------------------ */
+static Int decCompare(const decNumber *lhs, const decNumber *rhs,
+ Flag abs) {
+ Int result; /* result value */
+ Int sigr; /* rhs signum */
+ Int compare; /* work */
+
+ result=1; /* assume signum(lhs) */
+ if (ISZERO(lhs)) result=0;
+ if (abs) {
+ if (ISZERO(rhs)) return result; /* LHS wins or both 0 */
+ /* RHS is non-zero */
+ if (result==0) return -1; /* LHS is 0; RHS wins */
+ /* [here, both non-zero, result=1] */
}
-
- /* we must compare the coefficients, allowing for exponents */
- if (lhs->exponent > rhs->exponent)
- { /* LHS exponent larger */
- /* swap sides, and sign */
- decNumber *temp = lhs;
- lhs = rhs;
- rhs = temp;
- result = -result;
+ else { /* signs matter */
+ if (result && decNumberIsNegative(lhs)) result=-1;
+ sigr=1; /* compute signum(rhs) */
+ if (ISZERO(rhs)) sigr=0;
+ else if (decNumberIsNegative(rhs)) sigr=-1;
+ if (result > sigr) return +1; /* L > R, return 1 */
+ if (result < sigr) return -1; /* L < R, return -1 */
+ if (result==0) return 0; /* both 0 */
}
- compare = decUnitCompare (lhs->lsu, D2U (lhs->digits),
- rhs->lsu, D2U (rhs->digits),
- rhs->exponent - lhs->exponent);
-
- if (compare != BADINT)
- compare *= result; /* comparison succeeded */
- return compare; /* what we got */
-}
+ /* signums are the same; both are non-zero */
+ if ((lhs->bits | rhs->bits) & DECINF) { /* one or more infinities */
+ if (decNumberIsInfinite(rhs)) {
+ if (decNumberIsInfinite(lhs)) result=0;/* both infinite */
+ else result=-result; /* only rhs infinite */
+ }
+ return result;
+ }
+ /* must compare the coefficients, allowing for exponents */
+ if (lhs->exponent>rhs->exponent) { /* LHS exponent larger */
+ /* swap sides, and sign */
+ const decNumber *temp=lhs;
+ lhs=rhs;
+ rhs=temp;
+ result=-result;
+ }
+ compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
+ rhs->lsu, D2U(rhs->digits),
+ rhs->exponent-lhs->exponent);
+ if (compare!=BADINT) compare*=result; /* comparison succeeded */
+ return compare;
+ } /* decCompare */
/* ------------------------------------------------------------------ */
-/* decUnitCompare -- compare two >=0 integers in Unit arrays */
-/* */
+/* decUnitCompare -- compare two >=0 integers in Unit arrays */
+/* */
/* This routine compares A ? B*10**E where A and B are unit arrays */
-/* A is a plain integer */
-/* B has an exponent of E (which must be non-negative) */
-/* */
-/* Arg1 is A first Unit (lsu) */
-/* Arg2 is A length in Units */
-/* Arg3 is B first Unit (lsu) */
-/* Arg4 is B length in Units */
-/* Arg5 is E */
-/* */
+/* A is a plain integer */
+/* B has an exponent of E (which must be non-negative) */
+/* */
+/* Arg1 is A first Unit (lsu) */
+/* Arg2 is A length in Units */
+/* Arg3 is B first Unit (lsu) */
+/* Arg4 is B length in Units */
+/* Arg5 is E (0 if the units are aligned) */
+/* */
/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
-/* (the only possible failure is an allocation error) */
-/* ------------------------------------------------------------------ */
-static Int
-decUnitCompare (Unit * a, Int alength, Unit * b, Int blength, Int exp)
-{
- Unit *acc; /* accumulator for result */
- Unit accbuff[D2U (DECBUFFER + 1)]; /* local buffer */
- Unit *allocacc = NULL; /* -> allocated acc buffer, iff allocated */
- Int accunits, need; /* units in use or needed for acc */
- Unit *l, *r, *u; /* work */
- Int expunits, exprem, result; /* .. */
-
- if (exp == 0)
- { /* aligned; fastpath */
- if (alength > blength)
- return 1;
- if (alength < blength)
- return -1;
- /* same number of units in both -- need unit-by-unit compare */
- l = a + alength - 1;
- r = b + alength - 1;
- for (; l >= a; l--, r--)
- {
- if (*l > *r)
- return 1;
- if (*l < *r)
- return -1;
- }
- return 0; /* all units match */
- } /* aligned */
+/* (the only possible failure is an allocation error, which can */
+/* only occur if E!=0) */
+/* ------------------------------------------------------------------ */
+static Int decUnitCompare(const Unit *a, Int alength,
+ const Unit *b, Int blength, Int exp) {
+ Unit *acc; /* accumulator for result */
+ Unit accbuff[SD2U(DECBUFFER*2+1)]; /* local buffer */
+ Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
+ Int accunits, need; /* units in use or needed for acc */
+ const Unit *l, *r, *u; /* work */
+ Int expunits, exprem, result; /* .. */
+
+ if (exp==0) { /* aligned; fastpath */
+ if (alength>blength) return 1;
+ if (alength<blength) return -1;
+ /* same number of units in both -- need unit-by-unit compare */
+ l=a+alength-1;
+ r=b+alength-1;
+ for (;l>=a; l--, r--) {
+ if (*l>*r) return 1;
+ if (*l<*r) return -1;
+ }
+ return 0; /* all units match */
+ } /* aligned */
/* Unaligned. If one is >1 unit longer than the other, padded */
- /* approximately, then we can return easily */
- if (alength > blength + (Int) D2U (exp))
- return 1;
- if (alength + 1 < blength + (Int) D2U (exp))
- return -1;
-
- /* We need to do a real subtract. For this, we need a result buffer */
- /* even though we only are interested in the sign. Its length needs */
+ /* approximately, then can return easily */
+ if (alength>blength+(Int)D2U(exp)) return 1;
+ if (alength+1<blength+(Int)D2U(exp)) return -1;
+
+ /* Need to do a real subtract. For this, a result buffer is needed */
+ /* even though only the sign is of interest. Its length needs */
/* to be the larger of alength and padded blength, +2 */
- need = blength + D2U (exp); /* maximum real length of B */
- if (need < alength)
- need = alength;
- need += 2;
- acc = accbuff; /* assume use local buffer */
- if (need * sizeof (Unit) > sizeof (accbuff))
- {
- allocacc = (Unit *) malloc (need * sizeof (Unit));
- if (allocacc == NULL)
- return BADINT; /* hopeless -- abandon */
- acc = allocacc;
+ need=blength+D2U(exp); /* maximum real length of B */
+ if (need<alength) need=alength;
+ need+=2;
+ acc=accbuff; /* assume use local buffer */
+ if (need*sizeof(Unit)>sizeof(accbuff)) {
+ allocacc=(Unit *)malloc(need*sizeof(Unit));
+ if (allocacc==NULL) return BADINT; /* hopeless -- abandon */
+ acc=allocacc;
}
/* Calculate units and remainder from exponent. */
- expunits = exp / DECDPUN;
- exprem = exp % DECDPUN;
+ expunits=exp/DECDPUN;
+ exprem=exp%DECDPUN;
/* subtract [A+B*(-m)] */
- accunits = decUnitAddSub (a, alength, b, blength, expunits, acc,
- -(Int) powers[exprem]);
+ accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
+ -(Int)powers[exprem]);
/* [UnitAddSub result may have leading zeros, even on zero] */
- if (accunits < 0)
- result = -1; /* negative result */
- else
- { /* non-negative result */
- /* check units of the result before freeing any storage */
- for (u = acc; u < acc + accunits - 1 && *u == 0;)
- u++;
- result = (*u == 0 ? 0 : +1);
+ if (accunits<0) result=-1; /* negative result */
+ else { /* non-negative result */
+ /* check units of the result before freeing any storage */
+ for (u=acc; u<acc+accunits-1 && *u==0;) u++;
+ result=(*u==0 ? 0 : +1);
}
/* clean up and return the result */
- if (allocacc != NULL)
- free (allocacc); /* drop any storage we used */
+ if (allocacc!=NULL) free(allocacc); /* drop any storage used */
return result;
-}
+ } /* decUnitCompare */
/* ------------------------------------------------------------------ */
/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
-/* */
-/* This routine performs the calculation: */
-/* */
-/* C=A+(B*M) */
-/* */
-/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
-/* */
-/* A may be shorter or longer than B. */
-/* */
-/* Leading zeros are not removed after a calculation. The result is */
+/* */
+/* This routine performs the calculation: */
+/* */
+/* C=A+(B*M) */
+/* */
+/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
+/* */
+/* A may be shorter or longer than B. */
+/* */
+/* Leading zeros are not removed after a calculation. The result is */
/* either the same length as the longer of A and B (adding any */
/* shift), or one Unit longer than that (if a Unit carry occurred). */
-/* */
-/* A and B content are not altered unless C is also A or B. */
+/* */
+/* A and B content are not altered unless C is also A or B. */
/* C may be the same array as A or B, but only if no zero padding is */
-/* requested (that is, C may be B only if bshift==0). */
+/* requested (that is, C may be B only if bshift==0). */
/* C is filled from the lsu; only those units necessary to complete */
-/* the calculation are referenced. */
-/* */
-/* Arg1 is A first Unit (lsu) */
-/* Arg2 is A length in Units */
-/* Arg3 is B first Unit (lsu) */
-/* Arg4 is B length in Units */
+/* the calculation are referenced. */
+/* */
+/* Arg1 is A first Unit (lsu) */
+/* Arg2 is A length in Units */
+/* Arg3 is B first Unit (lsu) */
+/* Arg4 is B length in Units */
/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
-/* Arg6 is C first Unit (lsu) */
-/* Arg7 is M, the multiplier */
-/* */
+/* Arg6 is C first Unit (lsu) */
+/* Arg7 is M, the multiplier */
+/* */
/* returns the count of Units written to C, which will be non-zero */
/* and negated if the result is negative. That is, the sign of the */
/* returned Int is the sign of the result (positive for zero) and */
-/* the absolute value of the Int is the count of Units. */
-/* */
+/* the absolute value of the Int is the count of Units. */
+/* */
/* It is the caller's responsibility to make sure that C size is */
-/* safe, allowing space if necessary for a one-Unit carry. */
-/* */
+/* safe, allowing space if necessary for a one-Unit carry. */
+/* */
/* This routine is severely performance-critical; *any* change here */
/* must be measured (timed) to assure no performance degradation. */
/* In particular, trickery here tends to be counter-productive, as */
/* increased complexity of code hurts register optimizations on */
-/* register-poor architectures. Avoiding divisions is nearly */
-/* always a Good Idea, however. */
-/* */
+/* register-poor architectures. Avoiding divisions is nearly */
+/* always a Good Idea, however. */
+/* */
/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
/* (IBM Warwick, UK) for some of the ideas used in this routine. */
/* ------------------------------------------------------------------ */
-static Int
-decUnitAddSub (Unit * a, Int alength,
- Unit * b, Int blength, Int bshift, Unit * c, Int m)
-{
- Unit *alsu = a; /* A lsu [need to remember it] */
- Unit *clsu = c; /* C ditto */
- Unit *minC; /* low water mark for C */
- Unit *maxC; /* high water mark for C */
- eInt carry = 0; /* carry integer (could be Long) */
- Int add; /* work */
-#if DECDPUN==4 /* myriadal */
- Int est; /* estimated quotient */
-#endif
-
-#if DECTRACE
- if (alength < 1 || blength < 1)
- printf ("decUnitAddSub: alen blen m %d %d [%d]\n", alength, blength, m);
-#endif
-
- maxC = c + alength; /* A is usually the longer */
- minC = c + blength; /* .. and B the shorter */
- if (bshift != 0)
- { /* B is shifted; low As copy across */
- minC += bshift;
- /* if in place [common], skip copy unless there's a gap [rare] */
- if (a == c && bshift <= alength)
- {
- c += bshift;
- a += bshift;
- }
- else
- for (; c < clsu + bshift; a++, c++)
- { /* copy needed */
- if (a < alsu + alength)
- *c = *a;
- else
- *c = 0;
- }
+static Int decUnitAddSub(const Unit *a, Int alength,
+ const Unit *b, Int blength, Int bshift,
+ Unit *c, Int m) {
+ const Unit *alsu=a; /* A lsu [need to remember it] */
+ Unit *clsu=c; /* C ditto */
+ Unit *minC; /* low water mark for C */
+ Unit *maxC; /* high water mark for C */
+ eInt carry=0; /* carry integer (could be Long) */
+ Int add; /* work */
+ #if DECDPUN<=4 /* myriadal, millenary, etc. */
+ Int est; /* estimated quotient */
+ #endif
+
+ #if DECTRACE
+ if (alength<1 || blength<1)
+ printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
+ #endif
+
+ maxC=c+alength; /* A is usually the longer */
+ minC=c+blength; /* .. and B the shorter */
+ if (bshift!=0) { /* B is shifted; low As copy across */
+ minC+=bshift;
+ /* if in place [common], skip copy unless there's a gap [rare] */
+ if (a==c && bshift<=alength) {
+ c+=bshift;
+ a+=bshift;
+ }
+ else for (; c<clsu+bshift; a++, c++) { /* copy needed */
+ if (a<alsu+alength) *c=*a;
+ else *c=0;
+ }
}
- if (minC > maxC)
- { /* swap */
- Unit *hold = minC;
- minC = maxC;
- maxC = hold;
+ if (minC>maxC) { /* swap */
+ Unit *hold=minC;
+ minC=maxC;
+ maxC=hold;
}
- /* For speed, we do the addition as two loops; the first where both A */
+ /* For speed, do the addition as two loops; the first where both A */
/* and B contribute, and the second (if necessary) where only one or */
/* other of the numbers contribute. */
/* Carry handling is the same (i.e., duplicated) in each case. */
- for (; c < minC; c++)
- {
- carry += *a;
+ for (; c<minC; c++) {
+ carry+=*a;
+ a++;
+ carry+=((eInt)*b)*m; /* [special-casing m=1/-1 */
+ b++; /* here is not a win] */
+ /* here carry is new Unit of digits; it could be +ve or -ve */
+ if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
+ *c=(Unit)carry;
+ carry=0;
+ continue;
+ }
+ #if DECDPUN==4 /* use divide-by-multiply */
+ if (carry>=0) {
+ est=(((ueInt)carry>>11)*53687)>>18;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
+ carry=est; /* likely quotient [89%] */
+ if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
+ carry++;
+ *c-=DECDPUNMAX+1;
+ continue;
+ }
+ /* negative case */
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
+ est=(((ueInt)carry>>11)*53687)>>18;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
+ if (*c<DECDPUNMAX+1) continue; /* was OK */
+ carry++;
+ *c-=DECDPUNMAX+1;
+ #elif DECDPUN==3
+ if (carry>=0) {
+ est=(((ueInt)carry>>3)*16777)>>21;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
+ carry=est; /* likely quotient [99%] */
+ if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
+ carry++;
+ *c-=DECDPUNMAX+1;
+ continue;
+ }
+ /* negative case */
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
+ est=(((ueInt)carry>>3)*16777)>>21;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
+ if (*c<DECDPUNMAX+1) continue; /* was OK */
+ carry++;
+ *c-=DECDPUNMAX+1;
+ #elif DECDPUN<=2
+ /* Can use QUOT10 as carry <= 4 digits */
+ if (carry>=0) {
+ est=QUOT10(carry, DECDPUN);
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
+ carry=est; /* quotient */
+ continue;
+ }
+ /* negative case */
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
+ est=QUOT10(carry, DECDPUN);
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
+ #else
+ /* remainder operator is undefined if negative, so must test */
+ if ((ueInt)carry<(DECDPUNMAX+1)*2) { /* fastpath carry +1 */
+ *c=(Unit)(carry-(DECDPUNMAX+1)); /* [helps additions] */
+ carry=1;
+ continue;
+ }
+ if (carry>=0) {
+ *c=(Unit)(carry%(DECDPUNMAX+1));
+ carry=carry/(DECDPUNMAX+1);
+ continue;
+ }
+ /* negative case */
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
+ *c=(Unit)(carry%(DECDPUNMAX+1));
+ carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
+ #endif
+ } /* c */
+
+ /* now may have one or other to complete */
+ /* [pretest to avoid loop setup/shutdown] */
+ if (c<maxC) for (; c<maxC; c++) {
+ if (a<alsu+alength) { /* still in A */
+ carry+=*a;
a++;
- carry += ((eInt) * b) * m; /* [special-casing m=1/-1 */
- b++; /* here is not a win] */
- /* here carry is new Unit of digits; it could be +ve or -ve */
- if ((ueInt) carry <= DECDPUNMAX)
- { /* fastpath 0-DECDPUNMAX */
- *c = (Unit) carry;
- carry = 0;
- continue;
+ }
+ else { /* inside B */
+ carry+=((eInt)*b)*m;
+ b++;
+ }
+ /* here carry is new Unit of digits; it could be +ve or -ve and */
+ /* magnitude up to DECDPUNMAX squared */
+ if ((ueInt)carry<=DECDPUNMAX) { /* fastpath 0-DECDPUNMAX */
+ *c=(Unit)carry;
+ carry=0;
+ continue;
+ }
+ /* result for this unit is negative or >DECDPUNMAX */
+ #if DECDPUN==4 /* use divide-by-multiply */
+ if (carry>=0) {
+ est=(((ueInt)carry>>11)*53687)>>18;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
+ carry=est; /* likely quotient [79.7%] */
+ if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
+ carry++;
+ *c-=DECDPUNMAX+1;
+ continue;
}
- /* remainder operator is undefined if negative, so we must test */
-#if DECDPUN==4 /* use divide-by-multiply */
- if (carry >= 0)
- {
- est = (((ueInt) carry >> 11) * 53687) >> 18;
- *c = (Unit) (carry - est * (DECDPUNMAX + 1)); /* remainder */
- carry = est; /* likely quotient [89%] */
- if (*c < DECDPUNMAX + 1)
- continue; /* estimate was correct */
- carry++;
- *c -= DECDPUNMAX + 1;
- continue;
+ /* negative case */
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
+ est=(((ueInt)carry>>11)*53687)>>18;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
+ if (*c<DECDPUNMAX+1) continue; /* was OK */
+ carry++;
+ *c-=DECDPUNMAX+1;
+ #elif DECDPUN==3
+ if (carry>=0) {
+ est=(((ueInt)carry>>3)*16777)>>21;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
+ carry=est; /* likely quotient [99%] */
+ if (*c<DECDPUNMAX+1) continue; /* estimate was correct */
+ carry++;
+ *c-=DECDPUNMAX+1;
+ continue;
+ }
+ /* negative case */
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
+ est=(((ueInt)carry>>3)*16777)>>21;
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
+ if (*c<DECDPUNMAX+1) continue; /* was OK */
+ carry++;
+ *c-=DECDPUNMAX+1;
+ #elif DECDPUN<=2
+ if (carry>=0) {
+ est=QUOT10(carry, DECDPUN);
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); /* remainder */
+ carry=est; /* quotient */
+ continue;
}
/* negative case */
- carry = carry + (eInt) (DECDPUNMAX + 1) * (DECDPUNMAX + 1); /* make positive */
- est = (((ueInt) carry >> 11) * 53687) >> 18;
- *c = (Unit) (carry - est * (DECDPUNMAX + 1));
- carry = est - (DECDPUNMAX + 1); /* correctly negative */
- if (*c < DECDPUNMAX + 1)
- continue; /* was OK */
- carry++;
- *c -= DECDPUNMAX + 1;
-#else
- if ((ueInt) carry < (DECDPUNMAX + 1) * 2)
- { /* fastpath carry +1 */
- *c = (Unit) (carry - (DECDPUNMAX + 1)); /* [helps additions] */
- carry = 1;
- continue;
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
+ est=QUOT10(carry, DECDPUN);
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
+ #else
+ if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */
+ *c=(Unit)(carry-(DECDPUNMAX+1));
+ carry=1;
+ continue;
}
- if (carry >= 0)
- {
- *c = (Unit) (carry % (DECDPUNMAX + 1));
- carry = carry / (DECDPUNMAX + 1);
- continue;
+ /* remainder operator is undefined if negative, so must test */
+ if (carry>=0) {
+ *c=(Unit)(carry%(DECDPUNMAX+1));
+ carry=carry/(DECDPUNMAX+1);
+ continue;
}
/* negative case */
- carry = carry + (eInt) (DECDPUNMAX + 1) * (DECDPUNMAX + 1); /* make positive */
- *c = (Unit) (carry % (DECDPUNMAX + 1));
- carry = carry / (DECDPUNMAX + 1) - (DECDPUNMAX + 1);
-#endif
- } /* c */
-
- /* we now may have one or other to complete */
- /* [pretest to avoid loop setup/shutdown] */
- if (c < maxC)
- for (; c < maxC; c++)
- {
- if (a < alsu + alength)
- { /* still in A */
- carry += *a;
- a++;
- }
- else
- { /* inside B */
- carry += ((eInt) * b) * m;
- b++;
- }
- /* here carry is new Unit of digits; it could be +ve or -ve and */
- /* magnitude up to DECDPUNMAX squared */
- if ((ueInt) carry <= DECDPUNMAX)
- { /* fastpath 0-DECDPUNMAX */
- *c = (Unit) carry;
- carry = 0;
- continue;
- }
- /* result for this unit is negative or >DECDPUNMAX */
-#if DECDPUN==4 /* use divide-by-multiply */
- /* remainder is undefined if negative, so we must test */
- if (carry >= 0)
- {
- est = (((ueInt) carry >> 11) * 53687) >> 18;
- *c = (Unit) (carry - est * (DECDPUNMAX + 1)); /* remainder */
- carry = est; /* likely quotient [79.7%] */
- if (*c < DECDPUNMAX + 1)
- continue; /* estimate was correct */
- carry++;
- *c -= DECDPUNMAX + 1;
- continue;
- }
- /* negative case */
- carry = carry + (eInt) (DECDPUNMAX + 1) * (DECDPUNMAX + 1); /* make positive */
- est = (((ueInt) carry >> 11) * 53687) >> 18;
- *c = (Unit) (carry - est * (DECDPUNMAX + 1));
- carry = est - (DECDPUNMAX + 1); /* correctly negative */
- if (*c < DECDPUNMAX + 1)
- continue; /* was OK */
- carry++;
- *c -= DECDPUNMAX + 1;
-#else
- if ((ueInt) carry < (DECDPUNMAX + 1) * 2)
- { /* fastpath carry 1 */
- *c = (Unit) (carry - (DECDPUNMAX + 1));
- carry = 1;
- continue;
- }
- /* remainder is undefined if negative, so we must test */
- if (carry >= 0)
- {
- *c = (Unit) (carry % (DECDPUNMAX + 1));
- carry = carry / (DECDPUNMAX + 1);
- continue;
- }
- /* negative case */
- carry = carry + (eInt) (DECDPUNMAX + 1) * (DECDPUNMAX + 1); /* make positive */
- *c = (Unit) (carry % (DECDPUNMAX + 1));
- carry = carry / (DECDPUNMAX + 1) - (DECDPUNMAX + 1);
-#endif
- } /* c */
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); /* make positive */
+ *c=(Unit)(carry%(DECDPUNMAX+1));
+ carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
+ #endif
+ } /* c */
/* OK, all A and B processed; might still have carry or borrow */
/* return number of Units in the result, negated if a borrow */
- if (carry == 0)
- return c - clsu; /* no carry, we're done */
- if (carry > 0)
- { /* positive carry */
- *c = (Unit) carry; /* place as new unit */
- c++; /* .. */
- return c - clsu;
+ if (carry==0) return c-clsu; /* no carry, so no more to do */
+ if (carry>0) { /* positive carry */
+ *c=(Unit)carry; /* place as new unit */
+ c++; /* .. */
+ return c-clsu;
}
/* -ve carry: it's a borrow; complement needed */
- add = 1; /* temporary carry... */
- for (c = clsu; c < maxC; c++)
- {
- add = DECDPUNMAX + add - *c;
- if (add <= DECDPUNMAX)
- {
- *c = (Unit) add;
- add = 0;
- }
- else
- {
- *c = 0;
- add = 1;
- }
+ add=1; /* temporary carry... */
+ for (c=clsu; c<maxC; c++) {
+ add=DECDPUNMAX+add-*c;
+ if (add<=DECDPUNMAX) {
+ *c=(Unit)add;
+ add=0;
+ }
+ else {
+ *c=0;
+ add=1;
+ }
}
/* add an extra unit iff it would be non-zero */
-#if DECTRACE
- printf ("UAS borrow: add %d, carry %d\n", add, carry);
-#endif
- if ((add - carry - 1) != 0)
- {
- *c = (Unit) (add - carry - 1);
- c++; /* interesting, include it */
+ #if DECTRACE
+ printf("UAS borrow: add %ld, carry %ld\n", add, carry);
+ #endif
+ if ((add-carry-1)!=0) {
+ *c=(Unit)(add-carry-1);
+ c++; /* interesting, include it */
}
- return clsu - c; /* -ve result indicates borrowed */
-}
+ return clsu-c; /* -ve result indicates borrowed */
+ } /* decUnitAddSub */
/* ------------------------------------------------------------------ */
-/* decTrim -- trim trailing zeros or normalize */
-/* */
-/* dn is the number to trim or normalize */
+/* decTrim -- trim trailing zeros or normalize */
+/* */
+/* dn is the number to trim or normalize */
+/* set is the context to use to check for clamp */
/* all is 1 to remove all trailing zeros, 0 for just fraction ones */
-/* dropped returns the number of discarded trailing zeros */
-/* returns dn */
-/* */
-/* All fields are updated as required. This is a utility operation, */
-/* so special values are unchanged and no error is possible. */
-/* ------------------------------------------------------------------ */
-static decNumber *
-decTrim (decNumber * dn, Flag all, Int * dropped)
-{
- Int d, exp; /* work */
- uInt cut; /* .. */
- Unit *up; /* -> current Unit */
-
-#if DECCHECK
- if (decCheckOperands (dn, DECUNUSED, DECUNUSED, DECUNUSED))
+/* noclamp is 1 to unconditional (unclamped) trim */
+/* dropped returns the number of discarded trailing zeros */
+/* returns dn */
+/* */
+/* If clamp is set in the context then the number of zeros trimmed */
+/* may be limited if the exponent is high. */
+/* All fields are updated as required. This is a utility operation, */
+/* so special values are unchanged and no error is possible. */
+/* ------------------------------------------------------------------ */
+static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
+ Flag noclamp, Int *dropped) {
+ Int d, exp; /* work */
+ uInt cut; /* .. */
+ Unit *up; /* -> current Unit */
+
+ #if DECCHECK
+ if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
+ #endif
+
+ *dropped=0; /* assume no zeros dropped */
+ if ((dn->bits & DECSPECIAL) /* fast exit if special .. */
+ || (*dn->lsu & 0x01)) return dn; /* .. or odd */
+ if (ISZERO(dn)) { /* .. or 0 */
+ dn->exponent=0; /* (sign is preserved) */
return dn;
-#endif
-
- *dropped = 0; /* assume no zeros dropped */
- if ((dn->bits & DECSPECIAL) /* fast exit if special .. */
- || (*dn->lsu & 0x01))
- return dn; /* .. or odd */
- if (ISZERO (dn))
- { /* .. or 0 */
- dn->exponent = 0; /* (sign is preserved) */
- return dn;
}
- /* we have a finite number which is even */
- exp = dn->exponent;
- cut = 1; /* digit (1-DECDPUN) in Unit */
- up = dn->lsu; /* -> current Unit */
- for (d = 0; d < dn->digits - 1; d++)
- { /* [don't strip the final digit] */
- /* slice by powers */
-#if DECDPUN<=4
- uInt quot = QUOT10 (*up, cut);
- if ((*up - quot * powers[cut]) != 0)
- break; /* found non-0 digit */
-#else
- if (*up % powers[cut] != 0)
- break; /* found non-0 digit */
-#endif
- /* have a trailing 0 */
- if (!all)
- { /* trimming */
- /* [if exp>0 then all trailing 0s are significant for trim] */
- if (exp <= 0)
- { /* if digit might be significant */
- if (exp == 0)
- break; /* then quit */
- exp++; /* next digit might be significant */
- }
+ /* have a finite number which is even */
+ exp=dn->exponent;
+ cut=1; /* digit (1-DECDPUN) in Unit */
+ up=dn->lsu; /* -> current Unit */
+ for (d=0; d<dn->digits-1; d++) { /* [don't strip the final digit] */
+ /* slice by powers */
+ #if DECDPUN<=4
+ uInt quot=QUOT10(*up, cut);
+ if ((*up-quot*powers[cut])!=0) break; /* found non-0 digit */
+ #else
+ if (*up%powers[cut]!=0) break; /* found non-0 digit */
+ #endif
+ /* have a trailing 0 */
+ if (!all) { /* trimming */
+ /* [if exp>0 then all trailing 0s are significant for trim] */
+ if (exp<=0) { /* if digit might be significant */
+ if (exp==0) break; /* then quit */
+ exp++; /* next digit might be significant */
}
- cut++; /* next power */
- if (cut > DECDPUN)
- { /* need new Unit */
- up++;
- cut = 1;
- }
- } /* d */
- if (d == 0)
- return dn; /* none dropped */
+ }
+ cut++; /* next power */
+ if (cut>DECDPUN) { /* need new Unit */
+ up++;
+ cut=1;
+ }
+ } /* d */
+ if (d==0) return dn; /* none to drop */
+
+ /* may need to limit drop if clamping */
+ if (set->clamp && !noclamp) {
+ Int maxd=set->emax-set->digits+1-dn->exponent;
+ if (maxd<=0) return dn; /* nothing possible */
+ if (d>maxd) d=maxd;
+ }
/* effect the drop */
- decShiftToLeast (dn->lsu, D2U (dn->digits), d);
- dn->exponent += d; /* maintain numerical value */
- dn->digits -= d; /* new length */
- *dropped = d; /* report the count */
+ decShiftToLeast(dn->lsu, D2U(dn->digits), d);
+ dn->exponent+=d; /* maintain numerical value */
+ dn->digits-=d; /* new length */
+ *dropped=d; /* report the count */
return dn;
-}
+ } /* decTrim */
+
+/* ------------------------------------------------------------------ */
+/* decReverse -- reverse a Unit array in place */
+/* */
+/* ulo is the start of the array */
+/* uhi is the end of the array (highest Unit to include) */
+/* */
+/* The units ulo through uhi are reversed in place (if the number */
+/* of units is odd, the middle one is untouched). Note that the */
+/* digit(s) in each unit are unaffected. */
+/* ------------------------------------------------------------------ */
+static void decReverse(Unit *ulo, Unit *uhi) {
+ Unit temp;
+ for (; ulo<uhi; ulo++, uhi--) {
+ temp=*ulo;
+ *ulo=*uhi;
+ *uhi=temp;
+ }
+ return;
+ } /* decReverse */
/* ------------------------------------------------------------------ */
/* decShiftToMost -- shift digits in array towards most significant */
-/* */
-/* uar is the array */
-/* digits is the count of digits in use in the array */
+/* */
+/* uar is the array */
+/* digits is the count of digits in use in the array */
/* shift is the number of zeros to pad with (least significant); */
-/* it must be zero or positive */
-/* */
+/* it must be zero or positive */
+/* */
/* returns the new length of the integer in the array, in digits */
-/* */
+/* */
/* No overflow is permitted (that is, the uar array must be known to */
-/* be large enough to hold the result, after shifting). */
-/* ------------------------------------------------------------------ */
-static Int
-decShiftToMost (Unit * uar, Int digits, Int shift)
-{
- Unit *target, *source, *first; /* work */
- uInt rem; /* for division */
- Int cut; /* odd 0's to add */
- uInt next; /* work */
-
- if (shift == 0)
- return digits; /* [fastpath] nothing to do */
- if ((digits + shift) <= DECDPUN)
- { /* [fastpath] single-unit case */
- *uar = (Unit) (*uar * powers[shift]);
- return digits + shift;
- }
+/* be large enough to hold the result, after shifting). */
+/* ------------------------------------------------------------------ */
+static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
+ Unit *target, *source, *first; /* work */
+ Int cut; /* odd 0's to add */
+ uInt next; /* work */
- cut = (DECDPUN - shift % DECDPUN) % DECDPUN;
- source = uar + D2U (digits) - 1; /* where msu comes from */
- first = uar + D2U (digits + shift) - 1; /* where msu of source will end up */
- target = source + D2U (shift); /* where upper part of first cut goes */
- next = 0;
+ if (shift==0) return digits; /* [fastpath] nothing to do */
+ if ((digits+shift)<=DECDPUN) { /* [fastpath] single-unit case */
+ *uar=(Unit)(*uar*powers[shift]);
+ return digits+shift;
+ }
- for (; source >= uar; source--, target--)
- {
- /* split the source Unit and accumulate remainder for next */
-#if DECDPUN<=4
- uInt quot = QUOT10 (*source, cut);
- rem = *source - quot * powers[cut];
- next += quot;
-#else
- rem = *source % powers[cut];
- next += *source / powers[cut];
-#endif
- if (target <= first)
- *target = (Unit) next; /* write to target iff valid */
- next = rem * powers[DECDPUN - cut]; /* save remainder for next Unit */
+ next=0; /* all paths */
+ source=uar+D2U(digits)-1; /* where msu comes from */
+ target=source+D2U(shift); /* where upper part of first cut goes */
+ cut=DECDPUN-MSUDIGITS(shift); /* where to slice */
+ if (cut==0) { /* unit-boundary case */
+ for (; source>=uar; source--, target--) *target=*source;
}
- /* propagate to one below and clear the rest */
- for (; target >= uar; target--)
- {
- *target = (Unit) next;
- next = 0;
+ else {
+ first=uar+D2U(digits+shift)-1; /* where msu of source will end up */
+ for (; source>=uar; source--, target--) {
+ /* split the source Unit and accumulate remainder for next */
+ #if DECDPUN<=4
+ uInt quot=QUOT10(*source, cut);
+ uInt rem=*source-quot*powers[cut];
+ next+=quot;
+ #else
+ uInt rem=*source%powers[cut];
+ next+=*source/powers[cut];
+ #endif
+ if (target<=first) *target=(Unit)next; /* write to target iff valid */
+ next=rem*powers[DECDPUN-cut]; /* save remainder for next Unit */
+ }
+ } /* shift-move */
+
+ /* propagate any partial unit to one below and clear the rest */
+ for (; target>=uar; target--) {
+ *target=(Unit)next;
+ next=0;
}
- return digits + shift;
-}
+ return digits+shift;
+ } /* decShiftToMost */
/* ------------------------------------------------------------------ */
/* decShiftToLeast -- shift digits in array towards least significant */
-/* */
-/* uar is the array */
-/* units is length of the array, in units */
+/* */
+/* uar is the array */
+/* units is length of the array, in units */
/* shift is the number of digits to remove from the lsu end; it */
-/* must be zero or positive and less than units*DECDPUN. */
-/* */
+/* must be zero or positive and <= than units*DECDPUN. */
+/* */
/* returns the new length of the integer in the array, in units */
-/* */
+/* */
/* Removed digits are discarded (lost). Units not required to hold */
-/* the final result are unchanged. */
-/* ------------------------------------------------------------------ */
-static Int
-decShiftToLeast (Unit * uar, Int units, Int shift)
-{
- Unit *target, *up; /* work */
- Int cut, count; /* work */
- Int quot, rem; /* for division */
-
- if (shift == 0)
- return units; /* [fastpath] nothing to do */
-
- up = uar + shift / DECDPUN; /* source; allow for whole Units */
- cut = shift % DECDPUN; /* odd 0's to drop */
- target = uar; /* both paths */
- if (cut == 0)
- { /* whole units shift */
- for (; up < uar + units; target++, up++)
- *target = *up;
- return target - uar;
+/* the final result are unchanged. */
+/* ------------------------------------------------------------------ */
+static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
+ Unit *target, *up; /* work */
+ Int cut, count; /* work */
+ Int quot, rem; /* for division */
+
+ if (shift==0) return units; /* [fastpath] nothing to do */
+ if (shift==units*DECDPUN) { /* [fastpath] little to do */
+ *uar=0; /* all digits cleared gives zero */
+ return 1; /* leaves just the one */
+ }
+
+ target=uar; /* both paths */
+ cut=MSUDIGITS(shift);
+ if (cut==DECDPUN) { /* unit-boundary case; easy */
+ up=uar+D2U(shift);
+ for (; up<uar+units; target++, up++) *target=*up;
+ return target-uar;
}
+
/* messier */
- count = units * DECDPUN - shift; /* the maximum new length */
-#if DECDPUN<=4
- quot = QUOT10 (*up, cut);
-#else
- quot = *up / powers[cut];
-#endif
- for (;; target++)
- {
- *target = (Unit) quot;
- count -= (DECDPUN - cut);
- if (count <= 0)
- break;
- up++;
- quot = *up;
-#if DECDPUN<=4
- quot = QUOT10 (quot, cut);
- rem = *up - quot * powers[cut];
-#else
- rem = quot % powers[cut];
- quot = quot / powers[cut];
-#endif
- *target = (Unit) (*target + rem * powers[DECDPUN - cut]);
- count -= cut;
- if (count <= 0)
- break;
+ up=uar+D2U(shift-cut); /* source; correct to whole Units */
+ count=units*DECDPUN-shift; /* the maximum new length */
+ #if DECDPUN<=4
+ quot=QUOT10(*up, cut);
+ #else
+ quot=*up/powers[cut];
+ #endif
+ for (; ; target++) {
+ *target=(Unit)quot;
+ count-=(DECDPUN-cut);
+ if (count<=0) break;
+ up++;
+ quot=*up;
+ #if DECDPUN<=4
+ quot=QUOT10(quot, cut);
+ rem=*up-quot*powers[cut];
+ #else
+ rem=quot%powers[cut];
+ quot=quot/powers[cut];
+ #endif
+ *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
+ count-=cut;
+ if (count<=0) break;
}
- return target - uar + 1;
-}
+ return target-uar+1;
+ } /* decShiftToLeast */
#if DECSUBSET
/* ------------------------------------------------------------------ */
-/* decRoundOperand -- round an operand [used for subset only] */
-/* */
-/* dn is the number to round (dn->digits is > set->digits) */
-/* set is the relevant context */
-/* status is the status accumulator */
-/* */
-/* returns an allocated decNumber with the rounded result. */
-/* */
-/* lostDigits and other status may be set by this. */
-/* */
-/* Since the input is an operand, we are not permitted to modify it. */
-/* We therefore return an allocated decNumber, rounded as required. */
+/* decRoundOperand -- round an operand [used for subset only] */
+/* */
+/* dn is the number to round (dn->digits is > set->digits) */
+/* set is the relevant context */
+/* status is the status accumulator */
+/* */
+/* returns an allocated decNumber with the rounded result. */
+/* */
+/* lostDigits and other status may be set by this. */
+/* */
+/* Since the input is an operand, it must not be modified. */
+/* Instead, return an allocated decNumber, rounded as required. */
/* It is the caller's responsibility to free the allocated storage. */
-/* */
+/* */
/* If no storage is available then the result cannot be used, so NULL */
-/* is returned. */
+/* is returned. */
/* ------------------------------------------------------------------ */
-static decNumber *
-decRoundOperand (decNumber * dn, decContext * set, uInt * status)
-{
- decNumber *res; /* result structure */
- uInt newstatus = 0; /* status from round */
- Int residue = 0; /* rounding accumulator */
+static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
+ uInt *status) {
+ decNumber *res; /* result structure */
+ uInt newstatus=0; /* status from round */
+ Int residue=0; /* rounding accumulator */
/* Allocate storage for the returned decNumber, big enough for the */
/* length specified by the context */
- res = (decNumber *) malloc (sizeof (decNumber)
- + (D2U (set->digits) - 1) * sizeof (Unit));
- if (res == NULL)
- {
- *status |= DEC_Insufficient_storage;
- return NULL;
+ res=(decNumber *)malloc(sizeof(decNumber)
+ +(D2U(set->digits)-1)*sizeof(Unit));
+ if (res==NULL) {
+ *status|=DEC_Insufficient_storage;
+ return NULL;
}
- decCopyFit (res, dn, set, &residue, &newstatus);
- decApplyRound (res, set, residue, &newstatus);
+ decCopyFit(res, dn, set, &residue, &newstatus);
+ decApplyRound(res, set, residue, &newstatus);
- /* If that set Inexact then we "lost digits" */
- if (newstatus & DEC_Inexact)
- newstatus |= DEC_Lost_digits;
- *status |= newstatus;
+ /* If that set Inexact then "lost digits" is raised... */
+ if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
+ *status|=newstatus;
return res;
-}
+ } /* decRoundOperand */
#endif
/* ------------------------------------------------------------------ */
-/* decCopyFit -- copy a number, shortening the coefficient if needed */
-/* */
-/* dest is the target decNumber */
-/* src is the source decNumber */
+/* decCopyFit -- copy a number, truncating the coefficient if needed */
+/* */
+/* dest is the target decNumber */
+/* src is the source decNumber */
/* set is the context [used for length (digits) and rounding mode] */
-/* residue is the residue accumulator */
-/* status contains the current status to be updated */
-/* */
-/* (dest==src is allowed and will be a no-op if fits) */
-/* All fields are updated as required. */
-/* ------------------------------------------------------------------ */
-static void
-decCopyFit (decNumber * dest, decNumber * src, decContext * set,
- Int * residue, uInt * status)
-{
- dest->bits = src->bits;
- dest->exponent = src->exponent;
- decSetCoeff (dest, set, src->lsu, src->digits, residue, status);
-}
-
-/* ------------------------------------------------------------------ */
-/* decSetCoeff -- set the coefficient of a number */
-/* */
-/* dn is the number whose coefficient array is to be set. */
-/* It must have space for set->digits digits */
-/* set is the context [for size] */
-/* lsu -> lsu of the source coefficient [may be dn->lsu] */
+/* residue is the residue accumulator */
+/* status contains the current status to be updated */
+/* */
+/* (dest==src is allowed and will be a no-op if fits) */
+/* All fields are updated as required. */
+/* ------------------------------------------------------------------ */
+static void decCopyFit(decNumber *dest, const decNumber *src,
+ decContext *set, Int *residue, uInt *status) {
+ dest->bits=src->bits;
+ dest->exponent=src->exponent;
+ decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
+ } /* decCopyFit */
+
+/* ------------------------------------------------------------------ */
+/* decSetCoeff -- set the coefficient of a number */
+/* */
+/* dn is the number whose coefficient array is to be set. */
+/* It must have space for set->digits digits */
+/* set is the context [for size] */
+/* lsu -> lsu of the source coefficient [may be dn->lsu] */
/* len is digits in the source coefficient [may be dn->digits] */
/* residue is the residue accumulator. This has values as in */
-/* decApplyRound, and will be unchanged unless the */
-/* target size is less than len. In this case, the */
-/* coefficient is truncated and the residue is updated to */
-/* reflect the previous residue and the dropped digits. */
-/* status is the status accumulator, as usual */
-/* */
+/* decApplyRound, and will be unchanged unless the */
+/* target size is less than len. In this case, the */
+/* coefficient is truncated and the residue is updated to */
+/* reflect the previous residue and the dropped digits. */
+/* status is the status accumulator, as usual */
+/* */
/* The coefficient may already be in the number, or it can be an */
/* external intermediate array. If it is in the number, lsu must == */
-/* dn->lsu and len must == dn->digits. */
-/* */
+/* dn->lsu and len must == dn->digits. */
+/* */
/* Note that the coefficient length (len) may be < set->digits, and */
/* in this case this merely copies the coefficient (or is a no-op */
-/* if dn->lsu==lsu). */
-/* */
-/* Note also that (only internally, from decNumberRescale and */
+/* if dn->lsu==lsu). */
+/* */
+/* Note also that (only internally, from decQuantizeOp and */
/* decSetSubnormal) the value of set->digits may be less than one, */
-/* indicating a round to left. */
-/* This routine handles that case correctly; caller ensures space. */
-/* */
-/* dn->digits, dn->lsu (and as required), and dn->exponent are */
-/* updated as necessary. dn->bits (sign) is unchanged. */
-/* */
-/* DEC_Rounded status is set if any digits are discarded. */
+/* indicating a round to left. This routine handles that case */
+/* correctly; caller ensures space. */
+/* */
+/* dn->digits, dn->lsu (and as required), and dn->exponent are */
+/* updated as necessary. dn->bits (sign) is unchanged. */
+/* */
+/* DEC_Rounded status is set if any digits are discarded. */
/* DEC_Inexact status is set if any non-zero digits are discarded, or */
-/* incoming residue was non-0 (implies rounded) */
-/* ------------------------------------------------------------------ */
-/* mapping array: maps 0-9 to canonical residues, so that we can */
-/* adjust by a residue in range [-1, +1] and achieve correct rounding */
-/* 0 1 2 3 4 5 6 7 8 9 */
-static const uByte resmap[10] = { 0, 3, 3, 3, 3, 5, 7, 7, 7, 7 };
-static void
-decSetCoeff (decNumber * dn, decContext * set, Unit * lsu,
- Int len, Int * residue, uInt * status)
-{
- Int discard; /* number of digits to discard */
- uInt discard1; /* first discarded digit */
- uInt cut; /* cut point in Unit */
- uInt quot, rem; /* for divisions */
- Unit *up, *target; /* work */
- Int count; /* .. */
-#if DECDPUN<=4
- uInt temp; /* .. */
-#endif
-
- discard = len - set->digits; /* digits to discard */
- if (discard <= 0)
- { /* no digits are being discarded */
- if (dn->lsu != lsu)
- { /* copy needed */
- /* copy the coefficient array to the result number; no shift needed */
- up = lsu;
- for (target = dn->lsu; target < dn->lsu + D2U (len); target++, up++)
- {
- *target = *up;
- }
- dn->digits = len; /* set the new length */
- }
- /* dn->exponent and residue are unchanged */
- if (*residue != 0)
- *status |= (DEC_Inexact | DEC_Rounded); /* record inexactitude */
- return;
+/* incoming residue was non-0 (implies rounded) */
+/* ------------------------------------------------------------------ */
+/* mapping array: maps 0-9 to canonical residues, so that a residue */
+/* can be adjusted in the range [-1, +1] and achieve correct rounding */
+/* 0 1 2 3 4 5 6 7 8 9 */
+static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
+static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
+ Int len, Int *residue, uInt *status) {
+ Int discard; /* number of digits to discard */
+ uInt cut; /* cut point in Unit */
+ const Unit *up; /* work */
+ Unit *target; /* .. */
+ Int count; /* .. */
+ #if DECDPUN<=4
+ uInt temp; /* .. */
+ #endif
+
+ discard=len-set->digits; /* digits to discard */
+ if (discard<=0) { /* no digits are being discarded */
+ if (dn->lsu!=lsu) { /* copy needed */
+ /* copy the coefficient array to the result number; no shift needed */
+ count=len; /* avoids D2U */
+ up=lsu;
+ for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
+ *target=*up;
+ dn->digits=len; /* set the new length */
+ }
+ /* dn->exponent and residue are unchanged, record any inexactitude */
+ if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
+ return;
}
- /* we have to discard some digits */
- *status |= DEC_Rounded; /* accumulate Rounded status */
- if (*residue > 1)
- *residue = 1; /* previous residue now to right, so -1 to +1 */
-
- if (discard > len)
- { /* everything, +1, is being discarded */
- /* guard digit is 0 */
- /* residue is all the number [NB could be all 0s] */
- if (*residue <= 0)
- for (up = lsu + D2U (len) - 1; up >= lsu; up--)
- {
- if (*up != 0)
- { /* found a non-0 */
- *residue = 1;
- break; /* no need to check any others */
- }
- }
- if (*residue != 0)
- *status |= DEC_Inexact; /* record inexactitude */
- *dn->lsu = 0; /* coefficient will now be 0 */
- dn->digits = 1; /* .. */
- dn->exponent += discard; /* maintain numerical value */
- return;
- } /* total discard */
+ /* some digits must be discarded ... */
+ dn->exponent+=discard; /* maintain numerical value */
+ *status|=DEC_Rounded; /* accumulate Rounded status */
+ if (*residue>1) *residue=1; /* previous residue now to right, so reduce */
+
+ if (discard>len) { /* everything, +1, is being discarded */
+ /* guard digit is 0 */
+ /* residue is all the number [NB could be all 0s] */
+ if (*residue<=0) { /* not already positive */
+ count=len; /* avoids D2U */
+ for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { /* found non-0 */
+ *residue=1;
+ break; /* no need to check any others */
+ }
+ }
+ if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
+ *dn->lsu=0; /* coefficient will now be 0 */
+ dn->digits=1; /* .. */
+ return;
+ } /* total discard */
/* partial discard [most common case] */
/* here, at least the first (most significant) discarded digit exists */
- /* spin up the number, noting residue as we pass, until we get to */
- /* the Unit with the first discarded digit. When we get there, */
- /* extract it and remember where we're at */
- count = 0;
- for (up = lsu;; up++)
- {
- count += DECDPUN;
- if (count >= discard)
- break; /* full ones all checked */
- if (*up != 0)
- *residue = 1;
- } /* up */
-
- /* here up -> Unit with discarded digit */
- cut = discard - (count - DECDPUN) - 1;
- if (cut == DECDPUN - 1)
- { /* discard digit is at top */
-#if DECDPUN<=4
- discard1 = QUOT10 (*up, DECDPUN - 1);
- rem = *up - discard1 * powers[DECDPUN - 1];
-#else
- rem = *up % powers[DECDPUN - 1];
- discard1 = *up / powers[DECDPUN - 1];
-#endif
- if (rem != 0)
- *residue = 1;
- up++; /* move to next */
- cut = 0; /* bottom digit of result */
- quot = 0; /* keep a certain compiler happy */
- }
- else
- {
- /* discard digit is in low digit(s), not top digit */
- if (cut == 0)
- quot = *up;
- else /* cut>0 */
- { /* it's not at bottom of Unit */
-#if DECDPUN<=4
- quot = QUOT10 (*up, cut);
- rem = *up - quot * powers[cut];
-#else
- rem = *up % powers[cut];
- quot = *up / powers[cut];
-#endif
- if (rem != 0)
- *residue = 1;
- }
- /* discard digit is now at bottom of quot */
-#if DECDPUN<=4
- temp = (quot * 6554) >> 16; /* fast /10 */
+ /* spin up the number, noting residue during the spin, until get to */
+ /* the Unit with the first discarded digit. When reach it, extract */
+ /* it and remember its position */
+ count=0;
+ for (up=lsu;; up++) {
+ count+=DECDPUN;
+ if (count>=discard) break; /* full ones all checked */
+ if (*up!=0) *residue=1;
+ } /* up */
+
+ /* here up -> Unit with first discarded digit */
+ cut=discard-(count-DECDPUN)-1;
+ if (cut==DECDPUN-1) { /* unit-boundary case (fast) */
+ Unit half=(Unit)powers[DECDPUN]>>1;
+ /* set residue directly */
+ if (*up>=half) {
+ if (*up>half) *residue=7;
+ else *residue+=5; /* add sticky bit */
+ }
+ else { /* <half */
+ if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */
+ }
+ if (set->digits<=0) { /* special for Quantize/Subnormal :-( */
+ *dn->lsu=0; /* .. result is 0 */
+ dn->digits=1; /* .. */
+ }
+ else { /* shift to least */
+ count=set->digits; /* now digits to end up with */
+ dn->digits=count; /* set the new length */
+ up++; /* move to next */
+ /* on unit boundary, so shift-down copy loop is simple */
+ for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
+ *target=*up;
+ }
+ } /* unit-boundary case */
+
+ else { /* discard digit is in low digit(s), and not top digit */
+ uInt discard1; /* first discarded digit */
+ uInt quot, rem; /* for divisions */
+ if (cut==0) quot=*up; /* is at bottom of unit */
+ else /* cut>0 */ { /* it's not at bottom of unit */
+ #if DECDPUN<=4
+ quot=QUOT10(*up, cut);
+ rem=*up-quot*powers[cut];
+ #else
+ rem=*up%powers[cut];
+ quot=*up/powers[cut];
+ #endif
+ if (rem!=0) *residue=1;
+ }
+ /* discard digit is now at bottom of quot */
+ #if DECDPUN<=4
+ temp=(quot*6554)>>16; /* fast /10 */
/* Vowels algorithm here not a win (9 instructions) */
- discard1 = quot - X10 (temp);
- quot = temp;
-#else
- discard1 = quot % 10;
- quot = quot / 10;
-#endif
- cut++; /* update cut */
- }
-
- /* here: up -> Unit of the array with discarded digit */
- /* cut is the division point for each Unit */
- /* quot holds the uncut high-order digits for the current */
- /* Unit, unless cut==0 in which case it's still in *up */
- /* copy the coefficient array to the result number, shifting as we go */
- count = set->digits; /* digits to end up with */
- if (count <= 0)
- { /* special for Rescale/Subnormal :-( */
- *dn->lsu = 0; /* .. result is 0 */
- dn->digits = 1; /* .. */
- }
- else
- { /* shift to least */
- /* [this is similar to decShiftToLeast code, with copy] */
- dn->digits = count; /* set the new length */
- if (cut == 0)
- {
- /* on unit boundary, so simple shift down copy loop suffices */
- for (target = dn->lsu; target < dn->lsu + D2U (count);
- target++, up++)
- {
- *target = *up;
- }
- }
- else
- for (target = dn->lsu;; target++)
- {
- *target = (Unit) quot;
- count -= (DECDPUN - cut);
- if (count <= 0)
- break;
- up++;
- quot = *up;
-#if DECDPUN<=4
- quot = QUOT10 (quot, cut);
- rem = *up - quot * powers[cut];
-#else
- rem = quot % powers[cut];
- quot = quot / powers[cut];
-#endif
- *target = (Unit) (*target + rem * powers[DECDPUN - cut]);
- count -= cut;
- if (count <= 0)
- break;
- }
- } /* shift to least needed */
- dn->exponent += discard; /* maintain numerical value */
-
- /* here, discard1 is the guard digit, and residue is everything else */
- /* [use mapping to accumulate residue safely] */
- *residue += resmap[discard1];
-
- if (*residue != 0)
- *status |= DEC_Inexact; /* record inexactitude */
+ discard1=quot-X10(temp);
+ quot=temp;
+ #else
+ discard1=quot%10;
+ quot=quot/10;
+ #endif
+ /* here, discard1 is the guard digit, and residue is everything */
+ /* else [use mapping array to accumulate residue safely] */
+ *residue+=resmap[discard1];
+ cut++; /* update cut */
+ /* here: up -> Unit of the array with bottom digit */
+ /* cut is the division point for each Unit */
+ /* quot holds the uncut high-order digits for the current unit */
+ if (set->digits<=0) { /* special for Quantize/Subnormal :-( */
+ *dn->lsu=0; /* .. result is 0 */
+ dn->digits=1; /* .. */
+ }
+ else { /* shift to least needed */
+ count=set->digits; /* now digits to end up with */
+ dn->digits=count; /* set the new length */
+ /* shift-copy the coefficient array to the result number */
+ for (target=dn->lsu; ; target++) {
+ *target=(Unit)quot;
+ count-=(DECDPUN-cut);
+ if (count<=0) break;
+ up++;
+ quot=*up;
+ #if DECDPUN<=4
+ quot=QUOT10(quot, cut);
+ rem=*up-quot*powers[cut];
+ #else
+ rem=quot%powers[cut];
+ quot=quot/powers[cut];
+ #endif
+ *target=(Unit)(*target+rem*powers[DECDPUN-cut]);
+ count-=cut;
+ if (count<=0) break;
+ } /* shift-copy loop */
+ } /* shift to least */
+ } /* not unit boundary */
+
+ if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
return;
-}
-
-/* ------------------------------------------------------------------ */
-/* decApplyRound -- apply pending rounding to a number */
-/* */
-/* dn is the number, with space for set->digits digits */
-/* set is the context [for size and rounding mode] */
-/* residue indicates pending rounding, being any accumulated */
-/* guard and sticky information. It may be: */
-/* 6-9: rounding digit is >5 */
-/* 5: rounding digit is exactly half-way */
-/* 1-4: rounding digit is <5 and >0 */
-/* 0: the coefficient is exact */
-/* -1: as 1, but the hidden digits are subtractive, that */
-/* is, of the opposite sign to dn. In this case the */
-/* coefficient must be non-0. */
-/* status is the status accumulator, as usual */
-/* */
+ } /* decSetCoeff */
+
+/* ------------------------------------------------------------------ */
+/* decApplyRound -- apply pending rounding to a number */
+/* */
+/* dn is the number, with space for set->digits digits */
+/* set is the context [for size and rounding mode] */
+/* residue indicates pending rounding, being any accumulated */
+/* guard and sticky information. It may be: */
+/* 6-9: rounding digit is >5 */
+/* 5: rounding digit is exactly half-way */
+/* 1-4: rounding digit is <5 and >0 */
+/* 0: the coefficient is exact */
+/* -1: as 1, but the hidden digits are subtractive, that */
+/* is, of the opposite sign to dn. In this case the */
+/* coefficient must be non-0. This case occurs when */
+/* subtracting a small number (which can be reduced to */
+/* a sticky bit); see decAddOp. */
+/* status is the status accumulator, as usual */
+/* */
/* This routine applies rounding while keeping the length of the */
/* coefficient constant. The exponent and status are unchanged */
-/* except if: */
-/* */
+/* except if: */
+/* */
/* -- the coefficient was increased and is all nines (in which */
-/* case Overflow could occur, and is handled directly here so */
-/* the caller does not need to re-test for overflow) */
-/* */
+/* case Overflow could occur, and is handled directly here so */
+/* the caller does not need to re-test for overflow) */
+/* */
/* -- the coefficient was decreased and becomes all nines (in which */
-/* case Underflow could occur, and is also handled directly). */
-/* */
-/* All fields in dn are updated as required. */
-/* */
+/* case Underflow could occur, and is also handled directly). */
+/* */
+/* All fields in dn are updated as required. */
+/* */
/* ------------------------------------------------------------------ */
-static void
-decApplyRound (decNumber * dn, decContext * set, Int residue, uInt * status)
-{
- Int bump; /* 1 if coefficient needs to be incremented */
- /* -1 if coefficient needs to be decremented */
+static void decApplyRound(decNumber *dn, decContext *set, Int residue,
+ uInt *status) {
+ Int bump; /* 1 if coefficient needs to be incremented */
+ /* -1 if coefficient needs to be decremented */
- if (residue == 0)
- return; /* nothing to apply */
+ if (residue==0) return; /* nothing to apply */
- bump = 0; /* assume a smooth ride */
+ bump=0; /* assume a smooth ride */
/* now decide whether, and how, to round, depending on mode */
- switch (set->round)
- {
- case DEC_ROUND_DOWN:
- {
- /* no change, except if negative residue */
- if (residue < 0)
- bump = -1;
- break;
- } /* r-d */
+ switch (set->round) {
+ case DEC_ROUND_05UP: { /* round zero or five up (for reround) */
+ /* This is the same as DEC_ROUND_DOWN unless there is a */
+ /* positive residue and the lsd of dn is 0 or 5, in which case */
+ /* it is bumped; when residue is <0, the number is therefore */
+ /* bumped down unless the final digit was 1 or 6 (in which */
+ /* case it is bumped down and then up -- a no-op) */
+ Int lsd5=*dn->lsu%5; /* get lsd and quintate */
+ if (residue<0 && lsd5!=1) bump=-1;
+ else if (residue>0 && lsd5==0) bump=1;
+ /* [bump==1 could be applied directly; use common path for clarity] */
+ break;} /* r-05 */
+
+ case DEC_ROUND_DOWN: {
+ /* no change, except if negative residue */
+ if (residue<0) bump=-1;
+ break;} /* r-d */
+
+ case DEC_ROUND_HALF_DOWN: {
+ if (residue>5) bump=1;
+ break;} /* r-h-d */
+
+ case DEC_ROUND_HALF_EVEN: {
+ if (residue>5) bump=1; /* >0.5 goes up */
+ else if (residue==5) { /* exactly 0.5000... */
+ /* 0.5 goes up iff [new] lsd is odd */
+ if (*dn->lsu & 0x01) bump=1;
+ }
+ break;} /* r-h-e */
- case DEC_ROUND_HALF_DOWN:
- {
- if (residue > 5)
- bump = 1;
- break;
- } /* r-h-d */
-
- case DEC_ROUND_HALF_EVEN:
- {
- if (residue > 5)
- bump = 1; /* >0.5 goes up */
- else if (residue == 5)
- { /* exactly 0.5000... */
- /* 0.5 goes up iff [new] lsd is odd */
- if (*dn->lsu & 0x01)
- bump = 1;
- }
- break;
- } /* r-h-e */
+ case DEC_ROUND_HALF_UP: {
+ if (residue>=5) bump=1;
+ break;} /* r-h-u */
- case DEC_ROUND_HALF_UP:
- {
- if (residue >= 5)
- bump = 1;
- break;
- } /* r-h-u */
+ case DEC_ROUND_UP: {
+ if (residue>0) bump=1;
+ break;} /* r-u */
- case DEC_ROUND_UP:
- {
- if (residue > 0)
- bump = 1;
- break;
- } /* r-u */
-
- case DEC_ROUND_CEILING:
- {
- /* same as _UP for positive numbers, and as _DOWN for negatives */
- /* [negative residue cannot occur on 0] */
- if (decNumberIsNegative (dn))
- {
- if (residue < 0)
- bump = -1;
- }
- else
- {
- if (residue > 0)
- bump = 1;
- }
- break;
- } /* r-c */
-
- case DEC_ROUND_FLOOR:
- {
- /* same as _UP for negative numbers, and as _DOWN for positive */
- /* [negative residue cannot occur on 0] */
- if (!decNumberIsNegative (dn))
- {
- if (residue < 0)
- bump = -1;
- }
- else
- {
- if (residue > 0)
- bump = 1;
- }
- break;
- } /* r-f */
+ case DEC_ROUND_CEILING: {
+ /* same as _UP for positive numbers, and as _DOWN for negatives */
+ /* [negative residue cannot occur on 0] */
+ if (decNumberIsNegative(dn)) {
+ if (residue<0) bump=-1;
+ }
+ else {
+ if (residue>0) bump=1;
+ }
+ break;} /* r-c */
- default:
- { /* e.g., DEC_ROUND_MAX */
- *status |= DEC_Invalid_context;
-#if DECTRACE
- printf ("Unknown rounding mode: %d\n", set->round);
-#endif
- break;
- }
- } /* switch */
+ case DEC_ROUND_FLOOR: {
+ /* same as _UP for negative numbers, and as _DOWN for positive */
+ /* [negative residue cannot occur on 0] */
+ if (!decNumberIsNegative(dn)) {
+ if (residue<0) bump=-1;
+ }
+ else {
+ if (residue>0) bump=1;
+ }
+ break;} /* r-f */
+
+ default: { /* e.g., DEC_ROUND_MAX */
+ *status|=DEC_Invalid_context;
+ #if DECTRACE || (DECCHECK && DECVERB)
+ printf("Unknown rounding mode: %d\n", set->round);
+ #endif
+ break;}
+ } /* switch */
/* now bump the number, up or down, if need be */
- if (bump == 0)
- return; /* no action required */
+ if (bump==0) return; /* no action required */
- /* Simply use decUnitAddSub unless we are bumping up and the number */
- /* is all nines. In this special case we set to 1000... and adjust */
- /* the exponent by one (as otherwise we could overflow the array) */
+ /* Simply use decUnitAddSub unless bumping up and the number is */
+ /* all nines. In this special case set to 100... explicitly */
+ /* and adjust the exponent by one (as otherwise could overflow */
+ /* the array) */
/* Similarly handle all-nines result if bumping down. */
- if (bump > 0)
- {
- Unit *up; /* work */
- uInt count = dn->digits; /* digits to be checked */
- for (up = dn->lsu;; up++)
- {
- if (count <= DECDPUN)
- {
- /* this is the last Unit (the msu) */
- if (*up != powers[count] - 1)
- break; /* not still 9s */
- /* here if it, too, is all nines */
- *up = (Unit) powers[count - 1]; /* here 999 -> 100 etc. */
- for (up = up - 1; up >= dn->lsu; up--)
- *up = 0; /* others all to 0 */
- dn->exponent++; /* and bump exponent */
- /* [which, very rarely, could cause Overflow...] */
- if ((dn->exponent + dn->digits) > set->emax + 1)
- {
- decSetOverflow (dn, set, status);
- }
- return; /* done */
- }
- /* a full unit to check, with more to come */
- if (*up != DECDPUNMAX)
- break; /* not still 9s */
- count -= DECDPUN;
- } /* up */
- } /* bump>0 */
- else
- { /* -1 */
- /* here we are lookng for a pre-bump of 1000... (leading 1, */
- /* all other digits zero) */
- Unit *up, *sup; /* work */
- uInt count = dn->digits; /* digits to be checked */
- for (up = dn->lsu;; up++)
- {
- if (count <= DECDPUN)
- {
- /* this is the last Unit (the msu) */
- if (*up != powers[count - 1])
- break; /* not 100.. */
- /* here if we have the 1000... case */
- sup = up; /* save msu pointer */
- *up = (Unit) powers[count] - 1; /* here 100 in msu -> 999 */
- /* others all to all-nines, too */
- for (up = up - 1; up >= dn->lsu; up--)
- *up = (Unit) powers[DECDPUN] - 1;
- dn->exponent--; /* and bump exponent */
-
- /* iff the number was at the subnormal boundary (exponent=etiny) */
- /* then the exponent is now out of range, so it will in fact get */
- /* clamped to etiny and the final 9 dropped. */
- /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
- /* dn->exponent, set->digits); */
- if (dn->exponent + 1 == set->emin - set->digits + 1)
- {
- if (count == 1 && dn->digits == 1)
- *sup = 0; /* here 9 -> 0[.9] */
- else
- {
- *sup = (Unit) powers[count - 1] - 1; /* here 999.. in msu -> 99.. */
- dn->digits--;
- }
- dn->exponent++;
- *status |=
- DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
- }
- return; /* done */
+ if (bump>0) {
+ Unit *up; /* work */
+ uInt count=dn->digits; /* digits to be checked */
+ for (up=dn->lsu; ; up++) {
+ if (count<=DECDPUN) {
+ /* this is the last Unit (the msu) */
+ if (*up!=powers[count]-1) break; /* not still 9s */
+ /* here if it, too, is all nines */
+ *up=(Unit)powers[count-1]; /* here 999 -> 100 etc. */
+ for (up=up-1; up>=dn->lsu; up--) *up=0; /* others all to 0 */
+ dn->exponent++; /* and bump exponent */
+ /* [which, very rarely, could cause Overflow...] */
+ if ((dn->exponent+dn->digits)>set->emax+1) {
+ decSetOverflow(dn, set, status);
+ }
+ return; /* done */
+ }
+ /* a full unit to check, with more to come */
+ if (*up!=DECDPUNMAX) break; /* not still 9s */
+ count-=DECDPUN;
+ } /* up */
+ } /* bump>0 */
+ else { /* -1 */
+ /* here checking for a pre-bump of 1000... (leading 1, all */
+ /* other digits zero) */
+ Unit *up, *sup; /* work */
+ uInt count=dn->digits; /* digits to be checked */
+ for (up=dn->lsu; ; up++) {
+ if (count<=DECDPUN) {
+ /* this is the last Unit (the msu) */
+ if (*up!=powers[count-1]) break; /* not 100.. */
+ /* here if have the 1000... case */
+ sup=up; /* save msu pointer */
+ *up=(Unit)powers[count]-1; /* here 100 in msu -> 999 */
+ /* others all to all-nines, too */
+ for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
+ dn->exponent--; /* and bump exponent */
+
+ /* iff the number was at the subnormal boundary (exponent=etiny) */
+ /* then the exponent is now out of range, so it will in fact get */
+ /* clamped to etiny and the final 9 dropped. */
+ /* printf(">> emin=%d exp=%d sdig=%d\n", set->emin, */
+ /* dn->exponent, set->digits); */
+ if (dn->exponent+1==set->emin-set->digits+1) {
+ if (count==1 && dn->digits==1) *sup=0; /* here 9 -> 0[.9] */
+ else {
+ *sup=(Unit)powers[count-1]-1; /* here 999.. in msu -> 99.. */
+ dn->digits--;
}
+ dn->exponent++;
+ *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
+ }
+ return; /* done */
+ }
- /* a full unit to check, with more to come */
- if (*up != 0)
- break; /* not still 0s */
- count -= DECDPUN;
- } /* up */
+ /* a full unit to check, with more to come */
+ if (*up!=0) break; /* not still 0s */
+ count-=DECDPUN;
+ } /* up */
- } /* bump<0 */
+ } /* bump<0 */
/* Actual bump needed. Do it. */
- decUnitAddSub (dn->lsu, D2U (dn->digits), one, 1, 0, dn->lsu, bump);
-}
+ decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
+ } /* decApplyRound */
#if DECSUBSET
/* ------------------------------------------------------------------ */
-/* decFinish -- finish processing a number */
-/* */
-/* dn is the number */
-/* set is the context */
-/* residue is the rounding accumulator (as in decApplyRound) */
-/* status is the accumulator */
-/* */
-/* This finishes off the current number by: */
-/* 1. If not extended: */
-/* a. Converting a zero result to clean '0' */
-/* b. Reducing positive exponents to 0, if would fit in digits */
-/* 2. Checking for overflow and subnormals (always) */
-/* Note this is just Finalize when no subset arithmetic. */
-/* All fields are updated as required. */
-/* ------------------------------------------------------------------ */
-static void
-decFinish (decNumber * dn, decContext * set, Int * residue, uInt * status)
-{
- if (!set->extended)
- {
- if ISZERO
- (dn)
- { /* value is zero */
- dn->exponent = 0; /* clean exponent .. */
- dn->bits = 0; /* .. and sign */
- return; /* no error possible */
- }
- if (dn->exponent >= 0)
- { /* non-negative exponent */
- /* >0; reduce to integer if possible */
- if (set->digits >= (dn->exponent + dn->digits))
- {
- dn->digits = decShiftToMost (dn->lsu, dn->digits, dn->exponent);
- dn->exponent = 0;
- }
+/* decFinish -- finish processing a number */
+/* */
+/* dn is the number */
+/* set is the context */
+/* residue is the rounding accumulator (as in decApplyRound) */
+/* status is the accumulator */
+/* */
+/* This finishes off the current number by: */
+/* 1. If not extended: */
+/* a. Converting a zero result to clean '0' */
+/* b. Reducing positive exponents to 0, if would fit in digits */
+/* 2. Checking for overflow and subnormals (always) */
+/* Note this is just Finalize when no subset arithmetic. */
+/* All fields are updated as required. */
+/* ------------------------------------------------------------------ */
+static void decFinish(decNumber *dn, decContext *set, Int *residue,
+ uInt *status) {
+ if (!set->extended) {
+ if ISZERO(dn) { /* value is zero */
+ dn->exponent=0; /* clean exponent .. */
+ dn->bits=0; /* .. and sign */
+ return; /* no error possible */
+ }
+ if (dn->exponent>=0) { /* non-negative exponent */
+ /* >0; reduce to integer if possible */
+ if (set->digits >= (dn->exponent+dn->digits)) {
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
+ dn->exponent=0;
}
- } /* !extended */
+ }
+ } /* !extended */
- decFinalize (dn, set, residue, status);
-}
+ decFinalize(dn, set, residue, status);
+ } /* decFinish */
#endif
/* ------------------------------------------------------------------ */
-/* decFinalize -- final check, clamp, and round of a number */
-/* */
-/* dn is the number */
-/* set is the context */
-/* residue is the rounding accumulator (as in decApplyRound) */
-/* status is the status accumulator */
-/* */
+/* decFinalize -- final check, clamp, and round of a number */
+/* */
+/* dn is the number */
+/* set is the context */
+/* residue is the rounding accumulator (as in decApplyRound) */
+/* status is the status accumulator */
+/* */
/* This finishes off the current number by checking for subnormal */
/* results, applying any pending rounding, checking for overflow, */
-/* and applying any clamping. */
+/* and applying any clamping. */
/* Underflow and overflow conditions are raised as appropriate. */
-/* All fields are updated as required. */
+/* All fields are updated as required. */
/* ------------------------------------------------------------------ */
-static void
-decFinalize (decNumber * dn, decContext * set, Int * residue, uInt * status)
-{
- Int shift; /* shift needed if clamping */
+static void decFinalize(decNumber *dn, decContext *set, Int *residue,
+ uInt *status) {
+ Int shift; /* shift needed if clamping */
+ Int tinyexp=set->emin-dn->digits+1; /* precalculate subnormal boundary */
- /* We have to be careful when checking the exponent as the adjusted */
- /* exponent could overflow 31 bits [because it may already be up */
- /* to twice the expected]. */
+ /* Must be careful, here, when checking the exponent as the */
+ /* adjusted exponent could overflow 31 bits [because it may already */
+ /* be up to twice the expected]. */
- /* First test for subnormal. This must be done before any final */
+ /* First test for subnormal. This must be done before any final */
/* round as the result could be rounded to Nmin or 0. */
- if (dn->exponent < 0 /* negative exponent */
- && (dn->exponent < set->emin - dn->digits + 1))
- {
+ if (dn->exponent<=tinyexp) { /* prefilter */
+ Int comp;
+ decNumber nmin;
+ /* A very nasty case here is dn == Nmin and residue<0 */
+ if (dn->exponent<tinyexp) {
/* Go handle subnormals; this will apply round if needed. */
- decSetSubnormal (dn, set, residue, status);
+ decSetSubnormal(dn, set, residue, status);
+ return;
+ }
+ /* Equals case: only subnormal if dn=Nmin and negative residue */
+ decNumberZero(&nmin);
+ nmin.lsu[0]=1;
+ nmin.exponent=set->emin;
+ comp=decCompare(dn, &nmin, 1); /* (signless compare) */
+ if (comp==BADINT) { /* oops */
+ *status|=DEC_Insufficient_storage; /* abandon... */
+ return;
+ }
+ if (*residue<0 && comp==0) { /* neg residue and dn==Nmin */
+ decApplyRound(dn, set, *residue, status); /* might force down */
+ decSetSubnormal(dn, set, residue, status);
return;
+ }
}
/* now apply any pending round (this could raise overflow). */
- if (*residue != 0)
- decApplyRound (dn, set, *residue, status);
+ if (*residue!=0) decApplyRound(dn, set, *residue, status);
/* Check for overflow [redundant in the 'rare' case] or clamp */
- if (dn->exponent <= set->emax - set->digits + 1)
- return; /* neither needed */
+ if (dn->exponent<=set->emax-set->digits+1) return; /* neither needed */
- /* here when we might have an overflow or clamp to do */
- if (dn->exponent > set->emax - dn->digits + 1)
- { /* too big */
- decSetOverflow (dn, set, status);
- return;
+
+ /* here when might have an overflow or clamp to do */
+ if (dn->exponent>set->emax-dn->digits+1) { /* too big */
+ decSetOverflow(dn, set, status);
+ return;
}
/* here when the result is normal but in clamp range */
- if (!set->clamp)
- return;
+ if (!set->clamp) return;
- /* here when we need to apply the IEEE exponent clamp (fold-down) */
- shift = dn->exponent - (set->emax - set->digits + 1);
+ /* here when need to apply the IEEE exponent clamp (fold-down) */
+ shift=dn->exponent-(set->emax-set->digits+1);
/* shift coefficient (if non-zero) */
- if (!ISZERO (dn))
- {
- dn->digits = decShiftToMost (dn->lsu, dn->digits, shift);
+ if (!ISZERO(dn)) {
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
}
- dn->exponent -= shift; /* adjust the exponent to match */
- *status |= DEC_Clamped; /* and record the dirty deed */
+ dn->exponent-=shift; /* adjust the exponent to match */
+ *status|=DEC_Clamped; /* and record the dirty deed */
return;
-}
+ } /* decFinalize */
/* ------------------------------------------------------------------ */
-/* decSetOverflow -- set number to proper overflow value */
-/* */
-/* dn is the number (used for sign [only] and result) */
-/* set is the context [used for the rounding mode] */
-/* status contains the current status to be updated */
-/* */
-/* This sets the sign of a number and sets its value to either */
+/* decSetOverflow -- set number to proper overflow value */
+/* */
+/* dn is the number (used for sign [only] and result) */
+/* set is the context [used for the rounding mode, etc.] */
+/* status contains the current status to be updated */
+/* */
+/* This sets the sign of a number and sets its value to either */
/* Infinity or the maximum finite value, depending on the sign of */
-/* dn and therounding mode, following IEEE 854 rules. */
-/* ------------------------------------------------------------------ */
-static void
-decSetOverflow (decNumber * dn, decContext * set, uInt * status)
-{
- Flag needmax = 0; /* result is maximum finite value */
- uByte sign = dn->bits & DECNEG; /* clean and save sign bit */
-
- if (ISZERO (dn))
- { /* zero does not overflow magnitude */
- Int emax = set->emax; /* limit value */
- if (set->clamp)
- emax -= set->digits - 1; /* lower if clamping */
- if (dn->exponent > emax)
- { /* clamp required */
- dn->exponent = emax;
- *status |= DEC_Clamped;
- }
- return;
+/* dn and the rounding mode, following IEEE 754 rules. */
+/* ------------------------------------------------------------------ */
+static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
+ Flag needmax=0; /* result is maximum finite value */
+ uByte sign=dn->bits&DECNEG; /* clean and save sign bit */
+
+ if (ISZERO(dn)) { /* zero does not overflow magnitude */
+ Int emax=set->emax; /* limit value */
+ if (set->clamp) emax-=set->digits-1; /* lower if clamping */
+ if (dn->exponent>emax) { /* clamp required */
+ dn->exponent=emax;
+ *status|=DEC_Clamped;
+ }
+ return;
}
- decNumberZero (dn);
- switch (set->round)
- {
- case DEC_ROUND_DOWN:
- {
- needmax = 1; /* never Infinity */
- break;
- } /* r-d */
- case DEC_ROUND_CEILING:
- {
- if (sign)
- needmax = 1; /* Infinity if non-negative */
- break;
- } /* r-c */
- case DEC_ROUND_FLOOR:
- {
- if (!sign)
- needmax = 1; /* Infinity if negative */
- break;
- } /* r-f */
- default:
- break; /* Infinity in all other cases */
+ decNumberZero(dn);
+ switch (set->round) {
+ case DEC_ROUND_DOWN: {
+ needmax=1; /* never Infinity */
+ break;} /* r-d */
+ case DEC_ROUND_05UP: {
+ needmax=1; /* never Infinity */
+ break;} /* r-05 */
+ case DEC_ROUND_CEILING: {
+ if (sign) needmax=1; /* Infinity if non-negative */
+ break;} /* r-c */
+ case DEC_ROUND_FLOOR: {
+ if (!sign) needmax=1; /* Infinity if negative */
+ break;} /* r-f */
+ default: break; /* Infinity in all other cases */
}
- if (needmax)
- {
- Unit *up; /* work */
- Int count = set->digits; /* nines to add */
- dn->digits = count;
- /* fill in all nines to set maximum value */
- for (up = dn->lsu;; up++)
- {
- if (count > DECDPUN)
- *up = DECDPUNMAX; /* unit full o'nines */
- else
- { /* this is the msu */
- *up = (Unit) (powers[count] - 1);
- break;
- }
- count -= DECDPUN; /* we filled those digits */
- } /* up */
- dn->bits = sign; /* sign */
- dn->exponent = set->emax - set->digits + 1;
+ if (needmax) {
+ decSetMaxValue(dn, set);
+ dn->bits=sign; /* set sign */
}
- else
- dn->bits = sign | DECINF; /* Value is +/-Infinity */
- *status |= DEC_Overflow | DEC_Inexact | DEC_Rounded;
-}
+ else dn->bits=sign|DECINF; /* Value is +/-Infinity */
+ *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
+ } /* decSetOverflow */
+
+/* ------------------------------------------------------------------ */
+/* decSetMaxValue -- set number to +Nmax (maximum normal value) */
+/* */
+/* dn is the number to set */
+/* set is the context [used for digits and emax] */
+/* */
+/* This sets the number to the maximum positive value. */
+/* ------------------------------------------------------------------ */
+static void decSetMaxValue(decNumber *dn, decContext *set) {
+ Unit *up; /* work */
+ Int count=set->digits; /* nines to add */
+ dn->digits=count;
+ /* fill in all nines to set maximum value */
+ for (up=dn->lsu; ; up++) {
+ if (count>DECDPUN) *up=DECDPUNMAX; /* unit full o'nines */
+ else { /* this is the msu */
+ *up=(Unit)(powers[count]-1);
+ break;
+ }
+ count-=DECDPUN; /* filled those digits */
+ } /* up */
+ dn->bits=0; /* + sign */
+ dn->exponent=set->emax-set->digits+1;
+ } /* decSetMaxValue */
/* ------------------------------------------------------------------ */
-/* decSetSubnormal -- process value whose exponent is <Emin */
-/* */
+/* decSetSubnormal -- process value whose exponent is <Emin */
+/* */
/* dn is the number (used as input as well as output; it may have */
-/* an allowed subnormal value, which may need to be rounded) */
-/* set is the context [used for the rounding mode] */
-/* residue is any pending residue */
-/* status contains the current status to be updated */
-/* */
-/* If subset mode, set result to zero and set Underflow flags. */
-/* */
+/* an allowed subnormal value, which may need to be rounded) */
+/* set is the context [used for the rounding mode] */
+/* residue is any pending residue */
+/* status contains the current status to be updated */
+/* */
+/* If subset mode, set result to zero and set Underflow flags. */
+/* */
/* Value may be zero with a low exponent; this does not set Subnormal */
-/* but the exponent will be clamped to Etiny. */
-/* */
-/* Otherwise ensure exponent is not out of range, and round as */
-/* necessary. Underflow is set if the result is Inexact. */
-/* ------------------------------------------------------------------ */
-static void
-decSetSubnormal (decNumber * dn, decContext * set, Int * residue,
- uInt * status)
-{
- decContext workset; /* work */
- Int etiny, adjust; /* .. */
+/* but the exponent will be clamped to Etiny. */
+/* */
+/* Otherwise ensure exponent is not out of range, and round as */
+/* necessary. Underflow is set if the result is Inexact. */
+/* ------------------------------------------------------------------ */
+static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
+ uInt *status) {
+ decContext workset; /* work */
+ Int etiny, adjust; /* .. */
-#if DECSUBSET
+ #if DECSUBSET
/* simple set to zero and 'hard underflow' for subset */
- if (!set->extended)
- {
- decNumberZero (dn);
- /* always full overflow */
- *status |= DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
- return;
+ if (!set->extended) {
+ decNumberZero(dn);
+ /* always full overflow */
+ *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
+ return;
}
-#endif
+ #endif
/* Full arithmetic -- allow subnormals, rounded to minimum exponent */
/* (Etiny) if needed */
- etiny = set->emin - (set->digits - 1); /* smallest allowed exponent */
-
- if ISZERO
- (dn)
- { /* value is zero */
- /* residue can never be non-zero here */
-#if DECCHECK
- if (*residue != 0)
- {
- printf ("++ Subnormal 0 residue %d\n", *residue);
- *status |= DEC_Invalid_operation;
- }
-#endif
- if (dn->exponent < etiny)
- { /* clamp required */
- dn->exponent = etiny;
- *status |= DEC_Clamped;
+ etiny=set->emin-(set->digits-1); /* smallest allowed exponent */
+
+ if ISZERO(dn) { /* value is zero */
+ /* residue can never be non-zero here */
+ #if DECCHECK
+ if (*residue!=0) {
+ printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
+ *status|=DEC_Invalid_operation;
}
- return;
+ #endif
+ if (dn->exponent<etiny) { /* clamp required */
+ dn->exponent=etiny;
+ *status|=DEC_Clamped;
+ }
+ return;
}
- *status |= DEC_Subnormal; /* we have a non-zero subnormal */
-
- adjust = etiny - dn->exponent; /* calculate digits to remove */
- if (adjust <= 0)
- { /* not out of range; unrounded */
- /* residue can never be non-zero here, so fast-path out */
-#if DECCHECK
- if (*residue != 0)
- {
- printf ("++ Subnormal no-adjust residue %d\n", *residue);
- *status |= DEC_Invalid_operation;
- }
-#endif
- /* it may already be inexact (from setting the coefficient) */
- if (*status & DEC_Inexact)
- *status |= DEC_Underflow;
- return;
+ *status|=DEC_Subnormal; /* have a non-zero subnormal */
+ adjust=etiny-dn->exponent; /* calculate digits to remove */
+ if (adjust<=0) { /* not out of range; unrounded */
+ /* residue can never be non-zero here, except in the Nmin-residue */
+ /* case (which is a subnormal result), so can take fast-path here */
+ /* it may already be inexact (from setting the coefficient) */
+ if (*status&DEC_Inexact) *status|=DEC_Underflow;
+ return;
}
- /* adjust>0. we need to rescale the result so exponent becomes Etiny */
+ /* adjust>0, so need to rescale the result so exponent becomes Etiny */
/* [this code is similar to that in rescale] */
- workset = *set; /* clone rounding, etc. */
- workset.digits = dn->digits - adjust; /* set requested length */
- workset.emin -= adjust; /* and adjust emin to match */
+ workset=*set; /* clone rounding, etc. */
+ workset.digits=dn->digits-adjust; /* set requested length */
+ workset.emin-=adjust; /* and adjust emin to match */
/* [note that the latter can be <1, here, similar to Rescale case] */
- decSetCoeff (dn, &workset, dn->lsu, dn->digits, residue, status);
- decApplyRound (dn, &workset, *residue, status);
+ decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
+ decApplyRound(dn, &workset, *residue, status);
- /* Use 754R/854 default rule: Underflow is set iff Inexact */
+ /* Use 754 default rule: Underflow is set iff Inexact */
/* [independent of whether trapped] */
- if (*status & DEC_Inexact)
- *status |= DEC_Underflow;
-
- /* if we rounded up a 999s case, exponent will be off by one; adjust */
- /* back if so [it will fit, because we shortened] */
- if (dn->exponent > etiny)
- {
- dn->digits = decShiftToMost (dn->lsu, dn->digits, 1);
- dn->exponent--; /* (re)adjust the exponent. */
+ if (*status&DEC_Inexact) *status|=DEC_Underflow;
+
+ /* if rounded up a 999s case, exponent will be off by one; adjust */
+ /* back if so [it will fit, because it was shortened earlier] */
+ if (dn->exponent>etiny) {
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
+ dn->exponent--; /* (re)adjust the exponent. */
}
-}
-/* ------------------------------------------------------------------ */
-/* decGetInt -- get integer from a number */
-/* */
-/* dn is the number [which will not be altered] */
-/* set is the context [requested digits], subset only */
-/* returns the converted integer, or BADINT if error */
-/* */
+ /* if rounded to zero, it is by definition clamped... */
+ if (ISZERO(dn)) *status|=DEC_Clamped;
+ } /* decSetSubnormal */
+
+/* ------------------------------------------------------------------ */
+/* decCheckMath - check entry conditions for a math function */
+/* */
+/* This checks the context and the operand */
+/* */
+/* rhs is the operand to check */
+/* set is the context to check */
+/* status is unchanged if both are good */
+/* */
+/* returns non-zero if status is changed, 0 otherwise */
+/* */
+/* Restrictions enforced: */
+/* */
+/* digits, emax, and -emin in the context must be less than */
+/* DEC_MAX_MATH (999999), and A must be within these bounds if */
+/* non-zero. Invalid_operation is set in the status if a */
+/* restriction is violated. */
+/* ------------------------------------------------------------------ */
+static uInt decCheckMath(const decNumber *rhs, decContext *set,
+ uInt *status) {
+ uInt save=*status; /* record */
+ if (set->digits>DEC_MAX_MATH
+ || set->emax>DEC_MAX_MATH
+ || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
+ else if ((rhs->digits>DEC_MAX_MATH
+ || rhs->exponent+rhs->digits>DEC_MAX_MATH+1
+ || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
+ && !ISZERO(rhs)) *status|=DEC_Invalid_operation;
+ return (*status!=save);
+ } /* decCheckMath */
+
+/* ------------------------------------------------------------------ */
+/* decGetInt -- get integer from a number */
+/* */
+/* dn is the number [which will not be altered] */
+/* */
+/* returns one of: */
+/* BADINT if there is a non-zero fraction */
+/* the converted integer */
+/* BIGEVEN if the integer is even and magnitude > 2*10**9 */
+/* BIGODD if the integer is odd and magnitude > 2*10**9 */
+/* */
/* This checks and gets a whole number from the input decNumber. */
-/* The magnitude of the integer must be <2^31. */
-/* Any discarded fractional part must be 0. */
-/* If subset it must also fit in set->digits */
+/* The sign can be determined from dn by the caller when BIGEVEN or */
+/* BIGODD is returned. */
/* ------------------------------------------------------------------ */
-#if DECSUBSET
-static Int
-decGetInt (decNumber * dn, decContext * set)
-{
-#else
-static Int
-decGetInt (decNumber * dn)
-{
-#endif
- Int theInt; /* result accumulator */
- Unit *up; /* work */
- Int got; /* digits (real or not) processed */
- Int ilength = dn->digits + dn->exponent; /* integral length */
+static Int decGetInt(const decNumber *dn) {
+ Int theInt; /* result accumulator */
+ const Unit *up; /* work */
+ Int got; /* digits (real or not) processed */
+ Int ilength=dn->digits+dn->exponent; /* integral length */
+ Flag neg=decNumberIsNegative(dn); /* 1 if -ve */
/* The number must be an integer that fits in 10 digits */
/* Assert, here, that 10 is enough for any rescale Etiny */
-#if DEC_MAX_EMAX > 999999999
-#error GetInt may need updating [for Emax]
-#endif
-#if DEC_MIN_EMIN < -999999999
-#error GetInt may need updating [for Emin]
-#endif
- if (ISZERO (dn))
- return 0; /* zeros are OK, with any exponent */
- if (ilength > 10)
- return BADINT; /* always too big */
-#if DECSUBSET
- if (!set->extended && ilength > set->digits)
- return BADINT;
-#endif
-
- up = dn->lsu; /* ready for lsu */
- theInt = 0; /* ready to accumulate */
- if (dn->exponent >= 0)
- { /* relatively easy */
- /* no fractional part [usual]; allow for positive exponent */
- got = dn->exponent;
+ #if DEC_MAX_EMAX > 999999999
+ #error GetInt may need updating [for Emax]
+ #endif
+ #if DEC_MIN_EMIN < -999999999
+ #error GetInt may need updating [for Emin]
+ #endif
+ if (ISZERO(dn)) return 0; /* zeros are OK, with any exponent */
+
+ up=dn->lsu; /* ready for lsu */
+ theInt=0; /* ready to accumulate */
+ if (dn->exponent>=0) { /* relatively easy */
+ /* no fractional part [usual]; allow for positive exponent */
+ got=dn->exponent;
}
- else
- { /* -ve exponent; some fractional part to check and discard */
- Int count = -dn->exponent; /* digits to discard */
- /* spin up whole units until we get to the Unit with the unit digit */
- for (; count >= DECDPUN; up++)
- {
- if (*up != 0)
- return BADINT; /* non-zero Unit to discard */
- count -= DECDPUN;
- }
- if (count == 0)
- got = 0; /* [a multiple of DECDPUN] */
- else
- { /* [not multiple of DECDPUN] */
- Int rem; /* work */
- /* slice off fraction digits and check for non-zero */
-#if DECDPUN<=4
- theInt = QUOT10 (*up, count);
- rem = *up - theInt * powers[count];
-#else
- rem = *up % powers[count]; /* slice off discards */
- theInt = *up / powers[count];
-#endif
- if (rem != 0)
- return BADINT; /* non-zero fraction */
- /* OK, we're good */
- got = DECDPUN - count; /* number of digits so far */
- up++; /* ready for next */
- }
+ else { /* -ve exponent; some fractional part to check and discard */
+ Int count=-dn->exponent; /* digits to discard */
+ /* spin up whole units until reach the Unit with the unit digit */
+ for (; count>=DECDPUN; up++) {
+ if (*up!=0) return BADINT; /* non-zero Unit to discard */
+ count-=DECDPUN;
+ }
+ if (count==0) got=0; /* [a multiple of DECDPUN] */
+ else { /* [not multiple of DECDPUN] */
+ Int rem; /* work */
+ /* slice off fraction digits and check for non-zero */
+ #if DECDPUN<=4
+ theInt=QUOT10(*up, count);
+ rem=*up-theInt*powers[count];
+ #else
+ rem=*up%powers[count]; /* slice off discards */
+ theInt=*up/powers[count];
+ #endif
+ if (rem!=0) return BADINT; /* non-zero fraction */
+ /* it looks good */
+ got=DECDPUN-count; /* number of digits so far */
+ up++; /* ready for next */
+ }
+ }
+ /* now it's known there's no fractional part */
+
+ /* tricky code now, to accumulate up to 9.3 digits */
+ if (got==0) {theInt=*up; got+=DECDPUN; up++;} /* ensure lsu is there */
+
+ if (ilength<11) {
+ Int save=theInt;
+ /* collect any remaining unit(s) */
+ for (; got<ilength; up++) {
+ theInt+=*up*powers[got];
+ got+=DECDPUN;
+ }
+ if (ilength==10) { /* need to check for wrap */
+ if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
+ /* [that test also disallows the BADINT result case] */
+ else if (neg && theInt>1999999997) ilength=11;
+ else if (!neg && theInt>999999999) ilength=11;
+ if (ilength==11) theInt=save; /* restore correct low bit */
+ }
}
- /* collect the rest */
- for (; got < ilength; up++)
- {
- theInt += *up * powers[got];
- got += DECDPUN;
+
+ if (ilength>10) { /* too big */
+ if (theInt&1) return BIGODD; /* bottom bit 1 */
+ return BIGEVEN; /* bottom bit 0 */
}
- if ((ilength == 10) /* check no wrap */
- && (theInt / (Int) powers[got - DECDPUN] != *(up - 1)))
- return BADINT;
- /* [that test also disallows the BADINT result case] */
-
- /* apply any sign and return */
- if (decNumberIsNegative (dn))
- theInt = -theInt;
+
+ if (neg) theInt=-theInt; /* apply sign */
return theInt;
-}
-
-/* ------------------------------------------------------------------ */
-/* decStrEq -- caseless comparison of strings */
-/* */
-/* str1 is one of the strings to compare */
-/* str2 is the other */
-/* */
-/* returns 1 if strings caseless-compare equal, 0 otherwise */
-/* */
-/* Note that the strings must be the same length if they are to */
-/* compare equal; there is no padding. */
-/* ------------------------------------------------------------------ */
-/* [strcmpi is not in ANSI C] */
-static Flag
-decStrEq (const char *str1, const char *str2)
-{
- for (;; str1++, str2++)
- {
- if (*str1 == *str2)
- {
- if (*str1 == '\0')
- break;
- }
- else
- {
- if (tolower (*str1) != tolower (*str2))
- return 0;
- }
- } /* stepping */
+ } /* decGetInt */
+
+/* ------------------------------------------------------------------ */
+/* decDecap -- decapitate the coefficient of a number */
+/* */
+/* dn is the number to be decapitated */
+/* drop is the number of digits to be removed from the left of dn; */
+/* this must be <= dn->digits (if equal, the coefficient is */
+/* set to 0) */
+/* */
+/* Returns dn; dn->digits will be <= the initial digits less drop */
+/* (after removing drop digits there may be leading zero digits */
+/* which will also be removed). Only dn->lsu and dn->digits change. */
+/* ------------------------------------------------------------------ */
+static decNumber *decDecap(decNumber *dn, Int drop) {
+ Unit *msu; /* -> target cut point */
+ Int cut; /* work */
+ if (drop>=dn->digits) { /* losing the whole thing */
+ #if DECCHECK
+ if (drop>dn->digits)
+ printf("decDecap called with drop>digits [%ld>%ld]\n",
+ (LI)drop, (LI)dn->digits);
+ #endif
+ dn->lsu[0]=0;
+ dn->digits=1;
+ return dn;
+ }
+ msu=dn->lsu+D2U(dn->digits-drop)-1; /* -> likely msu */
+ cut=MSUDIGITS(dn->digits-drop); /* digits to be in use in msu */
+ if (cut!=DECDPUN) *msu%=powers[cut]; /* clear left digits */
+ /* that may have left leading zero digits, so do a proper count... */
+ dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
+ return dn;
+ } /* decDecap */
+
+/* ------------------------------------------------------------------ */
+/* decBiStr -- compare string with pairwise options */
+/* */
+/* targ is the string to compare */
+/* str1 is one of the strings to compare against (length may be 0) */
+/* str2 is the other; it must be the same length as str1 */
+/* */
+/* returns 1 if strings compare equal, (that is, it is the same */
+/* length as str1 and str2, and each character of targ is in either */
+/* str1 or str2 in the corresponding position), or 0 otherwise */
+/* */
+/* This is used for generic caseless compare, including the awkward */
+/* case of the Turkish dotted and dotless Is. Use as (for example): */
+/* if (decBiStr(test, "mike", "MIKE")) ... */
+/* ------------------------------------------------------------------ */
+static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
+ for (;;targ++, str1++, str2++) {
+ if (*targ!=*str1 && *targ!=*str2) return 0;
+ /* *targ has a match in one (or both, if terminator) */
+ if (*targ=='\0') break;
+ } /* forever */
return 1;
-}
-
-/* ------------------------------------------------------------------ */
-/* decNaNs -- handle NaN operand or operands */
-/* */
-/* res is the result number */
-/* lhs is the first operand */
-/* rhs is the second operand, or NULL if none */
-/* status contains the current status */
-/* returns res in case convenient */
-/* */
+ } /* decBiStr */
+
+/* ------------------------------------------------------------------ */
+/* decNaNs -- handle NaN operand or operands */
+/* */
+/* res is the result number */
+/* lhs is the first operand */
+/* rhs is the second operand, or NULL if none */
+/* context is used to limit payload length */
+/* status contains the current status */
+/* returns res in case convenient */
+/* */
/* Called when one or both operands is a NaN, and propagates the */
/* appropriate result to res. When an sNaN is found, it is changed */
-/* to a qNaN and Invalid operation is set. */
+/* to a qNaN and Invalid operation is set. */
/* ------------------------------------------------------------------ */
-static decNumber *
-decNaNs (decNumber * res, decNumber * lhs, decNumber * rhs, uInt * status)
-{
+static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set,
+ uInt *status) {
/* This decision tree ends up with LHS being the source pointer, */
/* and status updated if need be */
if (lhs->bits & DECSNAN)
- *status |= DEC_Invalid_operation | DEC_sNaN;
- else if (rhs == NULL);
- else if (rhs->bits & DECSNAN)
- {
- lhs = rhs;
- *status |= DEC_Invalid_operation | DEC_sNaN;
+ *status|=DEC_Invalid_operation | DEC_sNaN;
+ else if (rhs==NULL);
+ else if (rhs->bits & DECSNAN) {
+ lhs=rhs;
+ *status|=DEC_Invalid_operation | DEC_sNaN;
}
- else if (lhs->bits & DECNAN);
- else
- lhs = rhs;
-
- decNumberCopy (res, lhs);
- res->bits &= ~DECSNAN; /* convert any sNaN to NaN, while */
- res->bits |= DECNAN; /* .. preserving sign */
- res->exponent = 0; /* clean exponent */
- /* [coefficient was copied] */
+ else if (lhs->bits & DECNAN);
+ else lhs=rhs;
+
+ /* propagate the payload */
+ if (lhs->digits<=set->digits) decNumberCopy(res, lhs); /* easy */
+ else { /* too long */
+ const Unit *ul;
+ Unit *ur, *uresp1;
+ /* copy safe number of units, then decapitate */
+ res->bits=lhs->bits; /* need sign etc. */
+ uresp1=res->lsu+D2U(set->digits);
+ for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
+ res->digits=D2U(set->digits)*DECDPUN;
+ /* maybe still too long */
+ if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
+ }
+
+ res->bits&=~DECSNAN; /* convert any sNaN to NaN, while */
+ res->bits|=DECNAN; /* .. preserving sign */
+ res->exponent=0; /* clean exponent */
+ /* [coefficient was copied/decapitated] */
return res;
-}
+ } /* decNaNs */
/* ------------------------------------------------------------------ */
-/* decStatus -- apply non-zero status */
-/* */
-/* dn is the number to set if error */
-/* status contains the current status (not yet in context) */
-/* set is the context */
-/* */
+/* decStatus -- apply non-zero status */
+/* */
+/* dn is the number to set if error */
+/* status contains the current status (not yet in context) */
+/* set is the context */
+/* */
/* If the status is an error status, the number is set to a NaN, */
/* unless the error was an overflow, divide-by-zero, or underflow, */
-/* in which case the number will have already been set. */
-/* */
+/* in which case the number will have already been set. */
+/* */
/* The context status is then updated with the new status. Note that */
/* this may raise a signal, so control may never return from this */
/* routine (hence resources must be recovered before it is called). */
/* ------------------------------------------------------------------ */
-static void
-decStatus (decNumber * dn, uInt status, decContext * set)
-{
- if (status & DEC_NaNs)
- { /* error status -> NaN */
- /* if cause was an sNaN, clear and propagate [NaN is already set up] */
- if (status & DEC_sNaN)
- status &= ~DEC_sNaN;
- else
- {
- decNumberZero (dn); /* other error: clean throughout */
- dn->bits = DECNAN; /* and make a quiet NaN */
- }
+static void decStatus(decNumber *dn, uInt status, decContext *set) {
+ if (status & DEC_NaNs) { /* error status -> NaN */
+ /* if cause was an sNaN, clear and propagate [NaN is already set up] */
+ if (status & DEC_sNaN) status&=~DEC_sNaN;
+ else {
+ decNumberZero(dn); /* other error: clean throughout */
+ dn->bits=DECNAN; /* and make a quiet NaN */
+ }
}
- decContextSetStatus (set, status);
+ decContextSetStatus(set, status); /* [may not return] */
return;
-}
+ } /* decStatus */
/* ------------------------------------------------------------------ */
-/* decGetDigits -- count digits in a Units array */
-/* */
-/* uar is the Unit array holding the number [this is often an */
-/* accumulator of some sort] */
-/* len is the length of the array in units */
-/* */
-/* returns the number of (significant) digits in the array */
-/* */
+/* decGetDigits -- count digits in a Units array */
+/* */
+/* uar is the Unit array holding the number (this is often an */
+/* accumulator of some sort) */
+/* len is the length of the array in units [>=1] */
+/* */
+/* returns the number of (significant) digits in the array */
+/* */
/* All leading zeros are excluded, except the last if the array has */
-/* only zero Units. */
+/* only zero Units. */
/* ------------------------------------------------------------------ */
/* This may be called twice during some operations. */
-static Int
-decGetDigits (Unit * uar, Int len)
-{
- Unit *up = uar + len - 1; /* -> msu */
- Int digits = len * DECDPUN; /* maximum possible digits */
- uInt const *pow; /* work */
-
- for (; up >= uar; up--)
- {
- digits -= DECDPUN;
- if (*up == 0)
- { /* unit is 0 */
- if (digits != 0)
- continue; /* more to check */
- /* all units were 0 */
- digits++; /* .. so bump digits to 1 */
- break;
- }
- /* found the first non-zero Unit */
- digits++;
- if (*up < 10)
- break; /* fastpath 1-9 */
- digits++;
- for (pow = &powers[2]; *up >= *pow; pow++)
- digits++;
- break;
- } /* up */
-
+static Int decGetDigits(Unit *uar, Int len) {
+ Unit *up=uar+(len-1); /* -> msu */
+ Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */
+ #if DECDPUN>4
+ uInt const *pow; /* work */
+ #endif
+ /* (at least 1 in final msu) */
+ #if DECCHECK
+ if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
+ #endif
+
+ for (; up>=uar; up--) {
+ if (*up==0) { /* unit is all 0s */
+ if (digits==1) break; /* a zero has one digit */
+ digits-=DECDPUN; /* adjust for 0 unit */
+ continue;}
+ /* found the first (most significant) non-zero Unit */
+ #if DECDPUN>1 /* not done yet */
+ if (*up<10) break; /* is 1-9 */
+ digits++;
+ #if DECDPUN>2 /* not done yet */
+ if (*up<100) break; /* is 10-99 */
+ digits++;
+ #if DECDPUN>3 /* not done yet */
+ if (*up<1000) break; /* is 100-999 */
+ digits++;
+ #if DECDPUN>4 /* count the rest ... */
+ for (pow=&powers[4]; *up>=*pow; pow++) digits++;
+ #endif
+ #endif
+ #endif
+ #endif
+ break;
+ } /* up */
return digits;
-}
-
+ } /* decGetDigits */
#if DECTRACE | DECCHECK
/* ------------------------------------------------------------------ */
-/* decNumberShow -- display a number [debug aid] */
-/* dn is the number to show */
-/* */
-/* Shows: sign, exponent, coefficient (msu first), digits */
-/* or: sign, special-value */
+/* decNumberShow -- display a number [debug aid] */
+/* dn is the number to show */
+/* */
+/* Shows: sign, exponent, coefficient (msu first), digits */
+/* or: sign, special-value */
/* ------------------------------------------------------------------ */
/* this is public so other modules can use it */
-void
-decNumberShow (decNumber * dn)
-{
- Unit *up; /* work */
- uInt u, d; /* .. */
- Int cut; /* .. */
- char isign = '+'; /* main sign */
- if (dn == NULL)
- {
- printf ("NULL\n");
- return;
- }
- if (decNumberIsNegative (dn))
- isign = '-';
- printf (" >> %c ", isign);
- if (dn->bits & DECSPECIAL)
- { /* Is a special value */
- if (decNumberIsInfinite (dn))
- printf ("Infinity");
- else
- { /* a NaN */
- if (dn->bits & DECSNAN)
- printf ("sNaN"); /* signalling NaN */
- else
- printf ("NaN");
- }
- /* if coefficient and exponent are 0, we're done */
- if (dn->exponent == 0 && dn->digits == 1 && *dn->lsu == 0)
- {
- printf ("\n");
- return;
- }
- /* drop through to report other information */
- printf (" ");
+void decNumberShow(const decNumber *dn) {
+ const Unit *up; /* work */
+ uInt u, d; /* .. */
+ Int cut; /* .. */
+ char isign='+'; /* main sign */
+ if (dn==NULL) {
+ printf("NULL\n");
+ return;}
+ if (decNumberIsNegative(dn)) isign='-';
+ printf(" >> %c ", isign);
+ if (dn->bits&DECSPECIAL) { /* Is a special value */
+ if (decNumberIsInfinite(dn)) printf("Infinity");
+ else { /* a NaN */
+ if (dn->bits&DECSNAN) printf("sNaN"); /* signalling NaN */
+ else printf("NaN");
+ }
+ /* if coefficient and exponent are 0, no more to do */
+ if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
+ printf("\n");
+ return;}
+ /* drop through to report other information */
+ printf(" ");
}
/* now carefully display the coefficient */
- up = dn->lsu + D2U (dn->digits) - 1; /* msu */
- printf ("%d", *up);
- for (up = up - 1; up >= dn->lsu; up--)
- {
- u = *up;
- printf (":");
- for (cut = DECDPUN - 1; cut >= 0; cut--)
- {
- d = u / powers[cut];
- u -= d * powers[cut];
- printf ("%d", d);
- } /* cut */
- } /* up */
- if (dn->exponent != 0)
- {
- char esign = '+';
- if (dn->exponent < 0)
- esign = '-';
- printf (" E%c%d", esign, abs (dn->exponent));
+ up=dn->lsu+D2U(dn->digits)-1; /* msu */
+ printf("%ld", (LI)*up);
+ for (up=up-1; up>=dn->lsu; up--) {
+ u=*up;
+ printf(":");
+ for (cut=DECDPUN-1; cut>=0; cut--) {
+ d=u/powers[cut];
+ u-=d*powers[cut];
+ printf("%ld", (LI)d);
+ } /* cut */
+ } /* up */
+ if (dn->exponent!=0) {
+ char esign='+';
+ if (dn->exponent<0) esign='-';
+ printf(" E%c%ld", esign, (LI)abs(dn->exponent));
}
- printf (" [%d]\n", dn->digits);
-}
+ printf(" [%ld]\n", (LI)dn->digits);
+ } /* decNumberShow */
#endif
#if DECTRACE || DECCHECK
/* ------------------------------------------------------------------ */
-/* decDumpAr -- display a unit array [debug aid] */
-/* name is a single-character tag name */
-/* ar is the array to display */
-/* len is the length of the array in Units */
+/* decDumpAr -- display a unit array [debug/check aid] */
+/* name is a single-character tag name */
+/* ar is the array to display */
+/* len is the length of the array in Units */
/* ------------------------------------------------------------------ */
-static void
-decDumpAr (char name, Unit * ar, Int len)
-{
+static void decDumpAr(char name, const Unit *ar, Int len) {
Int i;
-#if DECDPUN==4
- char *spec = "%04d ";
-#else
- char *spec = "%d ";
-#endif
- printf (" :%c: ", name);
- for (i = len - 1; i >= 0; i--)
- {
- if (i == len - 1)
- printf ("%d ", ar[i]);
- else
- printf (spec, ar[i]);
+ const char *spec;
+ #if DECDPUN==9
+ spec="%09d ";
+ #elif DECDPUN==8
+ spec="%08d ";
+ #elif DECDPUN==7
+ spec="%07d ";
+ #elif DECDPUN==6
+ spec="%06d ";
+ #elif DECDPUN==5
+ spec="%05d ";
+ #elif DECDPUN==4
+ spec="%04d ";
+ #elif DECDPUN==3
+ spec="%03d ";
+ #elif DECDPUN==2
+ spec="%02d ";
+ #else
+ spec="%d ";
+ #endif
+ printf(" :%c: ", name);
+ for (i=len-1; i>=0; i--) {
+ if (i==len-1) printf("%ld ", (LI)ar[i]);
+ else printf(spec, ar[i]);
}
- printf ("\n");
- return;
-}
+ printf("\n");
+ return;}
#endif
#if DECCHECK
/* ------------------------------------------------------------------ */
-/* decCheckOperands -- check operand(s) to a routine */
+/* decCheckOperands -- check operand(s) to a routine */
/* res is the result structure (not checked; it will be set to */
-/* quiet NaN if error found (and it is not NULL)) */
-/* lhs is the first operand (may be DECUNUSED) */
-/* rhs is the second (may be DECUNUSED) */
-/* set is the context (may be DECUNUSED) */
+/* quiet NaN if error found (and it is not NULL)) */
+/* lhs is the first operand (may be DECUNRESU) */
+/* rhs is the second (may be DECUNUSED) */
+/* set is the context (may be DECUNCONT) */
/* returns 0 if both operands, and the context are clean, or 1 */
/* otherwise (in which case the context will show an error, */
/* unless NULL). Note that res is not cleaned; caller should */
-/* handle this so res=NULL case is safe. */
+/* handle this so res=NULL case is safe. */
/* The caller is expected to abandon immediately if 1 is returned. */
/* ------------------------------------------------------------------ */
-static Flag
-decCheckOperands (decNumber * res, decNumber * lhs,
- decNumber * rhs, decContext * set)
-{
- Flag bad = 0;
- if (set == NULL)
- { /* oops; hopeless */
-#if DECTRACE
- printf ("Context is NULL.\n");
-#endif
- bad = 1;
- return 1;
+static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
+ const decNumber *rhs, decContext *set) {
+ Flag bad=0;
+ if (set==NULL) { /* oops; hopeless */
+ #if DECTRACE || DECVERB
+ printf("Reference to context is NULL.\n");
+ #endif
+ bad=1;
+ return 1;}
+ else if (set!=DECUNCONT
+ && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
+ bad=1;
+ #if DECTRACE || DECVERB
+ printf("Bad context [digits=%ld round=%ld].\n",
+ (LI)set->digits, (LI)set->round);
+ #endif
}
- else if (set != DECUNUSED
- && (set->digits < 1 || set->round < 0
- || set->round >= DEC_ROUND_MAX))
- {
- bad = 1;
-#if DECTRACE
- printf ("Bad context [digits=%d round=%d].\n", set->digits, set->round);
-#endif
- }
- else
- {
- if (res == NULL)
- {
- bad = 1;
-#if DECTRACE
- printf ("Bad result [is NULL].\n");
-#endif
- }
- if (!bad && lhs != DECUNUSED)
- bad = (decCheckNumber (lhs, set));
- if (!bad && rhs != DECUNUSED)
- bad = (decCheckNumber (rhs, set));
+ else {
+ if (res==NULL) {
+ bad=1;
+ #if DECTRACE
+ /* this one not DECVERB as standard tests include NULL */
+ printf("Reference to result is NULL.\n");
+ #endif
+ }
+ if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
+ if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
}
- if (bad)
- {
- if (set != DECUNUSED)
- decContextSetStatus (set, DEC_Invalid_operation);
- if (res != DECUNUSED && res != NULL)
- {
- decNumberZero (res);
- res->bits = DECNAN; /* qNaN */
- }
+ if (bad) {
+ if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
+ if (res!=DECUNRESU && res!=NULL) {
+ decNumberZero(res);
+ res->bits=DECNAN; /* qNaN */
+ }
}
return bad;
-}
+ } /* decCheckOperands */
/* ------------------------------------------------------------------ */
-/* decCheckNumber -- check a number */
-/* dn is the number to check */
-/* set is the context (may be DECUNUSED) */
-/* returns 0 if the number is clean, or 1 otherwise */
-/* */
+/* decCheckNumber -- check a number */
+/* dn is the number to check */
+/* returns 0 if the number is clean, or 1 otherwise */
+/* */
/* The number is considered valid if it could be a result from some */
-/* operation in some valid context (not necessarily the current one). */
-/* ------------------------------------------------------------------ */
-Flag
-decCheckNumber (decNumber * dn, decContext * set)
-{
- Unit *up; /* work */
- uInt maxuint; /* .. */
- Int ae, d, digits; /* .. */
- Int emin, emax; /* .. */
-
- if (dn == NULL)
- { /* hopeless */
-#if DECTRACE
- printf ("Reference to decNumber is NULL.\n");
-#endif
- return 1;
- }
+/* operation in some valid context. */
+/* ------------------------------------------------------------------ */
+static Flag decCheckNumber(const decNumber *dn) {
+ const Unit *up; /* work */
+ uInt maxuint; /* .. */
+ Int ae, d, digits; /* .. */
+ Int emin, emax; /* .. */
- /* check special values */
- if (dn->bits & DECSPECIAL)
- {
- if (dn->exponent != 0)
- {
-#if DECTRACE
- printf ("Exponent %d (not 0) for a special value.\n", dn->exponent);
-#endif
- return 1;
- }
+ if (dn==NULL) { /* hopeless */
+ #if DECTRACE
+ /* this one not DECVERB as standard tests include NULL */
+ printf("Reference to decNumber is NULL.\n");
+ #endif
+ return 1;}
- /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
- if (decNumberIsInfinite (dn))
- {
- if (dn->digits != 1)
- {
-#if DECTRACE
- printf ("Digits %d (not 1) for an infinity.\n", dn->digits);
-#endif
- return 1;
- }
- if (*dn->lsu != 0)
- {
-#if DECTRACE
- printf ("LSU %d (not 0) for an infinity.\n", *dn->lsu);
-#endif
- return 1;
- }
- } /* Inf */
- /* 2002.12.26: negative NaNs can now appear through proposed IEEE */
- /* concrete formats (decimal64, etc.), though they are */
- /* never visible in strings. */
- return 0;
-
- /* if ((dn->bits & DECINF) || (dn->bits & DECNEG)==0) return 0; */
- /* #if DECTRACE */
- /* printf("Negative NaN in number.\n"); */
- /* #endif */
- /* return 1; */
+ /* check special values */
+ if (dn->bits & DECSPECIAL) {
+ if (dn->exponent!=0) {
+ #if DECTRACE || DECVERB
+ printf("Exponent %ld (not 0) for a special value [%02x].\n",
+ (LI)dn->exponent, dn->bits);
+ #endif
+ return 1;}
+
+ /* 2003.09.08: NaNs may now have coefficients, so next tests Inf only */
+ if (decNumberIsInfinite(dn)) {
+ if (dn->digits!=1) {
+ #if DECTRACE || DECVERB
+ printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
+ #endif
+ return 1;}
+ if (*dn->lsu!=0) {
+ #if DECTRACE || DECVERB
+ printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
+ #endif
+ decDumpAr('I', dn->lsu, D2U(dn->digits));
+ return 1;}
+ } /* Inf */
+ /* 2002.12.26: negative NaNs can now appear through proposed IEEE */
+ /* concrete formats (decimal64, etc.). */
+ return 0;
}
/* check the coefficient */
- if (dn->digits < 1 || dn->digits > DECNUMMAXP)
- {
-#if DECTRACE
- printf ("Digits %d in number.\n", dn->digits);
-#endif
- return 1;
- }
-
- d = dn->digits;
-
- for (up = dn->lsu; d > 0; up++)
- {
- if (d > DECDPUN)
- maxuint = DECDPUNMAX;
- else
- { /* we are at the msu */
- maxuint = powers[d] - 1;
- if (dn->digits > 1 && *up < powers[d - 1])
- {
-#if DECTRACE
- printf ("Leading 0 in number.\n");
- decNumberShow (dn);
-#endif
- return 1;
- }
- }
- if (*up > maxuint)
- {
-#if DECTRACE
- printf ("Bad Unit [%08x] in number at offset %d [maxuint %d].\n",
- *up, up - dn->lsu, maxuint);
-#endif
- return 1;
- }
- d -= DECDPUN;
+ if (dn->digits<1 || dn->digits>DECNUMMAXP) {
+ #if DECTRACE || DECVERB
+ printf("Digits %ld in number.\n", (LI)dn->digits);
+ #endif
+ return 1;}
+
+ d=dn->digits;
+
+ for (up=dn->lsu; d>0; up++) {
+ if (d>DECDPUN) maxuint=DECDPUNMAX;
+ else { /* reached the msu */
+ maxuint=powers[d]-1;
+ if (dn->digits>1 && *up<powers[d-1]) {
+ #if DECTRACE || DECVERB
+ printf("Leading 0 in number.\n");
+ decNumberShow(dn);
+ #endif
+ return 1;}
+ }
+ if (*up>maxuint) {
+ #if DECTRACE || DECVERB
+ printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
+ (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
+ #endif
+ return 1;}
+ d-=DECDPUN;
}
/* check the exponent. Note that input operands can have exponents */
/* which are out of the set->emin/set->emax and set->digits range */
/* (just as they can have more digits than set->digits). */
- ae = dn->exponent + dn->digits - 1; /* adjusted exponent */
- emax = DECNUMMAXE;
- emin = DECNUMMINE;
- digits = DECNUMMAXP;
- if (ae < emin - (digits - 1))
- {
-#if DECTRACE
- printf ("Adjusted exponent underflow [%d].\n", ae);
- decNumberShow (dn);
-#endif
- return 1;
- }
- if (ae > +emax)
- {
-#if DECTRACE
- printf ("Adjusted exponent overflow [%d].\n", ae);
- decNumberShow (dn);
-#endif
- return 1;
- }
-
- return 0; /* it's OK */
-}
+ ae=dn->exponent+dn->digits-1; /* adjusted exponent */
+ emax=DECNUMMAXE;
+ emin=DECNUMMINE;
+ digits=DECNUMMAXP;
+ if (ae<emin-(digits-1)) {
+ #if DECTRACE || DECVERB
+ printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
+ decNumberShow(dn);
+ #endif
+ return 1;}
+ if (ae>+emax) {
+ #if DECTRACE || DECVERB
+ printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
+ decNumberShow(dn);
+ #endif
+ return 1;}
+
+ return 0; /* it's OK */
+ } /* decCheckNumber */
+
+/* ------------------------------------------------------------------ */
+/* decCheckInexact -- check a normal finite inexact result has digits */
+/* dn is the number to check */
+/* set is the context (for status and precision) */
+/* sets Invalid operation, etc., if some digits are missing */
+/* [this check is not made for DECSUBSET compilation or when */
+/* subnormal is not set] */
+/* ------------------------------------------------------------------ */
+static void decCheckInexact(const decNumber *dn, decContext *set) {
+ #if !DECSUBSET && DECEXTFLAG
+ if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
+ && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
+ #if DECTRACE || DECVERB
+ printf("Insufficient digits [%ld] on normal Inexact result.\n",
+ (LI)dn->digits);
+ decNumberShow(dn);
+ #endif
+ decContextSetStatus(set, DEC_Invalid_operation);
+ }
+ #else
+ /* next is a noop for quiet compiler */
+ if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
+ #endif
+ return;
+ } /* decCheckInexact */
#endif
#if DECALLOC
#undef malloc
#undef free
/* ------------------------------------------------------------------ */
-/* decMalloc -- accountable allocation routine */
-/* n is the number of bytes to allocate */
-/* */
+/* decMalloc -- accountable allocation routine */
+/* n is the number of bytes to allocate */
+/* */
/* Semantics is the same as the stdlib malloc routine, but bytes */
/* allocated are accounted for globally, and corruption fences are */
-/* added before and after the 'actual' storage. */
+/* added before and after the 'actual' storage. */
/* ------------------------------------------------------------------ */
/* This routine allocates storage with an extra twelve bytes; 8 are */
-/* at the start and hold: */
-/* 0-3 the original length requested */
-/* 4-7 buffer corruption detection fence (DECFENCE, x4) */
+/* at the start and hold: */
+/* 0-3 the original length requested */
+/* 4-7 buffer corruption detection fence (DECFENCE, x4) */
/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
/* ------------------------------------------------------------------ */
-static void *
-decMalloc (uInt n)
-{
- uInt size = n + 12; /* true size */
- void *alloc; /* -> allocated storage */
- uInt *j; /* work */
- uByte *b, *b0; /* .. */
-
- alloc = malloc (size); /* -> allocated storage */
- if (alloc == NULL)
- return NULL; /* out of strorage */
- b0 = (uByte *) alloc; /* as bytes */
- decAllocBytes += n; /* account for storage */
- j = (uInt *) alloc; /* -> first four bytes */
- *j = n; /* save n */
- /* printf("++ alloc(%d)\n", n); */
- for (b = b0 + 4; b < b0 + 8; b++)
- *b = DECFENCE;
- for (b = b0 + n + 8; b < b0 + n + 12; b++)
- *b = DECFENCE;
- return b0 + 8; /* -> play area */
-}
-
-/* ------------------------------------------------------------------ */
-/* decFree -- accountable free routine */
-/* alloc is the storage to free */
-/* */
+static void *decMalloc(size_t n) {
+ uInt size=n+12; /* true size */
+ void *alloc; /* -> allocated storage */
+ uByte *b, *b0; /* work */
+ uInt uiwork; /* for macros */
+
+ alloc=malloc(size); /* -> allocated storage */
+ if (alloc==NULL) return NULL; /* out of strorage */
+ b0=(uByte *)alloc; /* as bytes */
+ decAllocBytes+=n; /* account for storage */
+ UBFROMUI(alloc, n); /* save n */
+ /* printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); */
+ for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
+ for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
+ return b0+8; /* -> play area */
+ } /* decMalloc */
+
+/* ------------------------------------------------------------------ */
+/* decFree -- accountable free routine */
+/* alloc is the storage to free */
+/* */
/* Semantics is the same as the stdlib malloc routine, except that */
-/* the global storage accounting is updated and the fences are */
+/* the global storage accounting is updated and the fences are */
/* checked to ensure that no routine has written 'out of bounds'. */
/* ------------------------------------------------------------------ */
/* This routine first checks that the fences have not been corrupted. */
/* It then frees the storage using the 'truw' storage address (that */
-/* is, offset by 8). */
-/* ------------------------------------------------------------------ */
-static void
-decFree (void *alloc)
-{
- uInt *j, n; /* pointer, original length */
- uByte *b, *b0; /* work */
-
- if (alloc == NULL)
- return; /* allowed; it's a nop */
- b0 = (uByte *) alloc; /* as bytes */
- b0 -= 8; /* -> true start of storage */
- j = (uInt *) b0; /* -> first four bytes */
- n = *j; /* lift */
- for (b = b0 + 4; b < b0 + 8; b++)
- if (*b != DECFENCE)
- printf ("=== Corrupt byte [%02x] at offset %d from %d ===\n", *b,
- b - b0 - 8, (Int) b0);
- for (b = b0 + n + 8; b < b0 + n + 12; b++)
- if (*b != DECFENCE)
- printf ("=== Corrupt byte [%02x] at offset +%d from %d, n=%d ===\n", *b,
- b - b0 - 8, (Int) b0, n);
- free (b0); /* drop the storage */
- decAllocBytes -= n; /* account for storage */
-}
+/* is, offset by 8). */
+/* ------------------------------------------------------------------ */
+static void decFree(void *alloc) {
+ uInt n; /* original length */
+ uByte *b, *b0; /* work */
+ uInt uiwork; /* for macros */
+
+ if (alloc==NULL) return; /* allowed; it's a nop */
+ b0=(uByte *)alloc; /* as bytes */
+ b0-=8; /* -> true start of storage */
+ n=UBTOUI(b0); /* lift length */
+ for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
+ printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
+ b-b0-8, (LI)b0);
+ for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
+ printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
+ b-b0-8, (LI)b0, (LI)n);
+ free(b0); /* drop the storage */
+ decAllocBytes-=n; /* account for storage */
+ /* printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n); */
+ } /* decFree */
+#define malloc(a) decMalloc(a)
+#define free(a) decFree(a)
#endif
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