/* Decimal number arithmetic module for the decNumber C Library.
- Copyright (C) 2005, 2007 Free Software Foundation, Inc.
+ 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.
- In addition to the permissions in the GNU General Public License,
- the Free Software Foundation gives you unlimited permission to link
- the compiled version of this file into combinations with other
- programs, and to distribute those combinations without any
- restriction coming from the use of this file. (The General Public
- License restrictions do apply in other respects; for example, they
- cover modification of the file, and distribution when not linked
- into a combine executable.)
-
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
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, 51 Franklin Street, Fifth Floor, Boston, MA
- 02110-1301, USA. */
+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 General Decimal Arithmetic */
-/* as defined in the specification which may be found on the */
-/* http://www2.hursley.ibm.com/decimal web pages. It implements both */
+/* 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: */
+/* Usage notes: */
/* */
/* 1. This code is ANSI C89 except: */
/* */
-/* If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */
+/* 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 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 */
+/* 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). Mathematical functions (for */
/* 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 */
+/* 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). */
/* */
/* */
/* 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). */
+/* Infinity or NaN). */
/* */
/* 6. The decNumber format is not an exchangeable concrete */
/* representation as it comprises fields which may be machine- */
/* Canonical conversions to and from strings are provided; other */
/* conversions are available in separate modules. */
/* */
-/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */
+/* 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 */
-/* 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.) */
/* */
/* */
/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */
/* ------------------------------------------------------------------ */
-/* Implementation notes for maintenance of this module: */
+/* 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., */
/* 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, */
+/* jump). Therefore all cleanup must be done first. In general, */
/* to achieve this status is accumulated and is only applied just */
/* before return by calling decContextSetStatus (via decStatus). */
/* */
/* */
/* 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 */
+/* the decFinalize function is called later. Multiplication and */
/* division, and intermediate calculations in exponentiation, */
-/* require more careful checks because of the risk of 31-bit */
+/* 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). */
/* */
/* 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 a floating-point or 64-bit multiply is */
-/* assumed to be available). */
+/* assumed to be available). */
/* */
-/* 8. Unusual abbreviations that may be used in the commentary: */
+/* 8. Unusual abbreviations that may be used in the commentary: */
/* lhs -- left hand side (operand, of an operation) */
-/* lsd -- least significant digit (of coefficient) */
+/* 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 */
+/* +ve -- positive */
+/* -ve -- negative */
/* ** -- raise to the power */
/* ------------------------------------------------------------------ */
#include <stdio.h> /* for printf [if needed] */
#include <string.h> /* for strcpy */
#include <ctype.h> /* for lower */
-#include "config.h" /* for GCC definitions */
+#include "dconfig.h" /* for GCC definitions */
#include "decNumber.h" /* base number library */
#include "decNumberLocal.h" /* decNumber local types, etc. */
/* Public lookup table used by the D2U macro */
const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
-#define DECVERB 1 /* set to 1 for verbose DECCHECK */
+#define DECVERB 1 /* set to 1 for verbose DECCHECK */
#define powers DECPOWERS /* old internal name */
/* 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 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 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 */
+#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 Int decShiftToMost(Unit *, Int, Int);
static void decStatus(decNumber *, uInt, decContext *);
static void decToString(const decNumber *, char[], Flag);
-static decNumber * decTrim(decNumber *, decContext *, Flag, Int *);
+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 DECCHECK
/* 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 */
+/* correctness. This roughly doubles the execution time of the */
/* fastest routines (and adds 600+ bytes), so should not normally be */
/* used in 'production'. */
/* decCheckInexact is used to check that inexact results have a full */
Int d; /* work */
const Unit *up; /* .. */
uInt hi=0, lo; /* .. */
- up=dn->lsu; /* -> lsu */
+ up=dn->lsu; /* -> lsu */
lo=*up; /* get 1 to 9 digits */
#if DECDPUN>1 /* split to higher */
hi=lo/10;
Int d; /* work */
const Unit *up; /* .. */
uInt hi=0, lo; /* .. */
- up=dn->lsu; /* -> lsu */
+ up=dn->lsu; /* -> lsu */
lo=*up; /* get 1 to 9 digits */
#if DECDPUN>1 /* split to higher */
hi=lo/10;
} /* decNumberToUInt32 */
/* ------------------------------------------------------------------ */
-/* to-scientific-string -- conversion to numeric string */
+/* to-scientific-string -- conversion to numeric string */
/* to-engineering-string -- conversion to numeric string */
/* */
/* decNumberToString(dn, string); */
/* to-number -- conversion from numeric string */
/* */
/* decNumberFromString -- convert string to decNumber */
-/* dn -- the number structure to fill */
+/* 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 */
+/* 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 */
-/* Overflow) can be reported or rounding applied, as necessary. */
+/* 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, const char chars[],
decContext *set) {
Int exponent=0; /* working exponent [assume 0] */
- uByte bits=0; /* working flags [assume +ve] */
+ 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 */
+ 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 */
do { /* status & malloc protection */
for (c=chars;; c++) { /* -> input character */
- if (*c>='0' && *c<='9') { /* test for Arabic digit */
+ if (*c>='0' && *c<='9') { /* test for Arabic digit */
last=c;
d++; /* count of real digits */
continue; /* still in decimal part */
if (!set->extended) break; /* hopeless */
#endif
/* Infinities and NaNs are possible, here */
- if (dotchar!=NULL) break; /* .. unless had a dot */
+ if (dotchar!=NULL) break; /* .. unless had a dot */
decNumberZero(dn); /* be optimistic */
if (decBiStr(c, "infinity", "INFINITY")
|| decBiStr(c, "inf", "INF")) {
/* 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 */
+ if (*c=='s' || *c=='S') { /* looks like an sNaN */
c++;
dn->bits=bits | DECSNAN;
}
if (d>set->digits) break;
} /* too many digits? */
/* good; drop through to convert the integer to coefficient */
- status=0; /* syntax is OK */
+ status=0; /* syntax is OK */
bits=dn->bits; /* for copy-back */
} /* last==NULL */
/* [up to 1999999999 is OK, for example 1E-1000000998] */
}
if (nege) exponent=-exponent; /* was negative */
- status=0; /* is OK */
+ 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 .] */
+ 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 */
/* Handle decimal point... */
if (dotchar!=NULL && dotchar<last) /* non-trailing '.' found? */
- exponent-=(last-dotchar); /* adjust exponent */
+ exponent-=(last-dotchar); /* adjust exponent */
/* [we can now ignore the .] */
/* OK, the digits string is good. Assemble in the decNumber, or in */
}
}
/* decNumberShow(dn); */
- } while(0); /* [for break] */
+ } while(0); /* [for break] */
if (allocres!=NULL) free(allocres); /* drop any storage used */
if (status!=0) decStatus(dn, status, set);
/* */
/* res is C, the result. C may be A */
/* rhs is A */
-/* set is the context */
+/* set is the context */
/* */
/* See also decNumberCopyAbs for a quiet bitwise version of this. */
/* C must have space for set->digits digits. */
#endif
decNumberZero(&dzero); /* set 0 */
- dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
+ 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
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* 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 */
+/* set is the context */
/* */
/* C must have space for one digit (or NaN). */
/* ------------------------------------------------------------------ */
/* 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 */
+/* set is the context */
/* */
/* C must have space for one digit (or NaN). */
/* ------------------------------------------------------------------ */
/* 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 */
+/* set is the context */
/* */
/* C must have space for one digit; the result will always be one of */
-/* -1, 0, or 1. */
+/* -1, 0, or 1. */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *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 */
+/* set is the context */
/* */
/* C must have space for one digit; the result will always be one of */
-/* -1, 0, or 1. */
+/* -1, 0, or 1. */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
a=allocbufa; /* use the allocated space */
}
decNumberCopy(a, lhs); /* copy content */
- a->bits&=~DECNEG; /* .. and clear the sign */
+ a->bits&=~DECNEG; /* .. and clear the sign */
lhs=a; /* use copy from here on */
}
if (decNumberIsNegative(rhs)) { /* rhs<0 */
b=allocbufb; /* use the allocated space */
}
decNumberCopy(b, rhs); /* copy content */
- b->bits&=~DECNEG; /* .. and clear the sign */
+ 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 */
+ } while(0); /* end protected */
if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
if (allocbufb!=NULL) free(allocbufb); /* .. */
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
} /* decNumberDivide */
/* ------------------------------------------------------------------ */
-/* decNumberDivideInteger -- divide and return integer quotient */
+/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* */
/* 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. */
+/* 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 */
}
#endif
decExpOp(res, rhs, set, &status);
- } while(0); /* end protected */
+ } while(0); /* end protected */
#if DECSUBSET
if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
/* lhs is A */
/* rhs is B */
/* fhs is C [far hand side] */
-/* set is the context */
+/* set is the context */
/* */
/* Mathematical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* 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 */
+ if (!(status&DEC_sNaN)) { /* but be true invalid */
decNumberZero(res); /* acc not yet set */
res->bits=DECNAN;
break;
}
#if DECCHECK
else { /* multiply was OK */
- if (status!=0) printf("Status=%08lx after FMA multiply\n", status);
+ 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 */
+ } while(0); /* end protected */
if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
if (status!=0) decStatus(res, status, set);
msudigs=MSUDIGITS(set->digits); /* [faster than remainder] */
for (; uc<=msuc; ua++, uc++) { /* Unit loop */
Unit a; /* extract unit */
- Int i, j; /* work */
+ Int i, j; /* work */
if (ua>msua) a=0;
else a=*ua;
*uc=0; /* can now write back */
/* */
/* 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. */
+/* 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 */
} /* extended=0 */
#endif
decLnOp(res, rhs, set, &status);
- } while(0); /* end protected */
+ } while(0); /* end protected */
#if DECSUBSET
if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
} /* decNumberLn */
/* ------------------------------------------------------------------ */
-/* decNumberLogB - get adjusted exponent, by 754r rules */
+/* decNumberLogB - get adjusted exponent, by 754 rules */
/* */
/* This computes C = adjustedexponent(A) */
/* */
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 */
+ decNumberZero(res); /* prepare for Infinity */
res->bits=DECNEG|DECINF; /* -Infinity */
- status|=DEC_Division_by_zero; /* as per 754r */
+ status|=DEC_Division_by_zero; /* as per 754 */
}
else { /* finite non-zero */
Int ae=rhs->exponent+rhs->digits-1; /* adjusted exponent */
/* ------------------------------------------------------------------ */
/* decNumberLog10 -- logarithm in base 10 */
/* */
-/* This computes C = log10(A) */
+/* This computes C = log10(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* */
/* 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. */
+/* 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 */
+/* (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,
decNumberFromInt32(w, w->exponent);
residue=0;
decCopyFit(res, w, set, &residue, &status); /* copy & round */
- decFinish(res, set, &residue, &status); /* cleanup/set flags */
+ decFinish(res, set, &residue, &status); /* cleanup/set flags */
break;
} /* not a power of 10 */
} /* not a candidate for exact */
aset.digits=set->digits; /* for final divide */
decDivideOp(res, a, b, &aset, DIVIDE, &status); /* into result */
- } while(0); /* [for break] */
+ } while(0); /* [for break] */
if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
if (allocbufb!=NULL) free(allocbufb); /* .. */
/* ------------------------------------------------------------------ */
/* decNumberMax -- compare two Numbers and return the maximum */
/* */
-/* This computes C = A ? B, returning the maximum by 754R rules */
+/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* ------------------------------------------------------------------ */
/* decNumberMaxMag -- compare and return the maximum by magnitude */
/* */
-/* This computes C = A ? B, returning the maximum by 754R rules */
+/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* ------------------------------------------------------------------ */
/* decNumberMin -- compare two Numbers and return the minimum */
/* */
-/* This computes C = A ? B, returning the minimum by 754R rules */
+/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* ------------------------------------------------------------------ */
/* decNumberMinMag -- compare and return the minimum by magnitude */
/* */
-/* This computes C = A ? B, returning the minimum by 754R rules */
+/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
-/* set is the context */
+/* set is the context */
/* */
/* See also decNumberCopyNegate for a quiet bitwise version of this. */
/* C must have space for set->digits digits. */
#endif
decNumberZero(&dzero); /* make 0 */
- dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
+ dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
decAddOp(res, &dzero, rhs, set, DECNEG, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
} /* decNumberMinus */
/* ------------------------------------------------------------------ */
-/* decNumberNextMinus -- next towards -Infinity */
+/* 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 */
+/* set is the context */
/* */
-/* This is a generalization of 754r NextDown. */
+/* This is a generalization of 754 NextDown. */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
decContext *set) {
/* */
/* res is C, the result. C may be A */
/* rhs is A */
-/* set is the context */
+/* set is the context */
/* */
-/* This is a generalization of 754r NextUp. */
+/* This is a generalization of 754 NextUp. */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
decContext *set) {
/* decNumberNextToward -- next towards rhs */
/* */
/* This computes C = A +/- infinitesimal, rounded towards */
-/* +/-Infinity in the direction of B, as per 754r nextafter rules */
+/* +/-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 */
+/* set is the context */
/* */
-/* This is a generalization of 754r NextAfter. */
+/* This is a generalization of 754-1985 NextAfter. */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
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 */
+ 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 */
+ return res; /* there is no status to set */
}
workset.round=DEC_ROUND_CEILING;
sub=0; /* add, please */
} /* plus */
- else { /* lhs>rhs, do nextminus */
+ 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 */
+ 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.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 */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
-/* set is the context */
+/* set is the context */
/* */
/* See also decNumberCopy for a quiet bitwise version of this. */
/* C must have space for set->digits digits. */
#endif
decNumberZero(&dzero); /* make 0 */
- dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
+ dzero.exponent=rhs->exponent; /* [no coefficient expansion] */
decAddOp(res, &dzero, rhs, set, 0, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* */
/* */
/* 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. */
+/* error in rare cases. */
/* ------------------------------------------------------------------ */
decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
Flag seenbit; /* seen a bit while powering */
Int residue=0; /* rounding residue */
uInt status=0; /* accumulators */
- uByte bits=0; /* result sign if errors */
+ 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] */
if (decNumberIsNegative(lhs) /* lhs<0 */
&& !decNumberIsZero(lhs)) /* .. */
status|=DEC_Invalid_operation;
- else { /* lhs >=0 */
+ else { /* lhs >=0 */
decNumberZero(&dnOne); /* set up 1 */
dnOne.lsu[0]=1;
decNumberCompare(dac, lhs, &dnOne, set); /* lhs ? 1 */
/* 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 */
+ 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 */
}
if (decNumberIsNegative(lhs) /* -x .. */
- && isoddint) bits=DECNEG; /* .. to an odd power */
+ && isoddint) bits=DECNEG; /* .. to an odd power */
/* handle LHS infinity */
if (decNumberIsInfinite(lhs)) { /* [NaNs already handled] */
uByte rbits=rhs->bits; /* save */
if (rbits & DECNEG) { /* was a 0**(-n) */
#if DECSUBSET
- if (!set->extended) { /* [bad if subset] */
+ if (!set->extended) { /* [bad if subset] */
status|=DEC_Invalid_operation;
break;}
#endif
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 */
+ /* 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 */
if (!rhsint) { /* add padding */
Int shift=set->digits-1;
dac->digits=decShiftToMost(dac->lsu, 1, shift);
- dac->exponent=-shift; /* make 1.0000... */
+ dac->exponent=-shift; /* make 1.0000... */
status|=DEC_Inexact|DEC_Rounded; /* deemed inexact */
}
}
/* 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 */
+ 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 */
}
/* [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 */
+ 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 */
+ if (!seenbit) continue; /* no need to square 1 */
decMultiplyOp(dac, dac, dac, &aset, &status); /* dac=dac*dac [square] */
} /*i*/ /* 32 bits */
decCopyFit(res, dac, set, &residue, &status);
decFinish(res, set, &residue, &status); /* final cleanup */
#if DECSUBSET
- if (!set->extended) decTrim(res, set, 0, &dropped); /* trailing zeros */
+ if (!set->extended) decTrim(res, set, 0, 1, &dropped); /* trailing zeros */
#endif
- } while(0); /* end protected */
+ } while(0); /* end protected */
if (allocdac!=NULL) free(allocdac); /* drop any storage used */
if (allocinv!=NULL) free(allocinv); /* .. */
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* */
/* ------------------------------------------------------------------ */
/* decNumberReduce -- remove trailing zeros */
/* */
-/* This computes C = 0 + A, and normalizes the result */
+/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
#endif
uInt status=0; /* as usual */
Int residue=0; /* as usual */
- Int dropped; /* work */
+ Int dropped; /* work */
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
/* 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, &dropped); /* normalize in place */
- } while(0); /* end protected */
+ decTrim(res, set, 1, 0, &dropped); /* normalize in place */
+ /* [may clamp] */
+ } while(0); /* end protected */
#if DECSUBSET
if (allocrhs !=NULL) free(allocrhs); /* .. */
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* */
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* 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) */
+/* 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 */
+/* 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 */
+/* set->digits the coefficient is padded with zeros on the left */
/* before the rotate. Any leading zeros in the result are removed */
/* as usual. */
/* */
&& !decNumberIsInfinite(res)) { /* lhs was infinite */
/* left-rotate to do; 0 < rotate < set->digits */
uInt units, shift; /* work */
- uInt msudigits; /* digits in result msu */
+ 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 */
+ 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 */
/* (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 */
+ 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 */
/* ------------------------------------------------------------------ */
/* decNumberSameQuantum -- test for equal exponents */
/* */
-/* res is the result number, which will contain either 0 or 1 */
+/* 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) */
/* */
} /* decNumberSameQuantum */
/* ------------------------------------------------------------------ */
-/* decNumberScaleB -- multiply by a power of 10 */
+/* decNumberScaleB -- multiply by a power of 10 */
/* */
-/* This computes C = A x 10**B where B is an integer (q=0) with */
+/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* */
const decNumber *rhs, decContext *set) {
Int reqexp; /* requested exponent change [B] */
uInt status=0; /* accumulator */
- Int residue; /* work */
+ Int residue; /* work */
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
/* 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 */
+/* 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 */
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 */
+ || 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 x < 0 then */
/* assert false */
/* else */
-/* result 0 */
+/* result 0 */
/* end if */
/* end if */
-/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
+/* 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 */
+/* if e mod 2 = 0 then */
/* approx := .259 + .819 * f % approx to root of f */
-/* else */
+/* else */
/* f := f/l0 % adjustments */
-/* e := e + 1 % for odd */
-/* approx := .0819 + 2.59 * f % exponent */
+/* e := e + 1 % for odd */
+/* approx := .0819 + 2.59 * f % exponent */
/* end if */
/* */
/* var p:= 3 */
/* const maxp := currentprecision + 2 */
-/* loop */
+/* loop */
/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
/* precision p */
-/* approx := .5 * (approx + f/approx) */
-/* exit when p = maxp */
+/* approx := .5 * (approx + f/approx) */
+/* exit when p = maxp */
/* end loop */
/* */
/* % approx is now within 1 ulp of the properly rounded square root */
Int workp; /* working precision */
Int residue=0; /* rounding residue */
uInt status=0, ignore=0; /* status accumulators */
- uInt rstatus; /* .. */
+ uInt rstatus; /* .. */
Int exp; /* working exponent */
Int ideal; /* ideal (preferred) exponent */
Int needbytes; /* work */
- Int dropped; /* .. */
+ Int dropped; /* .. */
#if DECSUBSET
decNumber *allocrhs=NULL; /* non-NULL if rounded rhs allocated */
}
/* calculate the ideal (preferred) exponent [floor(exp/2)] */
- /* [We would like to write: ideal=rhs->exponent>>1, but this */
+ /* [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 */
+ ideal=(rhs->exponent&~1)/2; /* target */
/* handle zeros */
if (ISZERO(rhs)) {
/* 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(bufa)) { /* [same applies to b] */
allocbufa=(decNumber *)malloc(needbytes);
allocbufb=(decNumber *)malloc(needbytes);
- if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */
+ if (allocbufa==NULL || allocbufb==NULL) { /* hopeless */
status|=DEC_Insufficient_storage;
break;}
a=allocbufa; /* use the allocated spaces */
/* 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.] */
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 */
+ if ((exp & 1)==0) { /* even exponent */
/* Set t=0.259, a=0.819 */
t->exponent=-3;
a->exponent=-3;
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 */
t->lsu[0]=5; /* .. */
t->exponent=-1; /* .. */
workset.digits=3; /* initial p */
- for (;;) {
+ for (; workset.digits<maxp;) {
/* 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;
+ 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 */
- if (a->digits==maxp) break; /* have required digits */
+ 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 */
/* correctly */
approxset=*set; /* get emin, emax, etc. */
approxset.round=DEC_ROUND_HALF_EVEN;
- a->exponent+=exp/2; /* set correct exponent */
-
+ a->exponent+=exp/2; /* set correct exponent */
rstatus=0; /* clear status */
residue=0; /* .. and accumulator */
decCopyFit(a, a, &approxset, &residue, &rstatus); /* reduce (if needed) */
status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
/* Carry out the Hull correction */
- a->exponent-=exp/2; /* back to 0.1->1 */
+ 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 */
/* estimation are irrelevant, so status was not accumulated] */
/* Here, 0.1 <= a < 1 (still), so adjust back */
- a->exponent+=exp/2; /* set correct exponent */
+ 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, &dropped); /* [drops trailing zeros] */
+ 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, */
- /* and it cannot have trailing zeros due to clamping, so these are */
- /* the only (relatively rare) conditions a careful check is needed */
- if (b->digits*2-1 > workp && !set->clamp) { /* cannot fit */
+ /* 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 */
else { /* plausible */
decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); /* b ? rhs */
if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; /* not equal */
- else { /* is Exact */
+ 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 */
+ 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;
}
decNumberCopy(res, a); /* a is now the result */
- } while(0); /* end protected */
+ } while(0); /* end protected */
- if (allocbuff!=NULL) free(allocbuff); /* drop any storage used */
- if (allocbufa!=NULL) free(allocbufa); /* .. */
- if (allocbufb!=NULL) free(allocbufb); /* .. */
+ 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
/* 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 */
+/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* */
/* res is the result */
/* rhs is input number */
-/* set is the context */
+/* set is the context */
/* */
/* res must have space for any value of rhs. */
/* */
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.digits=rhs->digits; /* no length rounding */
workset.traps=0; /* no traps */
- decNumberZero(&dn); /* make a number with exponent 0 */
+ decNumberZero(&dn); /* make a number with exponent 0 */
decNumberQuantize(res, rhs, &dn, &workset);
status|=workset.status;
}
/* ================================================================== */
/* ------------------------------------------------------------------ */
-/* decNumberClass -- return the decClass of a decNumber */
+/* decNumberClass -- return the decClass of a decNumber */
/* dn -- the decNumber to test */
-/* set -- the context to use for Emin */
+/* set -- the context to use for Emin */
/* returns the decClass enum */
/* ------------------------------------------------------------------ */
enum decClass decNumberClass(const decNumber *dn, decContext *set) {
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. */
+ /* 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;
/* ------------------------------------------------------------------ */
/* decNumberCopySign -- quiet copy and set sign operator */
/* */
-/* This sets C = A with the sign of B */
+/* This sets C = A with the sign of B */
/* */
/* res is C, the result. C may be A */
/* lhs is A */
/* ------------------------------------------------------------------ */
/* decNumberGetBCD -- get the coefficient in BCD8 */
-/* dn is the source decNumber */
+/* 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, uint8_t *bcd) {
+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 */
+ #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] */
/* ------------------------------------------------------------------ */
/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */
-/* dn is the target decNumber */
+/* 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 */
+/* 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 */
#if DECDPUN==1 /* trivial simple copy */
for (; ub<bcd+n; ub++, up--) *up=*ub;
- #else /* some assembly needed */
+ #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 */
cut=DECDPUN; /* next Unit has all digits */
}
#endif
- dn->digits=n; /* set digit count */
+ dn->digits=n; /* set digit count */
return dn;
} /* decNumberSetBCD */
/* ------------------------------------------------------------------ */
/* decNumberIsNormal -- test normality of a decNumber */
/* dn is the decNumber to test */
-/* set is the context to use for Emin */
+/* set is the context to use for Emin */
/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */
/* ------------------------------------------------------------------ */
Int decNumberIsNormal(const decNumber *dn, decContext *set) {
if (decNumberIsSpecial(dn)) return 0; /* not finite */
if (decNumberIsZero(dn)) return 0; /* not non-zero */
- ae=dn->exponent+dn->digits-1; /* adjusted exponent */
+ 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 */
+/* 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) {
if (decNumberIsSpecial(dn)) return 0; /* not finite */
if (decNumberIsZero(dn)) return 0; /* not non-zero */
- ae=dn->exponent+dn->digits-1; /* adjusted exponent */
+ 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 */
+/* returns dn */
/* */
/* All fields are updated as required. This is a utility operation, */
-/* so special values are unchanged and no error is possible. */
+/* so special values are unchanged and no error is possible. The */
+/* zeros are removed unconditionally. */
/* ------------------------------------------------------------------ */
decNumber * decNumberTrim(decNumber *dn) {
- Int dropped; /* work */
+ 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, &dropped);
+ return decTrim(dn, &set, 0, 1, &dropped);
} /* decNumberTrim */
/* ------------------------------------------------------------------ */
/* decNumberZero -- set a number to 0 */
/* */
/* dn is the number to set, with space for one digit */
-/* returns dn */
+/* returns dn */
/* */
/* No error is possible. */
/* ------------------------------------------------------------------ */
/* ------------------------------------------------------------------ */
/* decToString -- lay out a number into a string */
/* */
-/* dn is the number to lay out */
+/* dn is the number to lay out */
/* string is where to lay out the number */
/* eng is 1 if Engineering, 0 if Scientific */
/* */
/* If DECCHECK is enabled the string "?" is returned if a number is */
/* invalid. */
static void decToString(const decNumber *dn, char *string, Flag eng) {
- Int exp=dn->exponent; /* local copy */
+ Int exp=dn->exponent; /* local copy */
Int e; /* E-part value */
Int pre; /* digits before the '.' */
Int cut; /* for counting digits in a Unit */
}
if (dn->bits&DECSPECIAL) { /* Is a special value */
if (decNumberIsInfinite(dn)) {
- strcpy(c, "Inf");
+ strcpy(c, "Inf");
strcpy(c+3, "inity");
return;}
/* a NaN */
cut=MSUDIGITS(dn->digits); /* [faster than remainder] */
cut--; /* power of ten for digit */
- if (exp==0) { /* simple integer [common fastpath] */
+ 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);
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 */
+ 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 */
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) */
+ if (up==dn->lsu) break; /* out of input digits (pre>digits) */
up--;
cut=DECDPUN-1;
u=*up;
}
TODIGIT(u, cut, c, pow);
}
- if (n<dn->digits) { /* more to come, after '.' */
+ if (n<dn->digits) { /* more to come, after '.' */
*c='.'; c++;
for (;; c++, cut--) {
if (cut<0) { /* need new Unit */
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 */
+ if (up==dn->lsu) break; /* out of input digits */
up--;
cut=DECDPUN-1;
u=*up;
}
}
- /* Finally add the E-part, if needed. It will never be 0, has a
+ /* 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 anormal numbers */
if (e!=0) {
- Flag had=0; /* 1=had non-zero */
+ Flag had=0; /* 1=had non-zero */
*c='E'; c++;
*c='+'; c++; /* assume positive */
u=e; /* .. */
/* 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 */
+/* set is the context */
/* negate is DECNEG if rhs should be negated, or 0 otherwise */
/* status accumulates status for the caller */
/* */
/* Inexact in status must be 0 for correct Exact zero sign in result */
/* ------------------------------------------------------------------ */
/* If possible, the coefficient is calculated directly into C. */
-/* However, if: */
+/* However, if: */
/* -- a digits+1 calculation is needed because the numbers are */
-/* unaligned and span more than set->digits digits */
+/* 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 */
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 */
+ Unit *allocacc=NULL; /* -> allocated acc buffer, iff allocated */
Int reqdigits=set->digits; /* local copy; requested DIGITS */
Int padding; /* work */
else bits=(rhs->bits^negate) & DECNEG;/* RHS must be Infinity */
bits|=DECINF;
decNumberZero(res);
- res->bits=bits; /* set +/- infinity */
+ res->bits=bits; /* set +/- infinity */
} /* an infinity */
break;
}
#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 (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) {
/* 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 (adjust<0) { /* 0-padding needed */
if ((res->digits-adjust)>set->digits) {
adjust=res->digits-set->digits; /* to fit exactly */
*status|=DEC_Rounded; /* [but exact] */
/* 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 */
+ rhsshift=0; /* rhs shift to left (padding) in Units */
bits=lhs->bits; /* assume sign is that of LHS */
mult=1; /* likely multiplier */
/* 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 */
+ 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. */
+ res->exponent-=shift; /* adjust the exponent. */
}
/* flip the result sign if unswapped and rhs was negated */
if (!swapped) res->bits^=negate;
if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; /* sign - */
else res->bits&=~DECNEG; /* sign + */
}
- } while(0); /* end protected */
+ } while(0); /* end protected */
if (allocacc!=NULL) free(allocacc); /* drop any storage used */
#if DECSUBSET
/* 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. */
+/* 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. */
/* */
/* Prepare operands and handle special values */
/* Test for x/0 and then 0/x */
-/* Exp =Exp1 - Exp2 */
+/* Exp =Exp1 - Exp2 */
/* Exp =Exp +len(var1) -len(var2) */
/* Sign=Sign1 * Sign2 */
/* Pad accumulator (Var1) to double-length with 0's (pad1) */
/* this_unit=0 */
/* Do forever */
/* compare numbers */
-/* if <0 then leave inner_loop */
+/* 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 */
/* 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 */
+/* mult=tops1/tops2 -- Good and safe guess at divisor */
/* if mult=0 then mult=1 */
/* this_unit=this_unit+mult */
/* subtract */
/* exp=exp-1 */
/* end outer_loop */
/* exp=exp+1 -- set the proper exponent */
-/* if have=0 then generate answer=0 */
+/* if have=0 then generate answer=0 */
/* Return (Result is defined by Var1) */
/* */
/* ------------------------------------------------------------------ */
#endif
Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; /* local buffer */
Unit *acc=accbuff; /* -> accumulator array for result */
- Unit *allocacc=NULL; /* -> allocated buffer, iff allocated */
+ 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)*sizeof(Unit)]; /* buffer for var1 */
+ 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 *varalloc=NULL; /* -> allocated buffer, iff used */
Unit *msu1; /* -> msu of var1 */
const Unit *var2; /* -> var2 array */
/* result is [finished clone of] lhs */
decCopyFit(res, lhs, set, &residue, status);
}
- else { /* a division */
+ else { /* a division */
decNumberZero(res);
res->bits=bits; /* set +/- zero */
/* for DIVIDEINT the exponent is always 0. For DIVIDE, result */
decNumberZero(res); /* integer 0 */
res->bits=bits; /* sign as computed */
}
- else { /* a remainder */
+ 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 */
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) */
+ 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 */
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 */
+ /* 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. */
else cut=DECDPUN-exponent%DECDPUN;
decShiftToLeast(var1, var1units, cut);
exponent+=cut; /* maintain numerical value */
- var1initpad-=cut; /* .. and reduce padding */
+ 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 */
}
/* ---- start the long-division loops ------------------------------ */
- accunits=0; /* no units accumulated yet */
+ 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 */
/* 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 */
+ thisunit++; /* as though subtracted */
*var1=0; /* set var1 to 0 */
var1units=1; /* .. */
break; /* from inner */
}
if (mult==0) mult=1; /* must always be at least 1 */
/* subtraction needed; var1 is > var2 */
- thisunit=(Unit)(thisunit+mult); /* accumulate */
+ 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;
/* 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 */
+ if (accunits!=0 || thisunit!=0) { /* is first or non-zero */
*accnext=thisunit; /* store in accumulator */
/* account exactly for the new digits */
if (accunits==0) {
else accdigits+=DECDPUN;
accunits++; /* update count */
accnext--; /* ready for next */
- if (accdigits>reqdigits) break; /* have enough digits */
+ if (accdigits>reqdigits) break; /* have enough digits */
}
/* if the residue is zero, the operation is done (unless divide */
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 */
+ if (lsu%powers[drop+1]!=0) break; /* found non-0 digit */
#endif
exponent++;
}
Unit *quotlsu; /* for save */
Int quotdigits; /* .. */
- bits=lhs->bits; /* remainder sign is always as lhs */
+ 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 */
+ 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 */
accdigits=decGetDigits(var1, var1units);
accunits=D2U(accdigits);
- exponent=lhs->exponent; /* exponent is smaller of lhs & rhs */
+ 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 */
if (quotdigits>DECDPUN) {
if (*up!=DECDPUNMAX) break;/* non-nines */
}
- else { /* this is the last Unit */
+ else { /* this is the last Unit */
if (*up==powers[quotdigits]-1) allnines=1;
break;
}
*status|=DEC_Division_impossible;
break;}
- /* rem-rhs is needed; the sign will invert. Again, var1 */
+ /* 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 */
+ exp=rhs->exponent-exponent; /* RHS padding needed */
/* Calculate units and remainder from exponent. */
expunits=exp/DECDPUN;
exprem=exp%DECDPUN;
#if DECSUBSET
/* If a divide then strip trailing zeros if subset [after round] */
- if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, &dropped);
+ if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
#endif
- } while(0); /* end protected */
+ } while(0); /* end protected */
if (varalloc!=NULL) free(varalloc); /* drop any storage used */
if (allocacc!=NULL) free(allocacc); /* .. */
/* 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 */
+/* set is the context */
/* status is the usual accumulator */
/* */
/* C must have space for set->digits digits. */
/* 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 */
+/* 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. */
+/* of the operand coefficients. */
/* Static buffers are larger than needed just for multiply, to allow */
/* for calls from other operations (notably exp). */
/* ------------------------------------------------------------------ */
Int accunits; /* Units of accumulator in use */
Int exponent; /* work */
Int residue=0; /* rounding residue */
- uByte bits; /* result sign */
+ uByte bits; /* result sign */
Unit *acc; /* -> accumulator Unit array */
Int needbytes; /* size calculator */
- void *allocacc=NULL; /* -> allocated accumulator, iff allocated */
+ 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 */
/* [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 */
+ 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 */
+ 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 */
+ Int count; /* work */
const Unit *cup; /* .. */
Unit *up; /* .. */
uLong *lp; /* .. */
- Int p; /* .. */
+ Int p; /* .. */
#endif
#if DECSUBSET
#endif
/* [following code does not require input rounding] */
- #if FASTMUL /* fastpath can be used */
+ #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 */
+ #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] */
/* 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 */
+ /* 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. */
*status|=DEC_Insufficient_storage;
break;}
- acc=(Unit *)zacc; /* -> target Unit array */
+ acc=(Unit *)zacc; /* -> target Unit array */
#if DECDPUN==1
zacc+=zoff; /* start uLong accumulator to right */
#endif
carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); /* [inline] */
}
*(lp+1)+=carry; /* add to item above [inline] */
- *lp-=((uLong)FASTBASE*carry); /* [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 */
+ /* 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 */
/* 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 */
+ /* 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 */
/* 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 */
+ } while(0); /* end protected */
if (allocacc!=NULL) free(allocacc); /* drop any storage used */
#if DECSUBSET
/* Restrictions: */
/* */
/* digits, emax, and -emin in the context must be less than */
-/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */
+/* 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. */
+/* 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). */
/* 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- */
+/* 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, */
+/* 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). */
/* 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, */
+/* 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. */
*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 */
+ comp=decCompare(d, rhs, 1); /* signless compare */
if (comp==BADINT) {
*status|=DEC_Insufficient_storage;
break;}
/* 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 */
+ h+=lever; /* apply leverage selected */
if (h<0) { /* clamp */
- use+=h; /* [may end up subnormal] */
+ 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 */
+ 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 */
+ if (allocrhs==NULL) { /* hopeless -- abandon */
*status|=DEC_Insufficient_storage;
break;}
newrhs=allocrhs; /* use the allocated space */
/* 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 */
+ /* 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 */
/* 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 */
+ 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 */
/* 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",
- iterations, *status, p, x->digits);
+ (LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
#endif
} /* h<=8 */
/* 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 */
+ 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 */
+ if (!seenbit) continue; /* no need to square 1 */
decMultiplyOp(t, t, t, &aset, status); /* acc=acc*acc [square] */
} /*i*/ /* 32 bits */
/* decNumberShow(t); */
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 */
+ } while(0); /* end protected */
if (allocrhs !=NULL) free(allocrhs); /* drop any storage used */
if (allocbufa!=NULL) free(allocbufa); /* .. */
/* 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,
+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};
+ 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 */
/* */
/* 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. */
+/* 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, */
/* */
/* Implementation notes: */
/* */
-/* 1. This is separated out as decLnOp so it can be called from */
+/* 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. */
break;}
} /* integer and short */
- /* Determine the working precision. This is normally the */
+ /* 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 */
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 */
+ 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 */
/* [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 */
+ bset.digits=pp+rhs->digits; /* wider context */
for (;;) { /* iterate */
#if DECCHECK
iterations++;
- if (iterations>24) break; /* consider 9 * 2**24 */
+ if (iterations>24) break; /* consider 9 * 2**24 */
#endif
- /* calculate the adjustment (exp(-a)*x-1) into b. This is a */
+ /* 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 */
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 */
+ 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 */
/* just a sanity check; remove the test to show always */
if (iterations>24)
printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
- iterations, *status, p, rhs->digits);
+ (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
#endif
/* Copy and round the result to res */
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 */
+ } while(0); /* end protected */
if (allocbufa!=NULL) free(allocbufa); /* drop any storage used */
if (allocbufb!=NULL) free(allocbufb); /* .. */
/* */
/* 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 */
+/* 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) */
#endif
const decNumber *inrhs=rhs; /* save original rhs */
Int reqdigits=set->digits; /* requested DIGITS */
- Int reqexp; /* requested exponent [-scale] */
+ Int reqexp; /* requested exponent [-scale] */
Int residue=0; /* rounding residue */
Int etiny=set->emin-(reqdigits-1);
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 */
+ if (res->digits==reqdigits) { /* cannot shift by 1 */
*status&=~(DEC_Inexact | DEC_Rounded); /* [clean these] */
*status|=DEC_Invalid_operation;
break;
}
else {
decFinalize(res, set, &residue, status); /* set subnormal flags */
- *status&=~DEC_Underflow; /* suppress Underflow [754r] */
+ *status&=~DEC_Underflow; /* suppress Underflow [as per 754] */
}
- } while(0); /* end protected */
+ } while(0); /* end protected */
#if DECSUBSET
if (allocrhs!=NULL) free(allocrhs); /* drop any storage used */
/* 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. */
+/* Invalid operation. */
/* COMPMAX -- returns the larger of the operands, using the */
-/* 754r maxnum operation */
+/* 754 maxnum operation */
/* COMPMAXMAG -- ditto, comparing absolute values */
-/* COMPMIN -- the 754r minnum operation */
+/* COMPMIN -- the 754 minnum operation */
/* COMPMINMAG -- ditto, comparing absolute values */
-/* COMTOTAL -- returns the signum (as a number) giving the */
-/* result of a comparison using 754r total ordering */
+/* 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 */
+/* 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, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
+/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
/* ------------------------------------------------------------------ */
-/* The emphasis here is on speed for common cases, and avoiding */
+/* The emphasis here is on speed for common cases, and avoiding */
/* coefficient comparison if possible. */
/* ------------------------------------------------------------------ */
decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
decNumber *allocrhs=NULL; /* .., rhs */
#endif
Int result=0; /* default result value */
- uByte merged; /* work */
+ uByte merged; /* work */
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
/* 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 */
+ 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 */
else if (merged & DECSNAN); /* sNaN -> qNaN */
else { /* here if MIN or MAX and one or two quiet NaNs */
- /* min or max -- 754r rules ignore single NaN */
+ /* 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;
/* have numbers */
if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
else result=decCompare(lhs, rhs, 0); /* sign matters */
- } while(0); /* end protected */
+ } while(0); /* end protected */
if (result==BADINT) *status|=DEC_Insufficient_storage; /* rare */
else {
/* choose the operand for the result */
const decNumber *choice;
if (result==0) { /* operands are numerically equal */
- /* choose according to sign then exponent (see 754r) */
+ /* choose according to sign then exponent (see 754) */
uByte slhs=(lhs->bits & DECNEG);
uByte srhs=(rhs->bits & DECNEG);
#if DECSUBSET
else result=-1;
/* [if equal, use lhs, technically identical] */
}
- else { /* both positive */
+ else { /* both positive */
if (lhs->exponent>rhs->exponent) result=+1;
else result=-1;
/* [ditto] */
/* ------------------------------------------------------------------ */
static Int decCompare(const decNumber *lhs, const decNumber *rhs,
Flag abs) {
- Int result; /* result value */
+ Int result; /* result value */
Int sigr; /* rhs signum */
Int compare; /* work */
compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
rhs->lsu, D2U(rhs->digits),
rhs->exponent-lhs->exponent);
- if (compare!=BADINT) compare*=result; /* comparison succeeded */
+ if (compare!=BADINT) compare*=result; /* comparison succeeded */
return compare;
} /* decCompare */
/* */
/* 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) */
+/* B has an exponent of E (which must be non-negative) */
/* */
/* Arg1 is A first Unit (lsu) */
/* Arg2 is A length in Units */
/* */
/* 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, which can */
-/* only occur if E!=0) */
+/* 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 */
+ 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 (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 */
return 0; /* all units match */
} /* aligned */
- /* Unaligned. If one is >1 unit longer than the other, padded */
+ /* Unaligned. If one is >1 unit longer than the other, padded */
/* approximately, then can return easily */
if (alength>blength+(Int)D2U(exp)) return 1;
if (alength+1<blength+(Int)D2U(exp)) return -1;
/* 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 */
+/* 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. */
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 *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) */
+ eInt carry=0; /* carry integer (could be Long) */
Int add; /* work */
#if DECDPUN<=4 /* myriadal, millenary, etc. */
Int est; /* estimated quotient */
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 */
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
if (*c<DECDPUNMAX+1) continue; /* was OK */
carry++;
*c-=DECDPUNMAX+1;
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 */
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
if (*c<DECDPUNMAX+1) continue; /* was OK */
carry++;
*c-=DECDPUNMAX+1;
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 */
+ 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 */
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 */
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
if (*c<DECDPUNMAX+1) continue; /* was OK */
carry++;
*c-=DECDPUNMAX+1;
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 */
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
if (*c<DECDPUNMAX+1) continue; /* was OK */
carry++;
*c-=DECDPUNMAX+1;
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 */
+ carry=est-(DECDPUNMAX+1); /* correctly negative */
#else
if ((ueInt)carry<(DECDPUNMAX+1)*2){ /* fastpath carry 1 */
*c=(Unit)(carry-(DECDPUNMAX+1));
/* 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 */
+/* noclamp is 1 to unconditional (unclamped) trim */
/* dropped returns the number of discarded trailing zeros */
-/* returns dn */
+/* returns dn */
/* */
/* If clamp is set in the context then the number of zeros trimmed */
/* may be limited if the exponent is high. */
/* so special values are unchanged and no error is possible. */
/* ------------------------------------------------------------------ */
static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
- Int *dropped) {
- Int d, exp; /* work */
+ Flag noclamp, Int *dropped) {
+ Int d, exp; /* work */
uInt cut; /* .. */
Unit *up; /* -> current Unit */
if (*up%powers[cut]!=0) break; /* found non-0 digit */
#endif
/* have a trailing 0 */
- if (!all) { /* trimming */
+ 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 */
if (d==0) return dn; /* none to drop */
/* may need to limit drop if clamping */
- if (set->clamp) {
+ 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;
/* 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). */
+/* be large enough to hold the result, after shifting). */
/* ------------------------------------------------------------------ */
static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
Unit *target, *source, *first; /* work */
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 */
+ cut=DECDPUN-MSUDIGITS(shift); /* where to slice */
+ if (cut==0) { /* unit-boundary case */
for (; source>=uar; source--, target--) *target=*source;
}
else {
/* ------------------------------------------------------------------ */
/* decShiftToLeast -- shift digits in array towards least significant */
/* */
-/* uar is the array */
+/* 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 <= 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 */
+/* Removed digits are discarded (lost). Units not required to hold */
/* the final result are unchanged. */
/* ------------------------------------------------------------------ */
static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
/* 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. */
+/* 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(const decNumber *dn, decContext *set,
uInt *status) {
/* 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 */
+/* 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) */
/* ------------------------------------------------------------------ */
/* decSetCoeff -- set the coefficient of a number */
/* */
-/* dn is the number whose coefficient array is to be set. */
+/* 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 */
+/* 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 */
+/* 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 == */
+/* external intermediate array. If it is in the number, lsu must == */
/* dn->lsu and len must == dn->digits. */
/* */
/* Note that the coefficient length (len) may be < set->digits, and */
/* ------------------------------------------------------------------ */
/* 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 */
+/* 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) {
discard=len-set->digits; /* digits to discard */
if (discard<=0) { /* no digits are being discarded */
- if (dn->lsu!=lsu) { /* copy needed */
+ if (dn->lsu!=lsu) { /* copy needed */
/* copy the coefficient array to the result number; no shift needed */
count=len; /* avoids D2U */
up=lsu;
/* some digits must be discarded ... */
dn->exponent+=discard; /* maintain numerical value */
- *status|=DEC_Rounded; /* accumulate Rounded status */
+ *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 */
}
}
if (*residue!=0) *status|=DEC_Inexact; /* record inexactitude */
- *dn->lsu=0; /* coefficient will now be 0 */
+ *dn->lsu=0; /* coefficient will now be 0 */
dn->digits=1; /* .. */
return;
} /* total discard */
/* here up -> Unit with first discarded digit */
cut=discard-(count-DECDPUN)-1;
- if (cut==DECDPUN-1) { /* unit-boundary case (fast) */
+ 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 *residue+=5; /* add sticky bit */
}
else { /* <half */
if (*up!=0) *residue=3; /* [else is 0, leave as sticky bit] */
}
else { /* shift to least */
count=set->digits; /* now digits to end up with */
- dn->digits=count; /* set the new length */
+ 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)
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 */
+ else /* cut>0 */ { /* it's not at bottom of unit */
#if DECDPUN<=4
quot=QUOT10(*up, cut);
rem=*up-quot*powers[cut];
}
else { /* shift to least needed */
count=set->digits; /* now digits to end up with */
- dn->digits=count; /* set the new length */
+ dn->digits=count; /* set the new length */
/* shift-copy the coefficient array to the result number */
for (target=dn->lsu; ; target++) {
*target=(Unit)quot;
/* ------------------------------------------------------------------ */
/* decApplyRound -- apply pending rounding to a number */
/* */
-/* dn is the number, with space for set->digits digits */
+/* 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: */
/* 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 */
+/* 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 */
+/* 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 */
+/* coefficient constant. The exponent and status are unchanged */
/* except if: */
/* */
/* -- the coefficient was increased and is all nines (in which */
if (bump==0) return; /* no action required */
/* Simply use decUnitAddSub unless bumping up and the number is */
- /* all nines. In this special case set to 100... explicitly */
+ /* 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. */
/* 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 */
+ 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 */
+ return; /* done */
}
/* a full unit to check, with more to come */
if (*up!=DECDPUNMAX) break; /* not still 9s */
/* 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 */
+ 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 */
+ 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 */
dn->exponent++;
*status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
}
- return; /* done */
+ return; /* done */
}
/* a full unit to check, with more to come */
/* decFinish -- finish processing a number */
/* */
/* dn is the number */
-/* set is the context */
+/* set is the context */
/* residue is the rounding accumulator (as in decApplyRound) */
/* status is the accumulator */
/* */
/* decFinalize -- final check, clamp, and round of a number */
/* */
/* dn is the number */
-/* set is the context */
+/* 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. */
-/* Underflow and overflow conditions are raised as appropriate. */
+/* Underflow and overflow conditions are raised as appropriate. */
/* All fields are updated as required. */
/* ------------------------------------------------------------------ */
static void decFinalize(decNumber *dn, decContext *set, Int *residue,
nmin.lsu[0]=1;
nmin.exponent=set->emin;
comp=decCompare(dn, &nmin, 1); /* (signless compare) */
- if (comp==BADINT) { /* oops */
+ 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 */
+ decApplyRound(dn, set, *residue, status); /* might force down */
decSetSubnormal(dn, set, residue, status);
return;
}
dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
}
dn->exponent-=shift; /* adjust the exponent to match */
- *status|=DEC_Clamped; /* and record the dirty deed */
+ *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) */
+/* 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 the rounding mode, following IEEE 854 rules. */
+/* 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 */
+ 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;
} /* decSetOverflow */
/* ------------------------------------------------------------------ */
-/* decSetMaxValue -- set number to +Nmax (maximum normal value) */
+/* decSetMaxValue -- set number to +Nmax (maximum normal value) */
/* */
/* dn is the number to set */
/* set is the context [used for digits and emax] */
/* ------------------------------------------------------------------ */
static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
uInt *status) {
- Int dnexp; /* saves original exponent */
decContext workset; /* work */
Int etiny, adjust; /* .. */
/* adjust>0, so need to rescale the result so exponent becomes Etiny */
/* [this code is similar to that in rescale] */
- dnexp=dn->exponent; /* save exponent */
- workset=*set; /* clone rounding, etc. */
+ workset=*set; /* clone rounding, etc. */
workset.digits=dn->digits-adjust; /* set requested length */
- workset.emin-=adjust; /* and adjust emin to match */
+ 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);
- /* 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;
/* ------------------------------------------------------------------ */
/* decDecap -- decapitate the coefficient of a number */
/* */
-/* dn is the number to be decapitated */
+/* 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 */
+/* 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. */
+/* (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 */
/* ------------------------------------------------------------------ */
/* decStatus -- apply non-zero status */
/* */
-/* dn is the number to set if error */
+/* 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 */
/* ------------------------------------------------------------------ */
/* decGetDigits -- count digits in a Units array */
/* */
-/* uar is the Unit array holding the number (this is often an */
+/* 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] */
/* */
/* ------------------------------------------------------------------ */
/* This may be called twice during some operations. */
static Int decGetDigits(Unit *uar, Int len) {
- Unit *up=uar+(len-1); /* -> msu */
+ Unit *up=uar+(len-1); /* -> msu */
Int digits=(len-1)*DECDPUN+1; /* possible digits excluding msu */
#if DECDPUN>4
uInt const *pow; /* work */
if (*up<10) break; /* is 1-9 */
digits++;
#if DECDPUN>2 /* not done yet */
- if (*up<100) break; /* is 10-99 */
+ if (*up<100) break; /* is 10-99 */
digits++;
#if DECDPUN>3 /* not done yet */
if (*up<1000) break; /* is 100-999 */
}
/* now carefully display the coefficient */
- up=dn->lsu+D2U(dn->digits)-1; /* msu */
+ up=dn->lsu+D2U(dn->digits)-1; /* msu */
printf("%ld", (LI)*up);
for (up=up-1; up>=dn->lsu; up--) {
u=*up;
/* ------------------------------------------------------------------ */
/* decDumpAr -- display a unit array [debug/check aid] */
/* name is a single-character tag name */
-/* ar is the array to display */
+/* ar is the array to display */
/* len is the length of the array in Units */
/* ------------------------------------------------------------------ */
static void decDumpAr(char name, const Unit *ar, Int len) {
/* 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, */
+/* 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. */
/* The caller is expected to abandon immediately if 1 is returned. */
if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
if (res!=DECUNRESU && res!=NULL) {
decNumberZero(res);
- res->bits=DECNAN; /* qNaN */
+ res->bits=DECNAN; /* qNaN */
}
}
return bad;
/* ------------------------------------------------------------------ */
static Flag decCheckNumber(const decNumber *dn) {
const Unit *up; /* work */
- uInt maxuint; /* .. */
+ uInt maxuint; /* .. */
Int ae, d, digits; /* .. */
Int emin, emax; /* .. */
/* 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 */
+ ae=dn->exponent+dn->digits-1; /* adjusted exponent */
emax=DECNUMMAXE;
emin=DECNUMMINE;
digits=DECNUMMAXP;
/* */
/* 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: */
/* ------------------------------------------------------------------ */
static void *decMalloc(size_t n) {
uInt size=n+12; /* true size */
- void *alloc; /* -> allocated storage */
- uInt *j; /* work */
- uByte *b, *b0; /* .. */
+ 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 */
+ 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 ++ dAB: %ld (%d)\n", decAllocBytes, n); */
+ 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 */
/* is, offset by 8). */
/* ------------------------------------------------------------------ */
static void decFree(void *alloc) {
- uInt *j, n; /* pointer, original length */
+ 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 */
- j=(uInt *)b0; /* -> first four bytes */
- n=*j; /* lift */
+ 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, (Int)b0);
+ 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, (Int)b0, n);
+ 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); */
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