The GCC low-level runtime library
*********************************

GCC provides a low-level runtime library, libgcc.a or libgcc_s.so.1 on some platforms.  GCC generates calls to routines in this library automatically, whenever it needs to perform some operation that is too complicated to emit inline code for.

Most of the routines in libgcc handle arithmetic operations that the target processor cannot perform directly.  This includes integer multiply and divide on some machines, and all floating-point and fixed-point operations on other machines.  libgcc also includes routines for exception handling, and a handful of miscellaneous operations.

Some of these routines can be defined in mostly machine-independent C. Others must be hand-written in assembly language for each processor that needs them.

GCC will also generate calls to C library routines, such as memcpy and memset, in some cases.  The set of routines that GCC may possibly use is documented in Other Builtins (Using the GNU Compiler Collection (GCC)).

These routines take arguments and return values of a specific machine mode, not a specific C type.  See Machine Modes, for an explanation of this concept.  For illustrative purposes, in this chapter the floating point type float is assumed to correspond to SFmode; double to DFmode; and long double to both TFmode and XFmode.  Similarly, the integer types int and unsigned int correspond to SImode; long and unsigned long to DImode; and long long and unsigned long long to TImode.

Routines for integer arithmetic
===============================

The integer arithmetic routines are used on platforms that don't provide hardware support for arithmetic operations on some modes.

Arithmetic functions
--------------------

 -- Runtime Function: int __ashlsi3 (int A, int B)
 -- Runtime Function: long __ashldi3 (long A, int B)
 -- Runtime Function: long long __ashlti3 (long long A, int B)
     These functions return the result of shifting A left by B bits.

 -- Runtime Function: int __ashrsi3 (int A, int B)
 -- Runtime Function: long __ashrdi3 (long A, int B)
 -- Runtime Function: long long __ashrti3 (long long A, int B)
     These functions return the result of arithmetically shifting A right by B bits.

 -- Runtime Function: int __divsi3 (int A, int B)
 -- Runtime Function: long __divdi3 (long A, long B)
 -- Runtime Function: long long __divti3 (long long A, long long B)
     These functions return the quotient of the signed division of A and B.

 -- Runtime Function: int __lshrsi3 (int A, int B)
 -- Runtime Function: long __lshrdi3 (long A, int B)
 -- Runtime Function: long long __lshrti3 (long long A, int B)
     These functions return the result of logically shifting A right by B bits.

 -- Runtime Function: int __modsi3 (int A, int B)
 -- Runtime Function: long __moddi3 (long A, long B)
 -- Runtime Function: long long __modti3 (long long A, long long B)
     These functions return the remainder of the signed division of A and B.

 -- Runtime Function: int __mulsi3 (int A, int B)
 -- Runtime Function: long __muldi3 (long A, long B)
 -- Runtime Function: long long __multi3 (long long A, long long B)
     These functions return the product of A and B.

 -- Runtime Function: long __negdi2 (long A)
 -- Runtime Function: long long __negti2 (long long A)
     These functions return the negation of A.

 -- Runtime Function: unsigned int __udivsi3 (unsigned int A, unsigned int B)
 -- Runtime Function: unsigned long __udivdi3 (unsigned long A, unsigned long B)
 -- Runtime Function: unsigned long long __udivti3 (unsigned long long A, unsigned long long B)
     These functions return the quotient of the unsigned division of A and B.

 -- Runtime Function: unsigned long __udivmoddi3 (unsigned long A, unsigned long B, unsigned long *C)
 -- Runtime Function: unsigned long long __udivti3 (unsigned long long A, unsigned long long B, unsigned long long *C)
     These functions calculate both the quotient and remainder of the unsigned division of A and B.  The return value is the quotient, and the remainder is placed in variable pointed to by C.

 -- Runtime Function: unsigned int __umodsi3 (unsigned int A, unsigned int B)
 -- Runtime Function: unsigned long __umoddi3 (unsigned long A, unsigned long B)
 -- Runtime Function: unsigned long long __umodti3 (unsigned long long A, unsigned long long B)
     These functions return the remainder of the unsigned division of A and B.

Comparison functions
--------------------

The following functions implement integral comparisons.  These functions implement a low-level compare, upon which the higher level comparison operators (such as less than and greater than or equal to) can be constructed.  The returned values lie in the range zero to two, to allow the high-level operators to be implemented by testing the returned result using either signed or unsigned comparison.

 -- Runtime Function: int __cmpdi2 (long A, long B)
 -- Runtime Function: int __cmpti2 (long long A, long long B)
     These functions perform a signed comparison of A and B.  If A is less than B, they return 0; if A is greater than B, they return 2; and if A and B are equal they return 1.

 -- Runtime Function: int __ucmpdi2 (unsigned long A, unsigned long B)
 -- Runtime Function: int __ucmpti2 (unsigned long long A, unsigned long long B)
     These functions perform an unsigned comparison of A and B. If A is less than B, they return 0; if A is greater than B, they return 2; and if A and B are equal they return 1.

Trapping arithmetic functions
-----------------------------

The following functions implement trapping arithmetic.  These functions call the libc function abort upon signed arithmetic overflow.

 -- Runtime Function: int __absvsi2 (int A)
 -- Runtime Function: long __absvdi2 (long A)
     These functions return the absolute value of A.

 -- Runtime Function: int __addvsi3 (int A, int B)
 -- Runtime Function: long __addvdi3 (long A, long B)
     These functions return the sum of A and B; that is A + B.

 -- Runtime Function: int __mulvsi3 (int A, int B)
 -- Runtime Function: long __mulvdi3 (long A, long B)
     The functions return the product of A and B; that is A * B.

 -- Runtime Function: int __negvsi2 (int A)
 -- Runtime Function: long __negvdi2 (long A)
     These functions return the negation of A; that is -A.

 -- Runtime Function: int __subvsi3 (int A, int B)
 -- Runtime Function: long __subvdi3 (long A, long B)
     These functions return the difference between B and A; that is A - B.

Bit operations
--------------

 -- Runtime Function: int __clzsi2 (int A)
 -- Runtime Function: int __clzdi2 (long A)
 -- Runtime Function: int __clzti2 (long long A)
     These functions return the number of leading 0-bits in A, starting at the most significant bit position.  If A is zero, the result is undefined.

 -- Runtime Function: int __ctzsi2 (int A)
 -- Runtime Function: int __ctzdi2 (long A)
 -- Runtime Function: int __ctzti2 (long long A)
     These functions return the number of trailing 0-bits in A, starting at the least significant bit position.  If A is zero, the result is undefined.

 -- Runtime Function: int __ffsdi2 (long A)
 -- Runtime Function: int __ffsti2 (long long A)
     These functions return the index of the least significant 1-bit in A, or the value zero if A is zero.  The least significant bit is index one.

 -- Runtime Function: int __paritysi2 (int A)
 -- Runtime Function: int __paritydi2 (long A)
 -- Runtime Function: int __parityti2 (long long A)
     These functions return the value zero if the number of bits set in A is even, and the value one otherwise.

 -- Runtime Function: int __popcountsi2 (int A)
 -- Runtime Function: int __popcountdi2 (long A)
 -- Runtime Function: int __popcountti2 (long long A)
     These functions return the number of bits set in A.

 -- Runtime Function: int32_t __bswapsi2 (int32_t A)
 -- Runtime Function: int64_t __bswapdi2 (int64_t A)
     These functions return the A byteswapped.

Routines for floating point emulation
=====================================

The software floating point library is used on machines which do not have hardware support for floating point.  It is also used whenever -msoft-float is used to disable generation of floating point instructions.  (Not all targets support this switch.)

For compatibility with other compilers, the floating point emulation routines can be renamed with the DECLARE_LIBRARY_RENAMES macro (see Library Calls).  In this section, the default names are used.

Presently the library does not support XFmode, which is used for long double on some architectures.

Arithmetic functions
--------------------

 -- Runtime Function: float __addsf3 (float A, float B)
 -- Runtime Function: double __adddf3 (double A, double B)
 -- Runtime Function: long double __addtf3 (long double A, long double B)
 -- Runtime Function: long double __addxf3 (long double A, long double B)
     These functions return the sum of A and B.

 -- Runtime Function: float __subsf3 (float A, float B)
 -- Runtime Function: double __subdf3 (double A, double B)
 -- Runtime Function: long double __subtf3 (long double A, long double B)
 -- Runtime Function: long double __subxf3 (long double A, long double B)
     These functions return the difference between B and A; that is, A - B.

 -- Runtime Function: float __mulsf3 (float A, float B)
 -- Runtime Function: double __muldf3 (double A, double B)
 -- Runtime Function: long double __multf3 (long double A, long double B)
 -- Runtime Function: long double __mulxf3 (long double A, long double B)
     These functions return the product of A and B.

 -- Runtime Function: float __divsf3 (float A, float B)
 -- Runtime Function: double __divdf3 (double A, double B)
 -- Runtime Function: long double __divtf3 (long double A, long double B)
 -- Runtime Function: long double __divxf3 (long double A, long double B)
     These functions return the quotient of A and B; that is, A / B.

 -- Runtime Function: float __negsf2 (float A)
 -- Runtime Function: double __negdf2 (double A)
 -- Runtime Function: long double __negtf2 (long double A)
 -- Runtime Function: long double __negxf2 (long double A)
     These functions return the negation of A.  They simply flip the sign bit, so they can produce negative zero and negative NaN.

Conversion functions
--------------------

 -- Runtime Function: double __extendsfdf2 (float A)
 -- Runtime Function: long double __extendsftf2 (float A)
 -- Runtime Function: long double __extendsfxf2 (float A)
 -- Runtime Function: long double __extenddftf2 (double A)
 -- Runtime Function: long double __extenddfxf2 (double A)
     These functions extend A to the wider mode of their return type.

 -- Runtime Function: double __truncxfdf2 (long double A)
 -- Runtime Function: double __trunctfdf2 (long double A)
 -- Runtime Function: float __truncxfsf2 (long double A)
 -- Runtime Function: float __trunctfsf2 (long double A)
 -- Runtime Function: float __truncdfsf2 (double A)
     These functions truncate A to the narrower mode of their return type, rounding toward zero.

 -- Runtime Function: int __fixsfsi (float A)
 -- Runtime Function: int __fixdfsi (double A)
 -- Runtime Function: int __fixtfsi (long double A)
 -- Runtime Function: int __fixxfsi (long double A)
     These functions convert A to a signed integer, rounding toward zero.

 -- Runtime Function: long __fixsfdi (float A)
 -- Runtime Function: long __fixdfdi (double A)
 -- Runtime Function: long __fixtfdi (long double A)
 -- Runtime Function: long __fixxfdi (long double A)
     These functions convert A to a signed long, rounding toward zero.

 -- Runtime Function: long long __fixsfti (float A)
 -- Runtime Function: long long __fixdfti (double A)
 -- Runtime Function: long long __fixtfti (long double A)
 -- Runtime Function: long long __fixxfti (long double A)
     These functions convert A to a signed long long, rounding toward zero.

 -- Runtime Function: unsigned int __fixunssfsi (float A)
 -- Runtime Function: unsigned int __fixunsdfsi (double A)
 -- Runtime Function: unsigned int __fixunstfsi (long double A)
 -- Runtime Function: unsigned int __fixunsxfsi (long double A)
     These functions convert A to an unsigned integer, rounding toward zero.  Negative values all become zero.

 -- Runtime Function: unsigned long __fixunssfdi (float A)
 -- Runtime Function: unsigned long __fixunsdfdi (double A)
 -- Runtime Function: unsigned long __fixunstfdi (long double A)
 -- Runtime Function: unsigned long __fixunsxfdi (long double A)
     These functions convert A to an unsigned long, rounding toward zero.  Negative values all become zero.

 -- Runtime Function: unsigned long long __fixunssfti (float A)
 -- Runtime Function: unsigned long long __fixunsdfti (double A)
 -- Runtime Function: unsigned long long __fixunstfti (long double A)
 -- Runtime Function: unsigned long long __fixunsxfti (long double A)
     These functions convert A to an unsigned long long, rounding toward zero.  Negative values all become zero.

 -- Runtime Function: float __floatsisf (int I)
 -- Runtime Function: double __floatsidf (int I)
 -- Runtime Function: long double __floatsitf (int I)
 -- Runtime Function: long double __floatsixf (int I)
     These functions convert I, a signed integer, to floating point.

 -- Runtime Function: float __floatdisf (long I)
 -- Runtime Function: double __floatdidf (long I)
 -- Runtime Function: long double __floatditf (long I)
 -- Runtime Function: long double __floatdixf (long I)
     These functions convert I, a signed long, to floating point.

 -- Runtime Function: float __floattisf (long long I)
 -- Runtime Function: double __floattidf (long long I)
 -- Runtime Function: long double __floattitf (long long I)
 -- Runtime Function: long double __floattixf (long long I)
     These functions convert I, a signed long long, to floating point.

 -- Runtime Function: float __floatunsisf (unsigned int I)
 -- Runtime Function: double __floatunsidf (unsigned int I)
 -- Runtime Function: long double __floatunsitf (unsigned int I)
 -- Runtime Function: long double __floatunsixf (unsigned int I)
     These functions convert I, an unsigned integer, to floating point.

 -- Runtime Function: float __floatundisf (unsigned long I)
 -- Runtime Function: double __floatundidf (unsigned long I)
 -- Runtime Function: long double __floatunditf (unsigned long I)
 -- Runtime Function: long double __floatundixf (unsigned long I)
     These functions convert I, an unsigned long, to floating point.

 -- Runtime Function: float __floatuntisf (unsigned long long I)
 -- Runtime Function: double __floatuntidf (unsigned long long I)
 -- Runtime Function: long double __floatuntitf (unsigned long long I)
 -- Runtime Function: long double __floatuntixf (unsigned long long I)
     These functions convert I, an unsigned long long, to floating point.

Comparison functions
--------------------

There are two sets of basic comparison functions.

 -- Runtime Function: int __cmpsf2 (float A, float B)
 -- Runtime Function: int __cmpdf2 (double A, double B)
 -- Runtime Function: int __cmptf2 (long double A, long double B)
     These functions calculate a <=> b.  That is, if A is less than B, they return -1; if A is greater than B, they return 1; and if A and B are equal they return 0.  If either argument is NaN they return 1, but you should not rely on this; if NaN is a possibility, use one of the higher-level comparison functions.

 -- Runtime Function: int __unordsf2 (float A, float B)
 -- Runtime Function: int __unorddf2 (double A, double B)
 -- Runtime Function: int __unordtf2 (long double A, long double B)
     These functions return a nonzero value if either argument is NaN, otherwise 0.

There is also a complete group of higher level functions which correspond directly to comparison operators.  They implement the ISO C semantics for floating-point comparisons, taking NaN into account. Pay careful attention to the return values defined for each set. Under the hood, all of these routines are implemented as

       if (__unordXf2 (a, b))
         return E;
       return __cmpXf2 (a, b);

where E is a constant chosen to give the proper behavior for NaN.  Thus, the meaning of the return value is different for each set. Do not rely on this implementation; only the semantics documented below are guaranteed.

 -- Runtime Function: int __eqsf2 (float A, float B)
 -- Runtime Function: int __eqdf2 (double A, double B)
 -- Runtime Function: int __eqtf2 (long double A, long double B)
     These functions return zero if neither argument is NaN, and A and B are equal.

 -- Runtime Function: int __nesf2 (float A, float B)
 -- Runtime Function: int __nedf2 (double A, double B)
 -- Runtime Function: int __netf2 (long double A, long double B)
     These functions return a nonzero value if either argument is NaN, or if A and B are unequal.

 -- Runtime Function: int __gesf2 (float A, float B)
 -- Runtime Function: int __gedf2 (double A, double B)
 -- Runtime Function: int __getf2 (long double A, long double B)
     These functions return a value greater than or equal to zero if neither argument is NaN, and A is greater than or equal to B.

 -- Runtime Function: int __ltsf2 (float A, float B)
 -- Runtime Function: int __ltdf2 (double A, double B)
 -- Runtime Function: int __lttf2 (long double A, long double B)
     These functions return a value less than zero if neither argument is NaN, and A is strictly less than B.

 -- Runtime Function: int __lesf2 (float A, float B)
 -- Runtime Function: int __ledf2 (double A, double B)
 -- Runtime Function: int __letf2 (long double A, long double B)
     These functions return a value less than or equal to zero if neither argument is NaN, and A is less than or equal to B.

 -- Runtime Function: int __gtsf2 (float A, float B)
 -- Runtime Function: int __gtdf2 (double A, double B)
 -- Runtime Function: int __gttf2 (long double A, long double B)
     These functions return a value greater than zero if neither argument is NaN, and A is strictly greater than B.

Other floating-point functions
------------------------------

 -- Runtime Function: float __powisf2 (float A, int B)
 -- Runtime Function: double __powidf2 (double A, int B)
 -- Runtime Function: long double __powitf2 (long double A, int B)
 -- Runtime Function: long double __powixf2 (long double A, int B)
     These functions convert raise A to the power B.

 -- Runtime Function: complex float __mulsc3 (float A, float B, float C, float D)
 -- Runtime Function: complex double __muldc3 (double A, double B, double C, double D)
 -- Runtime Function: complex long double __multc3 (long double A, long double B, long double C, long double D)
 -- Runtime Function: complex long double __mulxc3 (long double A, long double B, long double C, long double D)
     These functions return the product of A + iB and C + iD, following the rules of C99 Annex G.

 -- Runtime Function: complex float __divsc3 (float A, float B, float C, float D)
 -- Runtime Function: complex double __divdc3 (double A, double B, double C, double D)
 -- Runtime Function: complex long double __divtc3 (long double A, long double B, long double C, long double D)
 -- Runtime Function: complex long double __divxc3 (long double A, long double B, long double C, long double D)
     These functions return the quotient of A + iB and C + iD (i.e., (A + iB) / (C + iD)), following the rules of C99 Annex G.

Routines for decimal floating point emulation
=============================================

The software decimal floating point library implements IEEE 754R decimal floating point arithmetic and is only activated on selected targets.

The software decimal floating point library supports either DPD (Densely Packed Decimal) or BID (Binary Integer Decimal) encoding as selected at configure time.

Arithmetic functions
--------------------

 -- Runtime Function: _Decimal32 __dpd_addsd3 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: _Decimal32 __bid_addsd3 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: _Decimal64 __dpd_adddd3 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: _Decimal64 __bid_adddd3 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: _Decimal128 __dpd_addtd3 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: _Decimal128 __bid_addtd3 (_Decimal128 A, _Decimal128 B)
     These functions return the sum of A and B.

 -- Runtime Function: _Decimal32 __dpd_subsd3 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: _Decimal32 __bid_subsd3 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: _Decimal64 __dpd_subdd3 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: _Decimal64 __bid_subdd3 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: _Decimal128 __dpd_subtd3 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: _Decimal128 __bid_subtd3 (_Decimal128 A, _Decimal128 B)
     These functions return the difference between B and A; that is, A - B.

 -- Runtime Function: _Decimal32 __dpd_mulsd3 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: _Decimal32 __bid_mulsd3 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: _Decimal64 __dpd_muldd3 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: _Decimal64 __bid_muldd3 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: _Decimal128 __dpd_multd3 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: _Decimal128 __bid_multd3 (_Decimal128 A, _Decimal128 B)
     These functions return the product of A and B.

 -- Runtime Function: _Decimal32 __dpd_divsd3 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: _Decimal32 __bid_divsd3 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: _Decimal64 __dpd_divdd3 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: _Decimal64 __bid_divdd3 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: _Decimal128 __dpd_divtd3 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: _Decimal128 __bid_divtd3 (_Decimal128 A, _Decimal128 B)
     These functions return the quotient of A and B; that is, A / B.

 -- Runtime Function: _Decimal32 __dpd_negsd2 (_Decimal32 A)
 -- Runtime Function: _Decimal32 __bid_negsd2 (_Decimal32 A)
 -- Runtime Function: _Decimal64 __dpd_negdd2 (_Decimal64 A)
 -- Runtime Function: _Decimal64 __bid_negdd2 (_Decimal64 A)
 -- Runtime Function: _Decimal128 __dpd_negtd2 (_Decimal128 A)
 -- Runtime Function: _Decimal128 __bid_negtd2 (_Decimal128 A)
     These functions return the negation of A.  They simply flip the sign bit, so they can produce negative zero and negative NaN.

Conversion functions
--------------------

 -- Runtime Function: _Decimal64 __dpd_extendsddd2 (_Decimal32 A)
 -- Runtime Function: _Decimal64 __bid_extendsddd2 (_Decimal32 A)
 -- Runtime Function: _Decimal128 __dpd_extendsdtd2 (_Decimal32 A)
 -- Runtime Function: _Decimal128 __bid_extendsdtd2 (_Decimal32 A)
 -- Runtime Function: _Decimal128 __dpd_extendddtd2 (_Decimal64 A)
 -- Runtime Function: _Decimal128 __bid_extendddtd2 (_Decimal64 A)
 -- Runtime Function: _Decimal32 __dpd_truncddsd2 (_Decimal64 A)
 -- Runtime Function: _Decimal32 __bid_truncddsd2 (_Decimal64 A)
 -- Runtime Function: _Decimal32 __dpd_trunctdsd2 (_Decimal128 A)
 -- Runtime Function: _Decimal32 __bid_trunctdsd2 (_Decimal128 A)
 -- Runtime Function: _Decimal64 __dpd_trunctddd2 (_Decimal128 A)
 -- Runtime Function: _Decimal64 __bid_trunctddd2 (_Decimal128 A)
     These functions convert the value A from one decimal floating type to another.

 -- Runtime Function: _Decimal64 __dpd_extendsfdd (float A)
 -- Runtime Function: _Decimal64 __bid_extendsfdd (float A)
 -- Runtime Function: _Decimal128 __dpd_extendsftd (float A)
 -- Runtime Function: _Decimal128 __bid_extendsftd (float A)
 -- Runtime Function: _Decimal128 __dpd_extenddftd (double A)
 -- Runtime Function: _Decimal128 __bid_extenddftd (double A)
 -- Runtime Function: _Decimal128 __dpd_extendxftd (long double A)
 -- Runtime Function: _Decimal128 __bid_extendxftd (long double A)
 -- Runtime Function: _Decimal32 __dpd_truncdfsd (double A)
 -- Runtime Function: _Decimal32 __bid_truncdfsd (double A)
 -- Runtime Function: _Decimal32 __dpd_truncxfsd (long double A)
 -- Runtime Function: _Decimal32 __bid_truncxfsd (long double A)
 -- Runtime Function: _Decimal32 __dpd_trunctfsd (long double A)
 -- Runtime Function: _Decimal32 __bid_trunctfsd (long double A)
 -- Runtime Function: _Decimal64 __dpd_truncxfdd (long double A)
 -- Runtime Function: _Decimal64 __bid_truncxfdd (long double A)
 -- Runtime Function: _Decimal64 __dpd_trunctfdd (long double A)
 -- Runtime Function: _Decimal64 __bid_trunctfdd (long double A)
     These functions convert the value of A from a binary floating type to a decimal floating type of a different size.

 -- Runtime Function: float __dpd_truncddsf (_Decimal64 A)
 -- Runtime Function: float __bid_truncddsf (_Decimal64 A)
 -- Runtime Function: float __dpd_trunctdsf (_Decimal128 A)
 -- Runtime Function: float __bid_trunctdsf (_Decimal128 A)
 -- Runtime Function: double __dpd_extendsddf (_Decimal32 A)
 -- Runtime Function: double __bid_extendsddf (_Decimal32 A)
 -- Runtime Function: double __dpd_trunctddf (_Decimal128 A)
 -- Runtime Function: double __bid_trunctddf (_Decimal128 A)
 -- Runtime Function: long double __dpd_extendsdxf (_Decimal32 A)
 -- Runtime Function: long double __bid_extendsdxf (_Decimal32 A)
 -- Runtime Function: long double __dpd_extendddxf (_Decimal64 A)
 -- Runtime Function: long double __bid_extendddxf (_Decimal64 A)
 -- Runtime Function: long double __dpd_trunctdxf (_Decimal128 A)
 -- Runtime Function: long double __bid_trunctdxf (_Decimal128 A)
 -- Runtime Function: long double __dpd_extendsdtf (_Decimal32 A)
 -- Runtime Function: long double __bid_extendsdtf (_Decimal32 A)
 -- Runtime Function: long double __dpd_extendddtf (_Decimal64 A)
 -- Runtime Function: long double __bid_extendddtf (_Decimal64 A)
     These functions convert the value of A from a decimal floating type to a binary floating type of a different size.

 -- Runtime Function: _Decimal32 __dpd_extendsfsd (float A)
 -- Runtime Function: _Decimal32 __bid_extendsfsd (float A)
 -- Runtime Function: _Decimal64 __dpd_extenddfdd (double A)
 -- Runtime Function: _Decimal64 __bid_extenddfdd (double A)
 -- Runtime Function: _Decimal128 __dpd_extendtftd (long double A)
 -- Runtime Function: _Decimal128 __bid_extendtftd (long double A)
 -- Runtime Function: float __dpd_truncsdsf (_Decimal32 A)
 -- Runtime Function: float __bid_truncsdsf (_Decimal32 A)
 -- Runtime Function: double __dpd_truncdddf (_Decimal64 A)
 -- Runtime Function: double __bid_truncdddf (_Decimal64 A)
 -- Runtime Function: long double __dpd_trunctdtf (_Decimal128 A)
 -- Runtime Function: long double __bid_trunctdtf (_Decimal128 A)
     These functions convert the value of A between decimal and binary floating types of the same size.

 -- Runtime Function: int __dpd_fixsdsi (_Decimal32 A)
 -- Runtime Function: int __bid_fixsdsi (_Decimal32 A)
 -- Runtime Function: int __dpd_fixddsi (_Decimal64 A)
 -- Runtime Function: int __bid_fixddsi (_Decimal64 A)
 -- Runtime Function: int __dpd_fixtdsi (_Decimal128 A)
 -- Runtime Function: int __bid_fixtdsi (_Decimal128 A)
     These functions convert A to a signed integer.

 -- Runtime Function: long __dpd_fixsddi (_Decimal32 A)
 -- Runtime Function: long __bid_fixsddi (_Decimal32 A)
 -- Runtime Function: long __dpd_fixdddi (_Decimal64 A)
 -- Runtime Function: long __bid_fixdddi (_Decimal64 A)
 -- Runtime Function: long __dpd_fixtddi (_Decimal128 A)
 -- Runtime Function: long __bid_fixtddi (_Decimal128 A)
     These functions convert A to a signed long.

 -- Runtime Function: unsigned int __dpd_fixunssdsi (_Decimal32 A)
 -- Runtime Function: unsigned int __bid_fixunssdsi (_Decimal32 A)
 -- Runtime Function: unsigned int __dpd_fixunsddsi (_Decimal64 A)
 -- Runtime Function: unsigned int __bid_fixunsddsi (_Decimal64 A)
 -- Runtime Function: unsigned int __dpd_fixunstdsi (_Decimal128 A)
 -- Runtime Function: unsigned int __bid_fixunstdsi (_Decimal128 A)
     These functions convert A to an unsigned integer.  Negative values all become zero.

 -- Runtime Function: unsigned long __dpd_fixunssddi (_Decimal32 A)
 -- Runtime Function: unsigned long __bid_fixunssddi (_Decimal32 A)
 -- Runtime Function: unsigned long __dpd_fixunsdddi (_Decimal64 A)
 -- Runtime Function: unsigned long __bid_fixunsdddi (_Decimal64 A)
 -- Runtime Function: unsigned long __dpd_fixunstddi (_Decimal128 A)
 -- Runtime Function: unsigned long __bid_fixunstddi (_Decimal128 A)
     These functions convert A to an unsigned long.  Negative values all become zero.

 -- Runtime Function: _Decimal32 __dpd_floatsisd (int I)
 -- Runtime Function: _Decimal32 __bid_floatsisd (int I)
 -- Runtime Function: _Decimal64 __dpd_floatsidd (int I)
 -- Runtime Function: _Decimal64 __bid_floatsidd (int I)
 -- Runtime Function: _Decimal128 __dpd_floatsitd (int I)
 -- Runtime Function: _Decimal128 __bid_floatsitd (int I)
     These functions convert I, a signed integer, to decimal floating point.

 -- Runtime Function: _Decimal32 __dpd_floatdisd (long I)
 -- Runtime Function: _Decimal32 __bid_floatdisd (long I)
 -- Runtime Function: _Decimal64 __dpd_floatdidd (long I)
 -- Runtime Function: _Decimal64 __bid_floatdidd (long I)
 -- Runtime Function: _Decimal128 __dpd_floatditd (long I)
 -- Runtime Function: _Decimal128 __bid_floatditd (long I)
     These functions convert I, a signed long, to decimal floating point.

 -- Runtime Function: _Decimal32 __dpd_floatunssisd (unsigned int I)
 -- Runtime Function: _Decimal32 __bid_floatunssisd (unsigned int I)
 -- Runtime Function: _Decimal64 __dpd_floatunssidd (unsigned int I)
 -- Runtime Function: _Decimal64 __bid_floatunssidd (unsigned int I)
 -- Runtime Function: _Decimal128 __dpd_floatunssitd (unsigned int I)
 -- Runtime Function: _Decimal128 __bid_floatunssitd (unsigned int I)
     These functions convert I, an unsigned integer, to decimal floating point.

 -- Runtime Function: _Decimal32 __dpd_floatunsdisd (unsigned long I)
 -- Runtime Function: _Decimal32 __bid_floatunsdisd (unsigned long I)
 -- Runtime Function: _Decimal64 __dpd_floatunsdidd (unsigned long I)
 -- Runtime Function: _Decimal64 __bid_floatunsdidd (unsigned long I)
 -- Runtime Function: _Decimal128 __dpd_floatunsditd (unsigned long I)
 -- Runtime Function: _Decimal128 __bid_floatunsditd (unsigned long I)
     These functions convert I, an unsigned long, to decimal floating point.

Comparison functions
--------------------

 -- Runtime Function: int __dpd_unordsd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __bid_unordsd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __dpd_unorddd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __bid_unorddd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __dpd_unordtd2 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: int __bid_unordtd2 (_Decimal128 A, _Decimal128 B)
     These functions return a nonzero value if either argument is NaN, otherwise 0.

There is also a complete group of higher level functions which correspond directly to comparison operators.  They implement the ISO C semantics for floating-point comparisons, taking NaN into account. Pay careful attention to the return values defined for each set. Under the hood, all of these routines are implemented as

       if (__bid_unordXd2 (a, b))
         return E;
       return __bid_cmpXd2 (a, b);

where E is a constant chosen to give the proper behavior for NaN.  Thus, the meaning of the return value is different for each set. Do not rely on this implementation; only the semantics documented below are guaranteed.

 -- Runtime Function: int __dpd_eqsd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __bid_eqsd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __dpd_eqdd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __bid_eqdd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __dpd_eqtd2 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: int __bid_eqtd2 (_Decimal128 A, _Decimal128 B)
     These functions return zero if neither argument is NaN, and A and B are equal.

 -- Runtime Function: int __dpd_nesd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __bid_nesd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __dpd_nedd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __bid_nedd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __dpd_netd2 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: int __bid_netd2 (_Decimal128 A, _Decimal128 B)
     These functions return a nonzero value if either argument is NaN, or if A and B are unequal.

 -- Runtime Function: int __dpd_gesd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __bid_gesd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __dpd_gedd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __bid_gedd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __dpd_getd2 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: int __bid_getd2 (_Decimal128 A, _Decimal128 B)
     These functions return a value greater than or equal to zero if neither argument is NaN, and A is greater than or equal to B.

 -- Runtime Function: int __dpd_ltsd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __bid_ltsd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __dpd_ltdd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __bid_ltdd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __dpd_lttd2 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: int __bid_lttd2 (_Decimal128 A, _Decimal128 B)
     These functions return a value less than zero if neither argument is NaN, and A is strictly less than B.

 -- Runtime Function: int __dpd_lesd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __bid_lesd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __dpd_ledd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __bid_ledd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __dpd_letd2 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: int __bid_letd2 (_Decimal128 A, _Decimal128 B)
     These functions return a value less than or equal to zero if neither argument is NaN, and A is less than or equal to B.

 -- Runtime Function: int __dpd_gtsd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __bid_gtsd2 (_Decimal32 A, _Decimal32 B)
 -- Runtime Function: int __dpd_gtdd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __bid_gtdd2 (_Decimal64 A, _Decimal64 B)
 -- Runtime Function: int __dpd_gttd2 (_Decimal128 A, _Decimal128 B)
 -- Runtime Function: int __bid_gttd2 (_Decimal128 A, _Decimal128 B)
     These functions return a value greater than zero if neither argument is NaN, and A is strictly greater than B.

Routines for fixed-point fractional emulation
=============================================

The software fixed-point library implements fixed-point fractional arithmetic, and is only activated on selected targets.

For ease of comprehension fract is an alias for the _Fract type, accum an alias for _Accum, and sat an alias for _Sat.

For illustrative purposes, in this section the fixed-point fractional type short fract is assumed to correspond to machine mode QQmode; unsigned short fract to UQQmode; fract to HQmode; unsigned fract to UHQmode; long fract to SQmode; unsigned long fract to USQmode; long long fract to DQmode; and unsigned long long fract to UDQmode. Similarly the fixed-point accumulator type short accum corresponds to HAmode; unsigned short accum to UHAmode; accum to SAmode; unsigned accum to USAmode; long accum to DAmode; unsigned long accum to UDAmode; long long accum to TAmode; and unsigned long long accum to UTAmode.

Arithmetic functions
--------------------

 -- Runtime Function: short fract __addqq3 (short fract A, short fract B)
 -- Runtime Function: fract __addhq3 (fract A, fract B)
 -- Runtime Function: long fract __addsq3 (long fract A, long fract B)
 -- Runtime Function: long long fract __adddq3 (long long fract A, long long fract B)
 -- Runtime Function: unsigned short fract __adduqq3 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: unsigned fract __adduhq3 (unsigned fract A, unsigned fract B)
 -- Runtime Function: unsigned long fract __addusq3 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: unsigned long long fract __addudq3 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: short accum __addha3 (short accum A, short accum B)
 -- Runtime Function: accum __addsa3 (accum A, accum B)
 -- Runtime Function: long accum __addda3 (long accum A, long accum B)
 -- Runtime Function: long long accum __addta3 (long long accum A, long long accum B)
 -- Runtime Function: unsigned short accum __adduha3 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: unsigned accum __addusa3 (unsigned accum A, unsigned accum B)
 -- Runtime Function: unsigned long accum __adduda3 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: unsigned long long accum __adduta3 (unsigned long long accum A, unsigned long long accum B)
     These functions return the sum of A and B.

 -- Runtime Function: short fract __ssaddqq3 (short fract A, short fract B)
 -- Runtime Function: fract __ssaddhq3 (fract A, fract B)
 -- Runtime Function: long fract __ssaddsq3 (long fract A, long fract B)
 -- Runtime Function: long long fract __ssadddq3 (long long fract A, long long fract B)
 -- Runtime Function: short accum __ssaddha3 (short accum A, short accum B)
 -- Runtime Function: accum __ssaddsa3 (accum A, accum B)
 -- Runtime Function: long accum __ssaddda3 (long accum A, long accum B)
 -- Runtime Function: long long accum __ssaddta3 (long long accum A, long long accum B)
     These functions return the sum of A and B with signed saturation.

 -- Runtime Function: unsigned short fract __usadduqq3 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: unsigned fract __usadduhq3 (unsigned fract A, unsigned fract B)
 -- Runtime Function: unsigned long fract __usaddusq3 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: unsigned long long fract __usaddudq3 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: unsigned short accum __usadduha3 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: unsigned accum __usaddusa3 (unsigned accum A, unsigned accum B)
 -- Runtime Function: unsigned long accum __usadduda3 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: unsigned long long accum __usadduta3 (unsigned long long accum A, unsigned long long accum B)
     These functions return the sum of A and B with unsigned saturation.

 -- Runtime Function: short fract __subqq3 (short fract A, short fract B)
 -- Runtime Function: fract __subhq3 (fract A, fract B)
 -- Runtime Function: long fract __subsq3 (long fract A, long fract B)
 -- Runtime Function: long long fract __subdq3 (long long fract A, long long fract B)
 -- Runtime Function: unsigned short fract __subuqq3 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: unsigned fract __subuhq3 (unsigned fract A, unsigned fract B)
 -- Runtime Function: unsigned long fract __subusq3 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: unsigned long long fract __subudq3 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: short accum __subha3 (short accum A, short accum B)
 -- Runtime Function: accum __subsa3 (accum A, accum B)
 -- Runtime Function: long accum __subda3 (long accum A, long accum B)
 -- Runtime Function: long long accum __subta3 (long long accum A, long long accum B)
 -- Runtime Function: unsigned short accum __subuha3 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: unsigned accum __subusa3 (unsigned accum A, unsigned accum B)
 -- Runtime Function: unsigned long accum __subuda3 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: unsigned long long accum __subuta3 (unsigned long long accum A, unsigned long long accum B)
     These functions return the difference of A and B; that is, A - B.

 -- Runtime Function: short fract __sssubqq3 (short fract A, short fract B)
 -- Runtime Function: fract __sssubhq3 (fract A, fract B)
 -- Runtime Function: long fract __sssubsq3 (long fract A, long fract B)
 -- Runtime Function: long long fract __sssubdq3 (long long fract A, long long fract B)
 -- Runtime Function: short accum __sssubha3 (short accum A, short accum B)
 -- Runtime Function: accum __sssubsa3 (accum A, accum B)
 -- Runtime Function: long accum __sssubda3 (long accum A, long accum B)
 -- Runtime Function: long long accum __sssubta3 (long long accum A, long long accum B)
     These functions return the difference of A and B with signed saturation;  that is, A - B.

 -- Runtime Function: unsigned short fract __ussubuqq3 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: unsigned fract __ussubuhq3 (unsigned fract A, unsigned fract B)
 -- Runtime Function: unsigned long fract __ussubusq3 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: unsigned long long fract __ussubudq3 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: unsigned short accum __ussubuha3 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: unsigned accum __ussubusa3 (unsigned accum A, unsigned accum B)
 -- Runtime Function: unsigned long accum __ussubuda3 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: unsigned long long accum __ussubuta3 (unsigned long long accum A, unsigned long long accum B)
     These functions return the difference of A and B with unsigned saturation;  that is, A - B.

 -- Runtime Function: short fract __mulqq3 (short fract A, short fract B)
 -- Runtime Function: fract __mulhq3 (fract A, fract B)
 -- Runtime Function: long fract __mulsq3 (long fract A, long fract B)
 -- Runtime Function: long long fract __muldq3 (long long fract A, long long fract B)
 -- Runtime Function: unsigned short fract __muluqq3 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: unsigned fract __muluhq3 (unsigned fract A, unsigned fract B)
 -- Runtime Function: unsigned long fract __mulusq3 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: unsigned long long fract __muludq3 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: short accum __mulha3 (short accum A, short accum B)
 -- Runtime Function: accum __mulsa3 (accum A, accum B)
 -- Runtime Function: long accum __mulda3 (long accum A, long accum B)
 -- Runtime Function: long long accum __multa3 (long long accum A, long long accum B)
 -- Runtime Function: unsigned short accum __muluha3 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: unsigned accum __mulusa3 (unsigned accum A, unsigned accum B)
 -- Runtime Function: unsigned long accum __muluda3 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: unsigned long long accum __muluta3 (unsigned long long accum A, unsigned long long accum B)
     These functions return the product of A and B.

 -- Runtime Function: short fract __ssmulqq3 (short fract A, short fract B)
 -- Runtime Function: fract __ssmulhq3 (fract A, fract B)
 -- Runtime Function: long fract __ssmulsq3 (long fract A, long fract B)
 -- Runtime Function: long long fract __ssmuldq3 (long long fract A, long long fract B)
 -- Runtime Function: short accum __ssmulha3 (short accum A, short accum B)
 -- Runtime Function: accum __ssmulsa3 (accum A, accum B)
 -- Runtime Function: long accum __ssmulda3 (long accum A, long accum B)
 -- Runtime Function: long long accum __ssmulta3 (long long accum A, long long accum B)
     These functions return the product of A and B with signed saturation.

 -- Runtime Function: unsigned short fract __usmuluqq3 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: unsigned fract __usmuluhq3 (unsigned fract A, unsigned fract B)
 -- Runtime Function: unsigned long fract __usmulusq3 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: unsigned long long fract __usmuludq3 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: unsigned short accum __usmuluha3 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: unsigned accum __usmulusa3 (unsigned accum A, unsigned accum B)
 -- Runtime Function: unsigned long accum __usmuluda3 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: unsigned long long accum __usmuluta3 (unsigned long long accum A, unsigned long long accum B)
     These functions return the product of A and B with unsigned saturation.

 -- Runtime Function: short fract __divqq3 (short fract A, short fract B)
 -- Runtime Function: fract __divhq3 (fract A, fract B)
 -- Runtime Function: long fract __divsq3 (long fract A, long fract B)
 -- Runtime Function: long long fract __divdq3 (long long fract A, long long fract B)
 -- Runtime Function: short accum __divha3 (short accum A, short accum B)
 -- Runtime Function: accum __divsa3 (accum A, accum B)
 -- Runtime Function: long accum __divda3 (long accum A, long accum B)
 -- Runtime Function: long long accum __divta3 (long long accum A, long long accum B)
     These functions return the quotient of the signed division of A and B.

 -- Runtime Function: unsigned short fract __udivuqq3 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: unsigned fract __udivuhq3 (unsigned fract A, unsigned fract B)
 -- Runtime Function: unsigned long fract __udivusq3 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: unsigned long long fract __udivudq3 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: unsigned short accum __udivuha3 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: unsigned accum __udivusa3 (unsigned accum A, unsigned accum B)
 -- Runtime Function: unsigned long accum __udivuda3 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: unsigned long long accum __udivuta3 (unsigned long long accum A, unsigned long long accum B)
     These functions return the quotient of the unsigned division of A and B.

 -- Runtime Function: short fract __ssdivqq3 (short fract A, short fract B)
 -- Runtime Function: fract __ssdivhq3 (fract A, fract B)
 -- Runtime Function: long fract __ssdivsq3 (long fract A, long fract B)
 -- Runtime Function: long long fract __ssdivdq3 (long long fract A, long long fract B)
 -- Runtime Function: short accum __ssdivha3 (short accum A, short accum B)
 -- Runtime Function: accum __ssdivsa3 (accum A, accum B)
 -- Runtime Function: long accum __ssdivda3 (long accum A, long accum B)
 -- Runtime Function: long long accum __ssdivta3 (long long accum A, long long accum B)
     These functions return the quotient of the signed division of A and B with signed saturation.

 -- Runtime Function: unsigned short fract __usdivuqq3 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: unsigned fract __usdivuhq3 (unsigned fract A, unsigned fract B)
 -- Runtime Function: unsigned long fract __usdivusq3 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: unsigned long long fract __usdivudq3 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: unsigned short accum __usdivuha3 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: unsigned accum __usdivusa3 (unsigned accum A, unsigned accum B)
 -- Runtime Function: unsigned long accum __usdivuda3 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: unsigned long long accum __usdivuta3 (unsigned long long accum A, unsigned long long accum B)
     These functions return the quotient of the unsigned division of A and B with unsigned saturation.

 -- Runtime Function: short fract __negqq2 (short fract A)
 -- Runtime Function: fract __neghq2 (fract A)
 -- Runtime Function: long fract __negsq2 (long fract A)
 -- Runtime Function: long long fract __negdq2 (long long fract A)
 -- Runtime Function: unsigned short fract __neguqq2 (unsigned short fract A)
 -- Runtime Function: unsigned fract __neguhq2 (unsigned fract A)
 -- Runtime Function: unsigned long fract __negusq2 (unsigned long fract A)
 -- Runtime Function: unsigned long long fract __negudq2 (unsigned long long fract A)
 -- Runtime Function: short accum __negha2 (short accum A)
 -- Runtime Function: accum __negsa2 (accum A)
 -- Runtime Function: long accum __negda2 (long accum A)
 -- Runtime Function: long long accum __negta2 (long long accum A)
 -- Runtime Function: unsigned short accum __neguha2 (unsigned short accum A)
 -- Runtime Function: unsigned accum __negusa2 (unsigned accum A)
 -- Runtime Function: unsigned long accum __neguda2 (unsigned long accum A)
 -- Runtime Function: unsigned long long accum __neguta2 (unsigned long long accum A)
     These functions return the negation of A.

 -- Runtime Function: short fract __ssnegqq2 (short fract A)
 -- Runtime Function: fract __ssneghq2 (fract A)
 -- Runtime Function: long fract __ssnegsq2 (long fract A)
 -- Runtime Function: long long fract __ssnegdq2 (long long fract A)
 -- Runtime Function: short accum __ssnegha2 (short accum A)
 -- Runtime Function: accum __ssnegsa2 (accum A)
 -- Runtime Function: long accum __ssnegda2 (long accum A)
 -- Runtime Function: long long accum __ssnegta2 (long long accum A)
     These functions return the negation of A with signed saturation.

 -- Runtime Function: unsigned short fract __usneguqq2 (unsigned short fract A)
 -- Runtime Function: unsigned fract __usneguhq2 (unsigned fract A)
 -- Runtime Function: unsigned long fract __usnegusq2 (unsigned long fract A)
 -- Runtime Function: unsigned long long fract __usnegudq2 (unsigned long long fract A)
 -- Runtime Function: unsigned short accum __usneguha2 (unsigned short accum A)
 -- Runtime Function: unsigned accum __usnegusa2 (unsigned accum A)
 -- Runtime Function: unsigned long accum __usneguda2 (unsigned long accum A)
 -- Runtime Function: unsigned long long accum __usneguta2 (unsigned long long accum A)
     These functions return the negation of A with unsigned saturation.

 -- Runtime Function: short fract __ashlqq3 (short fract A, int B)
 -- Runtime Function: fract __ashlhq3 (fract A, int B)
 -- Runtime Function: long fract __ashlsq3 (long fract A, int B)
 -- Runtime Function: long long fract __ashldq3 (long long fract A, int B)
 -- Runtime Function: unsigned short fract __ashluqq3 (unsigned short fract A, int B)
 -- Runtime Function: unsigned fract __ashluhq3 (unsigned fract A, int B)
 -- Runtime Function: unsigned long fract __ashlusq3 (unsigned long fract A, int B)
 -- Runtime Function: unsigned long long fract __ashludq3 (unsigned long long fract A, int B)
 -- Runtime Function: short accum __ashlha3 (short accum A, int B)
 -- Runtime Function: accum __ashlsa3 (accum A, int B)
 -- Runtime Function: long accum __ashlda3 (long accum A, int B)
 -- Runtime Function: long long accum __ashlta3 (long long accum A, int B)
 -- Runtime Function: unsigned short accum __ashluha3 (unsigned short accum A, int B)
 -- Runtime Function: unsigned accum __ashlusa3 (unsigned accum A, int B)
 -- Runtime Function: unsigned long accum __ashluda3 (unsigned long accum A, int B)
 -- Runtime Function: unsigned long long accum __ashluta3 (unsigned long long accum A, int B)
     These functions return the result of shifting A left by B bits.

 -- Runtime Function: short fract __ashrqq3 (short fract A, int B)
 -- Runtime Function: fract __ashrhq3 (fract A, int B)
 -- Runtime Function: long fract __ashrsq3 (long fract A, int B)
 -- Runtime Function: long long fract __ashrdq3 (long long fract A, int B)
 -- Runtime Function: short accum __ashrha3 (short accum A, int B)
 -- Runtime Function: accum __ashrsa3 (accum A, int B)
 -- Runtime Function: long accum __ashrda3 (long accum A, int B)
 -- Runtime Function: long long accum __ashrta3 (long long accum A, int B)
     These functions return the result of arithmetically shifting A right by B bits.

 -- Runtime Function: unsigned short fract __lshruqq3 (unsigned short fract A, int B)
 -- Runtime Function: unsigned fract __lshruhq3 (unsigned fract A, int B)
 -- Runtime Function: unsigned long fract __lshrusq3 (unsigned long fract A, int B)
 -- Runtime Function: unsigned long long fract __lshrudq3 (unsigned long long fract A, int B)
 -- Runtime Function: unsigned short accum __lshruha3 (unsigned short accum A, int B)
 -- Runtime Function: unsigned accum __lshrusa3 (unsigned accum A, int B)
 -- Runtime Function: unsigned long accum __lshruda3 (unsigned long accum A, int B)
 -- Runtime Function: unsigned long long accum __lshruta3 (unsigned long long accum A, int B)
     These functions return the result of logically shifting A right by B bits.

 -- Runtime Function: fract __ssashlhq3 (fract A, int B)
 -- Runtime Function: long fract __ssashlsq3 (long fract A, int B)
 -- Runtime Function: long long fract __ssashldq3 (long long fract A, int B)
 -- Runtime Function: short accum __ssashlha3 (short accum A, int B)
 -- Runtime Function: accum __ssashlsa3 (accum A, int B)
 -- Runtime Function: long accum __ssashlda3 (long accum A, int B)
 -- Runtime Function: long long accum __ssashlta3 (long long accum A, int B)
     These functions return the result of shifting A left by B bits with signed saturation.

 -- Runtime Function: unsigned short fract __usashluqq3 (unsigned short fract A, int B)
 -- Runtime Function: unsigned fract __usashluhq3 (unsigned fract A, int B)
 -- Runtime Function: unsigned long fract __usashlusq3 (unsigned long fract A, int B)
 -- Runtime Function: unsigned long long fract __usashludq3 (unsigned long long fract A, int B)
 -- Runtime Function: unsigned short accum __usashluha3 (unsigned short accum A, int B)
 -- Runtime Function: unsigned accum __usashlusa3 (unsigned accum A, int B)
 -- Runtime Function: unsigned long accum __usashluda3 (unsigned long accum A, int B)
 -- Runtime Function: unsigned long long accum __usashluta3 (unsigned long long accum A, int B)
     These functions return the result of shifting A left by B bits with unsigned saturation.

Comparison functions
--------------------

The following functions implement fixed-point comparisons.  These functions implement a low-level compare, upon which the higher level comparison operators (such as less than and greater than or equal to) can be constructed.  The returned values lie in the range zero to two, to allow the high-level operators to be implemented by testing the returned result using either signed or unsigned comparison.

 -- Runtime Function: int __cmpqq2 (short fract A, short fract B)
 -- Runtime Function: int __cmphq2 (fract A, fract B)
 -- Runtime Function: int __cmpsq2 (long fract A, long fract B)
 -- Runtime Function: int __cmpdq2 (long long fract A, long long fract B)
 -- Runtime Function: int __cmpuqq2 (unsigned short fract A, unsigned short fract B)
 -- Runtime Function: int __cmpuhq2 (unsigned fract A, unsigned fract B)
 -- Runtime Function: int __cmpusq2 (unsigned long fract A, unsigned long fract B)
 -- Runtime Function: int __cmpudq2 (unsigned long long fract A, unsigned long long fract B)
 -- Runtime Function: int __cmpha2 (short accum A, short accum B)
 -- Runtime Function: int __cmpsa2 (accum A, accum B)
 -- Runtime Function: int __cmpda2 (long accum A, long accum B)
 -- Runtime Function: int __cmpta2 (long long accum A, long long accum B)
 -- Runtime Function: int __cmpuha2 (unsigned short accum A, unsigned short accum B)
 -- Runtime Function: int __cmpusa2 (unsigned accum A, unsigned accum B)
 -- Runtime Function: int __cmpuda2 (unsigned long accum A, unsigned long accum B)
 -- Runtime Function: int __cmputa2 (unsigned long long accum A, unsigned long long accum B)
     These functions perform a signed or unsigned comparison of A and B (depending on the selected machine mode).  If A is less than B, they return 0; if A is greater than B, they return 2; and if A and B are equal they return 1.

Conversion functions
--------------------

 -- Runtime Function: fract __fractqqhq2 (short fract A)
 -- Runtime Function: long fract __fractqqsq2 (short fract A)
 -- Runtime Function: long long fract __fractqqdq2 (short fract A)
 -- Runtime Function: short accum __fractqqha (short fract A)
 -- Runtime Function: accum __fractqqsa (short fract A)
 -- Runtime Function: long accum __fractqqda (short fract A)
 -- Runtime Function: long long accum __fractqqta (short fract A)
 -- Runtime Function: unsigned short fract __fractqquqq (short fract A)
 -- Runtime Function: unsigned fract __fractqquhq (short fract A)
 -- Runtime Function: unsigned long fract __fractqqusq (short fract A)
 -- Runtime Function: unsigned long long fract __fractqqudq (short fract A)
 -- Runtime Function: unsigned short accum __fractqquha (short fract A)
 -- Runtime Function: unsigned accum __fractqqusa (short fract A)
 -- Runtime Function: unsigned long accum __fractqquda (short fract A)
 -- Runtime Function: unsigned long long accum __fractqquta (short fract A)
 -- Runtime Function: signed char __fractqqqi (short fract A)
 -- Runtime Function: short __fractqqhi (short fract A)
 -- Runtime Function: int __fractqqsi (short fract A)
 -- Runtime Function: long __fractqqdi (short fract A)
 -- Runtime Function: long long __fractqqti (short fract A)
 -- Runtime Function: float __fractqqsf (short fract A)
 -- Runtime Function: double __fractqqdf (short fract A)
 -- Runtime Function: short fract __fracthqqq2 (fract A)
 -- Runtime Function: long fract __fracthqsq2 (fract A)
 -- Runtime Function: long long fract __fracthqdq2 (fract A)
 -- Runtime Function: short accum __fracthqha (fract A)
 -- Runtime Function: accum __fracthqsa (fract A)
 -- Runtime Function: long accum __fracthqda (fract A)
 -- Runtime Function: long long accum __fracthqta (fract A)
 -- Runtime Function: unsigned short fract __fracthquqq (fract A)
 -- Runtime Function: unsigned fract __fracthquhq (fract A)
 -- Runtime Function: unsigned long fract __fracthqusq (fract A)
 -- Runtime Function: unsigned long long fract __fracthqudq (fract A)
 -- Runtime Function: unsigned short accum __fracthquha (fract A)
 -- Runtime Function: unsigned accum __fracthqusa (fract A)
 -- Runtime Function: unsigned long accum __fracthquda (fract A)
 -- Runtime Function: unsigned long long accum __fracthquta (fract A)
 -- Runtime Function: signed char __fracthqqi (fract A)
 -- Runtime Function: short __fracthqhi (fract A)
 -- Runtime Function: int __fracthqsi (fract A)
 -- Runtime Function: long __fracthqdi (fract A)
 -- Runtime Function: long long __fracthqti (fract A)
 -- Runtime Function: float __fracthqsf (fract A)
 -- Runtime Function: double __fracthqdf (fract A)
 -- Runtime Function: short fract __fractsqqq2 (long fract A)
 -- Runtime Function: fract __fractsqhq2 (long fract A)
 -- Runtime Function: long long fract __fractsqdq2 (long fract A)
 -- Runtime Function: short accum __fractsqha (long fract A)
 -- Runtime Function: accum __fractsqsa (long fract A)
 -- Runtime Function: long accum __fractsqda (long fract A)
 -- Runtime Function: long long accum __fractsqta (long fract A)
 -- Runtime Function: unsigned short fract __fractsquqq (long fract A)
 -- Runtime Function: unsigned fract __fractsquhq (long fract A)
 -- Runtime Function: unsigned long fract __fractsqusq (long fract A)
 -- Runtime Function: unsigned long long fract __fractsqudq (long fract A)
 -- Runtime Function: unsigned short accum __fractsquha (long fract A)
 -- Runtime Function: unsigned accum __fractsqusa (long fract A)
 -- Runtime Function: unsigned long accum __fractsquda (long fract A)
 -- Runtime Function: unsigned long long accum __fractsquta (long fract A)
 -- Runtime Function: signed char __fractsqqi (long fract A)
 -- Runtime Function: short __fractsqhi (long fract A)
 -- Runtime Function: int __fractsqsi (long fract A)
 -- Runtime Function: long __fractsqdi (long fract A)
 -- Runtime Function: long long __fractsqti (long fract A)
 -- Runtime Function: float __fractsqsf (long fract A)
 -- Runtime Function: double __fractsqdf (long fract A)
 -- Runtime Function: short fract __fractdqqq2 (long long fract A)
 -- Runtime Function: fract __fractdqhq2 (long long fract A)
 -- Runtime Function: long fract __fractdqsq2 (long long fract A)
 -- Runtime Function: short accum __fractdqha (long long fract A)
 -- Runtime Function: accum __fractdqsa (long long fract A)
 -- Runtime Function: long accum __fractdqda (long long fract A)
 -- Runtime Function: long long accum __fractdqta (long long fract A)
 -- Runtime Function: unsigned short fract __fractdquqq (long long fract A)
 -- Runtime Function: unsigned fract __fractdquhq (long long fract A)
 -- Runtime Function: unsigned long fract __fractdqusq (long long fract A)
 -- Runtime Function: unsigned long long fract __fractdqudq (long long fract A)
 -- Runtime Function: unsigned short accum __fractdquha (long long fract A)
 -- Runtime Function: unsigned accum __fractdqusa (long long fract A)
 -- Runtime Function: unsigned long accum __fractdquda (long long fract A)
 -- Runtime Function: unsigned long long accum __fractdquta (long long fract A)
 -- Runtime Function: signed char __fractdqqi (long long fract A)
 -- Runtime Function: short __fractdqhi (long long fract A)
 -- Runtime Function: int __fractdqsi (long long fract A)
 -- Runtime Function: long __fractdqdi (long long fract A)
 -- Runtime Function: long long __fractdqti (long long fract A)
 -- Runtime Function: float __fractdqsf (long long fract A)
 -- Runtime Function: double __fractdqdf (long long fract A)
 -- Runtime Function: short fract __fracthaqq (short accum A)
 -- Runtime Function: fract __fracthahq (short accum A)
 -- Runtime Function: long fract __fracthasq (short accum A)
 -- Runtime Function: long long fract __fracthadq (short accum A)
 -- Runtime Function: accum __fracthasa2 (short accum A)
 -- Runtime Function: long accum __fracthada2 (short accum A)
 -- Runtime Function: long long accum __fracthata2 (short accum A)
 -- Runtime Function: unsigned short fract __fracthauqq (short accum A)
 -- Runtime Function: unsigned fract __fracthauhq (short accum A)
 -- Runtime Function: unsigned long fract __fracthausq (short accum A)
 -- Runtime Function: unsigned long long fract __fracthaudq (short accum A)
 -- Runtime Function: unsigned short accum __fracthauha (short accum A)
 -- Runtime Function: unsigned accum __fracthausa (short accum A)
 -- Runtime Function: unsigned long accum __fracthauda (short accum A)
 -- Runtime Function: unsigned long long accum __fracthauta (short accum A)
 -- Runtime Function: signed char __fracthaqi (short accum A)
 -- Runtime Function: short __fracthahi (short accum A)
 -- Runtime Function: int __fracthasi (short accum A)
 -- Runtime Function: long __fracthadi (short accum A)
 -- Runtime Function: long long __fracthati (short accum A)
 -- Runtime Function: float __fracthasf (short accum A)
 -- Runtime Function: double __fracthadf (short accum A)
 -- Runtime Function: short fract __fractsaqq (accum A)
 -- Runtime Function: fract __fractsahq (accum A)
 -- Runtime Function: long fract __fractsasq (accum A)
 -- Runtime Function: long long fract __fractsadq (accum A)
 -- Runtime Function: short accum __fractsaha2 (accum A)
 -- Runtime Function: long accum __fractsada2 (accum A)
 -- Runtime Function: long long accum __fractsata2 (accum A)
 -- Runtime Function: unsigned short fract __fractsauqq (accum A)
 -- Runtime Function: unsigned fract __fractsauhq (accum A)
 -- Runtime Function: unsigned long fract __fractsausq (accum A)
 -- Runtime Function: unsigned long long fract __fractsaudq (accum A)
 -- Runtime Function: unsigned short accum __fractsauha (accum A)
 -- Runtime Function: unsigned accum __fractsausa (accum A)
 -- Runtime Function: unsigned long accum __fractsauda (accum A)
 -- Runtime Function: unsigned long long accum __fractsauta (accum A)
 -- Runtime Function: signed char __fractsaqi (accum A)
 -- Runtime Function: short __fractsahi (accum A)
 -- Runtime Function: int __fractsasi (accum A)
 -- Runtime Function: long __fractsadi (accum A)
 -- Runtime Function: long long __fractsati (accum A)
 -- Runtime Function: float __fractsasf (accum A)
 -- Runtime Function: double __fractsadf (accum A)
 -- Runtime Function: short fract __fractdaqq (long accum A)
 -- Runtime Function: fract __fractdahq (long accum A)
 -- Runtime Function: long fract __fractdasq (long accum A)
 -- Runtime Function: long long fract __fractdadq (long accum A)
 -- Runtime Function: short accum __fractdaha2 (long accum A)
 -- Runtime Function: accum __fractdasa2 (long accum A)
 -- Runtime Function: long long accum __fractdata2 (long accum A)
 -- Runtime Function: unsigned short fract __fractdauqq (long accum A)
 -- Runtime Function: unsigned fract __fractdauhq (long accum A)
 -- Runtime Function: unsigned long fract __fractdausq (long accum A)
 -- Runtime Function: unsigned long long fract __fractdaudq (long accum A)
 -- Runtime Function: unsigned short accum __fractdauha (long accum A)
 -- Runtime Function: unsigned accum __fractdausa (long accum A)
 -- Runtime Function: unsigned long accum __fractdauda (long accum A)
 -- Runtime Function: unsigned long long accum __fractdauta (long accum A)
 -- Runtime Function: signed char __fractdaqi (long accum A)
 -- Runtime Function: short __fractdahi (long accum A)
 -- Runtime Function: int __fractdasi (long accum A)
 -- Runtime Function: long __fractdadi (long accum A)
 -- Runtime Function: long long __fractdati (long accum A)
 -- Runtime Function: float __fractdasf (long accum A)
 -- Runtime Function: double __fractdadf (long accum A)
 -- Runtime Function: short fract __fracttaqq (long long accum A)
 -- Runtime Function: fract __fracttahq (long long accum A)
 -- Runtime Function: long fract __fracttasq (long long accum A)
 -- Runtime Function: long long fract __fracttadq (long long accum A)
 -- Runtime Function: short accum __fracttaha2 (long long accum A)
 -- Runtime Function: accum __fracttasa2 (long long accum A)
 -- Runtime Function: long accum __fracttada2 (long long accum A)
 -- Runtime Function: unsigned short fract __fracttauqq (long long accum A)
 -- Runtime Function: unsigned fract __fracttauhq (long long accum A)
 -- Runtime Function: unsigned long fract __fracttausq (long long accum A)
 -- Runtime Function: unsigned long long fract __fracttaudq (long long accum A)
 -- Runtime Function: unsigned short accum __fracttauha (long long accum A)
 -- Runtime Function: unsigned accum __fracttausa (long long accum A)
 -- Runtime Function: unsigned long accum __fracttauda (long long accum A)
 -- Runtime Function: unsigned long long accum __fracttauta (long long accum A)
 -- Runtime Function: signed char __fracttaqi (long long accum A)
 -- Runtime Function: short __fracttahi (long long accum A)
 -- Runtime Function: int __fracttasi (long long accum A)
 -- Runtime Function: long __fracttadi (long long accum A)
 -- Runtime Function: long long __fracttati (long long accum A)
 -- Runtime Function: float __fracttasf (long long accum A)
 -- Runtime Function: double __fracttadf (long long accum A)
 -- Runtime Function: short fract __fractuqqqq (unsigned short fract A)
 -- Runtime Function: fract __fractuqqhq (unsigned short fract A)
 -- Runtime Function: long fract __fractuqqsq (unsigned short fract A)
 -- Runtime Function: long long fract __fractuqqdq (unsigned short fract A)
 -- Runtime Function: short accum __fractuqqha (unsigned short fract A)
 -- Runtime Function: accum __fractuqqsa (unsigned short fract A)
 -- Runtime Function: long accum __fractuqqda (unsigned short fract A)
 -- Runtime Function: long long accum __fractuqqta (unsigned short fract A)
 -- Runtime Function: unsigned fract __fractuqquhq2 (unsigned short fract A)
 -- Runtime Function: unsigned long fract __fractuqqusq2 (unsigned short fract A)
 -- Runtime Function: unsigned long long fract __fractuqqudq2 (unsigned short fract A)
 -- Runtime Function: unsigned short accum __fractuqquha (unsigned short fract A)
 -- Runtime Function: unsigned accum __fractuqqusa (unsigned short fract A)
 -- Runtime Function: unsigned long accum __fractuqquda (unsigned short fract A)
 -- Runtime Function: unsigned long long accum __fractuqquta (unsigned short fract A)
 -- Runtime Function: signed char __fractuqqqi (unsigned short fract A)
 -- Runtime Function: short __fractuqqhi (unsigned short fract A)
 -- Runtime Function: int __fractuqqsi (unsigned short fract A)
 -- Runtime Function: long __fractuqqdi (unsigned short fract A)
 -- Runtime Function: long long __fractuqqti (unsigned short fract A)
 -- Runtime Function: float __fractuqqsf (unsigned short fract A)
 -- Runtime Function: double __fractuqqdf (unsigned short fract A)
 -- Runtime Function: short fract __fractuhqqq (unsigned fract A)
 -- Runtime Function: fract __fractuhqhq (unsigned fract A)
 -- Runtime Function: long fract __fractuhqsq (unsigned fract A)
 -- Runtime Function: long long fract __fractuhqdq (unsigned fract A)
 -- Runtime Function: short accum __fractuhqha (unsigned fract A)
 -- Runtime Function: accum __fractuhqsa (unsigned fract A)
 -- Runtime Function: long accum __fractuhqda (unsigned fract A)
 -- Runtime Function: long long accum __fractuhqta (unsigned fract A)
 -- Runtime Function: unsigned short fract __fractuhquqq2 (unsigned fract A)
 -- Runtime Function: unsigned long fract __fractuhqusq2 (unsigned fract A)
 -- Runtime Function: unsigned long long fract __fractuhqudq2 (unsigned fract A)
 -- Runtime Function: unsigned short accum __fractuhquha (unsigned fract A)
 -- Runtime Function: unsigned accum __fractuhqusa (unsigned fract A)
 -- Runtime Function: unsigned long accum __fractuhquda (unsigned fract A)
 -- Runtime Function: unsigned long long accum __fractuhquta (unsigned fract A)
 -- Runtime Function: signed char __fractuhqqi (unsigned fract A)
 -- Runtime Function: short __fractuhqhi (unsigned fract A)
 -- Runtime Function: int __fractuhqsi (unsigned fract A)
 -- Runtime Function: long __fractuhqdi (unsigned fract A)
 -- Runtime Function: long long __fractuhqti (unsigned fract A)
 -- Runtime Function: float __fractuhqsf (unsigned fract A)
 -- Runtime Function: double __fractuhqdf (unsigned fract A)
 -- Runtime Function: short fract __fractusqqq (unsigned long fract A)
 -- Runtime Function: fract __fractusqhq (unsigned long fract A)
 -- Runtime Function: long fract __fractusqsq (unsigned long fract A)
 -- Runtime Function: long long fract __fractusqdq (unsigned long fract A)
 -- Runtime Function: short accum __fractusqha (unsigned long fract A)
 -- Runtime Function: accum __fractusqsa (unsigned long fract A)
 -- Runtime Function: long accum __fractusqda (unsigned long fract A)
 -- Runtime Function: long long accum __fractusqta (unsigned long fract A)
 -- Runtime Function: unsigned short fract __fractusquqq2 (unsigned long fract A)
 -- Runtime Function: unsigned fract __fractusquhq2 (unsigned long fract A)
 -- Runtime Function: unsigned long long fract __fractusqudq2 (unsigned long fract A)
 -- Runtime Function: unsigned short accum __fractusquha (unsigned long fract A)
 -- Runtime Function: unsigned accum __fractusqusa (unsigned long fract A)
 -- Runtime Function: unsigned long accum __fractusquda (unsigned long fract A)
 -- Runtime Function: unsigned long long accum __fractusquta (unsigned long fract A)
 -- Runtime Function: signed char __fractusqqi (unsigned long fract A)
 -- Runtime Function: short __fractusqhi (unsigned long fract A)
 -- Runtime Function: int __fractusqsi (unsigned long fract A)
 -- Runtime Function: long __fractusqdi (unsigned long fract A)
 -- Runtime Function: long long __fractusqti (unsigned long fract A)
 -- Runtime Function: float __fractusqsf (unsigned long fract A)
 -- Runtime Function: double __fractusqdf (unsigned long fract A)
 -- Runtime Function: short fract __fractudqqq (unsigned long long fract A)
 -- Runtime Function: fract __fractudqhq (unsigned long long fract A)
 -- Runtime Function: long fract __fractudqsq (unsigned long long fract A)
 -- Runtime Function: long long fract __fractudqdq (unsigned long long fract A)
 -- Runtime Function: short accum __fractudqha (unsigned long long fract A)
 -- Runtime Function: accum __fractudqsa (unsigned long long fract A)
 -- Runtime Function: long accum __fractudqda (unsigned long long fract A)
 -- Runtime Function: long long accum __fractudqta (unsigned long long fract A)
 -- Runtime Function: unsigned short fract __fractudquqq2 (unsigned long long fract A)
 -- Runtime Function: unsigned fract __fractudquhq2 (unsigned long long fract A)
 -- Runtime Function: unsigned long fract __fractudqusq2 (unsigned long long fract A)
 -- Runtime Function: unsigned short accum __fractudquha (unsigned long long fract A)
 -- Runtime Function: unsigned accum __fractudqusa (unsigned long long fract A)
 -- Runtime Function: unsigned long accum __fractudquda (unsigned long long fract A)
 -- Runtime Function: unsigned long long accum __fractudquta (unsigned long long fract A)
 -- Runtime Function: signed char __fractudqqi (unsigned long long fract A)
 -- Runtime Function: short __fractudqhi (unsigned long long fract A)
 -- Runtime Function: int __fractudqsi (unsigned long long fract A)
 -- Runtime Function: long __fractudqdi (unsigned long long fract A)
 -- Runtime Function: long long __fractudqti (unsigned long long fract A)
 -- Runtime Function: float __fractudqsf (unsigned long long fract A)
 -- Runtime Function: double __fractudqdf (unsigned long long fract A)
 -- Runtime Function: short fract __fractuhaqq (unsigned short accum A)
 -- Runtime Function: fract __fractuhahq (unsigned short accum A)
 -- Runtime Function: long fract __fractuhasq (unsigned short accum A)
 -- Runtime Function: long long fract __fractuhadq (unsigned short accum A)
 -- Runtime Function: short accum __fractuhaha (unsigned short accum A)
 -- Runtime Function: accum __fractuhasa (unsigned short accum A)
 -- Runtime Function: long accum __fractuhada (unsigned short accum A)
 -- Runtime Function: long long accum __fractuhata (unsigned short accum A)
 -- Runtime Function: unsigned short fract __fractuhauqq (unsigned short accum A)
 -- Runtime Function: unsigned fract __fractuhauhq (unsigned short accum A)
 -- Runtime Function: unsigned long fract __fractuhausq (unsigned short accum A)
 -- Runtime Function: unsigned long long fract __fractuhaudq (unsigned short accum A)
 -- Runtime Function: unsigned accum __fractuhausa2 (unsigned short accum A)
 -- Runtime Function: unsigned long accum __fractuhauda2 (unsigned short accum A)
 -- Runtime Function: unsigned long long accum __fractuhauta2 (unsigned short accum A)
 -- Runtime Function: signed char __fractuhaqi (unsigned short accum A)
 -- Runtime Function: short __fractuhahi (unsigned short accum A)
 -- Runtime Function: int __fractuhasi (unsigned short accum A)
 -- Runtime Function: long __fractuhadi (unsigned short accum A)
 -- Runtime Function: long long __fractuhati (unsigned short accum A)
 -- Runtime Function: float __fractuhasf (unsigned short accum A)
 -- Runtime Function: double __fractuhadf (unsigned short accum A)
 -- Runtime Function: short fract __fractusaqq (unsigned accum A)
 -- Runtime Function: fract __fractusahq (unsigned accum A)
 -- Runtime Function: long fract __fractusasq (unsigned accum A)
 -- Runtime Function: long long fract __fractusadq (unsigned accum A)
 -- Runtime Function: short accum __fractusaha (unsigned accum A)
 -- Runtime Function: accum __fractusasa (unsigned accum A)
 -- Runtime Function: long accum __fractusada (unsigned accum A)
 -- Runtime Function: long long accum __fractusata (unsigned accum A)
 -- Runtime Function: unsigned short fract __fractusauqq (unsigned accum A)
 -- Runtime Function: unsigned fract __fractusauhq (unsigned accum A)
 -- Runtime Function: unsigned long fract __fractusausq (unsigned accum A)
 -- Runtime Function: unsigned long long fract __fractusaudq (unsigned accum A)
 -- Runtime Function: unsigned short accum __fractusauha2 (unsigned accum A)
 -- Runtime Function: unsigned long accum __fractusauda2 (unsigned accum A)
 -- Runtime Function: unsigned long long accum __fractusauta2 (unsigned accum A)
 -- Runtime Function: signed char __fractusaqi (unsigned accum A)
 -- Runtime Function: short __fractusahi (unsigned accum A)
 -- Runtime Function: int __fractusasi (unsigned accum A)
 -- Runtime Function: long __fractusadi (unsigned accum A)
 -- Runtime Function: long long __fractusati (unsigned accum A)
 -- Runtime Function: float __fractusasf (unsigned accum A)
 -- Runtime Function: double __fractusadf (unsigned accum A)
 -- Runtime Function: short fract __fractudaqq (unsigned long accum A)
 -- Runtime Function: fract __fractudahq (unsigned long accum A)
 -- Runtime Function: long fract __fractudasq (unsigned long accum A)
 -- Runtime Function: long long fract __fractudadq (unsigned long accum A)
 -- Runtime Function: short accum __fractudaha (unsigned long accum A)
 -- Runtime Function: accum __fractudasa (unsigned long accum A)
 -- Runtime Function: long accum __fractudada (unsigned long accum A)
 -- Runtime Function: long long accum __fractudata (unsigned long accum A)
 -- Runtime Function: unsigned short fract __fractudauqq (unsigned long accum A)
 -- Runtime Function: unsigned fract __fractudauhq (unsigned long accum A)
 -- Runtime Function: unsigned long fract __fractudausq (unsigned long accum A)
 -- Runtime Function: unsigned long long fract __fractudaudq (unsigned long accum A)
 -- Runtime Function: unsigned short accum __fractudauha2 (unsigned long accum A)
 -- Runtime Function: unsigned accum __fractudausa2 (unsigned long accum A)
 -- Runtime Function: unsigned long long accum __fractudauta2 (unsigned long accum A)
 -- Runtime Function: signed char __fractudaqi (unsigned long accum A)
 -- Runtime Function: short __fractudahi (unsigned long accum A)
 -- Runtime Function: int __fractudasi (unsigned long accum A)
 -- Runtime Function: long __fractudadi (unsigned long accum A)
 -- Runtime Function: long long __fractudati (unsigned long accum A)
 -- Runtime Function: float __fractudasf (unsigned long accum A)
 -- Runtime Function: double __fractudadf (unsigned long accum A)
 -- Runtime Function: short fract __fractutaqq (unsigned long long accum A)
 -- Runtime Function: fract __fractutahq (unsigned long long accum A)
 -- Runtime Function: long fract __fractutasq (unsigned long long accum A)
 -- Runtime Function: long long fract __fractutadq (unsigned long long accum A)
 -- Runtime Function: short accum __fractutaha (unsigned long long accum A)
 -- Runtime Function: accum __fractutasa (unsigned long long accum A)
 -- Runtime Function: long accum __fractutada (unsigned long long accum A)
 -- Runtime Function: long long accum __fractutata (unsigned long long accum A)
 -- Runtime Function: unsigned short fract __fractutauqq (unsigned long long accum A)
 -- Runtime Function: unsigned fract __fractutauhq (unsigned long long accum A)
 -- Runtime Function: unsigned long fract __fractutausq (unsigned long long accum A)
 -- Runtime Function: unsigned long long fract __fractutaudq (unsigned long long accum A)
 -- Runtime Function: unsigned short accum __fractutauha2 (unsigned long long accum A)
 -- Runtime Function: unsigned accum __fractutausa2 (unsigned long long accum A)
 -- Runtime Function: unsigned long accum __fractutauda2 (unsigned long long accum A)
 -- Runtime Function: signed char __fractutaqi (unsigned long long accum A)
 -- Runtime Function: short __fractutahi (unsigned long long accum A)
 -- Runtime Function: int __fractutasi (unsigned long long accum A)
 -- Runtime Function: long __fractutadi (unsigned long long accum A)
 -- Runtime Function: long long __fractutati (unsigned long long accum A)
 -- Runtime Function: float __fractutasf (unsigned long long accum A)
 -- Runtime Function: double __fractutadf (unsigned long long accum A)
 -- Runtime Function: short fract __fractqiqq (signed char A)
 -- Runtime Function: fract __fractqihq (signed char A)
 -- Runtime Function: long fract __fractqisq (signed char A)
 -- Runtime Function: long long fract __fractqidq (signed char A)
 -- Runtime Function: short accum __fractqiha (signed char A)
 -- Runtime Function: accum __fractqisa (signed char A)
 -- Runtime Function: long accum __fractqida (signed char A)
 -- Runtime Function: long long accum __fractqita (signed char A)
 -- Runtime Function: unsigned short fract __fractqiuqq (signed char A)
 -- Runtime Function: unsigned fract __fractqiuhq (signed char A)
 -- Runtime Function: unsigned long fract __fractqiusq (signed char A)
 -- Runtime Function: unsigned long long fract __fractqiudq (signed char A)
 -- Runtime Function: unsigned short accum __fractqiuha (signed char A)
 -- Runtime Function: unsigned accum __fractqiusa (signed char A)
 -- Runtime Function: unsigned long accum __fractqiuda (signed char A)
 -- Runtime Function: unsigned long long accum __fractqiuta (signed char A)
 -- Runtime Function: short fract __fracthiqq (short A)
 -- Runtime Function: fract __fracthihq (short A)
 -- Runtime Function: long fract __fracthisq (short A)
 -- Runtime Function: long long fract __fracthidq (short A)
 -- Runtime Function: short accum __fracthiha (short A)
 -- Runtime Function: accum __fracthisa (short A)
 -- Runtime Function: long accum __fracthida (short A)
 -- Runtime Function: long long accum __fracthita (short A)
 -- Runtime Function: unsigned short fract __fracthiuqq (short A)
 -- Runtime Function: unsigned fract __fracthiuhq (short A)
 -- Runtime Function: unsigned long fract __fracthiusq (short A)
 -- Runtime Function: unsigned long long fract __fracthiudq (short A)
 -- Runtime Function: unsigned short accum __fracthiuha (short A)
 -- Runtime Function: unsigned accum __fracthiusa (short A)
 -- Runtime Function: unsigned long accum __fracthiuda (short A)
 -- Runtime Function: unsigned long long accum __fracthiuta (short A)
 -- Runtime Function: short fract __fractsiqq (int A)
 -- Runtime Function: fract __fractsihq (int A)
 -- Runtime Function: long fract __fractsisq (int A)
 -- Runtime Function: long long fract __fractsidq (int A)
 -- Runtime Function: short accum __fractsiha (int A)
 -- Runtime Function: accum __fractsisa (int A)
 -- Runtime Function: long accum __fractsida (int A)
 -- Runtime Function: long long accum __fractsita (int A)
 -- Runtime Function: unsigned short fract __fractsiuqq (int A)
 -- Runtime Function: unsigned fract __fractsiuhq (int A)
 -- Runtime Function: unsigned long fract __fractsiusq (int A)
 -- Runtime Function: unsigned long long fract __fractsiudq (int A)
 -- Runtime Function: unsigned short accum __fractsiuha (int A)
 -- Runtime Function: unsigned accum __fractsiusa (int A)
 -- Runtime Function: unsigned long accum __fractsiuda (int A)
 -- Runtime Function: unsigned long long accum __fractsiuta (int A)
 -- Runtime Function: short fract __fractdiqq (long A)
 -- Runtime Function: fract __fractdihq (long A)
 -- Runtime Function: long fract __fractdisq (long A)
 -- Runtime Function: long long fract __fractdidq (long A)
 -- Runtime Function: short accum __fractdiha (long A)
 -- Runtime Function: accum __fractdisa (long A)
 -- Runtime Function: long accum __fractdida (long A)
 -- Runtime Function: long long accum __fractdita (long A)
 -- Runtime Function: unsigned short fract __fractdiuqq (long A)
 -- Runtime Function: unsigned fract __fractdiuhq (long A)
 -- Runtime Function: unsigned long fract __fractdiusq (long A)
 -- Runtime Function: unsigned long long fract __fractdiudq (long A)
 -- Runtime Function: unsigned short accum __fractdiuha (long A)
 -- Runtime Function: unsigned accum __fractdiusa (long A)
 -- Runtime Function: unsigned long accum __fractdiuda (long A)
 -- Runtime Function: unsigned long long accum __fractdiuta (long A)
 -- Runtime Function: short fract __fracttiqq (long long A)
 -- Runtime Function: fract __fracttihq (long long A)
 -- Runtime Function: long fract __fracttisq (long long A)
 -- Runtime Function: long long fract __fracttidq (long long A)
 -- Runtime Function: short accum __fracttiha (long long A)
 -- Runtime Function: accum __fracttisa (long long A)
 -- Runtime Function: long accum __fracttida (long long A)
 -- Runtime Function: long long accum __fracttita (long long A)
 -- Runtime Function: unsigned short fract __fracttiuqq (long long A)
 -- Runtime Function: unsigned fract __fracttiuhq (long long A)
 -- Runtime Function: unsigned long fract __fracttiusq (long long A)
 -- Runtime Function: unsigned long long fract __fracttiudq (long long A)
 -- Runtime Function: unsigned short accum __fracttiuha (long long A)
 -- Runtime Function: unsigned accum __fracttiusa (long long A)
 -- Runtime Function: unsigned long accum __fracttiuda (long long A)
 -- Runtime Function: unsigned long long accum __fracttiuta (long long A)
 -- Runtime Function: short fract __fractsfqq (float A)
 -- Runtime Function: fract __fractsfhq (float A)
 -- Runtime Function: long fract __fractsfsq (float A)
 -- Runtime Function: long long fract __fractsfdq (float A)
 -- Runtime Function: short accum __fractsfha (float A)
 -- Runtime Function: accum __fractsfsa (float A)
 -- Runtime Function: long accum __fractsfda (float A)
 -- Runtime Function: long long accum __fractsfta (float A)
 -- Runtime Function: unsigned short fract __fractsfuqq (float A)
 -- Runtime Function: unsigned fract __fractsfuhq (float A)
 -- Runtime Function: unsigned long fract __fractsfusq (float A)
 -- Runtime Function: unsigned long long fract __fractsfudq (float A)
 -- Runtime Function: unsigned short accum __fractsfuha (float A)
 -- Runtime Function: unsigned accum __fractsfusa (float A)
 -- Runtime Function: unsigned long accum __fractsfuda (float A)
 -- Runtime Function: unsigned long long accum __fractsfuta (float A)
 -- Runtime Function: short fract __fractdfqq (double A)
 -- Runtime Function: fract __fractdfhq (double A)
 -- Runtime Function: long fract __fractdfsq (double A)
 -- Runtime Function: long long fract __fractdfdq (double A)
 -- Runtime Function: short accum __fractdfha (double A)
 -- Runtime Function: accum __fractdfsa (double A)
 -- Runtime Function: long accum __fractdfda (double A)
 -- Runtime Function: long long accum __fractdfta (double A)
 -- Runtime Function: unsigned short fract __fractdfuqq (double A)
 -- Runtime Function: unsigned fract __fractdfuhq (double A)
 -- Runtime Function: unsigned long fract __fractdfusq (double A)
 -- Runtime Function: unsigned long long fract __fractdfudq (double A)
 -- Runtime Function: unsigned short accum __fractdfuha (double A)
 -- Runtime Function: unsigned accum __fractdfusa (double A)
 -- Runtime Function: unsigned long accum __fractdfuda (double A)
 -- Runtime Function: unsigned long long accum __fractdfuta (double A)
     These functions convert from fractional and signed non-fractionals to fractionals and signed non-fractionals, without saturation.

 -- Runtime Function: fract __satfractqqhq2 (short fract A)
 -- Runtime Function: long fract __satfractqqsq2 (short fract A)
 -- Runtime Function: long long fract __satfractqqdq2 (short fract A)
 -- Runtime Function: short accum __satfractqqha (short fract A)
 -- Runtime Function: accum __satfractqqsa (short fract A)
 -- Runtime Function: long accum __satfractqqda (short fract A)
 -- Runtime Function: long long accum __satfractqqta (short fract A)
 -- Runtime Function: unsigned short fract __satfractqquqq (short fract A)
 -- Runtime Function: unsigned fract __satfractqquhq (short fract A)
 -- Runtime Function: unsigned long fract __satfractqqusq (short fract A)
 -- Runtime Function: unsigned long long fract __satfractqqudq (short fract A)
 -- Runtime Function: unsigned short accum __satfractqquha (short fract A)
 -- Runtime Function: unsigned accum __satfractqqusa (short fract A)
 -- Runtime Function: unsigned long accum __satfractqquda (short fract A)
 -- Runtime Function: unsigned long long accum __satfractqquta (short fract A)
 -- Runtime Function: short fract __satfracthqqq2 (fract A)
 -- Runtime Function: long fract __satfracthqsq2 (fract A)
 -- Runtime Function: long long fract __satfracthqdq2 (fract A)
 -- Runtime Function: short accum __satfracthqha (fract A)
 -- Runtime Function: accum __satfracthqsa (fract A)
 -- Runtime Function: long accum __satfracthqda (fract A)
 -- Runtime Function: long long accum __satfracthqta (fract A)
 -- Runtime Function: unsigned short fract __satfracthquqq (fract A)
 -- Runtime Function: unsigned fract __satfracthquhq (fract A)
 -- Runtime Function: unsigned long fract __satfracthqusq (fract A)
 -- Runtime Function: unsigned long long fract __satfracthqudq (fract A)
 -- Runtime Function: unsigned short accum __satfracthquha (fract A)
 -- Runtime Function: unsigned accum __satfracthqusa (fract A)
 -- Runtime Function: unsigned long accum __satfracthquda (fract A)
 -- Runtime Function: unsigned long long accum __satfracthquta (fract A)
 -- Runtime Function: short fract __satfractsqqq2 (long fract A)
 -- Runtime Function: fract __satfractsqhq2 (long fract A)
 -- Runtime Function: long long fract __satfractsqdq2 (long fract A)
 -- Runtime Function: short accum __satfractsqha (long fract A)
 -- Runtime Function: accum __satfractsqsa (long fract A)
 -- Runtime Function: long accum __satfractsqda (long fract A)
 -- Runtime Function: long long accum __satfractsqta (long fract A)
 -- Runtime Function: unsigned short fract __satfractsquqq (long fract A)
 -- Runtime Function: unsigned fract __satfractsquhq (long fract A)
 -- Runtime Function: unsigned long fract __satfractsqusq (long fract A)
 -- Runtime Function: unsigned long long fract __satfractsqudq (long fract A)
 -- Runtime Function: unsigned short accum __satfractsquha (long fract A)
 -- Runtime Function: unsigned accum __satfractsqusa (long fract A)
 -- Runtime Function: unsigned long accum __satfractsquda (long fract A)
 -- Runtime Function: unsigned long long accum __satfractsquta (long fract A)
 -- Runtime Function: short fract __satfractdqqq2 (long long fract A)
 -- Runtime Function: fract __satfractdqhq2 (long long fract A)
 -- Runtime Function: long fract __satfractdqsq2 (long long fract A)
 -- Runtime Function: short accum __satfractdqha (long long fract A)
 -- Runtime Function: accum __satfractdqsa (long long fract A)
 -- Runtime Function: long accum __satfractdqda (long long fract A)
 -- Runtime Function: long long accum __satfractdqta (long long fract A)
 -- Runtime Function: unsigned short fract __satfractdquqq (long long fract A)
 -- Runtime Function: unsigned fract __satfractdquhq (long long fract A)
 -- Runtime Function: unsigned long fract __satfractdqusq (long long fract A)
 -- Runtime Function: unsigned long long fract __satfractdqudq (long long fract A)
 -- Runtime Function: unsigned short accum __satfractdquha (long long fract A)
 -- Runtime Function: unsigned accum __satfractdqusa (long long fract A)
 -- Runtime Function: unsigned long accum __satfractdquda (long long fract A)
 -- Runtime Function: unsigned long long accum __satfractdquta (long long fract A)
 -- Runtime Function: short fract __satfracthaqq (short accum A)
 -- Runtime Function: fract __satfracthahq (short accum A)
 -- Runtime Function: long fract __satfracthasq (short accum A)
 -- Runtime Function: long long fract __satfracthadq (short accum A)
 -- Runtime Function: accum __satfracthasa2 (short accum A)
 -- Runtime Function: long accum __satfracthada2 (short accum A)
 -- Runtime Function: long long accum __satfracthata2 (short accum A)
 -- Runtime Function: unsigned short fract __satfracthauqq (short accum A)
 -- Runtime Function: unsigned fract __satfracthauhq (short accum A)
 -- Runtime Function: unsigned long fract __satfracthausq (short accum A)
 -- Runtime Function: unsigned long long fract __satfracthaudq (short accum A)
 -- Runtime Function: unsigned short accum __satfracthauha (short accum A)
 -- Runtime Function: unsigned accum __satfracthausa (short accum A)
 -- Runtime Function: unsigned long accum __satfracthauda (short accum A)
 -- Runtime Function: unsigned long long accum __satfracthauta (short accum A)
 -- Runtime Function: short fract __satfractsaqq (accum A)
 -- Runtime Function: fract __satfractsahq (accum A)
 -- Runtime Function: long fract __satfractsasq (accum A)
 -- Runtime Function: long long fract __satfractsadq (accum A)
 -- Runtime Function: short accum __satfractsaha2 (accum A)
 -- Runtime Function: long accum __satfractsada2 (accum A)
 -- Runtime Function: long long accum __satfractsata2 (accum A)
 -- Runtime Function: unsigned short fract __satfractsauqq (accum A)
 -- Runtime Function: unsigned fract __satfractsauhq (accum A)
 -- Runtime Function: unsigned long fract __satfractsausq (accum A)
 -- Runtime Function: unsigned long long fract __satfractsaudq (accum A)
 -- Runtime Function: unsigned short accum __satfractsauha (accum A)
 -- Runtime Function: unsigned accum __satfractsausa (accum A)
 -- Runtime Function: unsigned long accum __satfractsauda (accum A)
 -- Runtime Function: unsigned long long accum __satfractsauta (accum A)
 -- Runtime Function: short fract __satfractdaqq (long accum A)
 -- Runtime Function: fract __satfractdahq (long accum A)
 -- Runtime Function: long fract __satfractdasq (long accum A)
 -- Runtime Function: long long fract __satfractdadq (long accum A)
 -- Runtime Function: short accum __satfractdaha2 (long accum A)
 -- Runtime Function: accum __satfractdasa2 (long accum A)
 -- Runtime Function: long long accum __satfractdata2 (long accum A)
 -- Runtime Function: unsigned short fract __satfractdauqq (long accum A)
 -- Runtime Function: unsigned fract __satfractdauhq (long accum A)
 -- Runtime Function: unsigned long fract __satfractdausq (long accum A)
 -- Runtime Function: unsigned long long fract __satfractdaudq (long accum A)
 -- Runtime Function: unsigned short accum __satfractdauha (long accum A)
 -- Runtime Function: unsigned accum __satfractdausa (long accum A)
 -- Runtime Function: unsigned long accum __satfractdauda (long accum A)
 -- Runtime Function: unsigned long long accum __satfractdauta (long accum A)
 -- Runtime Function: short fract __satfracttaqq (long long accum A)
 -- Runtime Function: fract __satfracttahq (long long accum A)
 -- Runtime Function: long fract __satfracttasq (long long accum A)
 -- Runtime Function: long long fract __satfracttadq (long long accum A)
 -- Runtime Function: short accum __satfracttaha2 (long long accum A)
 -- Runtime Function: accum __satfracttasa2 (long long accum A)
 -- Runtime Function: long accum __satfracttada2 (long long accum A)
 -- Runtime Function: unsigned short fract __satfracttauqq (long long accum A)
 -- Runtime Function: unsigned fract __satfracttauhq (long long accum A)
 -- Runtime Function: unsigned long fract __satfracttausq (long long accum A)
 -- Runtime Function: unsigned long long fract __satfracttaudq (long long accum A)
 -- Runtime Function: unsigned short accum __satfracttauha (long long accum A)
 -- Runtime Function: unsigned accum __satfracttausa (long long accum A)
 -- Runtime Function: unsigned long accum __satfracttauda (long long accum A)
 -- Runtime Function: unsigned long long accum __satfracttauta (long long accum A)
 -- Runtime Function: short fract __satfractuqqqq (unsigned short fract A)
 -- Runtime Function: fract __satfractuqqhq (unsigned short fract A)
 -- Runtime Function: long fract __satfractuqqsq (unsigned short fract A)
 -- Runtime Function: long long fract __satfractuqqdq (unsigned short fract A)
 -- Runtime Function: short accum __satfractuqqha (unsigned short fract A)
 -- Runtime Function: accum __satfractuqqsa (unsigned short fract A)
 -- Runtime Function: long accum __satfractuqqda (unsigned short fract A)
 -- Runtime Function: long long accum __satfractuqqta (unsigned short fract A)
 -- Runtime Function: unsigned fract __satfractuqquhq2 (unsigned short fract A)
 -- Runtime Function: unsigned long fract __satfractuqqusq2 (unsigned short fract A)
 -- Runtime Function: unsigned long long fract __satfractuqqudq2 (unsigned short fract A)
 -- Runtime Function: unsigned short accum __satfractuqquha (unsigned short fract A)
 -- Runtime Function: unsigned accum __satfractuqqusa (unsigned short fract A)
 -- Runtime Function: unsigned long accum __satfractuqquda (unsigned short fract A)
 -- Runtime Function: unsigned long long accum __satfractuqquta (unsigned short fract A)
 -- Runtime Function: short fract __satfractuhqqq (unsigned fract A)
 -- Runtime Function: fract __satfractuhqhq (unsigned fract A)
 -- Runtime Function: long fract __satfractuhqsq (unsigned fract A)
 -- Runtime Function: long long fract __satfractuhqdq (unsigned fract A)
 -- Runtime Function: short accum __satfractuhqha (unsigned fract A)
 -- Runtime Function: accum __satfractuhqsa (unsigned fract A)
 -- Runtime Function: long accum __satfractuhqda (unsigned fract A)
 -- Runtime Function: long long accum __satfractuhqta (unsigned fract A)
 -- Runtime Function: unsigned short fract __satfractuhquqq2 (unsigned fract A)
 -- Runtime Function: unsigned long fract __satfractuhqusq2 (unsigned fract A)
 -- Runtime Function: unsigned long long fract __satfractuhqudq2 (unsigned fract A)
 -- Runtime Function: unsigned short accum __satfractuhquha (unsigned fract A)
 -- Runtime Function: unsigned accum __satfractuhqusa (unsigned fract A)
 -- Runtime Function: unsigned long accum __satfractuhquda (unsigned fract A)
 -- Runtime Function: unsigned long long accum __satfractuhquta (unsigned fract A)
 -- Runtime Function: short fract __satfractusqqq (unsigned long fract A)
 -- Runtime Function: fract __satfractusqhq (unsigned long fract A)
 -- Runtime Function: long fract __satfractusqsq (unsigned long fract A)
 -- Runtime Function: long long fract __satfractusqdq (unsigned long fract A)
 -- Runtime Function: short accum __satfractusqha (unsigned long fract A)
 -- Runtime Function: accum __satfractusqsa (unsigned long fract A)
 -- Runtime Function: long accum __satfractusqda (unsigned long fract A)
 -- Runtime Function: long long accum __satfractusqta (unsigned long fract A)
 -- Runtime Function: unsigned short fract __satfractusquqq2 (unsigned long fract A)
 -- Runtime Function: unsigned fract __satfractusquhq2 (unsigned long fract A)
 -- Runtime Function: unsigned long long fract __satfractusqudq2 (unsigned long fract A)
 -- Runtime Function: unsigned short accum __satfractusquha (unsigned long fract A)
 -- Runtime Function: unsigned accum __satfractusqusa (unsigned long fract A)
 -- Runtime Function: unsigned long accum __satfractusquda (unsigned long fract A)
 -- Runtime Function: unsigned long long accum __satfractusquta (unsigned long fract A)
 -- Runtime Function: short fract __satfractudqqq (unsigned long long fract A)
 -- Runtime Function: fract __satfractudqhq (unsigned long long fract A)
 -- Runtime Function: long fract __satfractudqsq (unsigned long long fract A)
 -- Runtime Function: long long fract __satfractudqdq (unsigned long long fract A)
 -- Runtime Function: short accum __satfractudqha (unsigned long long fract A)
 -- Runtime Function: accum __satfractudqsa (unsigned long long fract A)
 -- Runtime Function: long accum __satfractudqda (unsigned long long fract A)
 -- Runtime Function: long long accum __satfractudqta (unsigned long long fract A)
 -- Runtime Function: unsigned short fract __satfractudquqq2 (unsigned long long fract A)
 -- Runtime Function: unsigned fract __satfractudquhq2 (unsigned long long fract A)
 -- Runtime Function: unsigned long fract __satfractudqusq2 (unsigned long long fract A)
 -- Runtime Function: unsigned short accum __satfractudquha (unsigned long long fract A)
 -- Runtime Function: unsigned accum __satfractudqusa (unsigned long long fract A)
 -- Runtime Function: unsigned long accum __satfractudquda (unsigned long long fract A)
 -- Runtime Function: unsigned long long accum __satfractudquta (unsigned long long fract A)
 -- Runtime Function: short fract __satfractuhaqq (unsigned short accum A)
 -- Runtime Function: fract __satfractuhahq (unsigned short accum A)
 -- Runtime Function: long fract __satfractuhasq (unsigned short accum A)
 -- Runtime Function: long long fract __satfractuhadq (unsigned short accum A)
 -- Runtime Function: short accum __satfractuhaha (unsigned short accum A)
 -- Runtime Function: accum __satfractuhasa (unsigned short accum A)
 -- Runtime Function: long accum __satfractuhada (unsigned short accum A)
 -- Runtime Function: long long accum __satfractuhata (unsigned short accum A)
 -- Runtime Function: unsigned short fract __satfractuhauqq (unsigned short accum A)
 -- Runtime Function: unsigned fract __satfractuhauhq (unsigned short accum A)
 -- Runtime Function: unsigned long fract __satfractuhausq (unsigned short accum A)
 -- Runtime Function: unsigned long long fract __satfractuhaudq (unsigned short accum A)
 -- Runtime Function: unsigned accum __satfractuhausa2 (unsigned short accum A)
 -- Runtime Function: unsigned long accum __satfractuhauda2 (unsigned short accum A)
 -- Runtime Function: unsigned long long accum __satfractuhauta2 (unsigned short accum A)
 -- Runtime Function: short fract __satfractusaqq (unsigned accum A)
 -- Runtime Function: fract __satfractusahq (unsigned accum A)
 -- Runtime Function: long fract __satfractusasq (unsigned accum A)
 -- Runtime Function: long long fract __satfractusadq (unsigned accum A)
 -- Runtime Function: short accum __satfractusaha (unsigned accum A)
 -- Runtime Function: accum __satfractusasa (unsigned accum A)
 -- Runtime Function: long accum __satfractusada (unsigned accum A)
 -- Runtime Function: long long accum __satfractusata (unsigned accum A)
 -- Runtime Function: unsigned short fract __satfractusauqq (unsigned accum A)
 -- Runtime Function: unsigned fract __satfractusauhq (unsigned accum A)
 -- Runtime Function: unsigned long fract __satfractusausq (unsigned accum A)
 -- Runtime Function: unsigned long long fract __satfractusaudq (unsigned accum A)
 -- Runtime Function: unsigned short accum __satfractusauha2 (unsigned accum A)
 -- Runtime Function: unsigned long accum __satfractusauda2 (unsigned accum A)
 -- Runtime Function: unsigned long long accum __satfractusauta2 (unsigned accum A)
 -- Runtime Function: short fract __satfractudaqq (unsigned long accum A)
 -- Runtime Function: fract __satfractudahq (unsigned long accum A)
 -- Runtime Function: long fract __satfractudasq (unsigned long accum A)
 -- Runtime Function: long long fract __satfractudadq (unsigned long accum A)
 -- Runtime Function: short accum __satfractudaha (unsigned long accum A)
 -- Runtime Function: accum __satfractudasa (unsigned long accum A)
 -- Runtime Function: long accum __satfractudada (unsigned long accum A)
 -- Runtime Function: long long accum __satfractudata (unsigned long accum A)
 -- Runtime Function: unsigned short fract __satfractudauqq (unsigned long accum A)
 -- Runtime Function: unsigned fract __satfractudauhq (unsigned long accum A)
 -- Runtime Function: unsigned long fract __satfractudausq (unsigned long accum A)
 -- Runtime Function: unsigned long long fract __satfractudaudq (unsigned long accum A)
 -- Runtime Function: unsigned short accum __satfractudauha2 (unsigned long accum A)
 -- Runtime Function: unsigned accum __satfractudausa2 (unsigned long accum A)
 -- Runtime Function: unsigned long long accum __satfractudauta2 (unsigned long accum A)
 -- Runtime Function: short fract __satfractutaqq (unsigned long long accum A)
 -- Runtime Function: fract __satfractutahq (unsigned long long accum A)
 -- Runtime Function: long fract __satfractutasq (unsigned long long accum A)
 -- Runtime Function: long long fract __satfractutadq (unsigned long long accum A)
 -- Runtime Function: short accum __satfractutaha (unsigned long long accum A)
 -- Runtime Function: accum __satfractutasa (unsigned long long accum A)
 -- Runtime Function: long accum __satfractutada (unsigned long long accum A)
 -- Runtime Function: long long accum __satfractutata (unsigned long long accum A)
 -- Runtime Function: unsigned short fract __satfractutauqq (unsigned long long accum A)
 -- Runtime Function: unsigned fract __satfractutauhq (unsigned long long accum A)
 -- Runtime Function: unsigned long fract __satfractutausq (unsigned long long accum A)
 -- Runtime Function: unsigned long long fract __satfractutaudq (unsigned long long accum A)
 -- Runtime Function: unsigned short accum __satfractutauha2 (unsigned long long accum A)
 -- Runtime Function: unsigned accum __satfractutausa2 (unsigned long long accum A)
 -- Runtime Function: unsigned long accum __satfractutauda2 (unsigned long long accum A)
 -- Runtime Function: short fract __satfractqiqq (signed char A)
 -- Runtime Function: fract __satfractqihq (signed char A)
 -- Runtime Function: long fract __satfractqisq (signed char A)
 -- Runtime Function: long long fract __satfractqidq (signed char A)
 -- Runtime Function: short accum __satfractqiha (signed char A)
 -- Runtime Function: accum __satfractqisa (signed char A)
 -- Runtime Function: long accum __satfractqida (signed char A)
 -- Runtime Function: long long accum __satfractqita (signed char A)
 -- Runtime Function: unsigned short fract __satfractqiuqq (signed char A)
 -- Runtime Function: unsigned fract __satfractqiuhq (signed char A)
 -- Runtime Function: unsigned long fract __satfractqiusq (signed char A)
 -- Runtime Function: unsigned long long fract __satfractqiudq (signed char A)
 -- Runtime Function: unsigned short accum __satfractqiuha (signed char A)
 -- Runtime Function: unsigned accum __satfractqiusa (signed char A)
 -- Runtime Function: unsigned long accum __satfractqiuda (signed char A)
 -- Runtime Function: unsigned long long accum __satfractqiuta (signed char A)
 -- Runtime Function: short fract __satfracthiqq (short A)
 -- Runtime Function: fract __satfracthihq (short A)
 -- Runtime Function: long fract __satfracthisq (short A)
 -- Runtime Function: long long fract __satfracthidq (short A)
 -- Runtime Function: short accum __satfracthiha (short A)
 -- Runtime Function: accum __satfracthisa (short A)
 -- Runtime Function: long accum __satfracthida (short A)
 -- Runtime Function: long long accum __satfracthita (short A)
 -- Runtime Function: unsigned short fract __satfracthiuqq (short A)
 -- Runtime Function: unsigned fract __satfracthiuhq (short A)
 -- Runtime Function: unsigned long fract __satfracthiusq (short A)
 -- Runtime Function: unsigned long long fract __satfracthiudq (short A)
 -- Runtime Function: unsigned short accum __satfracthiuha (short A)
 -- Runtime Function: unsigned accum __satfracthiusa (short A)
 -- Runtime Function: unsigned long accum __satfracthiuda (short A)
 -- Runtime Function: unsigned long long accum __satfracthiuta (short A)
 -- Runtime Function: short fract __satfractsiqq (int A)
 -- Runtime Function: fract __satfractsihq (int A)
 -- Runtime Function: long fract __satfractsisq (int A)
 -- Runtime Function: long long fract __satfractsidq (int A)
 -- Runtime Function: short accum __satfractsiha (int A)
 -- Runtime Function: accum __satfractsisa (int A)
 -- Runtime Function: long accum __satfractsida (int A)
 -- Runtime Function: long long accum __satfractsita (int A)
 -- Runtime Function: unsigned short fract __satfractsiuqq (int A)
 -- Runtime Function: unsigned fract __satfractsiuhq (int A)
 -- Runtime Function: unsigned long fract __satfractsiusq (int A)
 -- Runtime Function: unsigned long long fract __satfractsiudq (int A)
 -- Runtime Function: unsigned short accum __satfractsiuha (int A)
 -- Runtime Function: unsigned accum __satfractsiusa (int A)
 -- Runtime Function: unsigned long accum __satfractsiuda (int A)
 -- Runtime Function: unsigned long long accum __satfractsiuta (int A)
 -- Runtime Function: short fract __satfractdiqq (long A)
 -- Runtime Function: fract __satfractdihq (long A)
 -- Runtime Function: long fract __satfractdisq (long A)
 -- Runtime Function: long long fract __satfractdidq (long A)
 -- Runtime Function: short accum __satfractdiha (long A)
 -- Runtime Function: accum __satfractdisa (long A)
 -- Runtime Function: long accum __satfractdida (long A)
 -- Runtime Function: long long accum __satfractdita (long A)
 -- Runtime Function: unsigned short fract __satfractdiuqq (long A)
 -- Runtime Function: unsigned fract __satfractdiuhq (long A)
 -- Runtime Function: unsigned long fract __satfractdiusq (long A)
 -- Runtime Function: unsigned long long fract __satfractdiudq (long A)
 -- Runtime Function: unsigned short accum __satfractdiuha (long A)
 -- Runtime Function: unsigned accum __satfractdiusa (long A)
 -- Runtime Function: unsigned long accum __satfractdiuda (long A)
 -- Runtime Function: unsigned long long accum __satfractdiuta (long A)
 -- Runtime Function: short fract __satfracttiqq (long long A)
 -- Runtime Function: fract __satfracttihq (long long A)
 -- Runtime Function: long fract __satfracttisq (long long A)
 -- Runtime Function: long long fract __satfracttidq (long long A)
 -- Runtime Function: short accum __satfracttiha (long long A)
 -- Runtime Function: accum __satfracttisa (long long A)
 -- Runtime Function: long accum __satfracttida (long long A)
 -- Runtime Function: long long accum __satfracttita (long long A)
 -- Runtime Function: unsigned short fract __satfracttiuqq (long long A)
 -- Runtime Function: unsigned fract __satfracttiuhq (long long A)
 -- Runtime Function: unsigned long fract __satfracttiusq (long long A)
 -- Runtime Function: unsigned long long fract __satfracttiudq (long long A)
 -- Runtime Function: unsigned short accum __satfracttiuha (long long A)
 -- Runtime Function: unsigned accum __satfracttiusa (long long A)
 -- Runtime Function: unsigned long accum __satfracttiuda (long long A)
 -- Runtime Function: unsigned long long accum __satfracttiuta (long long A)
 -- Runtime Function: short fract __satfractsfqq (float A)
 -- Runtime Function: fract __satfractsfhq (float A)
 -- Runtime Function: long fract __satfractsfsq (float A)
 -- Runtime Function: long long fract __satfractsfdq (float A)
 -- Runtime Function: short accum __satfractsfha (float A)
 -- Runtime Function: accum __satfractsfsa (float A)
 -- Runtime Function: long accum __satfractsfda (float A)
 -- Runtime Function: long long accum __satfractsfta (float A)
 -- Runtime Function: unsigned short fract __satfractsfuqq (float A)
 -- Runtime Function: unsigned fract __satfractsfuhq (float A)
 -- Runtime Function: unsigned long fract __satfractsfusq (float A)
 -- Runtime Function: unsigned long long fract __satfractsfudq (float A)
 -- Runtime Function: unsigned short accum __satfractsfuha (float A)
 -- Runtime Function: unsigned accum __satfractsfusa (float A)
 -- Runtime Function: unsigned long accum __satfractsfuda (float A)
 -- Runtime Function: unsigned long long accum __satfractsfuta (float A)
 -- Runtime Function: short fract __satfractdfqq (double A)
 -- Runtime Function: fract __satfractdfhq (double A)
 -- Runtime Function: long fract __satfractdfsq (double A)
 -- Runtime Function: long long fract __satfractdfdq (double A)
 -- Runtime Function: short accum __satfractdfha (double A)
 -- Runtime Function: accum __satfractdfsa (double A)
 -- Runtime Function: long accum __satfractdfda (double A)
 -- Runtime Function: long long accum __satfractdfta (double A)
 -- Runtime Function: unsigned short fract __satfractdfuqq (double A)
 -- Runtime Function: unsigned fract __satfractdfuhq (double A)
 -- Runtime Function: unsigned long fract __satfractdfusq (double A)
 -- Runtime Function: unsigned long long fract __satfractdfudq (double A)
 -- Runtime Function: unsigned short accum __satfractdfuha (double A)
 -- Runtime Function: unsigned accum __satfractdfusa (double A)
 -- Runtime Function: unsigned long accum __satfractdfuda (double A)
 -- Runtime Function: unsigned long long accum __satfractdfuta (double A)
     The functions convert from fractional and signed non-fractionals to fractionals, with saturation.

 -- Runtime Function: unsigned char __fractunsqqqi (short fract A)
 -- Runtime Function: unsigned short __fractunsqqhi (short fract A)
 -- Runtime Function: unsigned int __fractunsqqsi (short fract A)
 -- Runtime Function: unsigned long __fractunsqqdi (short fract A)
 -- Runtime Function: unsigned long long __fractunsqqti (short fract A)
 -- Runtime Function: unsigned char __fractunshqqi (fract A)
 -- Runtime Function: unsigned short __fractunshqhi (fract A)
 -- Runtime Function: unsigned int __fractunshqsi (fract A)
 -- Runtime Function: unsigned long __fractunshqdi (fract A)
 -- Runtime Function: unsigned long long __fractunshqti (fract A)
 -- Runtime Function: unsigned char __fractunssqqi (long fract A)
 -- Runtime Function: unsigned short __fractunssqhi (long fract A)
 -- Runtime Function: unsigned int __fractunssqsi (long fract A)
 -- Runtime Function: unsigned long __fractunssqdi (long fract A)
 -- Runtime Function: unsigned long long __fractunssqti (long fract A)
 -- Runtime Function: unsigned char __fractunsdqqi (long long fract A)
 -- Runtime Function: unsigned short __fractunsdqhi (long long fract A)
 -- Runtime Function: unsigned int __fractunsdqsi (long long fract A)
 -- Runtime Function: unsigned long __fractunsdqdi (long long fract A)
 -- Runtime Function: unsigned long long __fractunsdqti (long long fract A)
 -- Runtime Function: unsigned char __fractunshaqi (short accum A)
 -- Runtime Function: unsigned short __fractunshahi (short accum A)
 -- Runtime Function: unsigned int __fractunshasi (short accum A)
 -- Runtime Function: unsigned long __fractunshadi (short accum A)
 -- Runtime Function: unsigned long long __fractunshati (short accum A)
 -- Runtime Function: unsigned char __fractunssaqi (accum A)
 -- Runtime Function: unsigned short __fractunssahi (accum A)
 -- Runtime Function: unsigned int __fractunssasi (accum A)
 -- Runtime Function: unsigned long __fractunssadi (accum A)
 -- Runtime Function: unsigned long long __fractunssati (accum A)
 -- Runtime Function: unsigned char __fractunsdaqi (long accum A)
 -- Runtime Function: unsigned short __fractunsdahi (long accum A)
 -- Runtime Function: unsigned int __fractunsdasi (long accum A)
 -- Runtime Function: unsigned long __fractunsdadi (long accum A)
 -- Runtime Function: unsigned long long __fractunsdati (long accum A)
 -- Runtime Function: unsigned char __fractunstaqi (long long accum A)
 -- Runtime Function: unsigned short __fractunstahi (long long accum A)
 -- Runtime Function: unsigned int __fractunstasi (long long accum A)
 -- Runtime Function: unsigned long __fractunstadi (long long accum A)
 -- Runtime Function: unsigned long long __fractunstati (long long accum A)
 -- Runtime Function: unsigned char __fractunsuqqqi (unsigned short fract A)
 -- Runtime Function: unsigned short __fractunsuqqhi (unsigned short fract A)
 -- Runtime Function: unsigned int __fractunsuqqsi (unsigned short fract A)
 -- Runtime Function: unsigned long __fractunsuqqdi (unsigned short fract A)
 -- Runtime Function: unsigned long long __fractunsuqqti (unsigned short fract A)
 -- Runtime Function: unsigned char __fractunsuhqqi (unsigned fract A)
 -- Runtime Function: unsigned short __fractunsuhqhi (unsigned fract A)
 -- Runtime Function: unsigned int __fractunsuhqsi (unsigned fract A)
 -- Runtime Function: unsigned long __fractunsuhqdi (unsigned fract A)
 -- Runtime Function: unsigned long long __fractunsuhqti (unsigned fract A)
 -- Runtime Function: unsigned char __fractunsusqqi (unsigned long fract A)
 -- Runtime Function: unsigned short __fractunsusqhi (unsigned long fract A)
 -- Runtime Function: unsigned int __fractunsusqsi (unsigned long fract A)
 -- Runtime Function: unsigned long __fractunsusqdi (unsigned long fract A)
 -- Runtime Function: unsigned long long __fractunsusqti (unsigned long fract A)
 -- Runtime Function: unsigned char __fractunsudqqi (unsigned long long fract A)
 -- Runtime Function: unsigned short __fractunsudqhi (unsigned long long fract A)
 -- Runtime Function: unsigned int __fractunsudqsi (unsigned long long fract A)
 -- Runtime Function: unsigned long __fractunsudqdi (unsigned long long fract A)
 -- Runtime Function: unsigned long long __fractunsudqti (unsigned long long fract A)
 -- Runtime Function: unsigned char __fractunsuhaqi (unsigned short accum A)
 -- Runtime Function: unsigned short __fractunsuhahi (unsigned short accum A)
 -- Runtime Function: unsigned int __fractunsuhasi (unsigned short accum A)
 -- Runtime Function: unsigned long __fractunsuhadi (unsigned short accum A)
 -- Runtime Function: unsigned long long __fractunsuhati (unsigned short accum A)
 -- Runtime Function: unsigned char __fractunsusaqi (unsigned accum A)
 -- Runtime Function: unsigned short __fractunsusahi (unsigned accum A)
 -- Runtime Function: unsigned int __fractunsusasi (unsigned accum A)
 -- Runtime Function: unsigned long __fractunsusadi (unsigned accum A)
 -- Runtime Function: unsigned long long __fractunsusati (unsigned accum A)
 -- Runtime Function: unsigned char __fractunsudaqi (unsigned long accum A)
 -- Runtime Function: unsigned short __fractunsudahi (unsigned long accum A)
 -- Runtime Function: unsigned int __fractunsudasi (unsigned long accum A)
 -- Runtime Function: unsigned long __fractunsudadi (unsigned long accum A)
 -- Runtime Function: unsigned long long __fractunsudati (unsigned long accum A)
 -- Runtime Function: unsigned char __fractunsutaqi (unsigned long long accum A)
 -- Runtime Function: unsigned short __fractunsutahi (unsigned long long accum A)
 -- Runtime Function: unsigned int __fractunsutasi (unsigned long long accum A)
 -- Runtime Function: unsigned long __fractunsutadi (unsigned long long accum A)
 -- Runtime Function: unsigned long long __fractunsutati (unsigned long long accum A)
 -- Runtime Function: short fract __fractunsqiqq (unsigned char A)
 -- Runtime Function: fract __fractunsqihq (unsigned char A)
 -- Runtime Function: long fract __fractunsqisq (unsigned char A)
 -- Runtime Function: long long fract __fractunsqidq (unsigned char A)
 -- Runtime Function: short accum __fractunsqiha (unsigned char A)
 -- Runtime Function: accum __fractunsqisa (unsigned char A)
 -- Runtime Function: long accum __fractunsqida (unsigned char A)
 -- Runtime Function: long long accum __fractunsqita (unsigned char A)
 -- Runtime Function: unsigned short fract __fractunsqiuqq (unsigned char A)
 -- Runtime Function: unsigned fract __fractunsqiuhq (unsigned char A)
 -- Runtime Function: unsigned long fract __fractunsqiusq (unsigned char A)
 -- Runtime Function: unsigned long long fract __fractunsqiudq (unsigned char A)
 -- Runtime Function: unsigned short accum __fractunsqiuha (unsigned char A)
 -- Runtime Function: unsigned accum __fractunsqiusa (unsigned char A)
 -- Runtime Function: unsigned long accum __fractunsqiuda (unsigned char A)
 -- Runtime Function: unsigned long long accum __fractunsqiuta (unsigned char A)
 -- Runtime Function: short fract __fractunshiqq (unsigned short A)
 -- Runtime Function: fract __fractunshihq (unsigned short A)
 -- Runtime Function: long fract __fractunshisq (unsigned short A)
 -- Runtime Function: long long fract __fractunshidq (unsigned short A)
 -- Runtime Function: short accum __fractunshiha (unsigned short A)
 -- Runtime Function: accum __fractunshisa (unsigned short A)
 -- Runtime Function: long accum __fractunshida (unsigned short A)
 -- Runtime Function: long long accum __fractunshita (unsigned short A)
 -- Runtime Function: unsigned short fract __fractunshiuqq (unsigned short A)
 -- Runtime Function: unsigned fract __fractunshiuhq (unsigned short A)
 -- Runtime Function: unsigned long fract __fractunshiusq (unsigned short A)
 -- Runtime Function: unsigned long long fract __fractunshiudq (unsigned short A)
 -- Runtime Function: unsigned short accum __fractunshiuha (unsigned short A)
 -- Runtime Function: unsigned accum __fractunshiusa (unsigned short A)
 -- Runtime Function: unsigned long accum __fractunshiuda (unsigned short A)
 -- Runtime Function: unsigned long long accum __fractunshiuta (unsigned short A)
 -- Runtime Function: short fract __fractunssiqq (unsigned int A)
 -- Runtime Function: fract __fractunssihq (unsigned int A)
 -- Runtime Function: long fract __fractunssisq (unsigned int A)
 -- Runtime Function: long long fract __fractunssidq (unsigned int A)
 -- Runtime Function: short accum __fractunssiha (unsigned int A)
 -- Runtime Function: accum __fractunssisa (unsigned int A)
 -- Runtime Function: long accum __fractunssida (unsigned int A)
 -- Runtime Function: long long accum __fractunssita (unsigned int A)
 -- Runtime Function: unsigned short fract __fractunssiuqq (unsigned int A)
 -- Runtime Function: unsigned fract __fractunssiuhq (unsigned int A)
 -- Runtime Function: unsigned long fract __fractunssiusq (unsigned int A)
 -- Runtime Function: unsigned long long fract __fractunssiudq (unsigned int A)
 -- Runtime Function: unsigned short accum __fractunssiuha (unsigned int A)
 -- Runtime Function: unsigned accum __fractunssiusa (unsigned int A)
 -- Runtime Function: unsigned long accum __fractunssiuda (unsigned int A)
 -- Runtime Function: unsigned long long accum __fractunssiuta (unsigned int A)
 -- Runtime Function: short fract __fractunsdiqq (unsigned long A)
 -- Runtime Function: fract __fractunsdihq (unsigned long A)
 -- Runtime Function: long fract __fractunsdisq (unsigned long A)
 -- Runtime Function: long long fract __fractunsdidq (unsigned long A)
 -- Runtime Function: short accum __fractunsdiha (unsigned long A)
 -- Runtime Function: accum __fractunsdisa (unsigned long A)
 -- Runtime Function: long accum __fractunsdida (unsigned long A)
 -- Runtime Function: long long accum __fractunsdita (unsigned long A)
 -- Runtime Function: unsigned short fract __fractunsdiuqq (unsigned long A)
 -- Runtime Function: unsigned fract __fractunsdiuhq (unsigned long A)
 -- Runtime Function: unsigned long fract __fractunsdiusq (unsigned long A)
 -- Runtime Function: unsigned long long fract __fractunsdiudq (unsigned long A)
 -- Runtime Function: unsigned short accum __fractunsdiuha (unsigned long A)
 -- Runtime Function: unsigned accum __fractunsdiusa (unsigned long A)
 -- Runtime Function: unsigned long accum __fractunsdiuda (unsigned long A)
 -- Runtime Function: unsigned long long accum __fractunsdiuta (unsigned long A)
 -- Runtime Function: short fract __fractunstiqq (unsigned long long A)
 -- Runtime Function: fract __fractunstihq (unsigned long long A)
 -- Runtime Function: long fract __fractunstisq (unsigned long long A)
 -- Runtime Function: long long fract __fractunstidq (unsigned long long A)
 -- Runtime Function: short accum __fractunstiha (unsigned long long A)
 -- Runtime Function: accum __fractunstisa (unsigned long long A)
 -- Runtime Function: long accum __fractunstida (unsigned long long A)
 -- Runtime Function: long long accum __fractunstita (unsigned long long A)
 -- Runtime Function: unsigned short fract __fractunstiuqq (unsigned long long A)
 -- Runtime Function: unsigned fract __fractunstiuhq (unsigned long long A)
 -- Runtime Function: unsigned long fract __fractunstiusq (unsigned long long A)
 -- Runtime Function: unsigned long long fract __fractunstiudq (unsigned long long A)
 -- Runtime Function: unsigned short accum __fractunstiuha (unsigned long long A)
 -- Runtime Function: unsigned accum __fractunstiusa (unsigned long long A)
 -- Runtime Function: unsigned long accum __fractunstiuda (unsigned long long A)
 -- Runtime Function: unsigned long long accum __fractunstiuta (unsigned long long A)
     These functions convert from fractionals to unsigned non-fractionals; and from unsigned non-fractionals to fractionals, without saturation.

 -- Runtime Function: short fract __satfractunsqiqq (unsigned char A)
 -- Runtime Function: fract __satfractunsqihq (unsigned char A)
 -- Runtime Function: long fract __satfractunsqisq (unsigned char A)
 -- Runtime Function: long long fract __satfractunsqidq (unsigned char A)
 -- Runtime Function: short accum __satfractunsqiha (unsigned char A)
 -- Runtime Function: accum __satfractunsqisa (unsigned char A)
 -- Runtime Function: long accum __satfractunsqida (unsigned char A)
 -- Runtime Function: long long accum __satfractunsqita (unsigned char A)
 -- Runtime Function: unsigned short fract __satfractunsqiuqq (unsigned char A)
 -- Runtime Function: unsigned fract __satfractunsqiuhq (unsigned char A)
 -- Runtime Function: unsigned long fract __satfractunsqiusq (unsigned char A)
 -- Runtime Function: unsigned long long fract __satfractunsqiudq (unsigned char A)
 -- Runtime Function: unsigned short accum __satfractunsqiuha (unsigned char A)
 -- Runtime Function: unsigned accum __satfractunsqiusa (unsigned char A)
 -- Runtime Function: unsigned long accum __satfractunsqiuda (unsigned char A)
 -- Runtime Function: unsigned long long accum __satfractunsqiuta (unsigned char A)
 -- Runtime Function: short fract __satfractunshiqq (unsigned short A)
 -- Runtime Function: fract __satfractunshihq (unsigned short A)
 -- Runtime Function: long fract __satfractunshisq (unsigned short A)
 -- Runtime Function: long long fract __satfractunshidq (unsigned short A)
 -- Runtime Function: short accum __satfractunshiha (unsigned short A)
 -- Runtime Function: accum __satfractunshisa (unsigned short A)
 -- Runtime Function: long accum __satfractunshida (unsigned short A)
 -- Runtime Function: long long accum __satfractunshita (unsigned short A)
 -- Runtime Function: unsigned short fract __satfractunshiuqq (unsigned short A)
 -- Runtime Function: unsigned fract __satfractunshiuhq (unsigned short A)
 -- Runtime Function: unsigned long fract __satfractunshiusq (unsigned short A)
 -- Runtime Function: unsigned long long fract __satfractunshiudq (unsigned short A)
 -- Runtime Function: unsigned short accum __satfractunshiuha (unsigned short A)
 -- Runtime Function: unsigned accum __satfractunshiusa (unsigned short A)
 -- Runtime Function: unsigned long accum __satfractunshiuda (unsigned short A)
 -- Runtime Function: unsigned long long accum __satfractunshiuta (unsigned short A)
 -- Runtime Function: short fract __satfractunssiqq (unsigned int A)
 -- Runtime Function: fract __satfractunssihq (unsigned int A)
 -- Runtime Function: long fract __satfractunssisq (unsigned int A)
 -- Runtime Function: long long fract __satfractunssidq (unsigned int A)
 -- Runtime Function: short accum __satfractunssiha (unsigned int A)
 -- Runtime Function: accum __satfractunssisa (unsigned int A)
 -- Runtime Function: long accum __satfractunssida (unsigned int A)
 -- Runtime Function: long long accum __satfractunssita (unsigned int A)
 -- Runtime Function: unsigned short fract __satfractunssiuqq (unsigned int A)
 -- Runtime Function: unsigned fract __satfractunssiuhq (unsigned int A)
 -- Runtime Function: unsigned long fract __satfractunssiusq (unsigned int A)
 -- Runtime Function: unsigned long long fract __satfractunssiudq (unsigned int A)
 -- Runtime Function: unsigned short accum __satfractunssiuha (unsigned int A)
 -- Runtime Function: unsigned accum __satfractunssiusa (unsigned int A)
 -- Runtime Function: unsigned long accum __satfractunssiuda (unsigned int A)
 -- Runtime Function: unsigned long long accum __satfractunssiuta (unsigned int A)
 -- Runtime Function: short fract __satfractunsdiqq (unsigned long A)
 -- Runtime Function: fract __satfractunsdihq (unsigned long A)
 -- Runtime Function: long fract __satfractunsdisq (unsigned long A)
 -- Runtime Function: long long fract __satfractunsdidq (unsigned long A)
 -- Runtime Function: short accum __satfractunsdiha (unsigned long A)
 -- Runtime Function: accum __satfractunsdisa (unsigned long A)
 -- Runtime Function: long accum __satfractunsdida (unsigned long A)
 -- Runtime Function: long long accum __satfractunsdita (unsigned long A)
 -- Runtime Function: unsigned short fract __satfractunsdiuqq (unsigned long A)
 -- Runtime Function: unsigned fract __satfractunsdiuhq (unsigned long A)
 -- Runtime Function: unsigned long fract __satfractunsdiusq (unsigned long A)
 -- Runtime Function: unsigned long long fract __satfractunsdiudq (unsigned long A)
 -- Runtime Function: unsigned short accum __satfractunsdiuha (unsigned long A)
 -- Runtime Function: unsigned accum __satfractunsdiusa (unsigned long A)
 -- Runtime Function: unsigned long accum __satfractunsdiuda (unsigned long A)
 -- Runtime Function: unsigned long long accum __satfractunsdiuta (unsigned long A)
 -- Runtime Function: short fract __satfractunstiqq (unsigned long long A)
 -- Runtime Function: fract __satfractunstihq (unsigned long long A)
 -- Runtime Function: long fract __satfractunstisq (unsigned long long A)
 -- Runtime Function: long long fract __satfractunstidq (unsigned long long A)
 -- Runtime Function: short accum __satfractunstiha (unsigned long long A)
 -- Runtime Function: accum __satfractunstisa (unsigned long long A)
 -- Runtime Function: long accum __satfractunstida (unsigned long long A)
 -- Runtime Function: long long accum __satfractunstita (unsigned long long A)
 -- Runtime Function: unsigned short fract __satfractunstiuqq (unsigned long long A)
 -- Runtime Function: unsigned fract __satfractunstiuhq (unsigned long long A)
 -- Runtime Function: unsigned long fract __satfractunstiusq (unsigned long long A)
 -- Runtime Function: unsigned long long fract __satfractunstiudq (unsigned long long A)
 -- Runtime Function: unsigned short accum __satfractunstiuha (unsigned long long A)
 -- Runtime Function: unsigned accum __satfractunstiusa (unsigned long long A)
 -- Runtime Function: unsigned long accum __satfractunstiuda (unsigned long long A)
 -- Runtime Function: unsigned long long accum __satfractunstiuta (unsigned long long A)
     These functions convert from unsigned non-fractionals to fractionals, with saturation.

Language-independent routines for exception handling
====================================================

document me!

       _Unwind_DeleteException
       _Unwind_Find_FDE
       _Unwind_ForcedUnwind
       _Unwind_GetGR
       _Unwind_GetIP
       _Unwind_GetLanguageSpecificData
       _Unwind_GetRegionStart
       _Unwind_GetTextRelBase
       _Unwind_GetDataRelBase
       _Unwind_RaiseException
       _Unwind_Resume
       _Unwind_SetGR
       _Unwind_SetIP
       _Unwind_FindEnclosingFunction
       _Unwind_SjLj_Register
       _Unwind_SjLj_Unregister
       _Unwind_SjLj_RaiseException
       _Unwind_SjLj_ForcedUnwind
       _Unwind_SjLj_Resume
       __deregister_frame
       __deregister_frame_info
       __deregister_frame_info_bases
       __register_frame
       __register_frame_info
       __register_frame_info_bases
       __register_frame_info_table
       __register_frame_info_table_bases
       __register_frame_table

Miscellaneous runtime library routines
======================================

Cache control functions
-----------------------

 -- Runtime Function: void __clear_cache (char *BEG, char *END)
     This function clears the instruction cache between BEG and END.