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@c Copyright (C) 2003, 2004, 2005, 2006, 2007, 2010

@c Free Software Foundation, Inc.

@c This is part of the GCC manual.

@c For copying conditions, see the file gcc.texi.

@c Contributed by Aldy Hernandez <aldy@quesejoda.com>

@node Libgcc

@chapter The GCC low-level runtime library

GCC provides a low-level runtime library, @file{libgcc.a} or

@file{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 @code{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.  @code{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

@code{memcpy} and @code{memset}, in some cases.  The set of routines

that GCC may possibly use is documented in @ref{Other

Builtins,,,gcc, Using the GNU Compiler Collection (GCC)}.

These routines take arguments and return values of a specific machine

mode, not a specific C type.  @xref{Machine Modes}, for an explanation

of this concept.  For illustrative purposes, in this chapter the

floating point type @code{float} is assumed to correspond to @code{SFmode};

@code{double} to @code{DFmode}; and @code{@w{long double}} to both

@code{TFmode} and @code{XFmode}.  Similarly, the integer types @code{int}

and @code{@w{unsigned int}} correspond to @code{SImode}; @code{long} and

@code{@w{unsigned long}} to @code{DImode}; and @code{@w{long long}} and

@code{@w{unsigned long long}} to @code{TImode}.

@menu

* Integer library routines::

* Soft float library routines::

* Decimal float library routines::

* Fixed-point fractional library routines::

* Exception handling routines::

* Miscellaneous routines::

@end menu

@node Integer library routines

@section Routines for integer arithmetic

The integer arithmetic routines are used on platforms that don't provide

hardware support for arithmetic operations on some modes.

@subsection Arithmetic functions

@deftypefn {Runtime Function} int __ashlsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __ashldi3 (long @var{a}, int @var{b})

@deftypefnx {Runtime Function} {long long} __ashlti3 (long long @var{a}, int @var{b})

These functions return the result of shifting @var{a} left by @var{b} bits.

@end deftypefn

@deftypefn {Runtime Function} int __ashrsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __ashrdi3 (long @var{a}, int @var{b})

@deftypefnx {Runtime Function} {long long} __ashrti3 (long long @var{a}, int @var{b})

These functions return the result of arithmetically shifting @var{a} right

by @var{b} bits.

@end deftypefn

@deftypefn {Runtime Function} int __divsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __divdi3 (long @var{a}, long @var{b})

@deftypefnx {Runtime Function} {long long} __divti3 (long long @var{a}, long long @var{b})

These functions return the quotient of the signed division of @var{a} and

@var{b}.

@end deftypefn

@deftypefn {Runtime Function} int __lshrsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __lshrdi3 (long @var{a}, int @var{b})

@deftypefnx {Runtime Function} {long long} __lshrti3 (long long @var{a}, int @var{b})

These functions return the result of logically shifting @var{a} right by

@var{b} bits.

@end deftypefn

@deftypefn {Runtime Function} int __modsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __moddi3 (long @var{a}, long @var{b})

@deftypefnx {Runtime Function} {long long} __modti3 (long long @var{a}, long long @var{b})

These functions return the remainder of the signed division of @var{a}

and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} int __mulsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __muldi3 (long @var{a}, long @var{b})

@deftypefnx {Runtime Function} {long long} __multi3 (long long @var{a}, long long @var{b})

These functions return the product of @var{a} and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} long __negdi2 (long @var{a})

@deftypefnx {Runtime Function} {long long} __negti2 (long long @var{a})

These functions return the negation of @var{a}.

@end deftypefn

@deftypefn {Runtime Function} {unsigned int} __udivsi3 (unsigned int @var{a}, unsigned int @var{b})

@deftypefnx {Runtime Function} {unsigned long} __udivdi3 (unsigned long @var{a}, unsigned long @var{b})

@deftypefnx {Runtime Function} {unsigned long long} __udivti3 (unsigned long long @var{a}, unsigned long long @var{b})

These functions return the quotient of the unsigned division of @var{a}

and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} {unsigned long} __udivmoddi4 (unsigned long @var{a}, unsigned long @var{b}, unsigned long *@var{c})

@deftypefnx {Runtime Function} {unsigned long long} __udivmodti4 (unsigned long long @var{a}, unsigned long long @var{b}, unsigned long long *@var{c})

These functions calculate both the quotient and remainder of the unsigned

division of @var{a} and @var{b}.  The return value is the quotient, and

the remainder is placed in variable pointed to by @var{c}.

@end deftypefn

@deftypefn {Runtime Function} {unsigned int} __umodsi3 (unsigned int @var{a}, unsigned int @var{b})

@deftypefnx {Runtime Function} {unsigned long} __umoddi3 (unsigned long @var{a}, unsigned long @var{b})

@deftypefnx {Runtime Function} {unsigned long long} __umodti3 (unsigned long long @var{a}, unsigned long long @var{b})

These functions return the remainder of the unsigned division of @var{a}

and @var{b}.

@end deftypefn

@subsection 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.

@deftypefn {Runtime Function} int __cmpdi2 (long @var{a}, long @var{b})

@deftypefnx {Runtime Function} int __cmpti2 (long long @var{a}, long long @var{b})

These functions perform a signed comparison of @var{a} and @var{b}.  If

@var{a} is less than @var{b}, they return 0; if @var{a} is greater than

@var{b}, they return 2; and if @var{a} and @var{b} are equal they return 1.

@end deftypefn

@deftypefn {Runtime Function} int __ucmpdi2 (unsigned long @var{a}, unsigned long @var{b})

@deftypefnx {Runtime Function} int __ucmpti2 (unsigned long long @var{a}, unsigned long long @var{b})

These functions perform an unsigned comparison of @var{a} and @var{b}.

If @var{a} is less than @var{b}, they return 0; if @var{a} is greater than

@var{b}, they return 2; and if @var{a} and @var{b} are equal they return 1.

@end deftypefn

@subsection Trapping arithmetic functions

The following functions implement trapping arithmetic.  These functions

call the libc function @code{abort} upon signed arithmetic overflow.

@deftypefn {Runtime Function} int __absvsi2 (int @var{a})

@deftypefnx {Runtime Function} long __absvdi2 (long @var{a})

These functions return the absolute value of @var{a}.

@end deftypefn

@deftypefn {Runtime Function} int __addvsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __addvdi3 (long @var{a}, long @var{b})

These functions return the sum of @var{a} and @var{b}; that is

@code{@var{a} + @var{b}}.

@end deftypefn

@deftypefn {Runtime Function} int __mulvsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __mulvdi3 (long @var{a}, long @var{b})

The functions return the product of @var{a} and @var{b}; that is

@code{@var{a} * @var{b}}.

@end deftypefn

@deftypefn {Runtime Function} int __negvsi2 (int @var{a})

@deftypefnx {Runtime Function} long __negvdi2 (long @var{a})

These functions return the negation of @var{a}; that is @code{-@var{a}}.

@end deftypefn

@deftypefn {Runtime Function} int __subvsi3 (int @var{a}, int @var{b})

@deftypefnx {Runtime Function} long __subvdi3 (long @var{a}, long @var{b})

These functions return the difference between @var{b} and @var{a};

that is @code{@var{a} - @var{b}}.

@end deftypefn

@subsection Bit operations

@deftypefn {Runtime Function} int __clzsi2 (int @var{a})

@deftypefnx {Runtime Function} int __clzdi2 (long @var{a})

@deftypefnx {Runtime Function} int __clzti2 (long long @var{a})

These functions return the number of leading 0-bits in @var{a}, starting

at the most significant bit position.  If @var{a} is zero, the result is

undefined.

@end deftypefn

@deftypefn {Runtime Function} int __ctzsi2 (int @var{a})

@deftypefnx {Runtime Function} int __ctzdi2 (long @var{a})

@deftypefnx {Runtime Function} int __ctzti2 (long long @var{a})

These functions return the number of trailing 0-bits in @var{a}, starting

at the least significant bit position.  If @var{a} is zero, the result is

undefined.

@end deftypefn

@deftypefn {Runtime Function} int __ffsdi2 (long @var{a})

@deftypefnx {Runtime Function} int __ffsti2 (long long @var{a})

These functions return the index of the least significant 1-bit in @var{a},

or the value zero if @var{a} is zero.  The least significant bit is index

one.

@end deftypefn

@deftypefn {Runtime Function} int __paritysi2 (int @var{a})

@deftypefnx {Runtime Function} int __paritydi2 (long @var{a})

@deftypefnx {Runtime Function} int __parityti2 (long long @var{a})

These functions return the value zero if the number of bits set in

@var{a} is even, and the value one otherwise.

@end deftypefn

@deftypefn {Runtime Function} int __popcountsi2 (int @var{a})

@deftypefnx {Runtime Function} int __popcountdi2 (long @var{a})

@deftypefnx {Runtime Function} int __popcountti2 (long long @var{a})

These functions return the number of bits set in @var{a}.

@end deftypefn

@deftypefn {Runtime Function} int32_t __bswapsi2 (int32_t @var{a})

@deftypefnx {Runtime Function} int64_t __bswapdi2 (int64_t @var{a})

These functions return the @var{a} byteswapped.

@end deftypefn

@node Soft float library routines

@section Routines for floating point emulation

@cindex soft float library

@cindex arithmetic library

@cindex math library

@opindex msoft-float

The software floating point library is used on machines which do not

have hardware support for floating point.  It is also used whenever

@option{-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 @code{DECLARE_LIBRARY_RENAMES} macro

(@pxref{Library Calls}).  In this section, the default names are used.

Presently the library does not support @code{XFmode}, which is used

for @code{long double} on some architectures.

@subsection Arithmetic functions

@deftypefn {Runtime Function} float __addsf3 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} double __adddf3 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} {long double} __addtf3 (long double @var{a}, long double @var{b})

@deftypefnx {Runtime Function} {long double} __addxf3 (long double @var{a}, long double @var{b})

These functions return the sum of @var{a} and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} float __subsf3 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} double __subdf3 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} {long double} __subtf3 (long double @var{a}, long double @var{b})

@deftypefnx {Runtime Function} {long double} __subxf3 (long double @var{a}, long double @var{b})

These functions return the difference between @var{b} and @var{a};

that is, @w{@math{@var{a} - @var{b}}}.

@end deftypefn

@deftypefn {Runtime Function} float __mulsf3 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} double __muldf3 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} {long double} __multf3 (long double @var{a}, long double @var{b})

@deftypefnx {Runtime Function} {long double} __mulxf3 (long double @var{a}, long double @var{b})

These functions return the product of @var{a} and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} float __divsf3 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} double __divdf3 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} {long double} __divtf3 (long double @var{a}, long double @var{b})

@deftypefnx {Runtime Function} {long double} __divxf3 (long double @var{a}, long double @var{b})

These functions return the quotient of @var{a} and @var{b}; that is,

@w{@math{@var{a} / @var{b}}}.

@end deftypefn

@deftypefn {Runtime Function} float __negsf2 (float @var{a})

@deftypefnx {Runtime Function} double __negdf2 (double @var{a})

@deftypefnx {Runtime Function} {long double} __negtf2 (long double @var{a})

@deftypefnx {Runtime Function} {long double} __negxf2 (long double @var{a})

These functions return the negation of @var{a}.  They simply flip the

sign bit, so they can produce negative zero and negative NaN@.

@end deftypefn

@subsection Conversion functions

@deftypefn {Runtime Function} double __extendsfdf2 (float @var{a})

@deftypefnx {Runtime Function} {long double} __extendsftf2 (float @var{a})

@deftypefnx {Runtime Function} {long double} __extendsfxf2 (float @var{a})

@deftypefnx {Runtime Function} {long double} __extenddftf2 (double @var{a})

@deftypefnx {Runtime Function} {long double} __extenddfxf2 (double @var{a})

These functions extend @var{a} to the wider mode of their return

type.

@end deftypefn

@deftypefn {Runtime Function} double __truncxfdf2 (long double @var{a})

@deftypefnx {Runtime Function} double __trunctfdf2 (long double @var{a})

@deftypefnx {Runtime Function} float __truncxfsf2 (long double @var{a})

@deftypefnx {Runtime Function} float __trunctfsf2 (long double @var{a})

@deftypefnx {Runtime Function} float __truncdfsf2 (double @var{a})

These functions truncate @var{a} to the narrower mode of their return

type, rounding toward zero.

@end deftypefn

@deftypefn {Runtime Function} int __fixsfsi (float @var{a})

@deftypefnx {Runtime Function} int __fixdfsi (double @var{a})

@deftypefnx {Runtime Function} int __fixtfsi (long double @var{a})

@deftypefnx {Runtime Function} int __fixxfsi (long double @var{a})

These functions convert @var{a} to a signed integer, rounding toward zero.

@end deftypefn

@deftypefn {Runtime Function} long __fixsfdi (float @var{a})

@deftypefnx {Runtime Function} long __fixdfdi (double @var{a})

@deftypefnx {Runtime Function} long __fixtfdi (long double @var{a})

@deftypefnx {Runtime Function} long __fixxfdi (long double @var{a})

These functions convert @var{a} to a signed long, rounding toward zero.

@end deftypefn

@deftypefn {Runtime Function} {long long} __fixsfti (float @var{a})

@deftypefnx {Runtime Function} {long long} __fixdfti (double @var{a})

@deftypefnx {Runtime Function} {long long} __fixtfti (long double @var{a})

@deftypefnx {Runtime Function} {long long} __fixxfti (long double @var{a})

These functions convert @var{a} to a signed long long, rounding toward zero.

@end deftypefn

@deftypefn {Runtime Function} {unsigned int} __fixunssfsi (float @var{a})

@deftypefnx {Runtime Function} {unsigned int} __fixunsdfsi (double @var{a})

@deftypefnx {Runtime Function} {unsigned int} __fixunstfsi (long double @var{a})

@deftypefnx {Runtime Function} {unsigned int} __fixunsxfsi (long double @var{a})

These functions convert @var{a} to an unsigned integer, rounding

toward zero.  Negative values all become zero.

@end deftypefn

@deftypefn {Runtime Function} {unsigned long} __fixunssfdi (float @var{a})

@deftypefnx {Runtime Function} {unsigned long} __fixunsdfdi (double @var{a})

@deftypefnx {Runtime Function} {unsigned long} __fixunstfdi (long double @var{a})

@deftypefnx {Runtime Function} {unsigned long} __fixunsxfdi (long double @var{a})

These functions convert @var{a} to an unsigned long, rounding

toward zero.  Negative values all become zero.

@end deftypefn

@deftypefn {Runtime Function} {unsigned long long} __fixunssfti (float @var{a})

@deftypefnx {Runtime Function} {unsigned long long} __fixunsdfti (double @var{a})

@deftypefnx {Runtime Function} {unsigned long long} __fixunstfti (long double @var{a})

@deftypefnx {Runtime Function} {unsigned long long} __fixunsxfti (long double @var{a})

These functions convert @var{a} to an unsigned long long, rounding

toward zero.  Negative values all become zero.

@end deftypefn

@deftypefn {Runtime Function} float __floatsisf (int @var{i})

@deftypefnx {Runtime Function} double __floatsidf (int @var{i})

@deftypefnx {Runtime Function} {long double} __floatsitf (int @var{i})

@deftypefnx {Runtime Function} {long double} __floatsixf (int @var{i})

These functions convert @var{i}, a signed integer, to floating point.

@end deftypefn

@deftypefn {Runtime Function} float __floatdisf (long @var{i})

@deftypefnx {Runtime Function} double __floatdidf (long @var{i})

@deftypefnx {Runtime Function} {long double} __floatditf (long @var{i})

@deftypefnx {Runtime Function} {long double} __floatdixf (long @var{i})

These functions convert @var{i}, a signed long, to floating point.

@end deftypefn

@deftypefn {Runtime Function} float __floattisf (long long @var{i})

@deftypefnx {Runtime Function} double __floattidf (long long @var{i})

@deftypefnx {Runtime Function} {long double} __floattitf (long long @var{i})

@deftypefnx {Runtime Function} {long double} __floattixf (long long @var{i})

These functions convert @var{i}, a signed long long, to floating point.

@end deftypefn

@deftypefn {Runtime Function} float __floatunsisf (unsigned int @var{i})

@deftypefnx {Runtime Function} double __floatunsidf (unsigned int @var{i})

@deftypefnx {Runtime Function} {long double} __floatunsitf (unsigned int @var{i})

@deftypefnx {Runtime Function} {long double} __floatunsixf (unsigned int @var{i})

These functions convert @var{i}, an unsigned integer, to floating point.

@end deftypefn

@deftypefn {Runtime Function} float __floatundisf (unsigned long @var{i})

@deftypefnx {Runtime Function} double __floatundidf (unsigned long @var{i})

@deftypefnx {Runtime Function} {long double} __floatunditf (unsigned long @var{i})

@deftypefnx {Runtime Function} {long double} __floatundixf (unsigned long @var{i})

These functions convert @var{i}, an unsigned long, to floating point.

@end deftypefn

@deftypefn {Runtime Function} float __floatuntisf (unsigned long long @var{i})

@deftypefnx {Runtime Function} double __floatuntidf (unsigned long long @var{i})

@deftypefnx {Runtime Function} {long double} __floatuntitf (unsigned long long @var{i})

@deftypefnx {Runtime Function} {long double} __floatuntixf (unsigned long long @var{i})

These functions convert @var{i}, an unsigned long long, to floating point.

@end deftypefn

@subsection Comparison functions

There are two sets of basic comparison functions.

@deftypefn {Runtime Function} int __cmpsf2 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} int __cmpdf2 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} int __cmptf2 (long double @var{a}, long double @var{b})

These functions calculate @math{a <=> b}.  That is, if @var{a} is less

than @var{b}, they return @minus{}1; if @var{a} is greater than @var{b}, they

return 1; and if @var{a} and @var{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.

@end deftypefn

@deftypefn {Runtime Function} int __unordsf2 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} int __unorddf2 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} int __unordtf2 (long double @var{a}, long double @var{b})

These functions return a nonzero value if either argument is NaN, otherwise 0.

@end deftypefn

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

@smallexample

  if (__unord@var{X}f2 (a, b))

    return @var{E};

  return __cmp@var{X}f2 (a, b);

@end smallexample

@noindent

where @var{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.

@deftypefn {Runtime Function} int __eqsf2 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} int __eqdf2 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} int __eqtf2 (long double @var{a}, long double @var{b})

These functions return zero if neither argument is NaN, and @var{a} and

@var{b} are equal.

@end deftypefn

@deftypefn {Runtime Function} int __nesf2 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} int __nedf2 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} int __netf2 (long double @var{a}, long double @var{b})

These functions return a nonzero value if either argument is NaN, or

if @var{a} and @var{b} are unequal.

@end deftypefn

@deftypefn {Runtime Function} int __gesf2 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} int __gedf2 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} int __getf2 (long double @var{a}, long double @var{b})

These functions return a value greater than or equal to zero if

neither argument is NaN, and @var{a} is greater than or equal to

@var{b}.

@end deftypefn

@deftypefn {Runtime Function} int __ltsf2 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} int __ltdf2 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} int __lttf2 (long double @var{a}, long double @var{b})

These functions return a value less than zero if neither argument is

NaN, and @var{a} is strictly less than @var{b}.

@end deftypefn

@deftypefn {Runtime Function} int __lesf2 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} int __ledf2 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} int __letf2 (long double @var{a}, long double @var{b})

These functions return a value less than or equal to zero if neither

argument is NaN, and @var{a} is less than or equal to @var{b}.

@end deftypefn

@deftypefn {Runtime Function} int __gtsf2 (float @var{a}, float @var{b})

@deftypefnx {Runtime Function} int __gtdf2 (double @var{a}, double @var{b})

@deftypefnx {Runtime Function} int __gttf2 (long double @var{a}, long double @var{b})

These functions return a value greater than zero if neither argument

is NaN, and @var{a} is strictly greater than @var{b}.

@end deftypefn

@subsection Other floating-point functions

@deftypefn {Runtime Function} float __powisf2 (float @var{a}, int @var{b})

@deftypefnx {Runtime Function} double __powidf2 (double @var{a}, int @var{b})

@deftypefnx {Runtime Function} {long double} __powitf2 (long double @var{a}, int @var{b})

@deftypefnx {Runtime Function} {long double} __powixf2 (long double @var{a}, int @var{b})

These functions convert raise @var{a} to the power @var{b}.

@end deftypefn

@deftypefn {Runtime Function} {complex float} __mulsc3 (float @var{a}, float @var{b}, float @var{c}, float @var{d})

@deftypefnx {Runtime Function} {complex double} __muldc3 (double @var{a}, double @var{b}, double @var{c}, double @var{d})

@deftypefnx {Runtime Function} {complex long double} __multc3 (long double @var{a}, long double @var{b}, long double @var{c}, long double @var{d})

@deftypefnx {Runtime Function} {complex long double} __mulxc3 (long double @var{a}, long double @var{b}, long double @var{c}, long double @var{d})

These functions return the product of @math{@var{a} + i@var{b}} and

@math{@var{c} + i@var{d}}, following the rules of C99 Annex G@.

@end deftypefn

@deftypefn {Runtime Function} {complex float} __divsc3 (float @var{a}, float @var{b}, float @var{c}, float @var{d})

@deftypefnx {Runtime Function} {complex double} __divdc3 (double @var{a}, double @var{b}, double @var{c}, double @var{d})

@deftypefnx {Runtime Function} {complex long double} __divtc3 (long double @var{a}, long double @var{b}, long double @var{c}, long double @var{d})

@deftypefnx {Runtime Function} {complex long double} __divxc3 (long double @var{a}, long double @var{b}, long double @var{c}, long double @var{d})

These functions return the quotient of @math{@var{a} + i@var{b}} and

@math{@var{c} + i@var{d}} (i.e., @math{(@var{a} + i@var{b}) / (@var{c}

+ i@var{d})}), following the rules of C99 Annex G@.

@end deftypefn

@node Decimal float library routines

@section Routines for decimal floating point emulation

@cindex decimal float library

@cindex IEEE 754-2008

The software decimal floating point library implements IEEE 754-2008

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.

@subsection Arithmetic functions

@deftypefn {Runtime Function} _Decimal32 __dpd_addsd3 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} _Decimal32 __bid_addsd3 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} _Decimal64 __dpd_adddd3 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} _Decimal64 __bid_adddd3 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} _Decimal128 __dpd_addtd3 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} _Decimal128 __bid_addtd3 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return the sum of @var{a} and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_subsd3 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} _Decimal32 __bid_subsd3 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} _Decimal64 __dpd_subdd3 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} _Decimal64 __bid_subdd3 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} _Decimal128 __dpd_subtd3 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} _Decimal128 __bid_subtd3 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return the difference between @var{b} and @var{a};

that is, @w{@math{@var{a} - @var{b}}}.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_mulsd3 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} _Decimal32 __bid_mulsd3 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} _Decimal64 __dpd_muldd3 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} _Decimal64 __bid_muldd3 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} _Decimal128 __dpd_multd3 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} _Decimal128 __bid_multd3 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return the product of @var{a} and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_divsd3 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} _Decimal32 __bid_divsd3 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} _Decimal64 __dpd_divdd3 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} _Decimal64 __bid_divdd3 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} _Decimal128 __dpd_divtd3 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} _Decimal128 __bid_divtd3 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return the quotient of @var{a} and @var{b}; that is,

@w{@math{@var{a} / @var{b}}}.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_negsd2 (_Decimal32 @var{a})

@deftypefnx {Runtime Function} _Decimal32 __bid_negsd2 (_Decimal32 @var{a})

@deftypefnx {Runtime Function} _Decimal64 __dpd_negdd2 (_Decimal64 @var{a})

@deftypefnx {Runtime Function} _Decimal64 __bid_negdd2 (_Decimal64 @var{a})

@deftypefnx {Runtime Function} _Decimal128 __dpd_negtd2 (_Decimal128 @var{a})

@deftypefnx {Runtime Function} _Decimal128 __bid_negtd2 (_Decimal128 @var{a})

These functions return the negation of @var{a}.  They simply flip the

sign bit, so they can produce negative zero and negative NaN@.

@end deftypefn

@subsection Conversion functions

@deftypefn {Runtime Function} _Decimal64 __dpd_extendsddd2 (_Decimal32 @var{a})

@deftypefnx {Runtime Function} _Decimal64 __bid_extendsddd2 (_Decimal32 @var{a})

@deftypefnx {Runtime Function} _Decimal128 __dpd_extendsdtd2 (_Decimal32 @var{a})

@deftypefnx {Runtime Function} _Decimal128 __bid_extendsdtd2 (_Decimal32 @var{a})

@deftypefnx {Runtime Function} _Decimal128 __dpd_extendddtd2 (_Decimal64 @var{a})

@deftypefnx {Runtime Function} _Decimal128 __bid_extendddtd2 (_Decimal64 @var{a})

@deftypefnx {Runtime Function} _Decimal32 __dpd_truncddsd2 (_Decimal64 @var{a})

@deftypefnx {Runtime Function} _Decimal32 __bid_truncddsd2 (_Decimal64 @var{a})

@deftypefnx {Runtime Function} _Decimal32 __dpd_trunctdsd2 (_Decimal128 @var{a})

@deftypefnx {Runtime Function} _Decimal32 __bid_trunctdsd2 (_Decimal128 @var{a})

@deftypefnx {Runtime Function} _Decimal64 __dpd_trunctddd2 (_Decimal128 @var{a})

@deftypefnx {Runtime Function} _Decimal64 __bid_trunctddd2 (_Decimal128 @var{a})

These functions convert the value @var{a} from one decimal floating type

to another.

@end deftypefn

@deftypefn {Runtime Function} _Decimal64 __dpd_extendsfdd (float @var{a})

@deftypefnx {Runtime Function} _Decimal64 __bid_extendsfdd (float @var{a})

@deftypefnx {Runtime Function} _Decimal128 __dpd_extendsftd (float @var{a})

@deftypefnx {Runtime Function} _Decimal128 __bid_extendsftd (float @var{a})

@deftypefnx {Runtime Function} _Decimal128 __dpd_extenddftd (double @var{a})

@deftypefnx {Runtime Function} _Decimal128 __bid_extenddftd (double @var{a})

@deftypefnx {Runtime Function} _Decimal128 __dpd_extendxftd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal128 __bid_extendxftd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal32 __dpd_truncdfsd (double @var{a})

@deftypefnx {Runtime Function} _Decimal32 __bid_truncdfsd (double @var{a})

@deftypefnx {Runtime Function} _Decimal32 __dpd_truncxfsd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal32 __bid_truncxfsd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal32 __dpd_trunctfsd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal32 __bid_trunctfsd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal64 __dpd_truncxfdd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal64 __bid_truncxfdd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal64 __dpd_trunctfdd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal64 __bid_trunctfdd ({long double} @var{a})

These functions convert the value of @var{a} from a binary floating type

to a decimal floating type of a different size.

@end deftypefn

@deftypefn {Runtime Function} float __dpd_truncddsf (_Decimal64 @var{a})

@deftypefnx {Runtime Function} float __bid_truncddsf (_Decimal64 @var{a})

@deftypefnx {Runtime Function} float __dpd_trunctdsf (_Decimal128 @var{a})

@deftypefnx {Runtime Function} float __bid_trunctdsf (_Decimal128 @var{a})

@deftypefnx {Runtime Function} double __dpd_extendsddf (_Decimal32 @var{a})

@deftypefnx {Runtime Function} double __bid_extendsddf (_Decimal32 @var{a})

@deftypefnx {Runtime Function} double __dpd_trunctddf (_Decimal128 @var{a})

@deftypefnx {Runtime Function} double __bid_trunctddf (_Decimal128 @var{a})

@deftypefnx {Runtime Function} {long double} __dpd_extendsdxf (_Decimal32 @var{a})

@deftypefnx {Runtime Function} {long double} __bid_extendsdxf (_Decimal32 @var{a})

@deftypefnx {Runtime Function} {long double} __dpd_extendddxf (_Decimal64 @var{a})

@deftypefnx {Runtime Function} {long double} __bid_extendddxf (_Decimal64 @var{a})

@deftypefnx {Runtime Function} {long double} __dpd_trunctdxf (_Decimal128 @var{a})

@deftypefnx {Runtime Function} {long double} __bid_trunctdxf (_Decimal128 @var{a})

@deftypefnx {Runtime Function} {long double} __dpd_extendsdtf (_Decimal32 @var{a})

@deftypefnx {Runtime Function} {long double} __bid_extendsdtf (_Decimal32 @var{a})

@deftypefnx {Runtime Function} {long double} __dpd_extendddtf (_Decimal64 @var{a})

@deftypefnx {Runtime Function} {long double} __bid_extendddtf (_Decimal64 @var{a})

These functions convert the value of @var{a} from a decimal floating type

to a binary floating type of a different size.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_extendsfsd (float @var{a})

@deftypefnx {Runtime Function} _Decimal32 __bid_extendsfsd (float @var{a})

@deftypefnx {Runtime Function} _Decimal64 __dpd_extenddfdd (double @var{a})

@deftypefnx {Runtime Function} _Decimal64 __bid_extenddfdd (double @var{a})

@deftypefnx {Runtime Function} _Decimal128 __dpd_extendtftd ({long double} @var{a})

@deftypefnx {Runtime Function} _Decimal128 __bid_extendtftd ({long double} @var{a})

@deftypefnx {Runtime Function} float __dpd_truncsdsf (_Decimal32 @var{a})

@deftypefnx {Runtime Function} float __bid_truncsdsf (_Decimal32 @var{a})

@deftypefnx {Runtime Function} double __dpd_truncdddf (_Decimal64 @var{a})

@deftypefnx {Runtime Function} double __bid_truncdddf (_Decimal64 @var{a})

@deftypefnx {Runtime Function} {long double} __dpd_trunctdtf (_Decimal128 @var{a})

@deftypefnx {Runtime Function} {long double} __bid_trunctdtf (_Decimal128 @var{a})

These functions convert the value of @var{a} between decimal and

binary floating types of the same size.

@end deftypefn

@deftypefn {Runtime Function} int __dpd_fixsdsi (_Decimal32 @var{a})

@deftypefnx {Runtime Function} int __bid_fixsdsi (_Decimal32 @var{a})

@deftypefnx {Runtime Function} int __dpd_fixddsi (_Decimal64 @var{a})

@deftypefnx {Runtime Function} int __bid_fixddsi (_Decimal64 @var{a})

@deftypefnx {Runtime Function} int __dpd_fixtdsi (_Decimal128 @var{a})

@deftypefnx {Runtime Function} int __bid_fixtdsi (_Decimal128 @var{a})

These functions convert @var{a} to a signed integer.

@end deftypefn

@deftypefn {Runtime Function} long __dpd_fixsddi (_Decimal32 @var{a})

@deftypefnx {Runtime Function} long __bid_fixsddi (_Decimal32 @var{a})

@deftypefnx {Runtime Function} long __dpd_fixdddi (_Decimal64 @var{a})

@deftypefnx {Runtime Function} long __bid_fixdddi (_Decimal64 @var{a})

@deftypefnx {Runtime Function} long __dpd_fixtddi (_Decimal128 @var{a})

@deftypefnx {Runtime Function} long __bid_fixtddi (_Decimal128 @var{a})

These functions convert @var{a} to a signed long.

@end deftypefn

@deftypefn {Runtime Function} {unsigned int} __dpd_fixunssdsi (_Decimal32 @var{a})

@deftypefnx {Runtime Function} {unsigned int} __bid_fixunssdsi (_Decimal32 @var{a})

@deftypefnx {Runtime Function} {unsigned int} __dpd_fixunsddsi (_Decimal64 @var{a})

@deftypefnx {Runtime Function} {unsigned int} __bid_fixunsddsi (_Decimal64 @var{a})

@deftypefnx {Runtime Function} {unsigned int} __dpd_fixunstdsi (_Decimal128 @var{a})

@deftypefnx {Runtime Function} {unsigned int} __bid_fixunstdsi (_Decimal128 @var{a})

These functions convert @var{a} to an unsigned integer.  Negative values all become zero.

@end deftypefn

@deftypefn {Runtime Function} {unsigned long} __dpd_fixunssddi (_Decimal32 @var{a})

@deftypefnx {Runtime Function} {unsigned long} __bid_fixunssddi (_Decimal32 @var{a})

@deftypefnx {Runtime Function} {unsigned long} __dpd_fixunsdddi (_Decimal64 @var{a})

@deftypefnx {Runtime Function} {unsigned long} __bid_fixunsdddi (_Decimal64 @var{a})

@deftypefnx {Runtime Function} {unsigned long} __dpd_fixunstddi (_Decimal128 @var{a})

@deftypefnx {Runtime Function} {unsigned long} __bid_fixunstddi (_Decimal128 @var{a})

These functions convert @var{a} to an unsigned long.  Negative values

all become zero.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_floatsisd (int @var{i})

@deftypefnx {Runtime Function} _Decimal32 __bid_floatsisd (int @var{i})

@deftypefnx {Runtime Function} _Decimal64 __dpd_floatsidd (int @var{i})

@deftypefnx {Runtime Function} _Decimal64 __bid_floatsidd (int @var{i})

@deftypefnx {Runtime Function} _Decimal128 __dpd_floatsitd (int @var{i})

@deftypefnx {Runtime Function} _Decimal128 __bid_floatsitd (int @var{i})

These functions convert @var{i}, a signed integer, to decimal floating point.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_floatdisd (long @var{i})

@deftypefnx {Runtime Function} _Decimal32 __bid_floatdisd (long @var{i})

@deftypefnx {Runtime Function} _Decimal64 __dpd_floatdidd (long @var{i})

@deftypefnx {Runtime Function} _Decimal64 __bid_floatdidd (long @var{i})

@deftypefnx {Runtime Function} _Decimal128 __dpd_floatditd (long @var{i})

@deftypefnx {Runtime Function} _Decimal128 __bid_floatditd (long @var{i})

These functions convert @var{i}, a signed long, to decimal floating point.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_floatunssisd (unsigned int @var{i})

@deftypefnx {Runtime Function} _Decimal32 __bid_floatunssisd (unsigned int @var{i})

@deftypefnx {Runtime Function} _Decimal64 __dpd_floatunssidd (unsigned int @var{i})

@deftypefnx {Runtime Function} _Decimal64 __bid_floatunssidd (unsigned int @var{i})

@deftypefnx {Runtime Function} _Decimal128 __dpd_floatunssitd (unsigned int @var{i})

@deftypefnx {Runtime Function} _Decimal128 __bid_floatunssitd (unsigned int @var{i})

These functions convert @var{i}, an unsigned integer, to decimal floating point.

@end deftypefn

@deftypefn {Runtime Function} _Decimal32 __dpd_floatunsdisd (unsigned long @var{i})

@deftypefnx {Runtime Function} _Decimal32 __bid_floatunsdisd (unsigned long @var{i})

@deftypefnx {Runtime Function} _Decimal64 __dpd_floatunsdidd (unsigned long @var{i})

@deftypefnx {Runtime Function} _Decimal64 __bid_floatunsdidd (unsigned long @var{i})

@deftypefnx {Runtime Function} _Decimal128 __dpd_floatunsditd (unsigned long @var{i})

@deftypefnx {Runtime Function} _Decimal128 __bid_floatunsditd (unsigned long @var{i})

These functions convert @var{i}, an unsigned long, to decimal floating point.

@end deftypefn

@subsection Comparison functions

@deftypefn {Runtime Function} int __dpd_unordsd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __bid_unordsd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __dpd_unorddd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __bid_unorddd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __dpd_unordtd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} int __bid_unordtd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return a nonzero value if either argument is NaN, otherwise 0.

@end deftypefn

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

@smallexample

  if (__bid_unord@var{X}d2 (a, b))

    return @var{E};

  return __bid_cmp@var{X}d2 (a, b);

@end smallexample

@noindent

where @var{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.

@deftypefn {Runtime Function} int __dpd_eqsd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __bid_eqsd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __dpd_eqdd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __bid_eqdd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __dpd_eqtd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} int __bid_eqtd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return zero if neither argument is NaN, and @var{a} and

@var{b} are equal.

@end deftypefn

@deftypefn {Runtime Function} int __dpd_nesd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __bid_nesd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __dpd_nedd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __bid_nedd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __dpd_netd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} int __bid_netd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return a nonzero value if either argument is NaN, or

if @var{a} and @var{b} are unequal.

@end deftypefn

@deftypefn {Runtime Function} int __dpd_gesd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __bid_gesd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __dpd_gedd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __bid_gedd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __dpd_getd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} int __bid_getd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return a value greater than or equal to zero if

neither argument is NaN, and @var{a} is greater than or equal to

@var{b}.

@end deftypefn

@deftypefn {Runtime Function} int __dpd_ltsd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __bid_ltsd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __dpd_ltdd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __bid_ltdd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __dpd_lttd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} int __bid_lttd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return a value less than zero if neither argument is

NaN, and @var{a} is strictly less than @var{b}.

@end deftypefn

@deftypefn {Runtime Function} int __dpd_lesd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __bid_lesd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __dpd_ledd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __bid_ledd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __dpd_letd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} int __bid_letd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return a value less than or equal to zero if neither

argument is NaN, and @var{a} is less than or equal to @var{b}.

@end deftypefn

@deftypefn {Runtime Function} int __dpd_gtsd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __bid_gtsd2 (_Decimal32 @var{a}, _Decimal32 @var{b})

@deftypefnx {Runtime Function} int __dpd_gtdd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __bid_gtdd2 (_Decimal64 @var{a}, _Decimal64 @var{b})

@deftypefnx {Runtime Function} int __dpd_gttd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

@deftypefnx {Runtime Function} int __bid_gttd2 (_Decimal128 @var{a}, _Decimal128 @var{b})

These functions return a value greater than zero if neither argument

is NaN, and @var{a} is strictly greater than @var{b}.

@end deftypefn

@node Fixed-point fractional library routines

@section Routines for fixed-point fractional emulation

@cindex fixed-point fractional library

@cindex fractional types

@cindex Embedded C

The software fixed-point library implements fixed-point fractional

arithmetic, and is only activated on selected targets.

For ease of comprehension @code{fract} is an alias for the

@code{_Fract} type, @code{accum} an alias for @code{_Accum}, and

@code{sat} an alias for @code{_Sat}.

For illustrative purposes, in this section the fixed-point fractional type

@code{@w{short fract}} is assumed to correspond to machine mode @code{QQmode};

@code{@w{unsigned short fract}} to @code{UQQmode};

@code{fract} to @code{HQmode};

@code{@w{unsigned fract}} to @code{UHQmode};

@code{@w{long fract}} to @code{SQmode};

@code{@w{unsigned long fract}} to @code{USQmode};

@code{@w{long long fract}} to @code{DQmode};

and @code{@w{unsigned long long fract}} to @code{UDQmode}.

Similarly the fixed-point accumulator type

@code{@w{short accum}} corresponds to @code{HAmode};

@code{@w{unsigned short accum}} to @code{UHAmode};

@code{accum} to @code{SAmode};

@code{@w{unsigned accum}} to @code{USAmode};

@code{@w{long accum}} to @code{DAmode};

@code{@w{unsigned long accum}} to @code{UDAmode};

@code{@w{long long accum}} to @code{TAmode};

and @code{@w{unsigned long long accum}} to @code{UTAmode}.

@subsection Arithmetic functions

@deftypefn {Runtime Function} {short fract} __addqq3 (short fract @var{a}, short fract @var{b})

@deftypefnx {Runtime Function} {fract} __addhq3 (fract @var{a}, fract @var{b})

@deftypefnx {Runtime Function} {long fract} __addsq3 (long fract @var{a}, long fract @var{b})

@deftypefnx {Runtime Function} {long long fract} __adddq3 (long long fract @var{a}, long long fract @var{b})

@deftypefnx {Runtime Function} {unsigned short fract} __adduqq3 (unsigned short fract @var{a}, unsigned short fract @var{b})

@deftypefnx {Runtime Function} {unsigned fract} __adduhq3 (unsigned fract @var{a}, unsigned fract @var{b})

@deftypefnx {Runtime Function} {unsigned long fract} __addusq3 (unsigned long fract @var{a}, unsigned long fract @var{b})

@deftypefnx {Runtime Function} {unsigned long long fract} __addudq3 (unsigned long long fract @var{a}, unsigned long long fract @var{b})

@deftypefnx {Runtime Function} {short accum} __addha3 (short accum @var{a}, short accum @var{b})

@deftypefnx {Runtime Function} {accum} __addsa3 (accum @var{a}, accum @var{b})

@deftypefnx {Runtime Function} {long accum} __addda3 (long accum @var{a}, long accum @var{b})

@deftypefnx {Runtime Function} {long long accum} __addta3 (long long accum @var{a}, long long accum @var{b})

@deftypefnx {Runtime Function} {unsigned short accum} __adduha3 (unsigned short accum @var{a}, unsigned short accum @var{b})

@deftypefnx {Runtime Function} {unsigned accum} __addusa3 (unsigned accum @var{a}, unsigned accum @var{b})

@deftypefnx {Runtime Function} {unsigned long accum} __adduda3 (unsigned long accum @var{a}, unsigned long accum @var{b})

@deftypefnx {Runtime Function} {unsigned long long accum} __adduta3 (unsigned long long accum @var{a}, unsigned long long accum @var{b})

These functions return the sum of @var{a} and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} {short fract} __ssaddqq3 (short fract @var{a}, short fract @var{b})

@deftypefnx {Runtime Function} {fract} __ssaddhq3 (fract @var{a}, fract @var{b})

@deftypefnx {Runtime Function} {long fract} __ssaddsq3 (long fract @var{a}, long fract @var{b})

@deftypefnx {Runtime Function} {long long fract} __ssadddq3 (long long fract @var{a}, long long fract @var{b})

@deftypefnx {Runtime Function} {short accum} __ssaddha3 (short accum @var{a}, short accum @var{b})

@deftypefnx {Runtime Function} {accum} __ssaddsa3 (accum @var{a}, accum @var{b})

@deftypefnx {Runtime Function} {long accum} __ssaddda3 (long accum @var{a}, long accum @var{b})

@deftypefnx {Runtime Function} {long long accum} __ssaddta3 (long long accum @var{a}, long long accum @var{b})

These functions return the sum of @var{a} and @var{b} with signed saturation.

@end deftypefn

@deftypefn {Runtime Function} {unsigned short fract} __usadduqq3 (unsigned short fract @var{a}, unsigned short fract @var{b})

@deftypefnx {Runtime Function} {unsigned fract} __usadduhq3 (unsigned fract @var{a}, unsigned fract @var{b})

@deftypefnx {Runtime Function} {unsigned long fract} __usaddusq3 (unsigned long fract @var{a}, unsigned long fract @var{b})

@deftypefnx {Runtime Function} {unsigned long long fract} __usaddudq3 (unsigned long long fract @var{a}, unsigned long long fract @var{b})

@deftypefnx {Runtime Function} {unsigned short accum} __usadduha3 (unsigned short accum @var{a}, unsigned short accum @var{b})

@deftypefnx {Runtime Function} {unsigned accum} __usaddusa3 (unsigned accum @var{a}, unsigned accum @var{b})

@deftypefnx {Runtime Function} {unsigned long accum} __usadduda3 (unsigned long accum @var{a}, unsigned long accum @var{b})

@deftypefnx {Runtime Function} {unsigned long long accum} __usadduta3 (unsigned long long accum @var{a}, unsigned long long accum @var{b})

These functions return the sum of @var{a} and @var{b} with unsigned saturation.

@end deftypefn

@deftypefn {Runtime Function} {short fract} __subqq3 (short fract @var{a}, short fract @var{b})

@deftypefnx {Runtime Function} {fract} __subhq3 (fract @var{a}, fract @var{b})

@deftypefnx {Runtime Function} {long fract} __subsq3 (long fract @var{a}, long fract @var{b})

@deftypefnx {Runtime Function} {long long fract} __subdq3 (long long fract @var{a}, long long fract @var{b})

@deftypefnx {Runtime Function} {unsigned short fract} __subuqq3 (unsigned short fract @var{a}, unsigned short fract @var{b})

@deftypefnx {Runtime Function} {unsigned fract} __subuhq3 (unsigned fract @var{a}, unsigned fract @var{b})

@deftypefnx {Runtime Function} {unsigned long fract} __subusq3 (unsigned long fract @var{a}, unsigned long fract @var{b})

@deftypefnx {Runtime Function} {unsigned long long fract} __subudq3 (unsigned long long fract @var{a}, unsigned long long fract @var{b})

@deftypefnx {Runtime Function} {short accum} __subha3 (short accum @var{a}, short accum @var{b})

@deftypefnx {Runtime Function} {accum} __subsa3 (accum @var{a}, accum @var{b})

@deftypefnx {Runtime Function} {long accum} __subda3 (long accum @var{a}, long accum @var{b})

@deftypefnx {Runtime Function} {long long accum} __subta3 (long long accum @var{a}, long long accum @var{b})

@deftypefnx {Runtime Function} {unsigned short accum} __subuha3 (unsigned short accum @var{a}, unsigned short accum @var{b})

@deftypefnx {Runtime Function} {unsigned accum} __subusa3 (unsigned accum @var{a}, unsigned accum @var{b})

@deftypefnx {Runtime Function} {unsigned long accum} __subuda3 (unsigned long accum @var{a}, unsigned long accum @var{b})

@deftypefnx {Runtime Function} {unsigned long long accum} __subuta3 (unsigned long long accum @var{a}, unsigned long long accum @var{b})

These functions return the difference of @var{a} and @var{b};

that is, @code{@var{a} - @var{b}}.

@end deftypefn

@deftypefn {Runtime Function} {short fract} __sssubqq3 (short fract @var{a}, short fract @var{b})

@deftypefnx {Runtime Function} {fract} __sssubhq3 (fract @var{a}, fract @var{b})

@deftypefnx {Runtime Function} {long fract} __sssubsq3 (long fract @var{a}, long fract @var{b})

@deftypefnx {Runtime Function} {long long fract} __sssubdq3 (long long fract @var{a}, long long fract @var{b})

@deftypefnx {Runtime Function} {short accum} __sssubha3 (short accum @var{a}, short accum @var{b})

@deftypefnx {Runtime Function} {accum} __sssubsa3 (accum @var{a}, accum @var{b})

@deftypefnx {Runtime Function} {long accum} __sssubda3 (long accum @var{a}, long accum @var{b})

@deftypefnx {Runtime Function} {long long accum} __sssubta3 (long long accum @var{a}, long long accum @var{b})

These functions return the difference of @var{a} and @var{b} with signed

saturation;  that is, @code{@var{a} - @var{b}}.

@end deftypefn

@deftypefn {Runtime Function} {unsigned short fract} __ussubuqq3 (unsigned short fract @var{a}, unsigned short fract @var{b})

@deftypefnx {Runtime Function} {unsigned fract} __ussubuhq3 (unsigned fract @var{a}, unsigned fract @var{b})

@deftypefnx {Runtime Function} {unsigned long fract} __ussubusq3 (unsigned long fract @var{a}, unsigned long fract @var{b})

@deftypefnx {Runtime Function} {unsigned long long fract} __ussubudq3 (unsigned long long fract @var{a}, unsigned long long fract @var{b})

@deftypefnx {Runtime Function} {unsigned short accum} __ussubuha3 (unsigned short accum @var{a}, unsigned short accum @var{b})

@deftypefnx {Runtime Function} {unsigned accum} __ussubusa3 (unsigned accum @var{a}, unsigned accum @var{b})

@deftypefnx {Runtime Function} {unsigned long accum} __ussubuda3 (unsigned long accum @var{a}, unsigned long accum @var{b})

@deftypefnx {Runtime Function} {unsigned long long accum} __ussubuta3 (unsigned long long accum @var{a}, unsigned long long accum @var{b})

These functions return the difference of @var{a} and @var{b} with unsigned

saturation;  that is, @code{@var{a} - @var{b}}.

@end deftypefn

@deftypefn {Runtime Function} {short fract} __mulqq3 (short fract @var{a}, short fract @var{b})

@deftypefnx {Runtime Function} {fract} __mulhq3 (fract @var{a}, fract @var{b})

@deftypefnx {Runtime Function} {long fract} __mulsq3 (long fract @var{a}, long fract @var{b})

@deftypefnx {Runtime Function} {long long fract} __muldq3 (long long fract @var{a}, long long fract @var{b})

@deftypefnx {Runtime Function} {unsigned short fract} __muluqq3 (unsigned short fract @var{a}, unsigned short fract @var{b})

@deftypefnx {Runtime Function} {unsigned fract} __muluhq3 (unsigned fract @var{a}, unsigned fract @var{b})

@deftypefnx {Runtime Function} {unsigned long fract} __mulusq3 (unsigned long fract @var{a}, unsigned long fract @var{b})

@deftypefnx {Runtime Function} {unsigned long long fract} __muludq3 (unsigned long long fract @var{a}, unsigned long long fract @var{b})

@deftypefnx {Runtime Function} {short accum} __mulha3 (short accum @var{a}, short accum @var{b})

@deftypefnx {Runtime Function} {accum} __mulsa3 (accum @var{a}, accum @var{b})

@deftypefnx {Runtime Function} {long accum} __mulda3 (long accum @var{a}, long accum @var{b})

@deftypefnx {Runtime Function} {long long accum} __multa3 (long long accum @var{a}, long long accum @var{b})

@deftypefnx {Runtime Function} {unsigned short accum} __muluha3 (unsigned short accum @var{a}, unsigned short accum @var{b})

@deftypefnx {Runtime Function} {unsigned accum} __mulusa3 (unsigned accum @var{a}, unsigned accum @var{b})

@deftypefnx {Runtime Function} {unsigned long accum} __muluda3 (unsigned long accum @var{a}, unsigned long accum @var{b})

@deftypefnx {Runtime Function} {unsigned long long accum} __muluta3 (unsigned long long accum @var{a}, unsigned long long accum @var{b})

These functions return the product of @var{a} and @var{b}.

@end deftypefn

@deftypefn {Runtime Function} {short fract} __ssmulqq3 (short fract @var{a}, short fract @var{b})