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|
/* file: libm_support.h */
/*
// Copyright (c) 2000 - 2004, Intel Corporation
// All rights reserved.
//
// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History: 02/02/2000 Initial version
// 2/28/2000 added tags for logb and nextafter
// 3/22/2000 Changes to support _LIB_VERSIONIMF variable
// and filled some enum gaps. Added support for C99.
// 5/31/2000 added prototypes for __libm_frexp_4l/8l
// 8/10/2000 Changed declaration of _LIB_VERSIONIMF to work for library
// builds and other application builds (precompiler directives).
// 8/11/2000 Added pointers-to-matherr-functions declarations to allow
// for user-defined matherr functions in the dll build.
// 12/07/2000 Added scalbn error_types values.
// 5/01/2001 Added error_types values for C99 nearest integer
// functions.
// 6/07/2001 Added error_types values for fdim.
// 6/18/2001 Added include of complex_support.h.
// 8/03/2001 Added error_types values for nexttoward, scalbln.
// 8/23/2001 Corrected tag numbers from 186 and higher.
// 8/27/2001 Added check for long int and long long int definitions.
// 12/10/2001 Added error_types for erfc.
// 12/27/2001 Added error_types for degree argument functions.
// 01/02/2002 Added error_types for tand, cotd.
// 01/04/2002 Delete include of complex_support.h
// 01/23/2002 Deleted prototypes for __libm_frexp*. Added check for
// multiple int, long int, and long long int definitions.
// 05/20/2002 Added error_types for cot.
// 06/27/2002 Added error_types for sinhcosh.
// 12/05/2002 Added error_types for annuity and compound
// 04/10/2003 Added error_types for tgammal/tgamma/tgammaf
// 05/16/2003 FP-treatment macros copied here from IA32 libm_support.h
// 06/02/2003 Added pad into struct fp80 (12/16 bytes).
// 08/01/2003 Added struct ker80 and macros for multiprecision addition,
// subtraction, multiplication, division, square root.
// 08/07/2003 History section updated.
// 09/03/2003 ALIGN(n) macro added.
// 10/01/2003 LDOUBLE_ALIGN and fp80 corrected on linux to 16 bytes.
// 11/24/2004 Added ifdef around definitions of INT32/64
// 12/15/2004 Added error_types for exp10, nextafter, nexttoward
// underflow. Moved error codes into libm_error_codes.h.
//
*/
#ifndef __LIBM_SUPPORT_H_INCLUDED__
#define __LIBM_SUPPORT_H_INCLUDED__
#ifndef _LIBC
#if !(defined(_WIN32) || defined(_WIN64))
# pragma const_seg(".rodata") /* place constant data in text (code) section */
#endif
#if defined(__ICC) || defined(__ICL) || defined(__ECC) || defined(__ECL)
# pragma warning( disable : 1682 ) /* #1682: ixplicit conversion of a 64-bit integral type to a smaller integral type (potential portability problem) */
# pragma warning( disable : 1683 ) /* #1683: explicit conversion of a 64-bit integral type to a smaller integral type (potential portability problem) */
#endif
#endif
/* macros to form a double value in hex representation (unsigned int type) */
#define DOUBLE_HEX(hi,lo) 0x##lo,0x##hi /*LITTLE_ENDIAN*/
#include "libm_cpu_defs.h"
#if !(defined (IA64))
# include "libm_dll.h"
# include "libm_dispatch.h"
#endif
#include "libm_error_codes.h"
struct exceptionf
{
int type;
char *name;
float arg1, arg2, retval;
};
# ifdef __cplusplus
struct __exception
{
int type;
char *name;
double arg1, arg2, retval;
};
# else
# ifndef _LIBC
struct exception
{
int type;
char *name;
double arg1, arg2, retval;
};
# endif
# endif
struct exceptionl
{
int type;
char *name;
long double arg1, arg2, retval;
};
#if (defined (_MS_) && defined (IA64))
#define MATHERR_F _matherrf
#define MATHERR_D _matherr
#else
#define MATHERR_F matherrf
#define MATHERR_D matherr
#endif
# ifdef __cplusplus
#define EXC_DECL_D __exception
#else
// exception is a reserved name in C++
#define EXC_DECL_D exception
#endif
extern int MATHERR_F(struct exceptionf*);
extern int MATHERR_D(struct EXC_DECL_D*);
extern int matherrl(struct exceptionl*);
#ifndef _LIBC
// Add code to support _LIB_VERSIONIMF
typedef enum
{
_IEEE_ = -1, // IEEE-like behavior
_SVID_, // SysV, Rel. 4 behavior
_XOPEN_, // Unix98
_POSIX_, // Posix
_ISOC_ // ISO C9X
} _LIB_VERSION_TYPE;
#endif
// This is a run-time variable and may affect
// floating point behavior of the libm functions
#if !defined( LIBM_BUILD )
#if defined( _DLL )
extern _LIB_VERSION_TYPE __declspec(dllimport) _LIB_VERSIONIMF;
#else
extern _LIB_VERSION_TYPE _LIB_VERSIONIMF;
#endif /* _DLL */
#else
extern int (*pmatherrf)(struct exceptionf*);
extern int (*pmatherr)(struct EXC_DECL_D*);
extern int (*pmatherrl)(struct exceptionl*);
#endif /* LIBM_BUILD */
/* memory format definitions (LITTLE_ENDIAN only) */
#if !(defined(SIZE_INT_32) || defined(SIZE_INT_64))
# error "You need to define SIZE_INT_32 or SIZE_INT_64"
#endif
#if (defined(SIZE_INT_32) && defined(SIZE_INT_64))
#error multiple integer size definitions; define SIZE_INT_32 or SIZE_INT_64
#endif
#if !(defined(SIZE_LONG_32) || defined(SIZE_LONG_64))
# error "You need to define SIZE_LONG_32 or SIZE_LONG_64"
#endif
#if (defined(SIZE_LONG_32) && defined(SIZE_LONG_64))
#error multiple integer size definitions; define SIZE_LONG_32 or SIZE_LONG_64
#endif
#if !defined(__USE_EXTERNAL_FPMEMTYP_H__)
#define BIAS_32 0x007F
#define BIAS_64 0x03FF
#define BIAS_80 0x3FFF
#define MAXEXP_32 0x00FE
#define MAXEXP_64 0x07FE
#define MAXEXP_80 0x7FFE
#define EXPINF_32 0x00FF
#define EXPINF_64 0x07FF
#define EXPINF_80 0x7FFF
struct fp32 { /*// sign:1 exponent:8 significand:23 (implied leading 1)*/
#if defined(SIZE_INT_32)
unsigned significand:23;
unsigned exponent:8;
unsigned sign:1;
#elif defined(SIZE_INT_64)
unsigned significand:23;
unsigned exponent:8;
unsigned sign:1;
#endif
};
struct fp64 { /*/ sign:1 exponent:11 significand:52 (implied leading 1)*/
#if defined(SIZE_INT_32)
unsigned lo_significand:32;
unsigned hi_significand:20;
unsigned exponent:11;
unsigned sign:1;
#elif defined(SIZE_INT_64)
unsigned significand:52;
unsigned exponent:11;
unsigned sign:1;
#endif
};
struct fp80 { /*/ sign:1 exponent:15 significand:64 (NO implied bits) */
#if defined(SIZE_INT_32)
unsigned lo_significand;
unsigned hi_significand;
unsigned exponent:15;
unsigned sign:1;
#elif defined(SIZE_INT_64)
unsigned significand;
unsigned exponent:15;
unsigned sign:1;
#endif
unsigned pad:16;
#if !(defined(__unix__) && defined(__i386__))
unsigned padwin:32;
#endif
};
#endif /*__USE_EXTERNAL_FPMEMTYP_H__*/
#if !(defined(opensource))
typedef __int32 INT32;
typedef signed __int32 SINT32;
typedef unsigned __int32 UINT32;
typedef __int64 INT64;
typedef signed __int64 SINT64;
typedef unsigned __int64 UINT64;
#else
typedef int INT32;
typedef signed int SINT32;
typedef unsigned int UINT32;
typedef long long INT64;
typedef signed long long SINT64;
typedef unsigned long long UINT64;
#endif
#if (defined(_WIN32) || defined(_WIN64)) /* Windows */
# define I64CONST(bits) 0x##bits##i64
# define U64CONST(bits) 0x##bits##ui64
#elif (defined(__linux__) && defined(_M_IA64)) /* Linux,64 */
# define I64CONST(bits) 0x##bits##L
# define U64CONST(bits) 0x##bits##uL
#else /* Linux,32 */
# define I64CONST(bits) 0x##bits##LL
# define U64CONST(bits) 0x##bits##uLL
#endif
struct ker80 {
union {
long double ldhi;
struct fp80 fphi;
};
union {
long double ldlo;
struct fp80 fplo;
};
int ex;
};
/* Addition: x+y */
/* The result is sum rhi+rlo */
/* Temporary variables: t1 */
/* All variables are in long double precision */
/* Correct if no overflow (algorithm by D.Knuth) */
#define __LIBM_ADDL1_K80( rhi,rlo,x,y, t1 ) \
rhi = x + y; \
rlo = rhi - x; \
t1 = rhi - rlo; \
rlo = y - rlo; \
t1 = x - t1; \
rlo = rlo + t1;
/* Addition: (xhi+xlo) + (yhi+ylo) */
/* The result is sum rhi+rlo */
/* Temporary variables: t1 */
/* All variables are in long double precision */
/* Correct if no overflow (algorithm by T.J.Dekker) */
#define __LIBM_ADDL2_K80( rhi,rlo,xhi,xlo,yhi,ylo, t1 ) \
rlo = xhi+yhi; \
if ( VALUE_GT_80(FP80(xhi),FP80(yhi)) ) { \
t1=xhi-rlo;t1=t1+yhi;t1=t1+ylo;t1=t1+xlo; \
} else { \
t1=yhi-rlo;t1=t1+xhi;t1=t1+xlo;t1=t1+ylo; \
} \
rhi=rlo+t1; \
rlo=rlo-rhi;rlo=rlo+t1;
/* Addition: r=x+y */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Temporary variables: t1 */
/* Correct if x and y belong to interval [2^-8000;2^8000], */
/* or when one or both of them are zero */
#if defined(SIZE_INT_32)
#define __LIBM_ADDL_K80(r,x,y, t1) \
if ( ((y)->ex+(y)->fphi.exponent-134 < \
(x)->ex+(x)->fphi.exponent) && \
((x)->ex+(x)->fphi.exponent < \
(y)->ex+(y)->fphi.exponent+134) && \
!SIGNIFICAND_ZERO_80(&((x)->fphi)) && \
!SIGNIFICAND_ZERO_80(&((y)->fphi)) ) \
{ \
/* y/2^134 < x < y*2^134, */ \
/* and x,y are nonzero finite numbers */ \
if ( (x)->ex != (y)->ex ) { \
/* adjust x->ex to y->ex */ \
/* t1 = 2^(x->ex - y->ex) */ \
FP80(t1)->sign = 0; \
FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
/* exponent is correct because */ \
/* |x->ex - y->ex| = */ \
/* = | (x->ex + x->fphi.exponent) - */ \
/* -(y->ex + y->fphi.exponent) + */ \
/* + y->fphi.exponent - */ \
/* - x->fphi.exponent | < */ \
/* < | (x->ex+x->fphi.exponent) - */ \
/* -(y->ex+y->fphi.exponent) | + */ \
/* +| y->fphi.exponent - */ \
/* -x->fphi.exponent | < */ \
/* < 134 + 16000 */ \
FP80(t1)->hi_significand = 0x80000000; \
FP80(t1)->lo_significand = 0x00000000; \
(x)->ex = (y)->ex; \
(x)->ldhi *= t1; \
(x)->ldlo *= t1; \
} \
/* r==x+y */ \
(r)->ex = (y)->ex; \
__LIBM_ADDL2_K80( (r)->ldhi,(r)->ldlo, \
(x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
} else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) || \
((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >= \
(x)->ex+(x)->fphi.exponent-BIAS_80) ) \
{ \
/* |x|<<|y| */ \
*(r) = *(y); \
} else { \
/* |y|<<|x| */ \
*(r) = *(x); \
}
#elif defined(SIZE_INT_64)
#define __LIBM_ADDL_K80(r,x,y, t1) \
if ( ((y)->ex+(y)->fphi.exponent-134 < \
(x)->ex+(x)->fphi.exponent) && \
((x)->ex+(x)->fphi.exponent < \
(y)->ex+(y)->fphi.exponent+134) && \
!SIGNIFICAND_ZERO_80(&((x)->fphi)) && \
!SIGNIFICAND_ZERO_80(&((y)->fphi)) ) \
{ \
/* y/2^134 < x < y*2^134, */ \
/* and x,y are nonzero finite numbers */ \
if ( (x)->ex != (y)->ex ) { \
/* adjust x->ex to y->ex */ \
/* t1 = 2^(x->ex - y->ex) */ \
FP80(t1)->sign = 0; \
FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
/* exponent is correct because */ \
/* |x->ex - y->ex| = */ \
/* = | (x->ex + x->fphi.exponent) - */ \
/* -(y->ex + y->fphi.exponent) + */ \
/* + y->fphi.exponent - */ \
/* - x->fphi.exponent | < */ \
/* < | (x->ex+x->fphi.exponent) - */ \
/* -(y->ex+y->fphi.exponent) | + */ \
/* +| y->fphi.exponent - */ \
/* -x->fphi.exponent | < */ \
/* < 134 + 16000 */ \
FP80(t1)->significand = 0x8000000000000000; \
(x)->ex = (y)->ex; \
(x)->ldhi *= t1; \
(x)->ldlo *= t1; \
} \
/* r==x+y */ \
(r)->ex = (y)->ex; \
__LIBM_ADDL2_K80( (r)->ldhi,(r)->ldlo, \
(x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
} else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) || \
((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >= \
(x)->ex+(x)->fphi.exponent-BIAS_80) ) \
{ \
/* |x|<<|y| */ \
*(r) = *(y); \
} else { \
/* |y|<<|x| */ \
*(r) = *(x); \
}
#endif
/* Addition: r=x+y */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Temporary variables: t1 */
/* Correct for any finite x and y */
#define __LIBM_ADDL_NORM_K80(r,x,y, t1) \
if ( ((x)->fphi.exponent-BIAS_80<-8000) || \
((x)->fphi.exponent-BIAS_80>+8000) || \
((y)->fphi.exponent-BIAS_80<-8000) || \
((y)->fphi.exponent-BIAS_80>+8000) ) \
{ \
__libm_normalizel_k80(x); \
__libm_normalizel_k80(y); \
} \
__LIBM_ADDL_K80(r,x,y, t1)
/* Subtraction: x-y */
/* The result is sum rhi+rlo */
/* Temporary variables: t1 */
/* All variables are in long double precision */
/* Correct if no overflow (algorithm by D.Knuth) */
#define __LIBM_SUBL1_K80( rhi, rlo, x, y, t1 ) \
rhi = x - y; \
rlo = rhi - x; \
t1 = rhi - rlo; \
rlo = y + rlo; \
t1 = x - t1; \
rlo = t1 - rlo;
/* Subtraction: (xhi+xlo) - (yhi+ylo) */
/* The result is sum rhi+rlo */
/* Temporary variables: t1 */
/* All variables are in long double precision */
/* Correct if no overflow (algorithm by T.J.Dekker) */
#define __LIBM_SUBL2_K80( rhi,rlo,xhi,xlo,yhi,ylo, t1 ) \
rlo = xhi-yhi; \
if ( VALUE_GT_80(FP80(xhi),FP80(yhi)) ) { \
t1=xhi-rlo;t1=t1-yhi;t1=t1-ylo;t1=t1+xlo; \
} else { \
t1=yhi+rlo;t1=xhi-t1;t1=t1+xlo;t1=t1-ylo; \
} \
rhi=rlo+t1; \
rlo=rlo-rhi;rlo=rlo+t1;
/* Subtraction: r=x-y */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Temporary variables: t1 */
/* Correct if x and y belong to interval [2^-8000;2^8000], */
/* or when one or both of them are zero */
#if defined(SIZE_INT_32)
#define __LIBM_SUBL_K80(r,x,y, t1) \
if ( ((y)->ex+(y)->fphi.exponent-134 < \
(x)->ex+(x)->fphi.exponent) && \
((x)->ex+(x)->fphi.exponent < \
(y)->ex+(y)->fphi.exponent+134) && \
!SIGNIFICAND_ZERO_80(&((x)->fphi)) && \
!SIGNIFICAND_ZERO_80(&((y)->fphi)) ) \
{ \
/* y/2^134 < x < y*2^134, */ \
/* and x,y are nonzero finite numbers */ \
if ( (x)->ex != (y)->ex ) { \
/* adjust x->ex to y->ex */ \
/* t1 = 2^(x->ex - y->ex) */ \
FP80(t1)->sign = 0; \
FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
/* exponent is correct because */ \
/* |x->ex - y->ex| = */ \
/* = | (x->ex + x->fphi.exponent) - */ \
/* -(y->ex + y->fphi.exponent) + */ \
/* + y->fphi.exponent - */ \
/* - x->fphi.exponent | < */ \
/* < | (x->ex+x->fphi.exponent) - */ \
/* -(y->ex+y->fphi.exponent) | + */ \
/* +| y->fphi.exponent - */ \
/* -x->fphi.exponent | < */ \
/* < 134 + 16000 */ \
FP80(t1)->hi_significand = 0x80000000; \
FP80(t1)->lo_significand = 0x00000000; \
(x)->ex = (y)->ex; \
(x)->ldhi *= t1; \
(x)->ldlo *= t1; \
} \
/* r==x+y */ \
(r)->ex = (y)->ex; \
__LIBM_SUBL2_K80( (r)->ldhi,(r)->ldlo, \
(x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
} else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) || \
((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >= \
(x)->ex+(x)->fphi.exponent-BIAS_80) ) \
{ \
/* |x|<<|y| */ \
(r)->ex = (y)->ex; \
(r)->ldhi = -((y)->ldhi); \
(r)->ldlo = -((y)->ldlo); \
} else { \
/* |y|<<|x| */ \
*(r) = *(x); \
}
#elif defined(SIZE_INT_64)
#define __LIBM_SUBL_K80(r,x,y, t1) \
if ( ((y)->ex+(y)->fphi.exponent-134 < \
(x)->ex+(x)->fphi.exponent) && \
((x)->ex+(x)->fphi.exponent < \
(y)->ex+(y)->fphi.exponent+134) && \
!SIGNIFICAND_ZERO_80(&((x)->fphi)) && \
!SIGNIFICAND_ZERO_80(&((y)->fphi)) ) \
{ \
/* y/2^134 < x < y*2^134, */ \
/* and x,y are nonzero finite numbers */ \
if ( (x)->ex != (y)->ex ) { \
/* adjust x->ex to y->ex */ \
/* t1 = 2^(x->ex - y->ex) */ \
FP80(t1)->sign = 0; \
FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
/* exponent is correct because */ \
/* |x->ex - y->ex| = */ \
/* = | (x->ex + x->fphi.exponent) - */ \
/* -(y->ex + y->fphi.exponent) + */ \
/* + y->fphi.exponent - */ \
/* - x->fphi.exponent | < */ \
/* < | (x->ex+x->fphi.exponent) - */ \
/* -(y->ex+y->fphi.exponent) | + */ \
/* +| y->fphi.exponent - */ \
/* -x->fphi.exponent | < */ \
/* < 134 + 16000 */ \
FP80(t1)->significand = 0x8000000000000000; \
(x)->ex = (y)->ex; \
(x)->ldhi *= t1; \
(x)->ldlo *= t1; \
} \
/* r==x+y */ \
(r)->ex = (y)->ex; \
__LIBM_SUBL2_K80( (r)->ldhi,(r)->ldlo, \
(x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
} else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) || \
((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >= \
(x)->ex+(x)->fphi.exponent-BIAS_80) ) \
{ \
/* |x|<<|y| */ \
(r)->ex = (y)->ex; \
(r)->ldhi = -((y)->ldhi); \
(r)->ldlo = -((y)->ldlo); \
} else { \
/* |y|<<|x| */ \
*(r) = *(x); \
}
#endif
/* Subtraction: r=x+y */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Temporary variables: t1 */
/* Correct for any finite x and y */
#define __LIBM_SUBL_NORM_K80(r,x,y, t1) \
if ( ((x)->fphi.exponent-BIAS_80<-8000) || \
((x)->fphi.exponent-BIAS_80>+8000) || \
((y)->fphi.exponent-BIAS_80<-8000) || \
((y)->fphi.exponent-BIAS_80>+8000) ) \
{ \
__libm_normalizel_k80(x); \
__libm_normalizel_k80(y); \
} \
__LIBM_SUBL_K80(r,x,y, t1)
/* Multiplication: x*y */
/* The result is sum rhi+rlo */
/* Here t32 is the constant 2^32+1 */
/* Temporary variables: t1,t2,t3,t4,t5,t6 */
/* All variables are in long double precision */
/* Correct if no over/underflow (algorithm by T.J.Dekker) */
#define __LIBM_MULL1_K80(rhi,rlo,x,y, \
t32,t1,t2,t3,t4,t5,t6) \
t1=(x)*(t32); t3=x-t1; t3=t3+t1; t4=x-t3; \
t1=(y)*(t32); t5=y-t1; t5=t5+t1; t6=y-t5; \
t1=(t3)*(t5); \
t2=(t3)*(t6)+(t4)*(t5); \
rhi=t1+t2; \
rlo=t1-rhi; rlo=rlo+t2; rlo=rlo+(t4*t6);
/* Multiplication: (xhi+xlo)*(yhi+ylo) */
/* The result is sum rhi+rlo */
/* Here t32 is the constant 2^32+1 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8 */
/* All variables are in long double precision */
/* Correct if no over/underflow (algorithm by T.J.Dekker) */
#define __LIBM_MULL2_K80(rhi,rlo,xhi,xlo,yhi,ylo, \
t32,t1,t2,t3,t4,t5,t6,t7,t8) \
__LIBM_MULL1_K80(t7,t8,xhi,yhi, t32,t1,t2,t3,t4,t5,t6) \
t1=(xhi)*(ylo)+(xlo)*(yhi); t1=t1+t8; \
rhi=t7+t1; \
rlo=t7-rhi; rlo=rlo+t1;
/* Multiplication: r=x*y */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Here t32 is the constant 2^32+1 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8 */
/* Correct if x and y belong to interval [2^-8000;2^8000] */
#define __LIBM_MULL_K80(r,x,y, t32,t1,t2,t3,t4,t5,t6,t7,t8) \
(r)->ex = (x)->ex + (y)->ex; \
__LIBM_MULL2_K80((r)->ldhi,(r)->ldlo, \
(x)->ldhi,(x)->ldlo,(y)->ldhi,(y)->ldlo, \
t32,t1,t2,t3,t4,t5,t6,t7,t8)
/* Multiplication: r=x*y */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Here t32 is the constant 2^32+1 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8 */
/* Correct for any finite x and y */
#define __LIBM_MULL_NORM_K80(r,x,y, \
t32,t1,t2,t3,t4,t5,t6,t7,t8) \
if ( ((x)->fphi.exponent-BIAS_80<-8000) || \
((x)->fphi.exponent-BIAS_80>+8000) || \
((y)->fphi.exponent-BIAS_80<-8000) || \
((y)->fphi.exponent-BIAS_80>+8000) ) \
{ \
__libm_normalizel_k80(x); \
__libm_normalizel_k80(y); \
} \
__LIBM_MULL_K80(r,x,y, t32,t1,t2,t3,t4,t5,t6,t7,t8)
/* Division: (xhi+xlo)/(yhi+ylo) */
/* The result is sum rhi+rlo */
/* Here t32 is the constant 2^32+1 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9 */
/* All variables are in long double precision */
/* Correct if no over/underflow (algorithm by T.J.Dekker) */
#define __LIBM_DIVL2_K80(rhi,rlo,xhi,xlo,yhi,ylo, \
t32,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
t7=(xhi)/(yhi); \
__LIBM_MULL1_K80(t8,t9,t7,yhi, t32,t1,t2,t3,t4,t5,t6) \
t1=xhi-t8; t1=t1-t9; t1=t1+xlo; t1=t1-(t7)*(ylo); \
t1=(t1)/(yhi); \
rhi=t7+t1; \
rlo=t7-rhi; rlo=rlo+t1;
/* Division: r=x/y */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Here t32 is the constant 2^32+1 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9 */
/* Correct if x and y belong to interval [2^-8000;2^8000] */
#define __LIBM_DIVL_K80(r,x,y, \
t32,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
(r)->ex = (x)->ex - (y)->ex; \
__LIBM_DIVL2_K80( (r)->ldhi,(r)->ldlo, \
(x)->ldhi,(x)->ldlo,(y)->ldhi,(y)->ldlo, \
t32,t1,t2,t3,t4,t5,t6,t7,t8,t9)
/* Division: r=x/y */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Here t32 is the constant 2^32+1 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8 */
/* Correct for any finite x and y */
#define __LIBM_DIVL_NORM_K80(r,x,y, \
t32,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
if ( ((x)->fphi.exponent-BIAS_80<-8000) || \
((x)->fphi.exponent-BIAS_80>+8000) || \
((y)->fphi.exponent-BIAS_80<-8000) || \
((y)->fphi.exponent-BIAS_80>+8000) ) \
{ \
__libm_normalizel_k80(x); \
__libm_normalizel_k80(y); \
} \
__LIBM_DIVL_K80(r,x,y, t32,t1,t2,t3,t4,t5,t6,t7,t8,t9)
/* Square root: sqrt(xhi+xlo) */
/* The result is sum rhi+rlo */
/* Here t32 is the constant 2^32+1 */
/* half is the constant 0.5 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9 */
/* All variables are in long double precision */
/* Correct for positive xhi+xlo (algorithm by T.J.Dekker) */
#define __LIBM_SQRTL2_NORM_K80(rhi,rlo,xhi,xlo, \
t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
t7=sqrtl(xhi); \
__LIBM_MULL1_K80(t8,t9,t7,t7, t32,t1,t2,t3,t4,t5,t6) \
t1=xhi-t8; t1=t1-t9; t1=t1+xlo; t1=(t1)*(half); \
t1=(t1)/(t7); \
rhi=t7+t1; \
rlo=t7-rhi; rlo=rlo+t1;
/* Square root: r=sqrt(x) */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Here t32 is the constant 2^32+1 */
/* half is the constant 0.5 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9 */
/* Correct if x belongs to interval [2^-16000;2^16000] */
#define __LIBM_SQRTL_K80(r,x, \
t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
if ( ((x)->ex & 1) == 1 ) { \
(x)->ex = (x)->ex + 1; \
(x)->ldhi *= half; \
(x)->ldlo *= half; \
} \
(r)->ex = (x)->ex >> 1; \
__LIBM_SQRTL2_NORM_K80( (r)->ldhi,(r)->ldlo, \
(x)->ldhi,(x)->ldlo, \
t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9)
/* Square root: r=sqrt(x) */
/* Variables r,x,y are pointers to struct ker80, */
/* all other variables are in long double precision */
/* Here t32 is the constant 2^32+1 */
/* half is the constant 0.5 */
/* Temporary variables: t1,t2,t3,t4,t5,t6,t7,t8,t9 */
/* Correct for any positive x */
#define __LIBM_SQRTL_NORM_K80(r,x, \
t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9) \
if ( ((x)->fphi.exponent-BIAS_80<-16000) || \
((x)->fphi.exponent-BIAS_80>+16000) ) \
{ \
__libm_normalizel_k80(x); \
} \
__LIBM_SQRTL_K80(r,x, t32,half,t1,t2,t3,t4,t5,t6,t7,t8,t9)
#ifdef __INTEL_COMPILER
#define ALIGN(n) __declspec(align(n))
#else /* __INTEL_COMPILER */
#define ALIGN(n)
#endif /* __INTEL_COMPILER */
/* macros to form a long double value in hex representation (unsigned short type) */
#if (defined(__unix__) && defined(__i386__))
# define LDOUBLE_ALIGN 12 /* IA32 Linux: 12-byte alignment */
#else /*__linux__ & IA32*/
# define LDOUBLE_ALIGN 16 /* EFI2/IA32 Win or IPF Win/Linux: 16-byte alignment */
#endif /*__linux__ & IA32*/
#if (LDOUBLE_ALIGN == 16)
#define _XPD_ ,0x0000,0x0000,0x0000
#else /*12*/
#define _XPD_ ,0x0000
#endif
#define LDOUBLE_HEX(w4,w3,w2,w1,w0) 0x##w0,0x##w1,0x##w2,0x##w3,0x##w4 _XPD_ /*LITTLE_ENDIAN*/
/* macros to sign-expand low 'num' bits of 'val' to native integer */
#if defined(SIZE_INT_32)
# define SIGN_EXPAND(val,num) ((int)(val) << (32-(num))) >> (32-(num)) /* sign expand of 'num' LSBs */
#elif defined(SIZE_INT_64)
# define SIGN_EXPAND(val,num) ((int)(val) << (64-(num))) >> (64-(num)) /* sign expand of 'num' LSBs */
#endif
/* macros to form pointers to FP number on-the-fly */
#define FP32(f) ((struct fp32 *)&f)
#define FP64(d) ((struct fp64 *)&d)
#define FP80(ld) ((struct fp80 *)&ld)
/* macros to extract signed low and high doubleword of long double */
#if defined(SIZE_INT_32)
# define HI_DWORD_80(ld) ((((FP80(ld)->sign << 15) | FP80(ld)->exponent) << 16) | \
((FP80(ld)->hi_significand >> 16) & 0xFFFF))
# define LO_DWORD_80(ld) SIGN_EXPAND(FP80(ld)->lo_significand, 32)
#elif defined(SIZE_INT_64)
# define HI_DWORD_80(ld) ((((FP80(ld)->sign << 15) | FP80(ld)->exponent) << 16) | \
((FP80(ld)->significand >> 48) & 0xFFFF))
# define LO_DWORD_80(ld) SIGN_EXPAND(FP80(ld)->significand, 32)
#endif
/* macros to extract hi bits of significand.
* note that explicit high bit do not count (returns as is)
*/
#if defined(SIZE_INT_32)
# define HI_SIGNIFICAND_80(X,NBITS) ((X)->hi_significand >> (31 - (NBITS)))
#elif defined(SIZE_INT_64)
# define HI_SIGNIFICAND_80(X,NBITS) ((X)->significand >> (63 - (NBITS)))
#endif
/* macros to check, whether a significand bits are all zero, or some of them are non-zero.
* note that SIGNIFICAND_ZERO_80 tests high bit also, but SIGNIFICAND_NONZERO_80 does not
*/
#define SIGNIFICAND_ZERO_32(X) ((X)->significand == 0)
#define SIGNIFICAND_NONZERO_32(X) ((X)->significand != 0)
#if defined(SIZE_INT_32)
# define SIGNIFICAND_ZERO_64(X) (((X)->hi_significand == 0) && ((X)->lo_significand == 0))
# define SIGNIFICAND_NONZERO_64(X) (((X)->hi_significand != 0) || ((X)->lo_significand != 0))
#elif defined(SIZE_INT_64)
# define SIGNIFICAND_ZERO_64(X) ((X)->significand == 0)
# define SIGNIFICAND_NONZERO_64(X) ((X)->significand != 0)
#endif
#if defined(SIZE_INT_32)
# define SIGNIFICAND_ZERO_80(X) (((X)->hi_significand == 0x00000000) && ((X)->lo_significand == 0))
# define SIGNIFICAND_NONZERO_80(X) (((X)->hi_significand != 0x80000000) || ((X)->lo_significand != 0))
#elif defined(SIZE_INT_64)
# define SIGNIFICAND_ZERO_80(X) ((X)->significand == 0x0000000000000000)
# define SIGNIFICAND_NONZERO_80(X) ((X)->significand != 0x8000000000000000)
#endif
/* macros to compare long double with constant value, represented as hex */
#define SIGNIFICAND_EQ_HEX_32(X,BITS) ((X)->significand == 0x ## BITS)
#define SIGNIFICAND_GT_HEX_32(X,BITS) ((X)->significand > 0x ## BITS)
#define SIGNIFICAND_GE_HEX_32(X,BITS) ((X)->significand >= 0x ## BITS)
#define SIGNIFICAND_LT_HEX_32(X,BITS) ((X)->significand < 0x ## BITS)
#define SIGNIFICAND_LE_HEX_32(X,BITS) ((X)->significand <= 0x ## BITS)
#if defined(SIZE_INT_32)
# define SIGNIFICAND_EQ_HEX_64(X,HI,LO) \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand == 0x ## LO))
# define SIGNIFICAND_GT_HEX_64(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand > 0x ## LO)))
# define SIGNIFICAND_GE_HEX_64(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >= 0x ## LO)))
# define SIGNIFICAND_LT_HEX_64(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand < 0x ## LO)))
# define SIGNIFICAND_LE_HEX_64(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <= 0x ## LO)))
#elif defined(SIZE_INT_64)
# define SIGNIFICAND_EQ_HEX_64(X,HI,LO) ((X)->significand == 0x ## HI ## LO)
# define SIGNIFICAND_GT_HEX_64(X,HI,LO) ((X)->significand > 0x ## HI ## LO)
# define SIGNIFICAND_GE_HEX_64(X,HI,LO) ((X)->significand >= 0x ## HI ## LO)
# define SIGNIFICAND_LT_HEX_64(X,HI,LO) ((X)->significand < 0x ## HI ## LO)
# define SIGNIFICAND_LE_HEX_64(X,HI,LO) ((X)->significand <= 0x ## HI ## LO)
#endif
#if defined(SIZE_INT_32)
# define SIGNIFICAND_EQ_HEX_80(X,HI,LO) \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand == 0x ## LO))
# define SIGNIFICAND_GT_HEX_80(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand > 0x ## LO)))
# define SIGNIFICAND_GE_HEX_80(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >= 0x ## LO)))
# define SIGNIFICAND_LT_HEX_80(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand < 0x ## LO)))
# define SIGNIFICAND_LE_HEX_80(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <= 0x ## LO)))
#elif defined(SIZE_INT_64)
# define SIGNIFICAND_EQ_HEX_80(X,HI,LO) ((X)->significand == 0x ## HI ## LO)
# define SIGNIFICAND_GT_HEX_80(X,HI,LO) ((X)->significand > 0x ## HI ## LO)
# define SIGNIFICAND_GE_HEX_80(X,HI,LO) ((X)->significand >= 0x ## HI ## LO)
# define SIGNIFICAND_LT_HEX_80(X,HI,LO) ((X)->significand < 0x ## HI ## LO)
# define SIGNIFICAND_LE_HEX_80(X,HI,LO) ((X)->significand <= 0x ## HI ## LO)
#endif
#define VALUE_EQ_HEX_32(X,EXP,BITS) \
(((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_32(X, BITS)))
#define VALUE_GT_HEX_32(X,EXP,BITS) (((X)->exponent > (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_32(X, BITS))))
#define VALUE_GE_HEX_32(X,EXP,BITS) (((X)->exponent > (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_32(X, BITS))))
#define VALUE_LT_HEX_32(X,EXP,BITS) (((X)->exponent < (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_32(X, BITS))))
#define VALUE_LE_HEX_32(X,EXP,BITS) (((X)->exponent < (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_32(X, BITS))))
#define VALUE_EQ_HEX_64(X,EXP,HI,LO) \
(((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_64(X, HI, LO)))
#define VALUE_GT_HEX_64(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_64(X, HI, LO))))
#define VALUE_GE_HEX_64(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_64(X, HI, LO))))
#define VALUE_LT_HEX_64(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_64(X, HI, LO))))
#define VALUE_LE_HEX_64(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_64(X, HI, LO))))
#define VALUE_EQ_HEX_80(X,EXP,HI,LO) \
(((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_80(X, HI, LO)))
#define VALUE_GT_HEX_80(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_80(X, HI, LO))))
#define VALUE_GE_HEX_80(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_80(X, HI, LO))))
#define VALUE_LT_HEX_80(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_80(X, HI, LO))))
#define VALUE_LE_HEX_80(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
(((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_80(X, HI, LO))))
/* macros to compare two long doubles */
#define SIGNIFICAND_EQ_32(X,Y) ((X)->significand == (Y)->significand)
#define SIGNIFICAND_GT_32(X,Y) ((X)->significand > (Y)->significand)
#define SIGNIFICAND_GE_32(X,Y) ((X)->significand >= (Y)->significand)
#define SIGNIFICAND_LT_32(X,Y) ((X)->significand < (Y)->significand)
#define SIGNIFICAND_LE_32(X,Y) ((X)->significand <= (Y)->significand)
#if defined(SIZE_INT_32)
# define SIGNIFICAND_EQ_64(X,Y) \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand == (Y)->lo_significand))
# define SIGNIFICAND_GT_64(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand > (Y)->lo_significand)))
# define SIGNIFICAND_GE_64(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand >= (Y)->lo_significand)))
# define SIGNIFICAND_LT_64(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand < (Y)->lo_significand)))
# define SIGNIFICAND_LE_64(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand <= (Y)->lo_significand)))
#elif defined(SIZE_INT_64)
# define SIGNIFICAND_EQ_64(X,Y) ((X)->significand == (Y)->significand)
# define SIGNIFICAND_GT_64(X,Y) ((X)->significand > (Y)->significand)
# define SIGNIFICAND_GE_64(X,Y) ((X)->significand >= (Y)->significand)
# define SIGNIFICAND_LT_64(X,Y) ((X)->significand < (Y)->significand)
# define SIGNIFICAND_LE_64(X,Y) ((X)->significand <= (Y)->significand)
#endif
#if defined(SIZE_INT_32)
# define SIGNIFICAND_EQ_80(X,Y) \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand == (Y)->lo_significand))
# define SIGNIFICAND_GT_80(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand > (Y)->lo_significand)))
# define SIGNIFICAND_GE_80(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand >= (Y)->lo_significand)))
# define SIGNIFICAND_LT_80(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand < (Y)->lo_significand)))
# define SIGNIFICAND_LE_80(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand <= (Y)->lo_significand)))
#elif defined(SIZE_INT_64)
# define SIGNIFICAND_EQ_80(X,Y) ((X)->significand == (Y)->significand)
# define SIGNIFICAND_GT_80(X,Y) ((X)->significand > (Y)->significand)
# define SIGNIFICAND_GE_80(X,Y) ((X)->significand >= (Y)->significand)
# define SIGNIFICAND_LT_80(X,Y) ((X)->significand < (Y)->significand)
# define SIGNIFICAND_LE_80(X,Y) ((X)->significand <= (Y)->significand)
#endif
#define VALUE_EQ_32(X,Y) \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_32(X, Y)))
#define VALUE_GT_32(X,Y) (((X)->exponent > (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_32(X, Y))))
#define VALUE_GE_32(X,Y) (((X)->exponent > (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_32(X, Y))))
#define VALUE_LT_32(X,Y) (((X)->exponent < (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_32(X, Y))))
#define VALUE_LE_32(X,Y) (((X)->exponent < (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_32(X, Y))))
#define VALUE_EQ_64(X,Y) \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_64(X, Y)))
#define VALUE_GT_64(X,Y) (((X)->exponent > (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_64(X, Y))))
#define VALUE_GE_64(X,Y) (((X)->exponent > (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_64(X, Y))))
#define VALUE_LT_64(X,Y) (((X)->exponent < (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_64(X, Y))))
#define VALUE_LE_64(X,Y) (((X)->exponent < (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_64(X, Y))))
#define VALUE_EQ_80(X,Y) \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_80(X, Y)))
#define VALUE_GT_80(X,Y) (((X)->exponent > (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_80(X, Y))))
#define VALUE_GE_80(X,Y) (((X)->exponent > (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_80(X, Y))))
#define VALUE_LT_80(X,Y) (((X)->exponent < (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_80(X, Y))))
#define VALUE_LE_80(X,Y) (((X)->exponent < (Y)->exponent) || \
(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_80(X, Y))))
/* add/subtract 1 ulp macros */
#if defined(SIZE_INT_32)
# define ADD_ULP_80(X) \
if ((++(X)->lo_significand == 0) && \
(++(X)->hi_significand == (((X)->exponent == 0) ? 0x80000000 : 0))) \
{ \
(X)->hi_significand |= 0x80000000; \
++(X)->exponent; \
}
# define SUB_ULP_80(X) \
if (--(X)->lo_significand == 0xFFFFFFFF) { \
--(X)->hi_significand; \
if (((X)->exponent != 0) && \
((X)->hi_significand == 0x7FFFFFFF) && \
(--(X)->exponent != 0)) \
{ \
(X)->hi_significand |= 0x80000000; \
} \
}
#elif defined(SIZE_INT_64)
# define ADD_ULP_80(X) \
if (++(X)->significand == (((X)->exponent == 0) ? 0x8000000000000000 : 0))) { \
(X)->significand |= 0x8000000000000000; \
++(X)->exponent; \
}
# define SUB_ULP_80(X) \
{ \
--(X)->significand; \
if (((X)->exponent != 0) && \
((X)->significand == 0x7FFFFFFFFFFFFFFF) && \
(--(X)->exponent != 0)) \
{ \
(X)->significand |= 0x8000000000000000; \
} \
}
#endif
/* error codes */
#define DOMAIN 1 /* argument domain error */
#define SING 2 /* argument singularity */
#define OVERFLOW 3 /* overflow range error */
#define UNDERFLOW 4 /* underflow range error */
#define TLOSS 5 /* total loss of precision */
#define PLOSS 6 /* partial loss of precision */
/* */
#define VOLATILE_32 /*volatile*/
#define VOLATILE_64 /*volatile*/
#define VOLATILE_80 /*volatile*/
#define QUAD_TYPE _Quad
#endif /*__LIBM_SUPPORT_H_INCLUDED__*/
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