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1052 lines
49 KiB
C
1052 lines
49 KiB
C
/* file: libm_support.h */
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/*
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// Copyright (c) 2000 - 2004, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2000 by the Intel Numerics Group, Intel Corporation
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History: 02/02/2000 Initial version
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// 2/28/2000 added tags for logb and nextafter
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// 3/22/2000 Changes to support _LIB_VERSIONIMF variable
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// and filled some enum gaps. Added support for C99.
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// 5/31/2000 added prototypes for __libm_frexp_4l/8l
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// 8/10/2000 Changed declaration of _LIB_VERSIONIMF to work for library
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// builds and other application builds (precompiler directives).
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// 8/11/2000 Added pointers-to-matherr-functions declarations to allow
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// for user-defined matherr functions in the dll build.
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// 12/07/2000 Added scalbn error_types values.
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// 5/01/2001 Added error_types values for C99 nearest integer
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// functions.
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// 6/07/2001 Added error_types values for fdim.
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// 6/18/2001 Added include of complex_support.h.
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// 8/03/2001 Added error_types values for nexttoward, scalbln.
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// 8/23/2001 Corrected tag numbers from 186 and higher.
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// 8/27/2001 Added check for long int and long long int definitions.
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// 12/10/2001 Added error_types for erfc.
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// 12/27/2001 Added error_types for degree argument functions.
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// 01/02/2002 Added error_types for tand, cotd.
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// 01/04/2002 Delete include of complex_support.h
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// 01/23/2002 Deleted prototypes for __libm_frexp*. Added check for
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// multiple int, long int, and long long int definitions.
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// 05/20/2002 Added error_types for cot.
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// 06/27/2002 Added error_types for sinhcosh.
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// 12/05/2002 Added error_types for annuity and compound
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// 04/10/2003 Added error_types for tgammal/tgamma/tgammaf
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// 05/16/2003 FP-treatment macros copied here from IA32 libm_support.h
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// 06/02/2003 Added pad into struct fp80 (12/16 bytes).
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// 08/01/2003 Added struct ker80 and macros for multiprecision addition,
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// subtraction, multiplication, division, square root.
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// 08/07/2003 History section updated.
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// 09/03/2003 ALIGN(n) macro added.
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// 10/01/2003 LDOUBLE_ALIGN and fp80 corrected on linux to 16 bytes.
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// 11/24/2004 Added ifdef around definitions of INT32/64
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// 12/15/2004 Added error_types for exp10, nextafter, nexttoward
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// underflow. Moved error codes into libm_error_codes.h.
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//
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*/
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#ifndef __LIBM_SUPPORT_H_INCLUDED__
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#define __LIBM_SUPPORT_H_INCLUDED__
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#ifndef _LIBC
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#if !(defined(_WIN32) || defined(_WIN64))
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# pragma const_seg(".rodata") /* place constant data in text (code) section */
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#endif
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#if defined(__ICC) || defined(__ICL) || defined(__ECC) || defined(__ECL)
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# pragma warning( disable : 1682 ) /* #1682: ixplicit conversion of a 64-bit integral type to a smaller integral type (potential portability problem) */
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# pragma warning( disable : 1683 ) /* #1683: explicit conversion of a 64-bit integral type to a smaller integral type (potential portability problem) */
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#endif
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#endif
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/* macros to form a double value in hex representation (unsigned int type) */
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#define DOUBLE_HEX(hi,lo) 0x##lo,0x##hi /*LITTLE_ENDIAN*/
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#include "libm_cpu_defs.h"
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#if !(defined (IA64))
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# include "libm_dll.h"
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# include "libm_dispatch.h"
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#endif
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#include "libm_error_codes.h"
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struct exceptionf
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{
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int type;
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char *name;
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float arg1, arg2, retval;
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};
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# ifdef __cplusplus
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struct __exception
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{
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int type;
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char *name;
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double arg1, arg2, retval;
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};
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# else
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# ifndef _LIBC
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struct exception
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{
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int type;
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char *name;
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double arg1, arg2, retval;
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};
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# endif
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# endif
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struct exceptionl
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{
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int type;
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char *name;
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long double arg1, arg2, retval;
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};
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#if (defined (_MS_) && defined (IA64))
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#define MATHERR_F _matherrf
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#define MATHERR_D _matherr
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#else
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#define MATHERR_F matherrf
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#define MATHERR_D matherr
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#endif
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# ifdef __cplusplus
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#define EXC_DECL_D __exception
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#else
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// exception is a reserved name in C++
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#define EXC_DECL_D exception
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#endif
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extern int MATHERR_F(struct exceptionf*);
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extern int MATHERR_D(struct EXC_DECL_D*);
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extern int matherrl(struct exceptionl*);
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#ifndef _LIBC
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// Add code to support _LIB_VERSIONIMF
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typedef enum
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{
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_IEEE_ = -1, // IEEE-like behavior
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_SVID_, // SysV, Rel. 4 behavior
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_XOPEN_, // Unix98
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_POSIX_, // Posix
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_ISOC_ // ISO C9X
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} _LIB_VERSION_TYPE;
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#endif
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// This is a run-time variable and may affect
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// floating point behavior of the libm functions
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#if !defined( LIBM_BUILD )
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#if defined( _DLL )
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extern _LIB_VERSION_TYPE __declspec(dllimport) _LIB_VERSIONIMF;
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#else
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extern _LIB_VERSION_TYPE _LIB_VERSIONIMF;
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#endif /* _DLL */
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#else
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extern int (*pmatherrf)(struct exceptionf*);
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extern int (*pmatherr)(struct EXC_DECL_D*);
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extern int (*pmatherrl)(struct exceptionl*);
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#endif /* LIBM_BUILD */
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/* memory format definitions (LITTLE_ENDIAN only) */
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#if !(defined(SIZE_INT_32) || defined(SIZE_INT_64))
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# error "You need to define SIZE_INT_32 or SIZE_INT_64"
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#endif
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#if (defined(SIZE_INT_32) && defined(SIZE_INT_64))
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#error multiple integer size definitions; define SIZE_INT_32 or SIZE_INT_64
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#endif
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#if !(defined(SIZE_LONG_32) || defined(SIZE_LONG_64))
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# error "You need to define SIZE_LONG_32 or SIZE_LONG_64"
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#endif
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#if (defined(SIZE_LONG_32) && defined(SIZE_LONG_64))
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#error multiple integer size definitions; define SIZE_LONG_32 or SIZE_LONG_64
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#endif
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#if !defined(__USE_EXTERNAL_FPMEMTYP_H__)
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#define BIAS_32 0x007F
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#define BIAS_64 0x03FF
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#define BIAS_80 0x3FFF
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#define MAXEXP_32 0x00FE
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#define MAXEXP_64 0x07FE
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#define MAXEXP_80 0x7FFE
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#define EXPINF_32 0x00FF
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#define EXPINF_64 0x07FF
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#define EXPINF_80 0x7FFF
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struct fp32 { /*// sign:1 exponent:8 significand:23 (implied leading 1)*/
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#if defined(SIZE_INT_32)
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unsigned significand:23;
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unsigned exponent:8;
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unsigned sign:1;
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#elif defined(SIZE_INT_64)
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unsigned significand:23;
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unsigned exponent:8;
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unsigned sign:1;
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#endif
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};
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struct fp64 { /*/ sign:1 exponent:11 significand:52 (implied leading 1)*/
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#if defined(SIZE_INT_32)
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unsigned lo_significand:32;
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unsigned hi_significand:20;
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unsigned exponent:11;
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unsigned sign:1;
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#elif defined(SIZE_INT_64)
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unsigned significand:52;
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unsigned exponent:11;
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unsigned sign:1;
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#endif
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};
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struct fp80 { /*/ sign:1 exponent:15 significand:64 (NO implied bits) */
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#if defined(SIZE_INT_32)
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unsigned lo_significand;
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unsigned hi_significand;
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unsigned exponent:15;
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unsigned sign:1;
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#elif defined(SIZE_INT_64)
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unsigned significand;
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unsigned exponent:15;
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unsigned sign:1;
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#endif
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unsigned pad:16;
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#if !(defined(__unix__) && defined(__i386__))
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unsigned padwin:32;
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#endif
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};
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#endif /*__USE_EXTERNAL_FPMEMTYP_H__*/
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#if !(defined(opensource))
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typedef __int32 INT32;
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typedef signed __int32 SINT32;
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typedef unsigned __int32 UINT32;
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typedef __int64 INT64;
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typedef signed __int64 SINT64;
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typedef unsigned __int64 UINT64;
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#else
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typedef int INT32;
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typedef signed int SINT32;
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typedef unsigned int UINT32;
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typedef long long INT64;
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typedef signed long long SINT64;
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typedef unsigned long long UINT64;
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#endif
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#if (defined(_WIN32) || defined(_WIN64)) /* Windows */
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# define I64CONST(bits) 0x##bits##i64
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# define U64CONST(bits) 0x##bits##ui64
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#elif (defined(__linux__) && defined(_M_IA64)) /* Linux,64 */
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# define I64CONST(bits) 0x##bits##L
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# define U64CONST(bits) 0x##bits##uL
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#else /* Linux,32 */
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# define I64CONST(bits) 0x##bits##LL
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# define U64CONST(bits) 0x##bits##uLL
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#endif
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struct ker80 {
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union {
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long double ldhi;
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struct fp80 fphi;
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};
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union {
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long double ldlo;
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struct fp80 fplo;
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};
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int ex;
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};
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/* Addition: x+y */
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/* The result is sum rhi+rlo */
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/* Temporary variables: t1 */
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/* All variables are in long double precision */
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/* Correct if no overflow (algorithm by D.Knuth) */
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#define __LIBM_ADDL1_K80( rhi,rlo,x,y, t1 ) \
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rhi = x + y; \
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rlo = rhi - x; \
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t1 = rhi - rlo; \
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rlo = y - rlo; \
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t1 = x - t1; \
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rlo = rlo + t1;
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/* Addition: (xhi+xlo) + (yhi+ylo) */
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/* The result is sum rhi+rlo */
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/* Temporary variables: t1 */
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/* All variables are in long double precision */
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/* Correct if no overflow (algorithm by T.J.Dekker) */
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#define __LIBM_ADDL2_K80( rhi,rlo,xhi,xlo,yhi,ylo, t1 ) \
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rlo = xhi+yhi; \
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if ( VALUE_GT_80(FP80(xhi),FP80(yhi)) ) { \
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t1=xhi-rlo;t1=t1+yhi;t1=t1+ylo;t1=t1+xlo; \
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} else { \
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t1=yhi-rlo;t1=t1+xhi;t1=t1+xlo;t1=t1+ylo; \
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} \
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rhi=rlo+t1; \
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rlo=rlo-rhi;rlo=rlo+t1;
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/* Addition: r=x+y */
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/* Variables r,x,y are pointers to struct ker80, */
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/* all other variables are in long double precision */
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/* Temporary variables: t1 */
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/* Correct if x and y belong to interval [2^-8000;2^8000], */
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/* or when one or both of them are zero */
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#if defined(SIZE_INT_32)
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#define __LIBM_ADDL_K80(r,x,y, t1) \
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if ( ((y)->ex+(y)->fphi.exponent-134 < \
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(x)->ex+(x)->fphi.exponent) && \
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((x)->ex+(x)->fphi.exponent < \
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(y)->ex+(y)->fphi.exponent+134) && \
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!SIGNIFICAND_ZERO_80(&((x)->fphi)) && \
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!SIGNIFICAND_ZERO_80(&((y)->fphi)) ) \
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{ \
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/* y/2^134 < x < y*2^134, */ \
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/* and x,y are nonzero finite numbers */ \
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if ( (x)->ex != (y)->ex ) { \
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/* adjust x->ex to y->ex */ \
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/* t1 = 2^(x->ex - y->ex) */ \
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FP80(t1)->sign = 0; \
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FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
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/* exponent is correct because */ \
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/* |x->ex - y->ex| = */ \
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/* = | (x->ex + x->fphi.exponent) - */ \
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/* -(y->ex + y->fphi.exponent) + */ \
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/* + y->fphi.exponent - */ \
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/* - x->fphi.exponent | < */ \
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/* < | (x->ex+x->fphi.exponent) - */ \
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/* -(y->ex+y->fphi.exponent) | + */ \
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/* +| y->fphi.exponent - */ \
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/* -x->fphi.exponent | < */ \
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/* < 134 + 16000 */ \
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FP80(t1)->hi_significand = 0x80000000; \
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FP80(t1)->lo_significand = 0x00000000; \
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(x)->ex = (y)->ex; \
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(x)->ldhi *= t1; \
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(x)->ldlo *= t1; \
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} \
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/* r==x+y */ \
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(r)->ex = (y)->ex; \
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__LIBM_ADDL2_K80( (r)->ldhi,(r)->ldlo, \
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(x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
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} else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) || \
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((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >= \
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(x)->ex+(x)->fphi.exponent-BIAS_80) ) \
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{ \
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/* |x|<<|y| */ \
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*(r) = *(y); \
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} else { \
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/* |y|<<|x| */ \
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*(r) = *(x); \
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}
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#elif defined(SIZE_INT_64)
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#define __LIBM_ADDL_K80(r,x,y, t1) \
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if ( ((y)->ex+(y)->fphi.exponent-134 < \
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(x)->ex+(x)->fphi.exponent) && \
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((x)->ex+(x)->fphi.exponent < \
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(y)->ex+(y)->fphi.exponent+134) && \
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!SIGNIFICAND_ZERO_80(&((x)->fphi)) && \
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!SIGNIFICAND_ZERO_80(&((y)->fphi)) ) \
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{ \
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/* y/2^134 < x < y*2^134, */ \
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/* and x,y are nonzero finite numbers */ \
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if ( (x)->ex != (y)->ex ) { \
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/* adjust x->ex to y->ex */ \
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/* t1 = 2^(x->ex - y->ex) */ \
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FP80(t1)->sign = 0; \
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FP80(t1)->exponent = BIAS_80 + (x)->ex-(y)->ex; \
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/* exponent is correct because */ \
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/* |x->ex - y->ex| = */ \
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/* = | (x->ex + x->fphi.exponent) - */ \
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/* -(y->ex + y->fphi.exponent) + */ \
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/* + y->fphi.exponent - */ \
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/* - x->fphi.exponent | < */ \
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/* < | (x->ex+x->fphi.exponent) - */ \
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/* -(y->ex+y->fphi.exponent) | + */ \
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/* +| y->fphi.exponent - */ \
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/* -x->fphi.exponent | < */ \
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/* < 134 + 16000 */ \
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FP80(t1)->significand = 0x8000000000000000; \
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(x)->ex = (y)->ex; \
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(x)->ldhi *= t1; \
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(x)->ldlo *= t1; \
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} \
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/* r==x+y */ \
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(r)->ex = (y)->ex; \
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__LIBM_ADDL2_K80( (r)->ldhi,(r)->ldlo, \
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(x)->ldhi,(x)->ldlo, (y)->ldhi,(y)->ldlo, t1 ); \
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} else if ( SIGNIFICAND_ZERO_80(&((x)->fphi)) || \
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((y)->ex+(y)->fphi.exponent-BIAS_80 - 134 >= \
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(x)->ex+(x)->fphi.exponent-BIAS_80) ) \
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{ \
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/* |x|<<|y| */ \
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*(r) = *(y); \
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} else { \
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/* |y|<<|x| */ \
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*(r) = *(x); \
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}
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#endif
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/* Addition: r=x+y */
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/* Variables r,x,y are pointers to struct ker80, */
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/* all other variables are in long double precision */
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/* Temporary variables: t1 */
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/* Correct for any finite x and y */
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#define __LIBM_ADDL_NORM_K80(r,x,y, t1) \
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if ( ((x)->fphi.exponent-BIAS_80<-8000) || \
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((x)->fphi.exponent-BIAS_80>+8000) || \
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((y)->fphi.exponent-BIAS_80<-8000) || \
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((y)->fphi.exponent-BIAS_80>+8000) ) \
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{ \
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__libm_normalizel_k80(x); \
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__libm_normalizel_k80(y); \
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} \
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__LIBM_ADDL_K80(r,x,y, t1)
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/* Subtraction: x-y */
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/* The result is sum rhi+rlo */
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/* Temporary variables: t1 */
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/* All variables are in long double precision */
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/* Correct if no overflow (algorithm by D.Knuth) */
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#define __LIBM_SUBL1_K80( rhi, rlo, x, y, t1 ) \
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rhi = x - y; \
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rlo = rhi - x; \
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|
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
|
|
*/
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#define SIGNIFICAND_ZERO_32(X) ((X)->significand == 0)
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#define SIGNIFICAND_NONZERO_32(X) ((X)->significand != 0)
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#if defined(SIZE_INT_32)
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# define SIGNIFICAND_ZERO_64(X) (((X)->hi_significand == 0) && ((X)->lo_significand == 0))
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# define SIGNIFICAND_NONZERO_64(X) (((X)->hi_significand != 0) || ((X)->lo_significand != 0))
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#elif defined(SIZE_INT_64)
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# define SIGNIFICAND_ZERO_64(X) ((X)->significand == 0)
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# define SIGNIFICAND_NONZERO_64(X) ((X)->significand != 0)
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#endif
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#if defined(SIZE_INT_32)
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# define SIGNIFICAND_ZERO_80(X) (((X)->hi_significand == 0x00000000) && ((X)->lo_significand == 0))
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# define SIGNIFICAND_NONZERO_80(X) (((X)->hi_significand != 0x80000000) || ((X)->lo_significand != 0))
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#elif defined(SIZE_INT_64)
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# define SIGNIFICAND_ZERO_80(X) ((X)->significand == 0x0000000000000000)
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# define SIGNIFICAND_NONZERO_80(X) ((X)->significand != 0x8000000000000000)
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#endif
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/* macros to compare long double with constant value, represented as hex */
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#define SIGNIFICAND_EQ_HEX_32(X,BITS) ((X)->significand == 0x ## BITS)
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#define SIGNIFICAND_GT_HEX_32(X,BITS) ((X)->significand > 0x ## BITS)
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#define SIGNIFICAND_GE_HEX_32(X,BITS) ((X)->significand >= 0x ## BITS)
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#define SIGNIFICAND_LT_HEX_32(X,BITS) ((X)->significand < 0x ## BITS)
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#define SIGNIFICAND_LE_HEX_32(X,BITS) ((X)->significand <= 0x ## BITS)
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#if defined(SIZE_INT_32)
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# define SIGNIFICAND_EQ_HEX_64(X,HI,LO) \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand == 0x ## LO))
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# define SIGNIFICAND_GT_HEX_64(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand > 0x ## LO)))
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# define SIGNIFICAND_GE_HEX_64(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >= 0x ## LO)))
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# define SIGNIFICAND_LT_HEX_64(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand < 0x ## LO)))
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# define SIGNIFICAND_LE_HEX_64(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <= 0x ## LO)))
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#elif defined(SIZE_INT_64)
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# define SIGNIFICAND_EQ_HEX_64(X,HI,LO) ((X)->significand == 0x ## HI ## LO)
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# define SIGNIFICAND_GT_HEX_64(X,HI,LO) ((X)->significand > 0x ## HI ## LO)
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# define SIGNIFICAND_GE_HEX_64(X,HI,LO) ((X)->significand >= 0x ## HI ## LO)
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# define SIGNIFICAND_LT_HEX_64(X,HI,LO) ((X)->significand < 0x ## HI ## LO)
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# define SIGNIFICAND_LE_HEX_64(X,HI,LO) ((X)->significand <= 0x ## HI ## LO)
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#endif
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#if defined(SIZE_INT_32)
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# define SIGNIFICAND_EQ_HEX_80(X,HI,LO) \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand == 0x ## LO))
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# define SIGNIFICAND_GT_HEX_80(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand > 0x ## LO)))
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# define SIGNIFICAND_GE_HEX_80(X,HI,LO) (((X)->hi_significand > 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >= 0x ## LO)))
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# define SIGNIFICAND_LT_HEX_80(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand < 0x ## LO)))
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# define SIGNIFICAND_LE_HEX_80(X,HI,LO) (((X)->hi_significand < 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <= 0x ## LO)))
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#elif defined(SIZE_INT_64)
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# define SIGNIFICAND_EQ_HEX_80(X,HI,LO) ((X)->significand == 0x ## HI ## LO)
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# define SIGNIFICAND_GT_HEX_80(X,HI,LO) ((X)->significand > 0x ## HI ## LO)
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# define SIGNIFICAND_GE_HEX_80(X,HI,LO) ((X)->significand >= 0x ## HI ## LO)
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# define SIGNIFICAND_LT_HEX_80(X,HI,LO) ((X)->significand < 0x ## HI ## LO)
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# define SIGNIFICAND_LE_HEX_80(X,HI,LO) ((X)->significand <= 0x ## HI ## LO)
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#endif
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#define VALUE_EQ_HEX_32(X,EXP,BITS) \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_32(X, BITS)))
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#define VALUE_GT_HEX_32(X,EXP,BITS) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_32(X, BITS))))
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#define VALUE_GE_HEX_32(X,EXP,BITS) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_32(X, BITS))))
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#define VALUE_LT_HEX_32(X,EXP,BITS) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_32(X, BITS))))
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#define VALUE_LE_HEX_32(X,EXP,BITS) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_32(X, BITS))))
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#define VALUE_EQ_HEX_64(X,EXP,HI,LO) \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_64(X, HI, LO)))
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#define VALUE_GT_HEX_64(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_64(X, HI, LO))))
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#define VALUE_GE_HEX_64(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_64(X, HI, LO))))
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#define VALUE_LT_HEX_64(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_64(X, HI, LO))))
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#define VALUE_LE_HEX_64(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_64(X, HI, LO))))
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#define VALUE_EQ_HEX_80(X,EXP,HI,LO) \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_EQ_HEX_80(X, HI, LO)))
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#define VALUE_GT_HEX_80(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_GT_HEX_80(X, HI, LO))))
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#define VALUE_GE_HEX_80(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_GE_HEX_80(X, HI, LO))))
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#define VALUE_LT_HEX_80(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_LT_HEX_80(X, HI, LO))))
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#define VALUE_LE_HEX_80(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_LE_HEX_80(X, HI, LO))))
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/* macros to compare two long doubles */
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#define SIGNIFICAND_EQ_32(X,Y) ((X)->significand == (Y)->significand)
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#define SIGNIFICAND_GT_32(X,Y) ((X)->significand > (Y)->significand)
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#define SIGNIFICAND_GE_32(X,Y) ((X)->significand >= (Y)->significand)
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#define SIGNIFICAND_LT_32(X,Y) ((X)->significand < (Y)->significand)
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#define SIGNIFICAND_LE_32(X,Y) ((X)->significand <= (Y)->significand)
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#if defined(SIZE_INT_32)
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# define SIGNIFICAND_EQ_64(X,Y) \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand == (Y)->lo_significand))
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# define SIGNIFICAND_GT_64(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand > (Y)->lo_significand)))
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# define SIGNIFICAND_GE_64(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand >= (Y)->lo_significand)))
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# define SIGNIFICAND_LT_64(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand < (Y)->lo_significand)))
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# define SIGNIFICAND_LE_64(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand <= (Y)->lo_significand)))
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#elif defined(SIZE_INT_64)
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# define SIGNIFICAND_EQ_64(X,Y) ((X)->significand == (Y)->significand)
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# define SIGNIFICAND_GT_64(X,Y) ((X)->significand > (Y)->significand)
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# define SIGNIFICAND_GE_64(X,Y) ((X)->significand >= (Y)->significand)
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# define SIGNIFICAND_LT_64(X,Y) ((X)->significand < (Y)->significand)
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# define SIGNIFICAND_LE_64(X,Y) ((X)->significand <= (Y)->significand)
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#endif
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#if defined(SIZE_INT_32)
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# define SIGNIFICAND_EQ_80(X,Y) \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand == (Y)->lo_significand))
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# define SIGNIFICAND_GT_80(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand > (Y)->lo_significand)))
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# define SIGNIFICAND_GE_80(X,Y) (((X)->hi_significand > (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand >= (Y)->lo_significand)))
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# define SIGNIFICAND_LT_80(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand < (Y)->lo_significand)))
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# define SIGNIFICAND_LE_80(X,Y) (((X)->hi_significand < (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand <= (Y)->lo_significand)))
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#elif defined(SIZE_INT_64)
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# define SIGNIFICAND_EQ_80(X,Y) ((X)->significand == (Y)->significand)
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# define SIGNIFICAND_GT_80(X,Y) ((X)->significand > (Y)->significand)
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# define SIGNIFICAND_GE_80(X,Y) ((X)->significand >= (Y)->significand)
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# define SIGNIFICAND_LT_80(X,Y) ((X)->significand < (Y)->significand)
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# define SIGNIFICAND_LE_80(X,Y) ((X)->significand <= (Y)->significand)
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#endif
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#define VALUE_EQ_32(X,Y) \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_32(X, Y)))
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#define VALUE_GT_32(X,Y) (((X)->exponent > (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_32(X, Y))))
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#define VALUE_GE_32(X,Y) (((X)->exponent > (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_32(X, Y))))
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#define VALUE_LT_32(X,Y) (((X)->exponent < (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_32(X, Y))))
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#define VALUE_LE_32(X,Y) (((X)->exponent < (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_32(X, Y))))
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#define VALUE_EQ_64(X,Y) \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_64(X, Y)))
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#define VALUE_GT_64(X,Y) (((X)->exponent > (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_64(X, Y))))
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#define VALUE_GE_64(X,Y) (((X)->exponent > (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_64(X, Y))))
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#define VALUE_LT_64(X,Y) (((X)->exponent < (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_64(X, Y))))
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#define VALUE_LE_64(X,Y) (((X)->exponent < (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_64(X, Y))))
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#define VALUE_EQ_80(X,Y) \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_EQ_80(X, Y)))
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#define VALUE_GT_80(X,Y) (((X)->exponent > (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GT_80(X, Y))))
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#define VALUE_GE_80(X,Y) (((X)->exponent > (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_GE_80(X, Y))))
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#define VALUE_LT_80(X,Y) (((X)->exponent < (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LT_80(X, Y))))
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#define VALUE_LE_80(X,Y) (((X)->exponent < (Y)->exponent) || \
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(((X)->exponent == (Y)->exponent) && (SIGNIFICAND_LE_80(X, Y))))
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/* add/subtract 1 ulp macros */
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#if defined(SIZE_INT_32)
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# define ADD_ULP_80(X) \
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if ((++(X)->lo_significand == 0) && \
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(++(X)->hi_significand == (((X)->exponent == 0) ? 0x80000000 : 0))) \
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{ \
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(X)->hi_significand |= 0x80000000; \
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++(X)->exponent; \
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}
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# define SUB_ULP_80(X) \
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if (--(X)->lo_significand == 0xFFFFFFFF) { \
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--(X)->hi_significand; \
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if (((X)->exponent != 0) && \
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((X)->hi_significand == 0x7FFFFFFF) && \
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(--(X)->exponent != 0)) \
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{ \
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(X)->hi_significand |= 0x80000000; \
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} \
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}
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#elif defined(SIZE_INT_64)
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# define ADD_ULP_80(X) \
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if (++(X)->significand == (((X)->exponent == 0) ? 0x8000000000000000 : 0))) { \
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(X)->significand |= 0x8000000000000000; \
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++(X)->exponent; \
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}
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# define SUB_ULP_80(X) \
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{ \
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--(X)->significand; \
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if (((X)->exponent != 0) && \
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((X)->significand == 0x7FFFFFFFFFFFFFFF) && \
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(--(X)->exponent != 0)) \
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{ \
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(X)->significand |= 0x8000000000000000; \
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} \
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}
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#endif
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/* error codes */
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#define DOMAIN 1 /* argument domain error */
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#define SING 2 /* argument singularity */
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#define OVERFLOW 3 /* overflow range error */
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#define UNDERFLOW 4 /* underflow range error */
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#define TLOSS 5 /* total loss of precision */
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#define PLOSS 6 /* partial loss of precision */
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/* */
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#define VOLATILE_32 /*volatile*/
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#define VOLATILE_64 /*volatile*/
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#define VOLATILE_80 /*volatile*/
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#define QUAD_TYPE _Quad
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#endif /*__LIBM_SUPPORT_H_INCLUDED__*/
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