756 lines
32 KiB
C
756 lines
32 KiB
C
/* file: libm_support.h */
|
|
|
|
|
|
// Copyright (c) 2000 - 2002, 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
|
|
//
|
|
|
|
void __libm_sincos_pi4(double,double*,double*,int);
|
|
void __libm_y0y1(double , double *, double *);
|
|
void __libm_j0j1(double , double *, double *);
|
|
double __libm_j0(double);
|
|
double __libm_j1(double);
|
|
double __libm_jn(int,double);
|
|
double __libm_y0(double);
|
|
double __libm_y1(double);
|
|
double __libm_yn(int,double);
|
|
double __libm_copysign (double, double);
|
|
float __libm_copysignf (float, float);
|
|
long double __libm_copysignl (long double, long double);
|
|
|
|
extern double sqrt(double);
|
|
extern double fabs(double);
|
|
extern double log(double);
|
|
extern double log1p(double);
|
|
extern double sqrt(double);
|
|
extern double sin(double);
|
|
extern double exp(double);
|
|
extern double modf(double, double *);
|
|
extern double asinh(double);
|
|
extern double acosh(double);
|
|
extern double atanh(double);
|
|
extern double tanh(double);
|
|
extern double erf(double);
|
|
extern double erfc(double);
|
|
extern double j0(double);
|
|
extern double j1(double);
|
|
extern double jn(int, double);
|
|
extern double y0(double);
|
|
extern double y1(double);
|
|
extern double yn(int, double);
|
|
|
|
extern float fabsf(float);
|
|
extern float asinhf(float);
|
|
extern float acoshf(float);
|
|
extern float atanhf(float);
|
|
extern float tanhf(float);
|
|
extern float erff(float);
|
|
extern float erfcf(float);
|
|
extern float j0f(float);
|
|
extern float j1f(float);
|
|
extern float jnf(int, float);
|
|
extern float y0f(float);
|
|
extern float y1f(float);
|
|
extern float ynf(int, float);
|
|
|
|
extern long double log1pl(long double);
|
|
extern long double logl(long double);
|
|
extern long double sqrtl(long double);
|
|
extern long double expl(long double);
|
|
extern long double fabsl(long double);
|
|
|
|
#if !(defined(SIZE_INT_32) || defined(SIZE_INT_64))
|
|
#error integer size not established; 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_INT_32) || defined(SIZE_LONG_INT_64))
|
|
#error long int size not established; define SIZE_LONG_INT_32 or SIZE_LONG_INT_64
|
|
#endif
|
|
|
|
#if (defined(SIZE_LONG_INT_32) && defined(SIZE_LONG_INT_64))
|
|
#error multiple long int size definitions; define SIZE_LONG_INT_32 or SIZE_LONG_INT_64
|
|
#endif
|
|
|
|
#if !(defined(SIZE_LONG_LONG_INT_32) || defined(SIZE_LONG_LONG_INT_64))
|
|
#error long long int size not established; define SIZE_LONG_LONG_INT_32 or SIZE_LONG_LONG_INT_64
|
|
#endif
|
|
|
|
#if (defined(SIZE_LONG_LONG_INT_32) && defined(SIZE_LONG_LONG_INT_64))
|
|
#error multiple long long int size definitions; define SIZE_LONG_LONG_INT_32 or SIZE_LONG_LONG_INT_64
|
|
#endif
|
|
|
|
typedef enum
|
|
{
|
|
logl_zero=0, logl_negative, /* 0, 1 */
|
|
log_zero, log_negative, /* 2, 3 */
|
|
logf_zero, logf_negative, /* 4, 5 */
|
|
log10l_zero, log10l_negative, /* 6, 7 */
|
|
log10_zero, log10_negative, /* 8, 9 */
|
|
log10f_zero, log10f_negative, /* 10, 11 */
|
|
expl_overflow, expl_underflow, /* 12, 13 */
|
|
exp_overflow, exp_underflow, /* 14, 15 */
|
|
expf_overflow, expf_underflow, /* 16, 17 */
|
|
powl_overflow, powl_underflow, /* 18, 19 */
|
|
powl_zero_to_zero, /* 20 */
|
|
powl_zero_to_negative, /* 21 */
|
|
powl_neg_to_non_integer, /* 22 */
|
|
powl_nan_to_zero, /* 23 */
|
|
pow_overflow, pow_underflow, /* 24, 25 */
|
|
pow_zero_to_zero, /* 26 */
|
|
pow_zero_to_negative, /* 27 */
|
|
pow_neg_to_non_integer, /* 28 */
|
|
pow_nan_to_zero, /* 29 */
|
|
powf_overflow, powf_underflow, /* 30, 31 */
|
|
powf_zero_to_zero, /* 32 */
|
|
powf_zero_to_negative, /* 33 */
|
|
powf_neg_to_non_integer, /* 34 */
|
|
powf_nan_to_zero, /* 35 */
|
|
atan2l_zero, /* 36 */
|
|
atan2_zero, /* 37 */
|
|
atan2f_zero, /* 38 */
|
|
expm1l_overflow, /* 39 */
|
|
expm1l_underflow, /* 40 */
|
|
expm1_overflow, /* 41 */
|
|
expm1_underflow, /* 42 */
|
|
expm1f_overflow, /* 43 */
|
|
expm1f_underflow, /* 44 */
|
|
hypotl_overflow, /* 45 */
|
|
hypot_overflow, /* 46 */
|
|
hypotf_overflow, /* 47 */
|
|
sqrtl_negative, /* 48 */
|
|
sqrt_negative, /* 49 */
|
|
sqrtf_negative, /* 50 */
|
|
scalbl_overflow, scalbl_underflow, /* 51, 52 */
|
|
scalb_overflow, scalb_underflow, /* 53, 54 */
|
|
scalbf_overflow, scalbf_underflow, /* 55, 56 */
|
|
acosl_gt_one, acos_gt_one, acosf_gt_one, /* 57, 58, 59 */
|
|
asinl_gt_one, asin_gt_one, asinf_gt_one, /* 60, 61, 62 */
|
|
coshl_overflow, cosh_overflow, coshf_overflow, /* 63, 64, 65 */
|
|
y0l_zero, y0l_negative,y0l_gt_loss, /* 66, 67, 68 */
|
|
y0_zero, y0_negative,y0_gt_loss, /* 69, 70, 71 */
|
|
y0f_zero, y0f_negative,y0f_gt_loss, /* 72, 73, 74 */
|
|
y1l_zero, y1l_negative,y1l_gt_loss, /* 75, 76, 77 */
|
|
y1_zero, y1_negative,y1_gt_loss, /* 78, 79, 80 */
|
|
y1f_zero, y1f_negative,y1f_gt_loss, /* 81, 82, 83 */
|
|
ynl_zero, ynl_negative,ynl_gt_loss, /* 84, 85, 86 */
|
|
yn_zero, yn_negative,yn_gt_loss, /* 87, 88, 89 */
|
|
ynf_zero, ynf_negative,ynf_gt_loss, /* 90, 91, 92 */
|
|
j0l_gt_loss, /* 93 */
|
|
j0_gt_loss, /* 94 */
|
|
j0f_gt_loss, /* 95 */
|
|
j1l_gt_loss, /* 96 */
|
|
j1_gt_loss, /* 97 */
|
|
j1f_gt_loss, /* 98 */
|
|
jnl_gt_loss, /* 99 */
|
|
jn_gt_loss, /* 100 */
|
|
jnf_gt_loss, /* 101 */
|
|
lgammal_overflow, lgammal_negative,lgammal_reserve, /* 102, 103, 104 */
|
|
lgamma_overflow, lgamma_negative,lgamma_reserve, /* 105, 106, 107 */
|
|
lgammaf_overflow, lgammaf_negative, lgammaf_reserve,/* 108, 109, 110 */
|
|
gammal_overflow,gammal_negative, gammal_reserve, /* 111, 112, 113 */
|
|
gamma_overflow, gamma_negative, gamma_reserve, /* 114, 115, 116 */
|
|
gammaf_overflow,gammaf_negative,gammaf_reserve, /* 117, 118, 119 */
|
|
fmodl_by_zero, /* 120 */
|
|
fmod_by_zero, /* 121 */
|
|
fmodf_by_zero, /* 122 */
|
|
remainderl_by_zero, /* 123 */
|
|
remainder_by_zero, /* 124 */
|
|
remainderf_by_zero, /* 125 */
|
|
sinhl_overflow, sinh_overflow, sinhf_overflow, /* 126, 127, 128 */
|
|
atanhl_gt_one, atanhl_eq_one, /* 129, 130 */
|
|
atanh_gt_one, atanh_eq_one, /* 131, 132 */
|
|
atanhf_gt_one, atanhf_eq_one, /* 133, 134 */
|
|
acoshl_lt_one, /* 135 */
|
|
acosh_lt_one, /* 136 */
|
|
acoshf_lt_one, /* 137 */
|
|
log1pl_zero, log1pl_negative, /* 138, 139 */
|
|
log1p_zero, log1p_negative, /* 140, 141 */
|
|
log1pf_zero, log1pf_negative, /* 142, 143 */
|
|
ldexpl_overflow, ldexpl_underflow, /* 144, 145 */
|
|
ldexp_overflow, ldexp_underflow, /* 146, 147 */
|
|
ldexpf_overflow, ldexpf_underflow, /* 148, 149 */
|
|
logbl_zero, logb_zero, logbf_zero, /* 150, 151, 152 */
|
|
nextafterl_overflow, nextafter_overflow,
|
|
nextafterf_overflow, /* 153, 154, 155 */
|
|
ilogbl_zero, ilogb_zero, ilogbf_zero, /* 156, 157, 158 */
|
|
exp2l_overflow, exp2l_underflow, /* 159, 160 */
|
|
exp2_overflow, exp2_underflow, /* 161, 162 */
|
|
exp2f_overflow, exp2f_underflow, /* 163, 164 */
|
|
exp10l_overflow, exp10_overflow,
|
|
exp10f_overflow, /* 165, 166, 167 */
|
|
log2l_zero, log2l_negative, /* 168, 169 */
|
|
log2_zero, log2_negative, /* 170, 171 */
|
|
log2f_zero, log2f_negative, /* 172, 173 */
|
|
scalbnl_overflow, scalbnl_underflow, /* 174, 175 */
|
|
scalbn_overflow, scalbn_underflow, /* 176, 177 */
|
|
scalbnf_overflow, scalbnf_underflow, /* 178, 179 */
|
|
remquol_by_zero, /* 180 */
|
|
remquo_by_zero, /* 181 */
|
|
remquof_by_zero, /* 182 */
|
|
lrintl_large, lrint_large, lrintf_large, /* 183, 184, 185 */
|
|
llrintl_large, llrint_large, llrintf_large, /* 186, 187, 188 */
|
|
lroundl_large, lround_large, lroundf_large, /* 189, 190, 191 */
|
|
llroundl_large, llround_large, llroundf_large, /* 192, 193, 194 */
|
|
fdiml_overflow, fdim_overflow, fdimf_overflow, /* 195, 196, 197 */
|
|
nexttowardl_overflow, nexttoward_overflow,
|
|
nexttowardf_overflow, /* 198, 199, 200 */
|
|
scalblnl_overflow, scalblnl_underflow, /* 201, 202 */
|
|
scalbln_overflow, scalbln_underflow, /* 203, 204 */
|
|
scalblnf_overflow, scalblnf_underflow, /* 205, 206 */
|
|
erfcl_underflow, erfc_underflow, erfcf_underflow, /* 207, 208, 209 */
|
|
acosdl_gt_one, acosd_gt_one, acosdf_gt_one, /* 210, 211, 212 */
|
|
asindl_gt_one, asind_gt_one, asindf_gt_one, /* 213, 214, 215 */
|
|
atan2dl_zero, atan2d_zero, atan2df_zero, /* 216, 217, 218 */
|
|
tandl_overflow, tand_overflow, tandf_overflow, /* 219, 220, 221 */
|
|
cotdl_overflow, cotd_overflow, cotdf_overflow, /* 222, 223, 224 */
|
|
cotl_overflow, cot_overflow, cotf_overflow, /* 225, 226, 227 */
|
|
sinhcoshl_overflow, sinhcosh_overflow, sinhcoshf_overflow, /* 228, 229, 230 */
|
|
annuityl_by_zero, annuity_by_zero, annuityf_by_zero, /* 231, 232, 233 */
|
|
annuityl_less_m1, annuity_less_m1, annuityf_less_m1, /* 234, 235, 236 */
|
|
annuityl_overflow, annuity_overflow, annuityf_overflow, /* 237, 238, 239 */
|
|
annuityl_underflow, annuity_underflow, annuityf_underflow, /* 240, 241, 242 */
|
|
compoundl_by_zero, compound_by_zero, compoundf_by_zero, /* 243, 244, 245 */
|
|
compoundl_less_m1, compound_less_m1, compoundf_less_m1, /* 246, 247, 248 */
|
|
compoundl_overflow, compound_overflow, compoundf_overflow, /* 249, 250, 251 */
|
|
compoundl_underflow, compound_underflow, compoundf_underflow, /* 252, 253, 254 */
|
|
tgammal_overflow, tgammal_negative, tgammal_reserve, /* 255, 256, 257 */
|
|
tgamma_overflow, tgamma_negative, tgamma_reserve, /* 258, 259, 260 */
|
|
tgammaf_overflow, tgammaf_negative, tgammaf_reserve, /* 261, 262, 263 */
|
|
} error_types;
|
|
|
|
void __libm_error_support(void*,void*,void*,error_types);
|
|
#ifdef _LIBC
|
|
libc_hidden_proto(__libm_error_support)
|
|
#endif
|
|
|
|
#define HI_SIGNIFICAND_LESS(X, HI) ((X)->hi_significand < 0x ## HI)
|
|
#define f64abs(x) ((x) < 0.0 ? -(x) : (x))
|
|
|
|
#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
|
|
};
|
|
|
|
#endif /*__USE_EXTERNAL_FPMEMTYP_H__*/
|
|
|
|
/* macros to form a double value in hex representation (unsigned int type) */
|
|
|
|
#define DOUBLE_HEX(hi,lo) 0x##lo,0x##hi /*LITTLE_ENDIAN*/
|
|
|
|
/* macros to form a long double value in hex representation (unsigned short type) */
|
|
|
|
#if defined(_WIN32) || defined(_WIN64)
|
|
#define LDOUBLE_ALIGN 16
|
|
#else
|
|
#define LDOUBLE_ALIGN 12
|
|
#endif
|
|
|
|
#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
|
|
|
|
|
|
|
|
#if (defined(_WIN32) && !defined(_WIN64))
|
|
|
|
#define FP80_DECLARE()
|
|
#define _FPC_64 0x0300
|
|
static unsigned short __wControlWord, __wNewControlWord;
|
|
#define FP80_SET() { \
|
|
__asm { fnstcw word ptr [__wControlWord] } \
|
|
__wNewControlWord = __wControlWord | _FPC_64; \
|
|
__asm { fldcw word ptr [__wNewControlWord] } \
|
|
}
|
|
#define FP80_RESET() { \
|
|
__asm { fldcw word ptr [__wControlWord] } \
|
|
}
|
|
#else /* defined(_WIN32) && !defined(_WIN64) */
|
|
|
|
#define FP80_DECLARE()
|
|
#define FP80_SET()
|
|
#define FP80_RESET()
|
|
|
|
#endif /* defined(_WIN32) && !defined(_WIN64) */
|
|
|
|
|
|
#ifdef _LIBC
|
|
# include <math.h>
|
|
#else
|
|
|
|
static const unsigned INF[] = {
|
|
DOUBLE_HEX(7ff00000, 00000000),
|
|
DOUBLE_HEX(fff00000, 00000000)
|
|
};
|
|
|
|
static const double _zeroo = 0.0;
|
|
static const double _bigg = 1.0e300;
|
|
static const double _ponee = 1.0;
|
|
static const double _nonee = -1.0;
|
|
|
|
#define INVALID (_zeroo * *((double*)&INF[0]))
|
|
#define PINF *((double*)&INF[0])
|
|
#define NINF -PINF
|
|
#define PINF_DZ (_ponee/_zeroo)
|
|
#define X_TLOSS 1.41484755040568800000e+16
|
|
#endif
|
|
|
|
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;
|
|
};
|
|
|
|
#ifdef _MS_
|
|
#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*);
|
|
|
|
|
|
/* Set these appropriately to make thread Safe */
|
|
#define ERRNO_RANGE errno = ERANGE
|
|
#define ERRNO_DOMAIN errno = EDOM
|
|
|
|
|
|
// Add code to support _LIB_VERSIONIMF
|
|
#ifndef _LIBC
|
|
typedef enum
|
|
{
|
|
_IEEE_ = -1, // IEEE-like behavior
|
|
_SVID_, // SysV, Rel. 4 behavior
|
|
_XOPEN_, // Unix98
|
|
_POSIX_, // Posix
|
|
_ISOC_ // ISO C9X
|
|
} _LIB_VERSION_TYPE;
|
|
|
|
|
|
#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 */
|
|
|
|
// This is a run-time variable and may affect
|
|
// floating point behavior of the libm functions
|
|
#endif
|