diff options
Diffstat (limited to 'sysdeps/ieee754')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/gamma_productf.c | 45 | ||||
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_gammaf_r.c | 321 | ||||
| -rw-r--r-- | sysdeps/ieee754/flt-32/math_config.h | 2 |
3 files changed, 130 insertions, 238 deletions
diff --git a/sysdeps/ieee754/dbl-64/gamma_productf.c b/sysdeps/ieee754/dbl-64/gamma_productf.c index f3596eeae4..1cc8931700 100644 --- a/sysdeps/ieee754/dbl-64/gamma_productf.c +++ b/sysdeps/ieee754/dbl-64/gamma_productf.c @@ -1,44 +1 @@ -/* Compute a product of X, X+1, ..., with an error estimate. - Copyright (C) 2013-2024 Free Software Foundation, Inc. - This file is part of the GNU C Library. - - The GNU C Library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. - - The GNU C Library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Lesser General Public License for more details. - - You should have received a copy of the GNU Lesser General Public - License along with the GNU C Library; if not, see - <https://www.gnu.org/licenses/>. */ - -#include <math.h> -#include <math-narrow-eval.h> -#include <math_private.h> -#include <float.h> - -/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N - - 1, in the form R * (1 + *EPS) where the return value R is an - approximation to the product and *EPS is set to indicate the - approximate error in the return value. X is such that all the - values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / - X is small enough that factors quadratic in it can be - neglected. */ - -float -__gamma_productf (float x, float x_eps, int n, float *eps) -{ - double x_full = (double) x + (double) x_eps; - double ret = x_full; - for (int i = 1; i < n; i++) - ret *= x_full + i; - - float fret = math_narrow_eval ((float) ret); - *eps = (ret - fret) / fret; - - return fret; -} +/* Not needed. */ diff --git a/sysdeps/ieee754/flt-32/e_gammaf_r.c b/sysdeps/ieee754/flt-32/e_gammaf_r.c index a9730d61c1..90ed3b4890 100644 --- a/sysdeps/ieee754/flt-32/e_gammaf_r.c +++ b/sysdeps/ieee754/flt-32/e_gammaf_r.c @@ -1,215 +1,150 @@ -/* Implementation of gamma function according to ISO C. - Copyright (C) 1997-2024 Free Software Foundation, Inc. - This file is part of the GNU C Library. +/* Implementation of the gamma function for binary32. - The GNU C Library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. +Copyright (c) 2023-2024 Alexei Sibidanov. - The GNU C Library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Lesser General Public License for more details. +The original version of this file was copied from the CORE-MATH +project (file src/binary32/tgamma/tgammaf.c, revision a48e352). - You should have received a copy of the GNU Lesser General Public - License along with the GNU C Library; if not, see - <https://www.gnu.org/licenses/>. */ +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: -#include <math.h> -#include <math-narrow-eval.h> -#include <math_private.h> -#include <fenv_private.h> -#include <math-underflow.h> -#include <float.h> -#include <libm-alias-finite.h> - -/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's - approximation to gamma function. */ +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. -static const float gamma_coeff[] = - { - 0x1.555556p-4f, - -0xb.60b61p-12f, - 0x3.403404p-12f, - }; +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. + */ -#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) +/* Changes with respect to the original CORE-MATH code: + - removed the dealing with errno + (this is done in the wrapper math/w_tgammaf_compat.c) + - usage of math_narrow_eval to deal with underflow/overflow + - deal with signgamp + */ -/* Return gamma (X), for positive X less than 42, in the form R * - 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to - avoid overflow or underflow in intermediate calculations. */ +#include <math.h> +#include <float.h> +#include <stdint.h> +#include <stddef.h> +#include <libm-alias-finite.h> +#include <math-narrow-eval.h> -static float -gammaf_positive (float x, int *exp2_adj) -{ - int local_signgam; - if (x < 0.5f) - { - *exp2_adj = 0; - return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x; - } - else if (x <= 1.5f) - { - *exp2_adj = 0; - return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam)); - } - else if (x < 2.5f) - { - *exp2_adj = 0; - float x_adj = x - 1; - return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam)) - * x_adj); - } - else - { - float eps = 0; - float x_eps = 0; - float x_adj = x; - float prod = 1; - if (x < 4.0f) - { - /* Adjust into the range for applying Stirling's - approximation. */ - float n = ceilf (4.0f - x); - x_adj = math_narrow_eval (x + n); - x_eps = (x - (x_adj - n)); - prod = __gamma_productf (x_adj - n, x_eps, n, &eps); - } - /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). - Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, - starting by computing pow (X_ADJ, X_ADJ) with a power of 2 - factored out. */ - float exp_adj = -eps; - float x_adj_int = roundf (x_adj); - float x_adj_frac = x_adj - x_adj_int; - int x_adj_log2; - float x_adj_mant = __frexpf (x_adj, &x_adj_log2); - if (x_adj_mant < M_SQRT1_2f) - { - x_adj_log2--; - x_adj_mant *= 2.0f; - } - *exp2_adj = x_adj_log2 * (int) x_adj_int; - float ret = (__ieee754_powf (x_adj_mant, x_adj) - * __ieee754_exp2f (x_adj_log2 * x_adj_frac) - * __ieee754_expf (-x_adj) - * sqrtf (2 * M_PIf / x_adj) - / prod); - exp_adj += x_eps * __ieee754_logf (x_adj); - float bsum = gamma_coeff[NCOEFF - 1]; - float x_adj2 = x_adj * x_adj; - for (size_t i = 1; i <= NCOEFF - 1; i++) - bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; - exp_adj += bsum / x_adj; - return ret + ret * __expm1f (exp_adj); - } -} +typedef union {float f; uint32_t u;} b32u32_u; +typedef union {double f; uint64_t u;} b64u64_u; float __ieee754_gammaf_r (float x, int *signgamp) { - int32_t hx; - float ret; + /* The wrapper in math/w_tgamma_template.c expects *signgamp to be set to a + non-negative value if the returned value is gamma(x), and to a negative + value if it is -gamma(x). + Since the code here directly computes gamma(x), we set it to 1. + */ + if (signgamp != NULL) + *signgamp = 1; - GET_FLOAT_WORD (hx, x); + /* List of exceptional cases. Each entry contains the 32-bit encoding u of x, + a binary32 approximation f of gamma(x), and a correction term df. */ + static const struct {uint32_t u; float f, df;} tb[] = { + {0x27de86a9u, 0x1.268266p+47f, 0x1p22f}, // x = 0x1.bd0d52p-48 + {0x27e05475u, 0x1.242422p+47f, 0x1p22f}, // x = 0x1.c0a8eap-48 + {0xb63befb3u, -0x1.5cb6e4p+18f, 0x1p-7f}, // x = -0x1.77df66p-19 + {0x3c7bb570u, 0x1.021d9p+6f, 0x1p-19f}, // x = 0x1.f76aep-7 + {0x41e886d1u, 0x1.33136ap+98f, 0x1p73f}, // x = 0x1.d10da2p+4 + {0xc067d177u, 0x1.f6850cp-3f, 0x1p-28f}, // x = -0x1.cfa2eep+1 + {0xbd99da31u, -0x1.befe66p+3, -0x1p-22f}, // x = -0x1.33b462p-4 + {0xbf54c45au, -0x1.a6b4ecp+2, +0x1p-23f}, // x = -0x1.a988b4p-1 + {0x41ee77feu, 0x1.d3631cp+101, -0x1p-76f}, // x = 0x1.dceffcp+4 + {0x3f843a64u, 0x1.f6c638p-1, 0x1p-26f}, // x = 0x1.0874c8p+0 + }; - if (__glibc_unlikely ((hx & 0x7fffffff) == 0)) - { - /* Return value for x == 0 is Inf with divide by zero exception. */ - *signgamp = 0; - return 1.0 / x; + b32u32_u t = {.f = x}; + uint32_t ax = t.u<<1; + if(__builtin_expect(ax>=(0xffu<<24), 0)){ /* x=NaN or +/-Inf */ + if(ax==(0xffu<<24)){ /* x=+/-Inf */ + if(t.u>>31){ /* x=-Inf */ + return x / x; /* will raise the "Invalid operation" exception */ + } + return x; /* x=+Inf */ } - if (__builtin_expect (hx < 0, 0) - && (uint32_t) hx < 0xff800000 && rintf (x) == x) - { - /* Return value for integer x < 0 is NaN with invalid exception. */ - *signgamp = 0; - return (x - x) / (x - x); + return x + x; /* x=NaN, where x+x ensures the "Invalid operation" + exception is set if x is sNaN */ + } + double z = x; + if(__builtin_expect(ax<0x6d000000u, 0)){ /* |x| < 0x1p-18 */ + volatile double d = (0x1.fa658c23b1578p-1 - 0x1.d0a118f324b63p-1*z)*z - 0x1.2788cfc6fb619p-1; + double f = 1.0/z + d; + float r = f; + b64u64_u rt = {.f = f}; + if(((rt.u+2)&0xfffffff) < 4){ + for(unsigned i=0;i<sizeof(tb)/sizeof(tb[0]);i++) + if(t.u==tb[i].u) return tb[i].f + tb[i].df; } - if (__glibc_unlikely (hx == 0xff800000)) - { - /* x == -Inf. According to ISO this is NaN. */ - *signgamp = 0; - return x - x; + return r; + } + float fx = __builtin_floorf(x); + if(__builtin_expect(x >= 0x1.18522p+5f, 0)){ + /* Overflow case. The original CORE-MATH code returns 0x1p127f * 0x1p127f, + but apparently some compilers replace this by +Inf. */ + return math_narrow_eval (x * 0x1p127f); + } + /* compute k only after the overflow check, otherwise the case to integer + might overflow */ + int k = fx; + if(__builtin_expect(fx==x, 0)){ /* x is integer */ + if(x == 0.0f){ + return 1.0f/x; } - if (__glibc_unlikely ((hx & 0x7f800000) == 0x7f800000)) - { - /* Positive infinity (return positive infinity) or NaN (return - NaN). */ - *signgamp = 0; - return x + x; + if(x < 0.0f){ + return 0.0f / 0.0f; /* should raise the "Invalid operation" exception */ } + double t0 = 1, x0 = 1; + for(int i=1; i<k; i++, x0 += 1.0) t0 *= x0; + return t0; + } + if(__builtin_expect(x<-42.0f, 0)){ /* negative non-integer */ + /* For x < -42, x non-integer, |gamma(x)| < 2^-151. */ + static const float sgn[2] = {0x1p-127f, -0x1p-127f}; + /* Underflows always happens */ + return math_narrow_eval (0x1p-127f * sgn[k&1]); + } + /* The array c[] stores a degree-15 polynomial approximation for gamma(x). */ + static const double c[] = + {0x1.c9a76be577123p+0, 0x1.8f2754ddcf90dp+0, 0x1.0d1191949419bp+0, 0x1.e1f42cf0ae4a1p-2, + 0x1.82b358a3ab638p-3, 0x1.e1f2b30cd907bp-5, 0x1.240f6d4071bd8p-6, 0x1.1522c9f3cd012p-8, + 0x1.1fd0051a0525bp-10, 0x1.9808a8b96c37ep-13, 0x1.b3f78e01152b5p-15, 0x1.49c85a7e1fd04p-18, + 0x1.471ca49184475p-19, -0x1.368f0b7ed9e36p-23, 0x1.882222f9049efp-23, -0x1.a69ed2042842cp-25}; - if (x >= 36.0f) - { - /* Overflow. */ - *signgamp = 0; - ret = math_narrow_eval (FLT_MAX * FLT_MAX); - return ret; - } - else - { - SET_RESTORE_ROUNDF (FE_TONEAREST); - if (x > 0.0f) - { - *signgamp = 0; - int exp2_adj; - float tret = gammaf_positive (x, &exp2_adj); - ret = __scalbnf (tret, exp2_adj); - } - else if (x >= -FLT_EPSILON / 4.0f) - { - *signgamp = 0; - ret = 1.0f / x; - } - else - { - float tx = truncf (x); - *signgamp = (tx == 2.0f * truncf (tx / 2.0f)) ? -1 : 1; - if (x <= -42.0f) - /* Underflow. */ - ret = FLT_MIN * FLT_MIN; - else - { - float frac = tx - x; - if (frac > 0.5f) - frac = 1.0f - frac; - float sinpix = (frac <= 0.25f - ? __sinf (M_PIf * frac) - : __cosf (M_PIf * (0.5f - frac))); - int exp2_adj; - float tret = M_PIf / (-x * sinpix - * gammaf_positive (-x, &exp2_adj)); - ret = __scalbnf (tret, -exp2_adj); - math_check_force_underflow_nonneg (ret); - } - } - ret = math_narrow_eval (ret); - } - if (isinf (ret) && x != 0) - { - if (*signgamp < 0) - { - ret = math_narrow_eval (-copysignf (FLT_MAX, ret) * FLT_MAX); - ret = -ret; - } - else - ret = math_narrow_eval (copysignf (FLT_MAX, ret) * FLT_MAX); - return ret; - } - else if (ret == 0) - { - if (*signgamp < 0) - { - ret = math_narrow_eval (-copysignf (FLT_MIN, ret) * FLT_MIN); - ret = -ret; - } - else - ret = math_narrow_eval (copysignf (FLT_MIN, ret) * FLT_MIN); - return ret; + double m = z - 0x1.7p+1, i = __builtin_roundeven(m), step = __builtin_copysign(1.0,i); + double d = m - i, d2 = d*d, d4 = d2*d2, d8 = d4*d4; + double f = (c[0] + d*c[1]) + d2*(c[2] + d*c[3]) + d4*((c[4] + d*c[5]) + d2*(c[6] + d*c[7])) + + d8*((c[8] + d*c[9]) + d2*(c[10] + d*c[11]) + d4*((c[12] + d*c[13]) + d2*(c[14] + d*c[15]))); + int jm = __builtin_fabs(i); + double w = 1; + if(jm){ + z -= 0.5 + step*0.5; + w = z; + for(int j=jm-1; j; j--) {z -= step; w *= z;} + } + if(i<=-0.5) w = 1/w; + f *= w; + b64u64_u rt = {.f = f}; + float r = f; + /* Deal with exceptional cases. */ + if(__builtin_expect(((rt.u+2)&0xfffffff) < 8, 0)){ + for(unsigned j=0;j<sizeof(tb)/sizeof(tb[0]);j++) { + if(t.u==tb[j].u) return tb[j].f + tb[j].df; } - else - return ret; + } + return r; } libm_alias_finite (__ieee754_gammaf_r, __gammaf_r) diff --git a/sysdeps/ieee754/flt-32/math_config.h b/sysdeps/ieee754/flt-32/math_config.h index 729f22cd4f..dc07ebd459 100644 --- a/sysdeps/ieee754/flt-32/math_config.h +++ b/sysdeps/ieee754/flt-32/math_config.h @@ -166,9 +166,9 @@ extern const struct exp2f_data uint64_t tab[1 << EXP2F_TABLE_BITS]; double shift_scaled; double poly[EXP2F_POLY_ORDER]; - double shift; double invln2_scaled; double poly_scaled[EXP2F_POLY_ORDER]; + double shift; } __exp2f_data attribute_hidden; #define LOGF_TABLE_BITS 4 |