diff options
Diffstat (limited to 'sysdeps/ieee754/flt-32/lgamma_negf.c')
-rw-r--r-- | sysdeps/ieee754/flt-32/lgamma_negf.c | 280 |
1 files changed, 0 insertions, 280 deletions
diff --git a/sysdeps/ieee754/flt-32/lgamma_negf.c b/sysdeps/ieee754/flt-32/lgamma_negf.c deleted file mode 100644 index 71bcbb0f9d..0000000000 --- a/sysdeps/ieee754/flt-32/lgamma_negf.c +++ /dev/null @@ -1,280 +0,0 @@ -/* lgammaf expanding around zeros. - Copyright (C) 2015-2017 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 - <http://www.gnu.org/licenses/>. */ - -#include <float.h> -#include <math.h> -#include <math_private.h> - -static const float lgamma_zeros[][2] = - { - { -0x2.74ff94p+0f, 0x1.3fe0f2p-24f }, - { -0x2.bf682p+0f, -0x1.437b2p-24f }, - { -0x3.24c1b8p+0f, 0x6.c34cap-28f }, - { -0x3.f48e2cp+0f, 0x1.707a04p-24f }, - { -0x4.0a13ap+0f, 0x1.e99aap-24f }, - { -0x4.fdd5ep+0f, 0x1.64454p-24f }, - { -0x5.021a98p+0f, 0x2.03d248p-24f }, - { -0x5.ffa4cp+0f, 0x2.9b82fcp-24f }, - { -0x6.005ac8p+0f, -0x1.625f24p-24f }, - { -0x6.fff3p+0f, 0x2.251e44p-24f }, - { -0x7.000dp+0f, 0x8.48078p-28f }, - { -0x7.fffe6p+0f, 0x1.fa98c4p-28f }, - { -0x8.0001ap+0f, -0x1.459fcap-28f }, - { -0x8.ffffdp+0f, -0x1.c425e8p-24f }, - { -0x9.00003p+0f, 0x1.c44b82p-24f }, - { -0xap+0f, 0x4.9f942p-24f }, - { -0xap+0f, -0x4.9f93b8p-24f }, - { -0xbp+0f, 0x6.b9916p-28f }, - { -0xbp+0f, -0x6.b9915p-28f }, - { -0xcp+0f, 0x8.f76c8p-32f }, - { -0xcp+0f, -0x8.f76c7p-32f }, - { -0xdp+0f, 0xb.09231p-36f }, - { -0xdp+0f, -0xb.09231p-36f }, - { -0xep+0f, 0xc.9cba5p-40f }, - { -0xep+0f, -0xc.9cba5p-40f }, - { -0xfp+0f, 0xd.73f9fp-44f }, - }; - -static const float e_hi = 0x2.b7e15p+0f, e_lo = 0x1.628aeep-24f; - -/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's - approximation to lgamma function. */ - -static const float lgamma_coeff[] = - { - 0x1.555556p-4f, - -0xb.60b61p-12f, - 0x3.403404p-12f, - }; - -#define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) - -/* Polynomial approximations to (|gamma(x)|-1)(x-n)/(x-x0), where n is - the integer end-point of the half-integer interval containing x and - x0 is the zero of lgamma in that half-integer interval. Each - polynomial is expressed in terms of x-xm, where xm is the midpoint - of the interval for which the polynomial applies. */ - -static const float poly_coeff[] = - { - /* Interval [-2.125, -2] (polynomial degree 5). */ - -0x1.0b71c6p+0f, - -0xc.73a1ep-4f, - -0x1.ec8462p-4f, - -0xe.37b93p-4f, - -0x1.02ed36p-4f, - -0xe.cbe26p-4f, - /* Interval [-2.25, -2.125] (polynomial degree 5). */ - -0xf.29309p-4f, - -0xc.a5cfep-4f, - 0x3.9c93fcp-4f, - -0x1.02a2fp+0f, - 0x9.896bep-4f, - -0x1.519704p+0f, - /* Interval [-2.375, -2.25] (polynomial degree 5). */ - -0xd.7d28dp-4f, - -0xe.6964cp-4f, - 0xb.0d4f1p-4f, - -0x1.9240aep+0f, - 0x1.dadabap+0f, - -0x3.1778c4p+0f, - /* Interval [-2.5, -2.375] (polynomial degree 6). */ - -0xb.74ea2p-4f, - -0x1.2a82cp+0f, - 0x1.880234p+0f, - -0x3.320c4p+0f, - 0x5.572a38p+0f, - -0x9.f92bap+0f, - 0x1.1c347ep+4f, - /* Interval [-2.625, -2.5] (polynomial degree 6). */ - -0x3.d10108p-4f, - 0x1.cd5584p+0f, - 0x3.819c24p+0f, - 0x6.84cbb8p+0f, - 0xb.bf269p+0f, - 0x1.57fb12p+4f, - 0x2.7b9854p+4f, - /* Interval [-2.75, -2.625] (polynomial degree 6). */ - -0x6.b5d25p-4f, - 0x1.28d604p+0f, - 0x1.db6526p+0f, - 0x2.e20b38p+0f, - 0x4.44c378p+0f, - 0x6.62a08p+0f, - 0x9.6db3ap+0f, - /* Interval [-2.875, -2.75] (polynomial degree 5). */ - -0x8.a41b2p-4f, - 0xc.da87fp-4f, - 0x1.147312p+0f, - 0x1.7617dap+0f, - 0x1.d6c13p+0f, - 0x2.57a358p+0f, - /* Interval [-3, -2.875] (polynomial degree 5). */ - -0xa.046d6p-4f, - 0x9.70b89p-4f, - 0xa.a89a6p-4f, - 0xd.2f2d8p-4f, - 0xd.e32b4p-4f, - 0xf.fb741p-4f, - }; - -static const size_t poly_deg[] = - { - 5, - 5, - 5, - 6, - 6, - 6, - 5, - 5, - }; - -static const size_t poly_end[] = - { - 5, - 11, - 17, - 24, - 31, - 38, - 44, - 50, - }; - -/* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ - -static float -lg_sinpi (float x) -{ - if (x <= 0.25f) - return __sinf ((float) M_PI * x); - else - return __cosf ((float) M_PI * (0.5f - x)); -} - -/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ - -static float -lg_cospi (float x) -{ - if (x <= 0.25f) - return __cosf ((float) M_PI * x); - else - return __sinf ((float) M_PI * (0.5f - x)); -} - -/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ - -static float -lg_cotpi (float x) -{ - return lg_cospi (x) / lg_sinpi (x); -} - -/* Compute lgamma of a negative argument -15 < X < -2, setting - *SIGNGAMP accordingly. */ - -float -__lgamma_negf (float x, int *signgamp) -{ - /* Determine the half-integer region X lies in, handle exact - integers and determine the sign of the result. */ - int i = __floorf (-2 * x); - if ((i & 1) == 0 && i == -2 * x) - return 1.0f / 0.0f; - float xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); - i -= 4; - *signgamp = ((i & 2) == 0 ? -1 : 1); - - SET_RESTORE_ROUNDF (FE_TONEAREST); - - /* Expand around the zero X0 = X0_HI + X0_LO. */ - float x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; - float xdiff = x - x0_hi - x0_lo; - - /* For arguments in the range -3 to -2, use polynomial - approximations to an adjusted version of the gamma function. */ - if (i < 2) - { - int j = __floorf (-8 * x) - 16; - float xm = (-33 - 2 * j) * 0.0625f; - float x_adj = x - xm; - size_t deg = poly_deg[j]; - size_t end = poly_end[j]; - float g = poly_coeff[end]; - for (size_t j = 1; j <= deg; j++) - g = g * x_adj + poly_coeff[end - j]; - return __log1pf (g * xdiff / (x - xn)); - } - - /* The result we want is log (sinpi (X0) / sinpi (X)) - + log (gamma (1 - X0) / gamma (1 - X)). */ - float x_idiff = fabsf (xn - x), x0_idiff = fabsf (xn - x0_hi - x0_lo); - float log_sinpi_ratio; - if (x0_idiff < x_idiff * 0.5f) - /* Use log not log1p to avoid inaccuracy from log1p of arguments - close to -1. */ - log_sinpi_ratio = __ieee754_logf (lg_sinpi (x0_idiff) - / lg_sinpi (x_idiff)); - else - { - /* Use log1p not log to avoid inaccuracy from log of arguments - close to 1. X0DIFF2 has positive sign if X0 is further from - XN than X is from XN, negative sign otherwise. */ - float x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5f; - float sx0d2 = lg_sinpi (x0diff2); - float cx0d2 = lg_cospi (x0diff2); - log_sinpi_ratio = __log1pf (2 * sx0d2 - * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); - } - - float log_gamma_ratio; - float y0 = math_narrow_eval (1 - x0_hi); - float y0_eps = -x0_hi + (1 - y0) - x0_lo; - float y = math_narrow_eval (1 - x); - float y_eps = -x + (1 - y); - /* We now wish to compute LOG_GAMMA_RATIO - = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF - accurately approximates the difference Y0 + Y0_EPS - Y - - Y_EPS. Use Stirling's approximation. */ - float log_gamma_high - = (xdiff * __log1pf ((y0 - e_hi - e_lo + y0_eps) / e_hi) - + (y - 0.5f + y_eps) * __log1pf (xdiff / y)); - /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ - float y0r = 1 / y0, yr = 1 / y; - float y0r2 = y0r * y0r, yr2 = yr * yr; - float rdiff = -xdiff / (y * y0); - float bterm[NCOEFF]; - float dlast = rdiff, elast = rdiff * yr * (yr + y0r); - bterm[0] = dlast * lgamma_coeff[0]; - for (size_t j = 1; j < NCOEFF; j++) - { - float dnext = dlast * y0r2 + elast; - float enext = elast * yr2; - bterm[j] = dnext * lgamma_coeff[j]; - dlast = dnext; - elast = enext; - } - float log_gamma_low = 0; - for (size_t j = 0; j < NCOEFF; j++) - log_gamma_low += bterm[NCOEFF - 1 - j]; - log_gamma_ratio = log_gamma_high + log_gamma_low; - - return log_sinpi_ratio + log_gamma_ratio; -} |