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Diffstat (limited to 'sysdeps/ieee754/flt-32/lgamma_negf.c')
| -rw-r--r-- | sysdeps/ieee754/flt-32/lgamma_negf.c | 280 |
1 files changed, 280 insertions, 0 deletions
diff --git a/sysdeps/ieee754/flt-32/lgamma_negf.c b/sysdeps/ieee754/flt-32/lgamma_negf.c new file mode 100644 index 0000000000..f15719b059 --- /dev/null +++ b/sysdeps/ieee754/flt-32/lgamma_negf.c @@ -0,0 +1,280 @@ +/* lgammaf expanding around zeros. + Copyright (C) 2015-2016 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; +} |