From c15a48dd9c2bb4e203a74347900fd86bb163df39 Mon Sep 17 00:00:00 2001 From: Jan Vesely Date: Tue, 6 Mar 2018 17:48:47 +0000 Subject: lgamma_r: Move code from .inc to .cl file Reviewed-by: Aaron Watry Signed-off-by: Jan Vesely llvm-svn: 326821 --- libclc/generic/lib/math/lgamma_r.cl | 491 +++++++++++++++++++++++++++++++++++ libclc/generic/lib/math/lgamma_r.inc | 480 +--------------------------------- 2 files changed, 496 insertions(+), 475 deletions(-) (limited to 'libclc/generic') diff --git a/libclc/generic/lib/math/lgamma_r.cl b/libclc/generic/lib/math/lgamma_r.cl index 3f07845eb9e..ff447386ac0 100644 --- a/libclc/generic/lib/math/lgamma_r.cl +++ b/libclc/generic/lib/math/lgamma_r.cl @@ -1,7 +1,498 @@ +/* + * Copyright (c) 2014 Advanced Micro Devices, Inc. + * Copyright (c) 2016 Aaron Watry + * + * 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: + * + * The above copyright notice and this permission notice shall be included in + * all copies or substantial portions of the Software. + * + * 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. + */ + #include #include "../clcmacro.h" #include "math.h" +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#define pi_f 3.1415927410e+00f /* 0x40490fdb */ + +#define a0_f 7.7215664089e-02f /* 0x3d9e233f */ +#define a1_f 3.2246702909e-01f /* 0x3ea51a66 */ +#define a2_f 6.7352302372e-02f /* 0x3d89f001 */ +#define a3_f 2.0580807701e-02f /* 0x3ca89915 */ +#define a4_f 7.3855509982e-03f /* 0x3bf2027e */ +#define a5_f 2.8905137442e-03f /* 0x3b3d6ec6 */ +#define a6_f 1.1927076848e-03f /* 0x3a9c54a1 */ +#define a7_f 5.1006977446e-04f /* 0x3a05b634 */ +#define a8_f 2.2086278477e-04f /* 0x39679767 */ +#define a9_f 1.0801156895e-04f /* 0x38e28445 */ +#define a10_f 2.5214456400e-05f /* 0x37d383a2 */ +#define a11_f 4.4864096708e-05f /* 0x383c2c75 */ + +#define tc_f 1.4616321325e+00f /* 0x3fbb16c3 */ + +#define tf_f -1.2148628384e-01f /* 0xbdf8cdcd */ +/* tt -(tail of tf) */ +#define tt_f 6.6971006518e-09f /* 0x31e61c52 */ + +#define t0_f 4.8383611441e-01f /* 0x3ef7b95e */ +#define t1_f -1.4758771658e-01f /* 0xbe17213c */ +#define t2_f 6.4624942839e-02f /* 0x3d845a15 */ +#define t3_f -3.2788541168e-02f /* 0xbd064d47 */ +#define t4_f 1.7970675603e-02f /* 0x3c93373d */ +#define t5_f -1.0314224288e-02f /* 0xbc28fcfe */ +#define t6_f 6.1005386524e-03f /* 0x3bc7e707 */ +#define t7_f -3.6845202558e-03f /* 0xbb7177fe */ +#define t8_f 2.2596477065e-03f /* 0x3b141699 */ +#define t9_f -1.4034647029e-03f /* 0xbab7f476 */ +#define t10_f 8.8108185446e-04f /* 0x3a66f867 */ +#define t11_f -5.3859531181e-04f /* 0xba0d3085 */ +#define t12_f 3.1563205994e-04f /* 0x39a57b6b */ +#define t13_f -3.1275415677e-04f /* 0xb9a3f927 */ +#define t14_f 3.3552918467e-04f /* 0x39afe9f7 */ + +#define u0_f -7.7215664089e-02f /* 0xbd9e233f */ +#define u1_f 6.3282704353e-01f /* 0x3f2200f4 */ +#define u2_f 1.4549225569e+00f /* 0x3fba3ae7 */ +#define u3_f 9.7771751881e-01f /* 0x3f7a4bb2 */ +#define u4_f 2.2896373272e-01f /* 0x3e6a7578 */ +#define u5_f 1.3381091878e-02f /* 0x3c5b3c5e */ + +#define v1_f 2.4559779167e+00f /* 0x401d2ebe */ +#define v2_f 2.1284897327e+00f /* 0x4008392d */ +#define v3_f 7.6928514242e-01f /* 0x3f44efdf */ +#define v4_f 1.0422264785e-01f /* 0x3dd572af */ +#define v5_f 3.2170924824e-03f /* 0x3b52d5db */ + +#define s0_f -7.7215664089e-02f /* 0xbd9e233f */ +#define s1_f 2.1498242021e-01f /* 0x3e5c245a */ +#define s2_f 3.2577878237e-01f /* 0x3ea6cc7a */ +#define s3_f 1.4635047317e-01f /* 0x3e15dce6 */ +#define s4_f 2.6642270386e-02f /* 0x3cda40e4 */ +#define s5_f 1.8402845599e-03f /* 0x3af135b4 */ +#define s6_f 3.1947532989e-05f /* 0x3805ff67 */ + +#define r1_f 1.3920053244e+00f /* 0x3fb22d3b */ +#define r2_f 7.2193557024e-01f /* 0x3f38d0c5 */ +#define r3_f 1.7193385959e-01f /* 0x3e300f6e */ +#define r4_f 1.8645919859e-02f /* 0x3c98bf54 */ +#define r5_f 7.7794247773e-04f /* 0x3a4beed6 */ +#define r6_f 7.3266842264e-06f /* 0x36f5d7bd */ + +#define w0_f 4.1893854737e-01f /* 0x3ed67f1d */ +#define w1_f 8.3333335817e-02f /* 0x3daaaaab */ +#define w2_f -2.7777778450e-03f /* 0xbb360b61 */ +#define w3_f 7.9365057172e-04f /* 0x3a500cfd */ +#define w4_f -5.9518753551e-04f /* 0xba1c065c */ +#define w5_f 8.3633989561e-04f /* 0x3a5b3dd2 */ +#define w6_f -1.6309292987e-03f /* 0xbad5c4e8 */ + +_CLC_OVERLOAD _CLC_DEF float lgamma_r(float x, private int *signp) { + int hx = as_int(x); + int ix = hx & 0x7fffffff; + float absx = as_float(ix); + + if (ix >= 0x7f800000) { + *signp = 1; + return x; + } + + if (absx < 0x1.0p-70f) { + *signp = hx < 0 ? -1 : 1; + return -log(absx); + } + + float r; + + if (absx == 1.0f | absx == 2.0f) + r = 0.0f; + + else if (absx < 2.0f) { + float y = 2.0f - absx; + int i = 0; + + int c = absx < 0x1.bb4c30p+0f; + float yt = absx - tc_f; + y = c ? yt : y; + i = c ? 1 : i; + + c = absx < 0x1.3b4c40p+0f; + yt = absx - 1.0f; + y = c ? yt : y; + i = c ? 2 : i; + + r = -log(absx); + yt = 1.0f - absx; + c = absx <= 0x1.ccccccp-1f; + r = c ? r : 0.0f; + y = c ? yt : y; + i = c ? 0 : i; + + c = absx < 0x1.769440p-1f; + yt = absx - (tc_f - 1.0f); + y = c ? yt : y; + i = c ? 1 : i; + + c = absx < 0x1.da6610p-3f; + y = c ? absx : y; + i = c ? 2 : i; + + float z, w, p1, p2, p3, p; + switch (i) { + case 0: + z = y * y; + p1 = mad(z, mad(z, mad(z, mad(z, mad(z, a10_f, a8_f), a6_f), a4_f), a2_f), a0_f); + p2 = z * mad(z, mad(z, mad(z, mad(z, mad(z, a11_f, a9_f), a7_f), a5_f), a3_f), a1_f); + p = mad(y, p1, p2); + r += mad(y, -0.5f, p); + break; + case 1: + z = y * y; + w = z * y; + p1 = mad(w, mad(w, mad(w, mad(w, t12_f, t9_f), t6_f), t3_f), t0_f); + p2 = mad(w, mad(w, mad(w, mad(w, t13_f, t10_f), t7_f), t4_f), t1_f); + p3 = mad(w, mad(w, mad(w, mad(w, t14_f, t11_f), t8_f), t5_f), t2_f); + p = mad(z, p1, -mad(w, -mad(y, p3, p2), tt_f)); + r += tf_f + p; + break; + case 2: + p1 = y * mad(y, mad(y, mad(y, mad(y, mad(y, u5_f, u4_f), u3_f), u2_f), u1_f), u0_f); + p2 = mad(y, mad(y, mad(y, mad(y, mad(y, v5_f, v4_f), v3_f), v2_f), v1_f), 1.0f); + r += mad(y, -0.5f, MATH_DIVIDE(p1, p2)); + break; + } + } else if (absx < 8.0f) { + int i = (int) absx; + float y = absx - (float) i; + float p = y * mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, s6_f, s5_f), s4_f), s3_f), s2_f), s1_f), s0_f); + float q = mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, r6_f, r5_f), r4_f), r3_f), r2_f), r1_f), 1.0f); + r = mad(y, 0.5f, MATH_DIVIDE(p, q)); + + float y6 = y + 6.0f; + float y5 = y + 5.0f; + float y4 = y + 4.0f; + float y3 = y + 3.0f; + float y2 = y + 2.0f; + + float z = 1.0f; + z *= i > 6 ? y6 : 1.0f; + z *= i > 5 ? y5 : 1.0f; + z *= i > 4 ? y4 : 1.0f; + z *= i > 3 ? y3 : 1.0f; + z *= i > 2 ? y2 : 1.0f; + + r += log(z); + } else if (absx < 0x1.0p+58f) { + float z = 1.0f / absx; + float y = z * z; + float w = mad(z, mad(y, mad(y, mad(y, mad(y, mad(y, w6_f, w5_f), w4_f), w3_f), w2_f), w1_f), w0_f); + r = mad(absx - 0.5f, log(absx) - 1.0f, w); + } else + // 2**58 <= x <= Inf + r = absx * (log(absx) - 1.0f); + + int s = 1; + + if (x < 0.0f) { + float t = sinpi(x); + r = log(pi_f / fabs(t * x)) - r; + r = t == 0.0f ? as_float(PINFBITPATT_SP32) : r; + s = t < 0.0f ? -1 : s; + } + + *signp = s; + return r; +} + +_CLC_V_V_VP_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, lgamma_r, float, private, int) + +#ifdef cl_khr_fp64 +#pragma OPENCL EXTENSION cl_khr_fp64 : enable +// ==================================================== +// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. +// +// Developed at SunPro, a Sun Microsystems, Inc. business. +// Permission to use, copy, modify, and distribute this +// software is freely granted, provided that this notice +// is preserved. +// ==================================================== + +// lgamma_r(x, i) +// Reentrant version of the logarithm of the Gamma function +// with user provide pointer for the sign of Gamma(x). +// +// Method: +// 1. Argument Reduction for 0 < x <= 8 +// Since gamma(1+s)=s*gamma(s), for x in [0,8], we may +// reduce x to a number in [1.5,2.5] by +// lgamma(1+s) = log(s) + lgamma(s) +// for example, +// lgamma(7.3) = log(6.3) + lgamma(6.3) +// = log(6.3*5.3) + lgamma(5.3) +// = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) +// 2. Polynomial approximation of lgamma around its +// minimun ymin=1.461632144968362245 to maintain monotonicity. +// On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use +// Let z = x-ymin; +// lgamma(x) = -1.214862905358496078218 + z^2*poly(z) +// where +// poly(z) is a 14 degree polynomial. +// 2. Rational approximation in the primary interval [2,3] +// We use the following approximation: +// s = x-2.0; +// lgamma(x) = 0.5*s + s*P(s)/Q(s) +// with accuracy +// |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 +// Our algorithms are based on the following observation +// +// zeta(2)-1 2 zeta(3)-1 3 +// lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... +// 2 3 +// +// where Euler = 0.5771... is the Euler constant, which is very +// close to 0.5. +// +// 3. For x>=8, we have +// lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... +// (better formula: +// lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) +// Let z = 1/x, then we approximation +// f(z) = lgamma(x) - (x-0.5)(log(x)-1) +// by +// 3 5 11 +// w = w0 + w1*z + w2*z + w3*z + ... + w6*z +// where +// |w - f(z)| < 2**-58.74 +// +// 4. For negative x, since (G is gamma function) +// -x*G(-x)*G(x) = pi/sin(pi*x), +// we have +// G(x) = pi/(sin(pi*x)*(-x)*G(-x)) +// since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 +// Hence, for x<0, signgam = sign(sin(pi*x)) and +// lgamma(x) = log(|Gamma(x)|) +// = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); +// Note: one should avoid compute pi*(-x) directly in the +// computation of sin(pi*(-x)). +// +// 5. Special Cases +// lgamma(2+s) ~ s*(1-Euler) for tiny s +// lgamma(1)=lgamma(2)=0 +// lgamma(x) ~ -log(x) for tiny x +// lgamma(0) = lgamma(inf) = inf +// lgamma(-integer) = +-inf +// +#define pi 3.14159265358979311600e+00 /* 0x400921FB, 0x54442D18 */ + +#define a0 7.72156649015328655494e-02 /* 0x3FB3C467, 0xE37DB0C8 */ +#define a1 3.22467033424113591611e-01 /* 0x3FD4A34C, 0xC4A60FAD */ +#define a2 6.73523010531292681824e-02 /* 0x3FB13E00, 0x1A5562A7 */ +#define a3 2.05808084325167332806e-02 /* 0x3F951322, 0xAC92547B */ +#define a4 7.38555086081402883957e-03 /* 0x3F7E404F, 0xB68FEFE8 */ +#define a5 2.89051383673415629091e-03 /* 0x3F67ADD8, 0xCCB7926B */ +#define a6 1.19270763183362067845e-03 /* 0x3F538A94, 0x116F3F5D */ +#define a7 5.10069792153511336608e-04 /* 0x3F40B6C6, 0x89B99C00 */ +#define a8 2.20862790713908385557e-04 /* 0x3F2CF2EC, 0xED10E54D */ +#define a9 1.08011567247583939954e-04 /* 0x3F1C5088, 0x987DFB07 */ +#define a10 2.52144565451257326939e-05 /* 0x3EFA7074, 0x428CFA52 */ +#define a11 4.48640949618915160150e-05 /* 0x3F07858E, 0x90A45837 */ + +#define tc 1.46163214496836224576e+00 /* 0x3FF762D8, 0x6356BE3F */ +#define tf -1.21486290535849611461e-01 /* 0xBFBF19B9, 0xBCC38A42 */ +#define tt -3.63867699703950536541e-18 /* 0xBC50C7CA, 0xA48A971F */ + +#define t0 4.83836122723810047042e-01 /* 0x3FDEF72B, 0xC8EE38A2 */ +#define t1 -1.47587722994593911752e-01 /* 0xBFC2E427, 0x8DC6C509 */ +#define t2 6.46249402391333854778e-02 /* 0x3FB08B42, 0x94D5419B */ +#define t3 -3.27885410759859649565e-02 /* 0xBFA0C9A8, 0xDF35B713 */ +#define t4 1.79706750811820387126e-02 /* 0x3F9266E7, 0x970AF9EC */ +#define t5 -1.03142241298341437450e-02 /* 0xBF851F9F, 0xBA91EC6A */ +#define t6 6.10053870246291332635e-03 /* 0x3F78FCE0, 0xE370E344 */ +#define t7 -3.68452016781138256760e-03 /* 0xBF6E2EFF, 0xB3E914D7 */ +#define t8 2.25964780900612472250e-03 /* 0x3F6282D3, 0x2E15C915 */ +#define t9 -1.40346469989232843813e-03 /* 0xBF56FE8E, 0xBF2D1AF1 */ +#define t10 8.81081882437654011382e-04 /* 0x3F4CDF0C, 0xEF61A8E9 */ +#define t11 -5.38595305356740546715e-04 /* 0xBF41A610, 0x9C73E0EC */ +#define t12 3.15632070903625950361e-04 /* 0x3F34AF6D, 0x6C0EBBF7 */ +#define t13 -3.12754168375120860518e-04 /* 0xBF347F24, 0xECC38C38 */ +#define t14 3.35529192635519073543e-04 /* 0x3F35FD3E, 0xE8C2D3F4 */ + +#define u0 -7.72156649015328655494e-02 /* 0xBFB3C467, 0xE37DB0C8 */ +#define u1 6.32827064025093366517e-01 /* 0x3FE4401E, 0x8B005DFF */ +#define u2 1.45492250137234768737e+00 /* 0x3FF7475C, 0xD119BD6F */ +#define u3 9.77717527963372745603e-01 /* 0x3FEF4976, 0x44EA8450 */ +#define u4 2.28963728064692451092e-01 /* 0x3FCD4EAE, 0xF6010924 */ +#define u5 1.33810918536787660377e-02 /* 0x3F8B678B, 0xBF2BAB09 */ + +#define v1 2.45597793713041134822e+00 /* 0x4003A5D7, 0xC2BD619C */ +#define v2 2.12848976379893395361e+00 /* 0x40010725, 0xA42B18F5 */ +#define v3 7.69285150456672783825e-01 /* 0x3FE89DFB, 0xE45050AF */ +#define v4 1.04222645593369134254e-01 /* 0x3FBAAE55, 0xD6537C88 */ +#define v5 3.21709242282423911810e-03 /* 0x3F6A5ABB, 0x57D0CF61 */ + +#define s0 -7.72156649015328655494e-02 /* 0xBFB3C467, 0xE37DB0C8 */ +#define s1 2.14982415960608852501e-01 /* 0x3FCB848B, 0x36E20878 */ +#define s2 3.25778796408930981787e-01 /* 0x3FD4D98F, 0x4F139F59 */ +#define s3 1.46350472652464452805e-01 /* 0x3FC2BB9C, 0xBEE5F2F7 */ +#define s4 2.66422703033638609560e-02 /* 0x3F9B481C, 0x7E939961 */ +#define s5 1.84028451407337715652e-03 /* 0x3F5E26B6, 0x7368F239 */ +#define s6 3.19475326584100867617e-05 /* 0x3F00BFEC, 0xDD17E945 */ + +#define r1 1.39200533467621045958e+00 /* 0x3FF645A7, 0x62C4AB74 */ +#define r2 7.21935547567138069525e-01 /* 0x3FE71A18, 0x93D3DCDC */ +#define r3 1.71933865632803078993e-01 /* 0x3FC601ED, 0xCCFBDF27 */ +#define r4 1.86459191715652901344e-02 /* 0x3F9317EA, 0x742ED475 */ +#define r5 7.77942496381893596434e-04 /* 0x3F497DDA, 0xCA41A95B */ +#define r6 7.32668430744625636189e-06 /* 0x3EDEBAF7, 0xA5B38140 */ + +#define w0 4.18938533204672725052e-01 /* 0x3FDACFE3, 0x90C97D69 */ +#define w1 8.33333333333329678849e-02 /* 0x3FB55555, 0x5555553B */ +#define w2 -2.77777777728775536470e-03 /* 0xBF66C16C, 0x16B02E5C */ +#define w3 7.93650558643019558500e-04 /* 0x3F4A019F, 0x98CF38B6 */ +#define w4 -5.95187557450339963135e-04 /* 0xBF4380CB, 0x8C0FE741 */ +#define w5 8.36339918996282139126e-04 /* 0x3F4B67BA, 0x4CDAD5D1 */ +#define w6 -1.63092934096575273989e-03 /* 0xBF5AB89D, 0x0B9E43E4 */ + +_CLC_OVERLOAD _CLC_DEF double lgamma_r(double x, private int *ip) { + ulong ux = as_ulong(x); + ulong ax = ux & EXSIGNBIT_DP64; + double absx = as_double(ax); + + if (ax >= 0x7ff0000000000000UL) { + // +-Inf, NaN + *ip = 1; + return absx; + } + + if (absx < 0x1.0p-70) { + *ip = ax == ux ? 1 : -1; + return -log(absx); + } + + // Handle rest of range + double r; + + if (absx < 2.0) { + int i = 0; + double y = 2.0 - absx; + + int c = absx < 0x1.bb4c3p+0; + double t = absx - tc; + i = c ? 1 : i; + y = c ? t : y; + + c = absx < 0x1.3b4c4p+0; + t = absx - 1.0; + i = c ? 2 : i; + y = c ? t : y; + + c = absx <= 0x1.cccccp-1; + t = -log(absx); + r = c ? t : 0.0; + t = 1.0 - absx; + i = c ? 0 : i; + y = c ? t : y; + + c = absx < 0x1.76944p-1; + t = absx - (tc - 1.0); + i = c ? 1 : i; + y = c ? t : y; + + c = absx < 0x1.da661p-3; + i = c ? 2 : i; + y = c ? absx : y; + + double p, q; + + switch (i) { + case 0: + p = fma(y, fma(y, fma(y, fma(y, a11, a10), a9), a8), a7); + p = fma(y, fma(y, fma(y, fma(y, p, a6), a5), a4), a3); + p = fma(y, fma(y, fma(y, p, a2), a1), a0); + r = fma(y, p - 0.5, r); + break; + case 1: + p = fma(y, fma(y, fma(y, fma(y, t14, t13), t12), t11), t10); + p = fma(y, fma(y, fma(y, fma(y, fma(y, p, t9), t8), t7), t6), t5); + p = fma(y, fma(y, fma(y, fma(y, fma(y, p, t4), t3), t2), t1), t0); + p = fma(y*y, p, -tt); + r += (tf + p); + break; + case 2: + p = y * fma(y, fma(y, fma(y, fma(y, fma(y, u5, u4), u3), u2), u1), u0); + q = fma(y, fma(y, fma(y, fma(y, fma(y, v5, v4), v3), v2), v1), 1.0); + r += fma(-0.5, y, p / q); + } + } else if (absx < 8.0) { + int i = absx; + double y = absx - (double) i; + double p = y * fma(y, fma(y, fma(y, fma(y, fma(y, fma(y, s6, s5), s4), s3), s2), s1), s0); + double q = fma(y, fma(y, fma(y, fma(y, fma(y, fma(y, r6, r5), r4), r3), r2), r1), 1.0); + r = fma(0.5, y, p / q); + double z = 1.0; + // lgamma(1+s) = log(s) + lgamma(s) + double y6 = y + 6.0; + double y5 = y + 5.0; + double y4 = y + 4.0; + double y3 = y + 3.0; + double y2 = y + 2.0; + z *= i > 6 ? y6 : 1.0; + z *= i > 5 ? y5 : 1.0; + z *= i > 4 ? y4 : 1.0; + z *= i > 3 ? y3 : 1.0; + z *= i > 2 ? y2 : 1.0; + r += log(z); + } else { + double z = 1.0 / absx; + double z2 = z * z; + double w = fma(z, fma(z2, fma(z2, fma(z2, fma(z2, fma(z2, w6, w5), w4), w3), w2), w1), w0); + r = (absx - 0.5) * (log(absx) - 1.0) + w; + } + + if (x < 0.0) { + double t = sinpi(x); + r = log(pi / fabs(t * x)) - r; + r = t == 0.0 ? as_double(PINFBITPATT_DP64) : r; + *ip = t < 0.0 ? -1 : 1; + } else + *ip = 1; + + return r; +} + +_CLC_V_V_VP_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, lgamma_r, double, private, int) +#endif + + +#define __CLC_ADDRSPACE global +#define __CLC_BODY +#include +#undef __CLC_ADDRSPACE + +#define __CLC_ADDRSPACE local #define __CLC_BODY #include +#undef __CLC_ADDRSPACE diff --git a/libclc/generic/lib/math/lgamma_r.inc b/libclc/generic/lib/math/lgamma_r.inc index b4f73f6dc6b..316d4fa1539 100644 --- a/libclc/generic/lib/math/lgamma_r.inc +++ b/libclc/generic/lib/math/lgamma_r.inc @@ -21,480 +21,10 @@ * THE SOFTWARE. */ -#if __CLC_FPSIZE == 32 -#ifdef __CLC_SCALAR -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#define pi_f 3.1415927410e+00f /* 0x40490fdb */ - -#define a0_f 7.7215664089e-02f /* 0x3d9e233f */ -#define a1_f 3.2246702909e-01f /* 0x3ea51a66 */ -#define a2_f 6.7352302372e-02f /* 0x3d89f001 */ -#define a3_f 2.0580807701e-02f /* 0x3ca89915 */ -#define a4_f 7.3855509982e-03f /* 0x3bf2027e */ -#define a5_f 2.8905137442e-03f /* 0x3b3d6ec6 */ -#define a6_f 1.1927076848e-03f /* 0x3a9c54a1 */ -#define a7_f 5.1006977446e-04f /* 0x3a05b634 */ -#define a8_f 2.2086278477e-04f /* 0x39679767 */ -#define a9_f 1.0801156895e-04f /* 0x38e28445 */ -#define a10_f 2.5214456400e-05f /* 0x37d383a2 */ -#define a11_f 4.4864096708e-05f /* 0x383c2c75 */ - -#define tc_f 1.4616321325e+00f /* 0x3fbb16c3 */ - -#define tf_f -1.2148628384e-01f /* 0xbdf8cdcd */ -/* tt -(tail of tf) */ -#define tt_f 6.6971006518e-09f /* 0x31e61c52 */ - -#define t0_f 4.8383611441e-01f /* 0x3ef7b95e */ -#define t1_f -1.4758771658e-01f /* 0xbe17213c */ -#define t2_f 6.4624942839e-02f /* 0x3d845a15 */ -#define t3_f -3.2788541168e-02f /* 0xbd064d47 */ -#define t4_f 1.7970675603e-02f /* 0x3c93373d */ -#define t5_f -1.0314224288e-02f /* 0xbc28fcfe */ -#define t6_f 6.1005386524e-03f /* 0x3bc7e707 */ -#define t7_f -3.6845202558e-03f /* 0xbb7177fe */ -#define t8_f 2.2596477065e-03f /* 0x3b141699 */ -#define t9_f -1.4034647029e-03f /* 0xbab7f476 */ -#define t10_f 8.8108185446e-04f /* 0x3a66f867 */ -#define t11_f -5.3859531181e-04f /* 0xba0d3085 */ -#define t12_f 3.1563205994e-04f /* 0x39a57b6b */ -#define t13_f -3.1275415677e-04f /* 0xb9a3f927 */ -#define t14_f 3.3552918467e-04f /* 0x39afe9f7 */ - -#define u0_f -7.7215664089e-02f /* 0xbd9e233f */ -#define u1_f 6.3282704353e-01f /* 0x3f2200f4 */ -#define u2_f 1.4549225569e+00f /* 0x3fba3ae7 */ -#define u3_f 9.7771751881e-01f /* 0x3f7a4bb2 */ -#define u4_f 2.2896373272e-01f /* 0x3e6a7578 */ -#define u5_f 1.3381091878e-02f /* 0x3c5b3c5e */ - -#define v1_f 2.4559779167e+00f /* 0x401d2ebe */ -#define v2_f 2.1284897327e+00f /* 0x4008392d */ -#define v3_f 7.6928514242e-01f /* 0x3f44efdf */ -#define v4_f 1.0422264785e-01f /* 0x3dd572af */ -#define v5_f 3.2170924824e-03f /* 0x3b52d5db */ - -#define s0_f -7.7215664089e-02f /* 0xbd9e233f */ -#define s1_f 2.1498242021e-01f /* 0x3e5c245a */ -#define s2_f 3.2577878237e-01f /* 0x3ea6cc7a */ -#define s3_f 1.4635047317e-01f /* 0x3e15dce6 */ -#define s4_f 2.6642270386e-02f /* 0x3cda40e4 */ -#define s5_f 1.8402845599e-03f /* 0x3af135b4 */ -#define s6_f 3.1947532989e-05f /* 0x3805ff67 */ - -#define r1_f 1.3920053244e+00f /* 0x3fb22d3b */ -#define r2_f 7.2193557024e-01f /* 0x3f38d0c5 */ -#define r3_f 1.7193385959e-01f /* 0x3e300f6e */ -#define r4_f 1.8645919859e-02f /* 0x3c98bf54 */ -#define r5_f 7.7794247773e-04f /* 0x3a4beed6 */ -#define r6_f 7.3266842264e-06f /* 0x36f5d7bd */ - -#define w0_f 4.1893854737e-01f /* 0x3ed67f1d */ -#define w1_f 8.3333335817e-02f /* 0x3daaaaab */ -#define w2_f -2.7777778450e-03f /* 0xbb360b61 */ -#define w3_f 7.9365057172e-04f /* 0x3a500cfd */ -#define w4_f -5.9518753551e-04f /* 0xba1c065c */ -#define w5_f 8.3633989561e-04f /* 0x3a5b3dd2 */ -#define w6_f -1.6309292987e-03f /* 0xbad5c4e8 */ - -_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE lgamma_r(float x, private int *signp) { - int hx = as_int(x); - int ix = hx & 0x7fffffff; - float absx = as_float(ix); - - if (ix >= 0x7f800000) { - *signp = 1; - return x; - } - - if (absx < 0x1.0p-70f) { - *signp = hx < 0 ? -1 : 1; - return -log(absx); - } - float r; - - if (absx == 1.0f | absx == 2.0f) - r = 0.0f; - - else if (absx < 2.0f) { - float y = 2.0f - absx; - int i = 0; - - int c = absx < 0x1.bb4c30p+0f; - float yt = absx - tc_f; - y = c ? yt : y; - i = c ? 1 : i; - - c = absx < 0x1.3b4c40p+0f; - yt = absx - 1.0f; - y = c ? yt : y; - i = c ? 2 : i; - - r = -log(absx); - yt = 1.0f - absx; - c = absx <= 0x1.ccccccp-1f; - r = c ? r : 0.0f; - y = c ? yt : y; - i = c ? 0 : i; - - c = absx < 0x1.769440p-1f; - yt = absx - (tc_f - 1.0f); - y = c ? yt : y; - i = c ? 1 : i; - - c = absx < 0x1.da6610p-3f; - y = c ? absx : y; - i = c ? 2 : i; - - float z, w, p1, p2, p3, p; - switch (i) { - case 0: - z = y * y; - p1 = mad(z, mad(z, mad(z, mad(z, mad(z, a10_f, a8_f), a6_f), a4_f), a2_f), a0_f); - p2 = z * mad(z, mad(z, mad(z, mad(z, mad(z, a11_f, a9_f), a7_f), a5_f), a3_f), a1_f); - p = mad(y, p1, p2); - r += mad(y, -0.5f, p); - break; - case 1: - z = y * y; - w = z * y; - p1 = mad(w, mad(w, mad(w, mad(w, t12_f, t9_f), t6_f), t3_f), t0_f); - p2 = mad(w, mad(w, mad(w, mad(w, t13_f, t10_f), t7_f), t4_f), t1_f); - p3 = mad(w, mad(w, mad(w, mad(w, t14_f, t11_f), t8_f), t5_f), t2_f); - p = mad(z, p1, -mad(w, -mad(y, p3, p2), tt_f)); - r += tf_f + p; - break; - case 2: - p1 = y * mad(y, mad(y, mad(y, mad(y, mad(y, u5_f, u4_f), u3_f), u2_f), u1_f), u0_f); - p2 = mad(y, mad(y, mad(y, mad(y, mad(y, v5_f, v4_f), v3_f), v2_f), v1_f), 1.0f); - r += mad(y, -0.5f, MATH_DIVIDE(p1, p2)); - break; - } - } else if (absx < 8.0f) { - int i = (int) absx; - float y = absx - (float) i; - float p = y * mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, s6_f, s5_f), s4_f), s3_f), s2_f), s1_f), s0_f); - float q = mad(y, mad(y, mad(y, mad(y, mad(y, mad(y, r6_f, r5_f), r4_f), r3_f), r2_f), r1_f), 1.0f); - r = mad(y, 0.5f, MATH_DIVIDE(p, q)); - - float y6 = y + 6.0f; - float y5 = y + 5.0f; - float y4 = y + 4.0f; - float y3 = y + 3.0f; - float y2 = y + 2.0f; - - float z = 1.0f; - z *= i > 6 ? y6 : 1.0f; - z *= i > 5 ? y5 : 1.0f; - z *= i > 4 ? y4 : 1.0f; - z *= i > 3 ? y3 : 1.0f; - z *= i > 2 ? y2 : 1.0f; - - r += log(z); - } else if (absx < 0x1.0p+58f) { - float z = 1.0f / absx; - float y = z * z; - float w = mad(z, mad(y, mad(y, mad(y, mad(y, mad(y, w6_f, w5_f), w4_f), w3_f), w2_f), w1_f), w0_f); - r = mad(absx - 0.5f, log(absx) - 1.0f, w); - } else - // 2**58 <= x <= Inf - r = absx * (log(absx) - 1.0f); - - int s = 1; - - if (x < 0.0f) { - float t = sinpi(x); - r = log(pi_f / fabs(t * x)) - r; - r = t == 0.0f ? as_float(PINFBITPATT_SP32) : r; - s = t < 0.0f ? -1 : s; - } - - *signp = s; - return r; +_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE lgamma_r(__CLC_GENTYPE x, __CLC_ADDRSPACE __CLC_INTN *iptr) { + __CLC_INTN private_iptr; + __CLC_GENTYPE ret = lgamma_r(x, &private_iptr); + *iptr = private_iptr; + return ret; } - -_CLC_V_V_VP_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, lgamma_r, float, private, int) - -#endif -#endif - -#if __CLC_FPSIZE == 64 -#ifdef __CLC_SCALAR -// ==================================================== -// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. -// -// Developed at SunPro, a Sun Microsystems, Inc. business. -// Permission to use, copy, modify, and distribute this -// software is freely granted, provided that this notice -// is preserved. -// ==================================================== - -// lgamma_r(x, i) -// Reentrant version of the logarithm of the Gamma function -// with user provide pointer for the sign of Gamma(x). -// -// Method: -// 1. Argument Reduction for 0 < x <= 8 -// Since gamma(1+s)=s*gamma(s), for x in [0,8], we may -// reduce x to a number in [1.5,2.5] by -// lgamma(1+s) = log(s) + lgamma(s) -// for example, -// lgamma(7.3) = log(6.3) + lgamma(6.3) -// = log(6.3*5.3) + lgamma(5.3) -// = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) -// 2. Polynomial approximation of lgamma around its -// minimun ymin=1.461632144968362245 to maintain monotonicity. -// On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use -// Let z = x-ymin; -// lgamma(x) = -1.214862905358496078218 + z^2*poly(z) -// where -// poly(z) is a 14 degree polynomial. -// 2. Rational approximation in the primary interval [2,3] -// We use the following approximation: -// s = x-2.0; -// lgamma(x) = 0.5*s + s*P(s)/Q(s) -// with accuracy -// |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 -// Our algorithms are based on the following observation -// -// zeta(2)-1 2 zeta(3)-1 3 -// lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... -// 2 3 -// -// where Euler = 0.5771... is the Euler constant, which is very -// close to 0.5. -// -// 3. For x>=8, we have -// lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... -// (better formula: -// lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) -// Let z = 1/x, then we approximation -// f(z) = lgamma(x) - (x-0.5)(log(x)-1) -// by -// 3 5 11 -// w = w0 + w1*z + w2*z + w3*z + ... + w6*z -// where -// |w - f(z)| < 2**-58.74 -// -// 4. For negative x, since (G is gamma function) -// -x*G(-x)*G(x) = pi/sin(pi*x), -// we have -// G(x) = pi/(sin(pi*x)*(-x)*G(-x)) -// since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 -// Hence, for x<0, signgam = sign(sin(pi*x)) and -// lgamma(x) = log(|Gamma(x)|) -// = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); -// Note: one should avoid compute pi*(-x) directly in the -// computation of sin(pi*(-x)). -// -// 5. Special Cases -// lgamma(2+s) ~ s*(1-Euler) for tiny s -// lgamma(1)=lgamma(2)=0 -// lgamma(x) ~ -log(x) for tiny x -// lgamma(0) = lgamma(inf) = inf -// lgamma(-integer) = +-inf -// -#define pi 3.14159265358979311600e+00 /* 0x400921FB, 0x54442D18 */ - -#define a0 7.72156649015328655494e-02 /* 0x3FB3C467, 0xE37DB0C8 */ -#define a1 3.22467033424113591611e-01 /* 0x3FD4A34C, 0xC4A60FAD */ -#define a2 6.73523010531292681824e-02 /* 0x3FB13E00, 0x1A5562A7 */ -#define a3 2.05808084325167332806e-02 /* 0x3F951322, 0xAC92547B */ -#define a4 7.38555086081402883957e-03 /* 0x3F7E404F, 0xB68FEFE8 */ -#define a5 2.89051383673415629091e-03 /* 0x3F67ADD8, 0xCCB7926B */ -#define a6 1.19270763183362067845e-03 /* 0x3F538A94, 0x116F3F5D */ -#define a7 5.10069792153511336608e-04 /* 0x3F40B6C6, 0x89B99C00 */ -#define a8 2.20862790713908385557e-04 /* 0x3F2CF2EC, 0xED10E54D */ -#define a9 1.08011567247583939954e-04 /* 0x3F1C5088, 0x987DFB07 */ -#define a10 2.52144565451257326939e-05 /* 0x3EFA7074, 0x428CFA52 */ -#define a11 4.48640949618915160150e-05 /* 0x3F07858E, 0x90A45837 */ - -#define tc 1.46163214496836224576e+00 /* 0x3FF762D8, 0x6356BE3F */ -#define tf -1.21486290535849611461e-01 /* 0xBFBF19B9, 0xBCC38A42 */ -#define tt -3.63867699703950536541e-18 /* 0xBC50C7CA, 0xA48A971F */ - -#define t0 4.83836122723810047042e-01 /* 0x3FDEF72B, 0xC8EE38A2 */ -#define t1 -1.47587722994593911752e-01 /* 0xBFC2E427, 0x8DC6C509 */ -#define t2 6.46249402391333854778e-02 /* 0x3FB08B42, 0x94D5419B */ -#define t3 -3.27885410759859649565e-02 /* 0xBFA0C9A8, 0xDF35B713 */ -#define t4 1.79706750811820387126e-02 /* 0x3F9266E7, 0x970AF9EC */ -#define t5 -1.03142241298341437450e-02 /* 0xBF851F9F, 0xBA91EC6A */ -#define t6 6.10053870246291332635e-03 /* 0x3F78FCE0, 0xE370E344 */ -#define t7 -3.68452016781138256760e-03 /* 0xBF6E2EFF, 0xB3E914D7 */ -#define t8 2.25964780900612472250e-03 /* 0x3F6282D3, 0x2E15C915 */ -#define t9 -1.40346469989232843813e-03 /* 0xBF56FE8E, 0xBF2D1AF1 */ -#define t10 8.81081882437654011382e-04 /* 0x3F4CDF0C, 0xEF61A8E9 */ -#define t11 -5.38595305356740546715e-04 /* 0xBF41A610, 0x9C73E0EC */ -#define t12 3.15632070903625950361e-04 /* 0x3F34AF6D, 0x6C0EBBF7 */ -#define t13 -3.12754168375120860518e-04 /* 0xBF347F24, 0xECC38C38 */ -#define t14 3.35529192635519073543e-04 /* 0x3F35FD3E, 0xE8C2D3F4 */ - -#define u0 -7.72156649015328655494e-02 /* 0xBFB3C467, 0xE37DB0C8 */ -#define u1 6.32827064025093366517e-01 /* 0x3FE4401E, 0x8B005DFF */ -#define u2 1.45492250137234768737e+00 /* 0x3FF7475C, 0xD119BD6F */ -#define u3 9.77717527963372745603e-01 /* 0x3FEF4976, 0x44EA8450 */ -#define u4 2.28963728064692451092e-01 /* 0x3FCD4EAE, 0xF6010924 */ -#define u5 1.33810918536787660377e-02 /* 0x3F8B678B, 0xBF2BAB09 */ - -#define v1 2.45597793713041134822e+00 /* 0x4003A5D7, 0xC2BD619C */ -#define v2 2.12848976379893395361e+00 /* 0x40010725, 0xA42B18F5 */ -#define v3 7.69285150456672783825e-01 /* 0x3FE89DFB, 0xE45050AF */ -#define v4 1.04222645593369134254e-01 /* 0x3FBAAE55, 0xD6537C88 */ -#define v5 3.21709242282423911810e-03 /* 0x3F6A5ABB, 0x57D0CF61 */ - -#define s0 -7.72156649015328655494e-02 /* 0xBFB3C467, 0xE37DB0C8 */ -#define s1 2.14982415960608852501e-01 /* 0x3FCB848B, 0x36E20878 */ -#define s2 3.25778796408930981787e-01 /* 0x3FD4D98F, 0x4F139F59 */ -#define s3 1.46350472652464452805e-01 /* 0x3FC2BB9C, 0xBEE5F2F7 */ -#define s4 2.66422703033638609560e-02 /* 0x3F9B481C, 0x7E939961 */ -#define s5 1.84028451407337715652e-03 /* 0x3F5E26B6, 0x7368F239 */ -#define s6 3.19475326584100867617e-05 /* 0x3F00BFEC, 0xDD17E945 */ - -#define r1 1.39200533467621045958e+00 /* 0x3FF645A7, 0x62C4AB74 */ -#define r2 7.21935547567138069525e-01 /* 0x3FE71A18, 0x93D3DCDC */ -#define r3 1.71933865632803078993e-01 /* 0x3FC601ED, 0xCCFBDF27 */ -#define r4 1.86459191715652901344e-02 /* 0x3F9317EA, 0x742ED475 */ -#define r5 7.77942496381893596434e-04 /* 0x3F497DDA, 0xCA41A95B */ -#define r6 7.32668430744625636189e-06 /* 0x3EDEBAF7, 0xA5B38140 */ - -#define w0 4.18938533204672725052e-01 /* 0x3FDACFE3, 0x90C97D69 */ -#define w1 8.33333333333329678849e-02 /* 0x3FB55555, 0x5555553B */ -#define w2 -2.77777777728775536470e-03 /* 0xBF66C16C, 0x16B02E5C */ -#define w3 7.93650558643019558500e-04 /* 0x3F4A019F, 0x98CF38B6 */ -#define w4 -5.95187557450339963135e-04 /* 0xBF4380CB, 0x8C0FE741 */ -#define w5 8.36339918996282139126e-04 /* 0x3F4B67BA, 0x4CDAD5D1 */ -#define w6 -1.63092934096575273989e-03 /* 0xBF5AB89D, 0x0B9E43E4 */ - -_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE lgamma_r(__CLC_GENTYPE x, private __CLC_INTN *ip) { - ulong ux = as_ulong(x); - ulong ax = ux & EXSIGNBIT_DP64; - double absx = as_double(ax); - - if (ax >= 0x7ff0000000000000UL) { - // +-Inf, NaN - *ip = 1; - return absx; - } - - if (absx < 0x1.0p-70) { - *ip = ax == ux ? 1 : -1; - return -log(absx); - } - - // Handle rest of range - double r; - - if (absx < 2.0) { - int i = 0; - double y = 2.0 - absx; - - int c = absx < 0x1.bb4c3p+0; - double t = absx - tc; - i = c ? 1 : i; - y = c ? t : y; - - c = absx < 0x1.3b4c4p+0; - t = absx - 1.0; - i = c ? 2 : i; - y = c ? t : y; - - c = absx <= 0x1.cccccp-1; - t = -log(absx); - r = c ? t : 0.0; - t = 1.0 - absx; - i = c ? 0 : i; - y = c ? t : y; - - c = absx < 0x1.76944p-1; - t = absx - (tc - 1.0); - i = c ? 1 : i; - y = c ? t : y; - - c = absx < 0x1.da661p-3; - i = c ? 2 : i; - y = c ? absx : y; - - double p, q; - - switch (i) { - case 0: - p = fma(y, fma(y, fma(y, fma(y, a11, a10), a9), a8), a7); - p = fma(y, fma(y, fma(y, fma(y, p, a6), a5), a4), a3); - p = fma(y, fma(y, fma(y, p, a2), a1), a0); - r = fma(y, p - 0.5, r); - break; - case 1: - p = fma(y, fma(y, fma(y, fma(y, t14, t13), t12), t11), t10); - p = fma(y, fma(y, fma(y, fma(y, fma(y, p, t9), t8), t7), t6), t5); - p = fma(y, fma(y, fma(y, fma(y, fma(y, p, t4), t3), t2), t1), t0); - p = fma(y*y, p, -tt); - r += (tf + p); - break; - case 2: - p = y * fma(y, fma(y, fma(y, fma(y, fma(y, u5, u4), u3), u2), u1), u0); - q = fma(y, fma(y, fma(y, fma(y, fma(y, v5, v4), v3), v2), v1), 1.0); - r += fma(-0.5, y, p / q); - } - } else if (absx < 8.0) { - int i = absx; - double y = absx - (double) i; - double p = y * fma(y, fma(y, fma(y, fma(y, fma(y, fma(y, s6, s5), s4), s3), s2), s1), s0); - double q = fma(y, fma(y, fma(y, fma(y, fma(y, fma(y, r6, r5), r4), r3), r2), r1), 1.0); - r = fma(0.5, y, p / q); - double z = 1.0; - // lgamma(1+s) = log(s) + lgamma(s) - double y6 = y + 6.0; - double y5 = y + 5.0; - double y4 = y + 4.0; - double y3 = y + 3.0; - double y2 = y + 2.0; - z *= i > 6 ? y6 : 1.0; - z *= i > 5 ? y5 : 1.0; - z *= i > 4 ? y4 : 1.0; - z *= i > 3 ? y3 : 1.0; - z *= i > 2 ? y2 : 1.0; - r += log(z); - } else { - double z = 1.0 / absx; - double z2 = z * z; - double w = fma(z, fma(z2, fma(z2, fma(z2, fma(z2, fma(z2, w6, w5), w4), w3), w2), w1), w0); - r = (absx - 0.5) * (log(absx) - 1.0) + w; - } - - if (x < 0.0) { - double t = sinpi(x); - r = log(pi / fabs(t * x)) - r; - r = t == 0.0 ? as_double(PINFBITPATT_DP64) : r; - *ip = t < 0.0 ? -1 : 1; - } else - *ip = 1; - - return r; -} - -_CLC_V_V_VP_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, lgamma_r, double, private, int) -#endif -#endif - -#define __CLC_LGAMMA_R_DEF(addrspace) \ - _CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE lgamma_r(__CLC_GENTYPE x, addrspace __CLC_INTN *iptr) { \ - __CLC_INTN private_iptr; \ - __CLC_GENTYPE ret = lgamma_r(x, &private_iptr); \ - *iptr = private_iptr; \ - return ret; \ -} -__CLC_LGAMMA_R_DEF(local); -__CLC_LGAMMA_R_DEF(global); - -#undef __CLC_LGAMMA_R_DEF -- cgit v1.2.1