1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)e_lgamma_r.c 1.3 95/01/18 */ 3b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* 4b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ==================================================== 5b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 7b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Developed at SunSoft, a Sun Microsystems, Inc. business. 8b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Permission to use, copy, modify, and distribute this 9b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * software is freely granted, provided that this notice 10b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * is preserved. 11b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ==================================================== 12b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 13b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 14b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 15b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* __ieee754_lgamma_r(x, signgamp) 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Reentrant version of the logarithm of the Gamma function 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * with user provide pointer for the sign of Gamma(x). 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Method: 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1. Argument Reduction for 0 < x <= 8 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Since ieee_gamma(1+s)=s*ieee_gamma(s), for x in [0,8], we may 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * reduce x to a number in [1.5,2.5] by 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(1+s) = ieee_log(s) + ieee_lgamma(s) 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for example, 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(7.3) = ieee_log(6.3) + ieee_lgamma(6.3) 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = ieee_log(6.3*5.3) + ieee_lgamma(5.3) 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = ieee_log(6.3*5.3*4.3*3.3*2.3) + ieee_lgamma(2.3) 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2. Polynomial approximation of lgamma around its 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * minimun ymin=1.461632144968362245 to maintain monotonicity. 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Let z = x-ymin; 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * poly(z) is a 14 degree polynomial. 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2. Rational approximation in the primary interval [2,3] 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * We use the following approximation: 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * s = x-2.0; 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(x) = 0.5*s + s*P(s)/Q(s) 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * with accuracy 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * |P/Q - (ieee_lgamma(x)-0.5s)| < 2**-61.71 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Our algorithms are based on the following observation 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * zeta(2)-1 2 zeta(3)-1 3 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2 3 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where Euler = 0.5771... is the Euler constant, which is very 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * close to 0.5. 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3. For x>=8, we have 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(x)~(x-0.5)log(x)-x+0.5*ieee_log(2pi)+1/(12x)-1/(360x**3)+.... 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (better formula: 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_lgamma(x)~(x-0.5)*(ieee_log(x)-1)-.5*(ieee_log(2pi)-1) + ...) 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Let z = 1/x, then we approximation 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * f(z) = ieee_lgamma(x) - (x-0.5)(ieee_log(x)-1) 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * by 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3 5 11 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * w = w0 + w1*z + w2*z + w3*z + ... + w6*z 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * |w - f(z)| < 2**-58.74 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 4. For negative x, since (G is gamma function) 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * -x*G(-x)*G(x) = pi/ieee_sin(pi*x), 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * we have 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * G(x) = pi/(ieee_sin(pi*x)*(-x)*G(-x)) 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * since G(-x) is positive, sign(G(x)) = sign(ieee_sin(pi*x)) for x<0 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Hence, for x<0, signgam = sign(ieee_sin(pi*x)) and 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(x) = ieee_log(|Gamma(x)|) 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = ieee_log(pi/(|x*ieee_sin(pi*x)|)) - ieee_lgamma(-x); 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Note: one should avoid compute pi*(-x) directly in the 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * computation of ieee_sin(pi*(-x)). 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 5. Special Cases 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(2+s) ~ s*(1-Euler) for tiny s 75b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(1)=ieee_lgamma(2)=0 76b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(x) ~ -ieee_log(x) for tiny x 77b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(0) = ieee_lgamma(inf) = inf 78b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * lgamma(-integer) = +-inf 79b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 80b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 81b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 82b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 83b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 84b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 85b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double 86b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 87b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double 88b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 89b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttwo52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ 90b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecthalf= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 91b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectone = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 92b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectpi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 93b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ 94b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ 95b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ 96b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ 97b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ 98b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ 99b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ 100b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ 101b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ 102b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ 103b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ 104b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecta11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ 105b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ 106b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ 107b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* tt = -(tail of tf) */ 108b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ 109b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ 110b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ 111b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ 112b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ 113b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ 114b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ 115b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ 116b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ 117b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ 118b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ 119b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ 120b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ 121b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ 122b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ 123b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectt14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ 124b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectu0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ 125b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectu1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ 126b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectu2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ 127b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectu3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ 128b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectu4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ 129b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectu5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ 130b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectv1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ 131b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectv2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ 132b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectv3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ 133b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectv4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ 134b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectv5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ 135b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ 136b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ 137b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ 138b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ 139b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ 140b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ 141b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ 142b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ 143b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ 144b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ 145b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ 146b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ 147b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ 148b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectw0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ 149b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectw1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ 150b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectw2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ 151b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectw3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ 152b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectw4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ 153b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectw5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ 154b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectw6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ 155b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 156b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double zero= 0.00000000000000000000e+00; 157b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 158b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 159b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project static double sin_pi(double x) 160b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 161b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project static double sin_pi(x) 162b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x; 163b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 164b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 165b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double y,z; 166b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int n,ix; 167b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 168b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = 0x7fffffff&__HI(x); 169b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 170b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); 171b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = -x; /* x is assume negative */ 172b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 173b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* 174b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * argument reduction, make sure inexact flag not raised if input 175b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * is an integer 176b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 177b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = ieee_floor(y); 178b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(z!=y) { /* inexact anyway */ 179b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y *= 0.5; 180b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = 2.0*(y - ieee_floor(y)); /* y = |x| mod 2.0 */ 181b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project n = (int) (y*4.0); 182b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 183b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x43400000) { 184b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = zero; n = 0; /* y must be even */ 185b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 186b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x43300000) z = y+two52; /* exact */ 187b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project n = __LO(z)&1; /* lower word of z */ 188b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = n; 189b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project n<<= 2; 190b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 191b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 192b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project switch (n) { 193b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 0: y = __kernel_sin(pi*y,zero,0); break; 194b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 1: 195b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 2: y = __kernel_cos(pi*(0.5-y),zero); break; 196b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 3: 197b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 4: y = __kernel_sin(pi*(one-y),zero,0); break; 198b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 5: 199b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; 200b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project default: y = __kernel_sin(pi*(y-2.0),zero,0); break; 201b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 202b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return -y; 203b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 204b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 205b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 206b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 207b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_lgamma_r(double x, int *signgamp) 208b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 209b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_lgamma_r(x,signgamp) 210b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x; int *signgamp; 211b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 212b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 213b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double t,y,z,nadj,p,p1,p2,p3,q,r,w; 214b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int i,hx,lx,ix; 215b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 216b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx = __HI(x); 217b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project lx = __LO(x); 218b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 219b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* purge off +-inf, NaN, +-0, and negative arguments */ 220b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project *signgamp = 1; 221b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = hx&0x7fffffff; 222b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x7ff00000) return x*x; 223b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((ix|lx)==0) return one/zero; 224b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x3b900000) { /* |x|<2**-70, return -ieee_log(|x|) */ 225b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx<0) { 226b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project *signgamp = -1; 227b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return -__ieee754_log(-x); 228b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else return -__ieee754_log(x); 229b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 230b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx<0) { 231b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ 232b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return one/zero; 233b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t = sin_pi(x); 234b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(t==zero) return one/zero; /* -integer */ 235b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project nadj = __ieee754_log(pi/ieee_fabs(t*x)); 236b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(t<zero) *signgamp = -1; 237b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project x = -x; 238b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 239b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 240b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* purge off 1 and 2 */ 241b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0; 242b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* for x < 2.0 */ 243b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix<0x40000000) { 244b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<=0x3feccccc) { /* ieee_lgamma(x) = ieee_lgamma(x+1)-ieee_log(x) */ 245b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = -__ieee754_log(x); 246b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x3FE76944) {y = one-x; i= 0;} 247b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} 248b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else {y = x; i=2;} 249b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 250b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = zero; 251b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ 252b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ 253b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else {y=x-one;i=2;} 254b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 255b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project switch(i) { 256b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 0: 257b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = y*y; 258b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); 259b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); 260b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p = y*p1+p2; 261b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r += (p-0.5*y); break; 262b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 1: 263b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = y*y; 264b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = z*y; 265b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ 266b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); 267b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); 268b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p = z*p1-(tt-w*(p2+y*p3)); 269b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r += (tf + p); break; 270b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 2: 271b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); 272b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); 273b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r += (-0.5*y + p1/p2); 274b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 275b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 276b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix<0x40200000) { /* x < 8.0 */ 277b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project i = (int)x; 278b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t = zero; 279b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = x-(double)i; 280b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); 281b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); 282b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = half*y+p/q; 283b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = one; /* ieee_lgamma(1+s) = ieee_log(s) + ieee_lgamma(s) */ 284b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project switch(i) { 285b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 7: z *= (y+6.0); /* FALLTHRU */ 286b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 6: z *= (y+5.0); /* FALLTHRU */ 287b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 5: z *= (y+4.0); /* FALLTHRU */ 288b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 4: z *= (y+3.0); /* FALLTHRU */ 289b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 3: z *= (y+2.0); /* FALLTHRU */ 290b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r += __ieee754_log(z); break; 291b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 292b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* 8.0 <= x < 2**58 */ 293b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else if (ix < 0x43900000) { 294b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t = __ieee754_log(x); 295b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = one/x; 296b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = z*z; 297b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); 298b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = (x-half)*(t-one)+w; 299b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else 300b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* 2**58 <= x <= inf */ 301b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = x*(__ieee754_log(x)-one); 302b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx<0) r = nadj - r; 303b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return r; 304b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 305