1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)e_j1.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/* __ieee754_j1(x), __ieee754_y1(x) 15b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Bessel function of the first and second kinds of order zero. 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Method -- ieee_j1(x): 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1. For tiny x, we use ieee_j1(x) = x/2 - x^3/16 + x^5/384 - ... 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2. Reduce x to |x| since ieee_j1(x)=-ieee_j1(-x), and 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for x in (0,2) 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * j1(x) = x/2 + x*z*R0/S0, where z = x*x; 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for x in (2,inf) 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * j1(x) = ieee_sqrt(2/(pi*x))*(p1(x)*ieee_cos(x1)-q1(x)*ieee_sin(x1)) 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y1(x) = ieee_sqrt(2/(pi*x))*(p1(x)*ieee_sin(x1)+q1(x)*ieee_cos(x1)) 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where x1 = x-3*pi/4. It is better to compute ieee_sin(x1),cos(x1) 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * as follow: 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * cos(x1) = ieee_cos(x)cos(3pi/4)+ieee_sin(x)sin(3pi/4) 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = 1/ieee_sqrt(2) * (ieee_sin(x) - ieee_cos(x)) 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * sin(x1) = ieee_sin(x)cos(3pi/4)-ieee_cos(x)sin(3pi/4) 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = -1/ieee_sqrt(2) * (ieee_sin(x) + ieee_cos(x)) 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (To avoid cancellation, use 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * sin(x) +- ieee_cos(x) = -ieee_cos(2x)/(ieee_sin(x) -+ ieee_cos(x)) 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * to compute the worse one.) 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3 Special cases 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * j1(nan)= nan 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * j1(0) = 0 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * j1(inf) = 0 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Method -- ieee_y1(x): 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1. screen out x<=0 cases: ieee_y1(0)=-inf, ieee_y1(x<0)=NaN 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2. For x<2. 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Since 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y1(x) = 2/pi*(ieee_j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * therefore ieee_y1(x)-2/pi*ieee_j1(x)*ln(x)-1/x is an odd function. 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * We use the following function to approximate y1, 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y1(x) = x*U(z)/V(z) + (2/pi)*(ieee_j1(x)*ln(x)-1/x), z= x^2 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where for x in [0,2] (abs err less than 2**-65.89) 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Note: For tiny x, 1/x dominate y1 and hence 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3. For x>=2. 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y1(x) = ieee_sqrt(2/(pi*x))*(p1(x)*ieee_sin(x1)+q1(x)*ieee_cos(x1)) 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where x1 = x-3*pi/4. It is better to compute ieee_sin(x1),cos(x1) 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * by method mentioned above. 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double pone(double), qone(double); 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double pone(), qone(); 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecthuge = 1e300, 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectone = 1.0, 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectinvsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 75b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 76b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* R0/S0 on [0,2] */ 77b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ 78b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ 79b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ 80b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectr03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ 81b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ 82b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ 83b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ 84b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ 85b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projects05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ 86b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 87b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double zero = 0.0; 88b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 89b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 90b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_j1(double x) 91b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 92b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_j1(x) 93b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x; 94b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 95b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 96b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double z, s,c,ss,cc,r,u,v,y; 97b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int hx,ix; 98b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 99b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx = __HI(x); 100b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = hx&0x7fffffff; 101b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x7ff00000) return one/x; 102b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y = ieee_fabs(x); 103b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix >= 0x40000000) { /* |x| >= 2.0 */ 104b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project s = ieee_sin(y); 105b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project c = ieee_cos(y); 106b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ss = -s-c; 107b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project cc = s-c; 108b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x7fe00000) { /* make sure y+y not overflow */ 109b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = ieee_cos(y+y); 110b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if ((s*c)>zero) cc = z/ss; 111b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else ss = z/cc; 112b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 113b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* 114b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_j1(x) = 1/ieee_sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / ieee_sqrt(x) 115b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_y1(x) = 1/ieee_sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / ieee_sqrt(x) 116b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 117b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>0x48000000) z = (invsqrtpi*cc)/ieee_sqrt(y); 118b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else { 119b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project u = pone(y); v = qone(y); 120b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = invsqrtpi*(u*cc-v*ss)/ieee_sqrt(y); 121b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 122b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx<0) return -z; 123b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else return z; 124b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 125b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x3e400000) { /* |x|<2**-27 */ 126b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ 127b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 128b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = x*x; 129b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = z*(r00+z*(r01+z*(r02+z*r03))); 130b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); 131b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r *= x; 132b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return(x*0.5+r/s); 133b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 134b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 135b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 136b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double U0[5] = { 137b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 138b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double U0[5] = { 139b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 140b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ 141b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ 142b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ 143b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ 144b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ 145b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 146b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 147b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double V0[5] = { 148b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 149b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double V0[5] = { 150b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 151b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ 152b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ 153b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ 154b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ 155b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ 156b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 157b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 158b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 159b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_y1(double x) 160b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 161b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_y1(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 z, s,c,ss,cc,u,v; 166b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int hx,ix,lx; 167b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 168b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx = __HI(x); 169b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = 0x7fffffff&hx; 170b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project lx = __LO(x); 171b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ 172b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x7ff00000) return one/(x+x*x); 173b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((ix|lx)==0) return -one/zero; 174b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx<0) return zero/zero; 175b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix >= 0x40000000) { /* |x| >= 2.0 */ 176b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project s = ieee_sin(x); 177b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project c = ieee_cos(x); 178b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ss = -s-c; 179b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project cc = s-c; 180b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x7fe00000) { /* make sure x+x not overflow */ 181b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = ieee_cos(x+x); 182b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if ((s*c)>zero) cc = z/ss; 183b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else ss = z/cc; 184b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 185b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* ieee_y1(x) = ieee_sqrt(2/(pi*x))*(p1(x)*ieee_sin(x0)+q1(x)*ieee_cos(x0)) 186b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where x0 = x-3pi/4 187b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Better formula: 188b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_cos(x0) = ieee_cos(x)cos(3pi/4)+ieee_sin(x)sin(3pi/4) 189b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = 1/ieee_sqrt(2) * (ieee_sin(x) - ieee_cos(x)) 190b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_sin(x0) = ieee_sin(x)cos(3pi/4)-ieee_cos(x)sin(3pi/4) 191b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = -1/ieee_sqrt(2) * (ieee_cos(x) + ieee_sin(x)) 192b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * To avoid cancellation, use 193b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_sin(x) +- ieee_cos(x) = -ieee_cos(2x)/(ieee_sin(x) -+ ieee_cos(x)) 194b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * to compute the worse one. 195b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 196b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>0x48000000) z = (invsqrtpi*ss)/ieee_sqrt(x); 197b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else { 198b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project u = pone(x); v = qone(x); 199b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = invsqrtpi*(u*ss+v*cc)/ieee_sqrt(x); 200b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 201b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return z; 202b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 203b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<=0x3c900000) { /* x < 2**-54 */ 204b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return(-tpi/x); 205b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 206b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = x*x; 207b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); 208b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); 209b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); 210b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 211b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 212b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* For x >= 8, the asymptotic expansions of pone is 213b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. 214b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * We approximate pone by 215b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * pone(x) = 1 + (R/S) 216b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 217b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * S = 1 + ps0*s^2 + ... + ps4*s^10 218b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * and 219b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * | pone(x)-1-R/S | <= 2 ** ( -60.06) 220b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 221b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 222b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 223b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 224b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 225b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 226b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 227b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 228b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ 229b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ 230b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ 231b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ 232b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ 233b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 234b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 235b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double ps8[5] = { 236b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 237b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double ps8[5] = { 238b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 239b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ 240b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ 241b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ 242b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ 243b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ 244b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 245b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 246b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 247b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 248b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 249b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 250b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 251b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ 252b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ 253b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ 254b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ 255b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ 256b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ 257b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 258b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 259b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double ps5[5] = { 260b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 261b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double ps5[5] = { 262b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 263b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ 264b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ 265b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ 266b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ 267b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ 268b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 269b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 270b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 271b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double pr3[6] = { 272b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 273b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 274b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 275b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ 276b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ 277b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ 278b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ 279b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ 280b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ 281b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 282b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 283b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double ps3[5] = { 284b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 285b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double ps3[5] = { 286b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 287b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ 288b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ 289b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ 290b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ 291b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ 292b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 293b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 294b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 295b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 296b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 297b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 298b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 299b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ 300b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ 301b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ 302b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ 303b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ 304b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ 305b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 306b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 307b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double ps2[5] = { 308b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 309b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double ps2[5] = { 310b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 311b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ 312b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ 313b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ 314b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ 315b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ 316b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 317b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 318b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 319b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project static double pone(double x) 320b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 321b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project static double pone(x) 322b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x; 323b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 324b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 325b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 326b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project const double *p,*q; 327b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 328b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double *p,*q; 329b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 330b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double z,r,s; 331b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int ix; 332b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = 0x7fffffff&__HI(x); 333b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x40200000) {p = pr8; q= ps8;} 334b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix>=0x40122E8B){p = pr5; q= ps5;} 335b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix>=0x4006DB6D){p = pr3; q= ps3;} 336b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix>=0x40000000){p = pr2; q= ps2;} 337b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = one/(x*x); 338b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 339b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 340b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return one+ r/s; 341b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 342b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 343b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 344b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* For x >= 8, the asymptotic expansions of qone is 345b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. 346b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * We approximate pone by 347b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * qone(x) = s*(0.375 + (R/S)) 348b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 349b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * S = 1 + qs1*s^2 + ... + qs6*s^12 350b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * and 351b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) 352b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 353b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 354b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 355b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 356b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 357b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 358b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 359b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 360b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ 361b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ 362b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ 363b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ 364b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ 365b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 366b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 367b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double qs8[6] = { 368b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 369b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double qs8[6] = { 370b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 371b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ 372b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ 373b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ 374b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ 375b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ 376b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ 377b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 378b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 379b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 380b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 381b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 382b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 383b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 384b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ 385b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ 386b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ 387b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ 388b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ 389b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ 390b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 391b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 392b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double qs5[6] = { 393b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 394b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double qs5[6] = { 395b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 396b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ 397b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ 398b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ 399b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ 400b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ 401b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ 402b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 403b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 404b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 405b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double qr3[6] = { 406b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 407b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 408b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 409b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ 410b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ 411b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ 412b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ 413b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ 414b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ 415b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 416b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 417b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double qs3[6] = { 418b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 419b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double qs3[6] = { 420b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 421b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ 422b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ 423b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ 424b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ 425b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ 426b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ 427b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 428b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 429b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 430b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 431b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 432b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 433b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 434b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ 435b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ 436b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ 437b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ 438b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ 439b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ 440b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 441b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 442b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double qs2[6] = { 443b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 444b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double qs2[6] = { 445b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 446b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ 447b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ 448b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ 449b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ 450b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ 451b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ 452b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 453b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 454b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 455b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project static double qone(double x) 456b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 457b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project static double qone(x) 458b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x; 459b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 460b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 461b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 462b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project const double *p,*q; 463b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 464b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double *p,*q; 465b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 466b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double s,r,z; 467b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int ix; 468b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = 0x7fffffff&__HI(x); 469b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x40200000) {p = qr8; q= qs8;} 470b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix>=0x40122E8B){p = qr5; q= qs5;} 471b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix>=0x4006DB6D){p = qr3; q= qs3;} 472b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(ix>=0x40000000){p = qr2; q= qs2;} 473b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = one/(x*x); 474b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 475b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 476b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return (.375 + r/s)/x; 477b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 478