1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)e_jn.c 1.4 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_jn(n, x), __ieee754_yn(n, x) 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * floating point Bessel's function of the 1st and 2nd kind 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * of order n 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Special cases: 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y0(0)=ieee_y1(0)=ieee_yn(n,0) = -inf with division by zero signal; 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y0(-ve)=ieee_y1(-ve)=ieee_yn(n,-ve) are NaN with invalid signal. 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Note 2. About ieee_jn(n,x), ieee_yn(n,x) 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * For n=0, ieee_j0(x) is called, 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for n=1, ieee_j1(x) is called, 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for n<x, forward recursion us used starting 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * from values of ieee_j0(x) and ieee_j1(x). 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for n>x, a continued fraction approximation to 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * j(n,x)/j(n-1,x) is evaluated and then backward 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * recursion is used starting from a supposed value 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for j(n,x). The resulting value of j(0,x) is 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * compared with the actual value to correct the 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * supposed value of j(n,x). 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * yn(n,x) is similar in all respects, except 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * that forward recursion is used for all 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * values of n>1. 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectinvsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttwo = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectone = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double zero = 0.00000000000000000000e+00; 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_jn(int n, double x) 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_jn(n,x) 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int n; double x; 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int i,hx,ix,lx, sgn; 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double a, b, temp, di; 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double z, w; 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Thus, J(-n,x) = J(n,-x) 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx = __HI(x); 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = 0x7fffffff&hx; 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project lx = __LO(x); 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* if J(n,NaN) is NaN */ 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x; 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(n<0){ 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project n = -n; 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project x = -x; 75b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx ^= 0x80000000; 76b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 77b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(n==0) return(__ieee754_j0(x)); 78b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(n==1) return(__ieee754_j1(x)); 79b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ 80b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project x = ieee_fabs(x); 81b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ 82b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = zero; 83b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if((double)n<=x) { 84b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ 85b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x52D00000) { /* x > 2**302 */ 86b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* (x >> n**2) 87b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Jn(x) = ieee_cos(x-(2n+1)*pi/4)*ieee_sqrt(2/x*pi) 88b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Yn(x) = ieee_sin(x-(2n+1)*pi/4)*ieee_sqrt(2/x*pi) 89b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Let s=ieee_sin(x), c=ieee_cos(x), 90b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * xn=x-(2n+1)*pi/4, sqt2 = ieee_sqrt(2),then 91b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 92b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * n sin(xn)*sqt2 cos(xn)*sqt2 93b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ---------------------------------- 94b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 0 s-c c+s 95b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 -s-c -c+s 96b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2 -s+c -c-s 97b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3 s+c c-s 98b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 99b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project switch(n&3) { 100b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 0: temp = ieee_cos(x)+ieee_sin(x); break; 101b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 1: temp = -ieee_cos(x)+ieee_sin(x); break; 102b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 2: temp = -ieee_cos(x)-ieee_sin(x); break; 103b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 3: temp = ieee_cos(x)-ieee_sin(x); break; 104b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 105b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = invsqrtpi*temp/ieee_sqrt(x); 106b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 107b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = __ieee754_j0(x); 108b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = __ieee754_j1(x); 109b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=1;i<n;i++){ 110b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project temp = b; 111b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = b*((double)(i+i)/x) - a; /* avoid underflow */ 112b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = temp; 113b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 114b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 115b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 116b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x3e100000) { /* x < 2**-29 */ 117b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* x is tiny, return the first Taylor expansion of J(n,x) 118b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * J(n,x) = 1/n!*(x/2)^n - ... 119b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 120b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(n>33) /* underflow */ 121b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = zero; 122b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else { 123b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project temp = x*0.5; b = temp; 124b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (a=one,i=2;i<=n;i++) { 125b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a *= (double)i; /* a = n! */ 126b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b *= temp; /* b = (x/2)^n */ 127b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 128b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = b/a; 129b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 130b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 131b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* use backward recurrence */ 132b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* x x^2 x^2 133b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * J(n,x)/J(n-1,x) = ---- ------ ------ ..... 134b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2n - 2(n+1) - 2(n+2) 135b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 136b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 1 1 137b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (for large x) = ---- ------ ------ ..... 138b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2n 2(n+1) 2(n+2) 139b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * -- - ------ - ------ - 140b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * x x x 141b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 142b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Let w = 2n/x and h=2/x, then the above quotient 143b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * is equal to the continued fraction: 144b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 145b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = ----------------------- 146b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 147b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * w - ----------------- 148b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 149b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * w+h - --------- 150b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * w+2h - ... 151b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 152b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * To determine how many terms needed, let 153b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Q(0) = w, Q(1) = w(w+h) - 1, 154b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), 155b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * When Q(k) > 1e4 good for single 156b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * When Q(k) > 1e9 good for double 157b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * When Q(k) > 1e17 good for quadruple 158b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 159b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* determine k */ 160b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double t,v; 161b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double q0,q1,h,tmp; int k,m; 162b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = (n+n)/(double)x; h = 2.0/(double)x; 163b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q0 = w; z = w+h; q1 = w*z - 1.0; k=1; 164b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project while(q1<1.0e9) { 165b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project k += 1; z += h; 166b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project tmp = z*q1 - q0; 167b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q0 = q1; 168b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q1 = tmp; 169b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 170b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project m = n+n; 171b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); 172b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = t; 173b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = one; 174b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* estimate ieee_log((2/x)^n*n!) = n*ieee_log(2/x)+n*ln(n) 175b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Hence, if n*(ieee_log(2n/x)) > ... 176b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * single 8.8722839355e+01 177b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * double 7.09782712893383973096e+02 178b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * long double 1.1356523406294143949491931077970765006170e+04 179b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * then recurrent value may overflow and the result is 180b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * likely underflow to zero 181b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 182b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project tmp = n; 183b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project v = two/x; 184b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project tmp = tmp*__ieee754_log(ieee_fabs(v*tmp)); 185b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(tmp<7.09782712893383973096e+02) { 186b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=n-1,di=(double)(i+i);i>0;i--){ 187b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project temp = b; 188b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b *= di; 189b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = b/x - a; 190b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = temp; 191b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project di -= two; 192b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 193b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 194b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=n-1,di=(double)(i+i);i>0;i--){ 195b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project temp = b; 196b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b *= di; 197b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = b/x - a; 198b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = temp; 199b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project di -= two; 200b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* scale b to avoid spurious overflow */ 201b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(b>1e100) { 202b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a /= b; 203b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project t /= b; 204b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = one; 205b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 206b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 207b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 208b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = (t*__ieee754_j0(x)/b); 209b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 210b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 211b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(sgn==1) return -b; else return b; 212b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 213b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 214b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 215b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_yn(int n, double x) 216b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 217b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_yn(n,x) 218b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int n; double x; 219b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 220b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 221b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int i,hx,ix,lx; 222b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int sign; 223b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double a, b, temp; 224b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 225b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx = __HI(x); 226b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = 0x7fffffff&hx; 227b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project lx = __LO(x); 228b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* if Y(n,NaN) is NaN */ 229b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x; 230b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if((ix|lx)==0) return -one/zero; 231b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx<0) return zero/zero; 232b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project sign = 1; 233b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(n<0){ 234b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project n = -n; 235b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project sign = 1 - ((n&1)<<1); 236b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 237b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(n==0) return(__ieee754_y0(x)); 238b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(n==1) return(sign*__ieee754_y1(x)); 239b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix==0x7ff00000) return zero; 240b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x52D00000) { /* x > 2**302 */ 241b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* (x >> n**2) 242b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Jn(x) = ieee_cos(x-(2n+1)*pi/4)*ieee_sqrt(2/x*pi) 243b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Yn(x) = ieee_sin(x-(2n+1)*pi/4)*ieee_sqrt(2/x*pi) 244b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Let s=ieee_sin(x), c=ieee_cos(x), 245b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * xn=x-(2n+1)*pi/4, sqt2 = ieee_sqrt(2),then 246b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 247b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * n sin(xn)*sqt2 cos(xn)*sqt2 248b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ---------------------------------- 249b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 0 s-c c+s 250b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 -s-c -c+s 251b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2 -s+c -c-s 252b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3 s+c c-s 253b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 254b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project switch(n&3) { 255b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 0: temp = ieee_sin(x)-ieee_cos(x); break; 256b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 1: temp = -ieee_sin(x)-ieee_cos(x); break; 257b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 2: temp = -ieee_sin(x)+ieee_cos(x); break; 258b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 3: temp = ieee_sin(x)+ieee_cos(x); break; 259b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 260b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = invsqrtpi*temp/ieee_sqrt(x); 261b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 262b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = __ieee754_y0(x); 263b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = __ieee754_y1(x); 264b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* quit if b is -inf */ 265b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=1;i<n&&(__HI(b) != 0xfff00000);i++){ 266b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project temp = b; 267b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project b = ((double)(i+i)/x)*b - a; 268b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = temp; 269b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 270b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 271b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(sign>0) return b; else return -b; 272b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 273