1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)k_rem_pio2.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 * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * double x[],y[]; int e0,nx,prec; int ipio2[]; 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * __kernel_rem_pio2 return the last three digits of N with 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y = x - N*pi/2 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * so that |y| < pi/2. 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * The method is to compute the integer (mod 8) and fraction parts of 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (2/pi)*x without doing the full multiplication. In general we 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * skip the part of the product that are known to be a huge integer ( 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * more accurately, = 0 mod 8 ). Thus the number of operations are 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * independent of the exponent of the input. 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * (2/pi) is represented by an array of 24-bit integers in ipio2[]. 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Input parameters: 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * x[] The input value (must be positive) is broken into nx 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * pieces of 24-bit integers in double precision format. 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * x[i] will be the i-th 24 bit of x. The scaled exponent 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * match x's up to 24 bits. 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Example of breaking a double positive z into x[0]+x[1]+x[2]: 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * e0 = ieee_ilogb(z)-23 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * z = ieee_scalbn(z,-e0) 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for i = 0,1,2 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * x[i] = ieee_floor(z) 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * z = (z-x[i])*2**24 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * y[] ouput result in an array of double precision numbers. 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * The dimension of y[] is: 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 24-bit precision 1 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 53-bit precision 2 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 64-bit precision 2 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 113-bit precision 3 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * The actual value is the sum of them. Thus for 113-bit 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * precison, one may have to do something like: 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * long double t,w,r_head, r_tail; 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * t = (long double)y[2] + (long double)y[1]; 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * w = (long double)y[0]; 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * r_head = t+w; 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * r_tail = w - (r_head - t); 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * e0 The exponent of x[0] 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * nx dimension of x[] 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * prec an integer indicating the precision: 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 0 24 bits (single) 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1 53 bits (double) 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2 64 bits (extended) 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3 113 bits (quad) 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ipio2[] 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * integer array, contains the (24*i)-th to (24*i+23)-th 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * bit of 2/pi after binary point. The corresponding 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * floating value is 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 75b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ipio2[i] * 2^(-24(i+1)). 76b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 77b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * External function: 78b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * double ieee_scalbn(), ieee_floor(); 79b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 80b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 81b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Here is the description of some local variables: 82b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 83b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * jk jk+1 is the initial number of terms of ipio2[] needed 84b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * in the computation. The recommended value is 2,3,4, 85b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 6 for single, double, extended,and quad. 86b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 87b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * jz local integer variable indicating the number of 88b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * terms of ipio2[] used. 89b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 90b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * jx nx - 1 91b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 92b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * jv index for pointing to the suitable ipio2[] for the 93b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * computation. In general, we want 94b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 95b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * is an integer. Thus 96b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * e0-3-24*jv >= 0 or (e0-3)/24 >= jv 97b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Hence jv = max(0,(e0-3)/24). 98b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 99b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. 100b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 101b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * q[] double array with integral value, representing the 102b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 24-bits chunk of the product of x and 2/pi. 103b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 104b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * q0 the corresponding exponent of q[0]. Note that the 105b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * exponent for q[i] would be q0-24*i. 106b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 107b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * PIo2[] double precision array, obtained by cutting pi/2 108b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * into 24 bits chunks. 109b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 110b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * f[] ipio2[] in floating point 111b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 112b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * iq[] integer array by breaking up q[] in 24-bits chunk. 113b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 114b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] 115b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 116b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ih integer. If >0 it indicates q[] is >= 0.5, hence 117b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * it also indicates the *sign* of the result. 118b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 119b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 120b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 121b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 122b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* 123b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Constants: 124b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * The hexadecimal values are the intended ones for the following 125b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * constants. The decimal values may be used, provided that the 126b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * compiler will convert from decimal to binary accurately enough 127b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * to produce the hexadecimal values shown. 128b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 129b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 130b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 131b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 132b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 133b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const int init_jk[] = {2,3,4,6}; /* initial value for jk */ 134b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 135b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic int init_jk[] = {2,3,4,6}; 136b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 137b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 138b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 139b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double PIo2[] = { 140b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 141b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double PIo2[] = { 142b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 143b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ 144b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ 145b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ 146b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ 147b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ 148b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ 149b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ 150b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ 151b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project}; 152b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 153b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 154b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double 155b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 156b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double 157b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 158b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectzero = 0.0, 159b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectone = 1.0, 160b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 161b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projecttwon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ 162b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 163b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 164b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) 165b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 166b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) 167b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x[], y[]; int e0,nx,prec; int ipio2[]; 168b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 169b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 170b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 171b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double z,fw,f[20],fq[20],q[20]; 172b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 173b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* initialize jk*/ 174b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project jk = init_jk[prec]; 175b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project jp = jk; 176b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 177b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* determine jx,jv,q0, note that 3>q0 */ 178b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project jx = nx-1; 179b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project jv = (e0-3)/24; if(jv<0) jv=0; 180b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q0 = e0-24*(jv+1); 181b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 182b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 183b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project j = jv-jx; m = jx+jk; 184b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; 185b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 186b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* compute q[0],q[1],...q[jk] */ 187b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (i=0;i<=jk;i++) { 188b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 189b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 190b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 191b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project jz = jk; 192b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectrecompute: 193b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* distill q[] into iq[] reversingly */ 194b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 195b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fw = (double)((int)(twon24* z)); 196b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project iq[i] = (int)(z-two24*fw); 197b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = q[j-1]+fw; 198b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 199b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 200b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* compute n */ 201b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = ieee_scalbn(z,q0); /* actual value of z */ 202b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z -= 8.0*ieee_floor(z*0.125); /* trim off integer >= 8 */ 203b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project n = (int) z; 204b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z -= (double)n; 205b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ih = 0; 206b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(q0>0) { /* need iq[jz-1] to determine n */ 207b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project i = (iq[jz-1]>>(24-q0)); n += i; 208b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project iq[jz-1] -= i<<(24-q0); 209b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ih = iq[jz-1]>>(23-q0); 210b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 211b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(q0==0) ih = iq[jz-1]>>23; 212b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else if(z>=0.5) ih=2; 213b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 214b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ih>0) { /* q > 0.5 */ 215b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project n += 1; carry = 0; 216b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=0;i<jz ;i++) { /* compute 1-q */ 217b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project j = iq[i]; 218b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(carry==0) { 219b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(j!=0) { 220b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project carry = 1; iq[i] = 0x1000000- j; 221b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 222b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else iq[i] = 0xffffff - j; 223b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 224b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(q0>0) { /* rare case: chance is 1 in 12 */ 225b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project switch(q0) { 226b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 1: 227b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project iq[jz-1] &= 0x7fffff; break; 228b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 2: 229b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project iq[jz-1] &= 0x3fffff; break; 230b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 231b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 232b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ih==2) { 233b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = one - z; 234b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(carry!=0) z -= ieee_scalbn(one,q0); 235b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 236b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 237b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 238b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* check if recomputation is needed */ 239b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(z==zero) { 240b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project j = 0; 241b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (i=jz-1;i>=jk;i--) j |= iq[i]; 242b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(j==0) { /* need recomputation */ 243b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 244b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 245b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 246b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project f[jx+i] = (double) ipio2[jv+i]; 247b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 248b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q[i] = fw; 249b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 250b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project jz += k; 251b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project goto recompute; 252b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 253b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 254b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 255b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* chop off zero terms */ 256b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(z==0.0) { 257b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project jz -= 1; q0 -= 24; 258b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project while(iq[jz]==0) { jz--; q0-=24;} 259b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { /* break z into 24-bit if necessary */ 260b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = ieee_scalbn(z,-q0); 261b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(z>=two24) { 262b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fw = (double)((int)(twon24*z)); 263b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project iq[jz] = (int)(z-two24*fw); 264b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project jz += 1; q0 += 24; 265b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project iq[jz] = (int) fw; 266b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else iq[jz] = (int) z ; 267b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 268b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 269b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* convert integer "bit" chunk to floating-point value */ 270b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fw = ieee_scalbn(one,q0); 271b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=jz;i>=0;i--) { 272b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q[i] = fw*(double)iq[i]; fw*=twon24; 273b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 274b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 275b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* compute PIo2[0,...,jp]*q[jz,...,0] */ 276b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(i=jz;i>=0;i--) { 277b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 278b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fq[jz-i] = fw; 279b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 280b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 281b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project /* compress fq[] into y[] */ 282b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project switch(prec) { 283b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 0: 284b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fw = 0.0; 285b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (i=jz;i>=0;i--) fw += fq[i]; 286b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y[0] = (ih==0)? fw: -fw; 287b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project break; 288b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 1: 289b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 2: 290b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fw = 0.0; 291b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (i=jz;i>=0;i--) fw += fq[i]; 292b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y[0] = (ih==0)? fw: -fw; 293b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fw = fq[0]-fw; 294b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (i=1;i<=jz;i++) fw += fq[i]; 295b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y[1] = (ih==0)? fw: -fw; 296b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project break; 297b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project case 3: /* painful */ 298b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (i=jz;i>0;i--) { 299b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fw = fq[i-1]+fq[i]; 300b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fq[i] += fq[i-1]-fw; 301b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fq[i-1] = fw; 302b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 303b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (i=jz;i>1;i--) { 304b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fw = fq[i-1]+fq[i]; 305b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fq[i] += fq[i-1]-fw; 306b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project fq[i-1] = fw; 307b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 308b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 309b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ih==0) { 310b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 311b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 312b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 313b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 314b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 315b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return n&7; 316b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 317