1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)k_cos.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_cos( x, y ) 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Input x is assumed to be bounded by ~pi/4 in magnitude. 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Input y is the tail of x. 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Algorithm 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 1. Since ieee_cos(-x) = ieee_cos(x), we need only to consider positive x. 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 3. ieee_cos(x) is approximated by a polynomial of degree 14 on 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * [0,pi/4] 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 4 14 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where the remez error is 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * | 2 4 6 8 10 12 14 | -58 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * |ieee_cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * | | 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 4 6 8 10 12 14 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ieee_cos(x) = 1 - x*x/2 + r 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * since ieee_cos(x+y) ~ ieee_cos(x) - ieee_sin(x)*y 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * ~ ieee_cos(x) - x*y, 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * a correction term is necessary in ieee_cos(x) and hence 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * cos(x+y) = 1 - (x*x/2 - (r - x*y)) 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * For better accuracy when x > 0.3, let qx = |x|/4 with 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Then 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Note that 1-qx and (x*x/2-qx) is EXACT here, and the 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * magnitude of the latter is at least a quarter of x*x/2, 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * thus, reducing the rounding error in the subtraction. 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectone = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectC1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectC2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectC3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectC4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectC5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectC6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __kernel_cos(double x, double y) 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __kernel_cos(x, y) 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x,y; 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double a,hz,z,r,qx; 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int ix; 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/ 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x3e400000) { /* if x < 2**27 */ 75b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(((int)x)==0) return one; /* generate inexact */ 76b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 77b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = x*x; 78b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); 79b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix < 0x3FD33333) /* if |x| < 0.3 */ 80b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return one - (0.5*z - (z*r - x*y)); 81b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else { 82b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix > 0x3fe90000) { /* x > 0.78125 */ 83b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project qx = 0.28125; 84b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { 85b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __HI(qx) = ix-0x00200000; /* x/4 */ 86b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __LO(qx) = 0; 87b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 88b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hz = 0.5*z-qx; 89b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project a = one-qx; 90b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return a - (hz - (z*r-x*y)); 91b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 92b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 93