1b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 2b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project/* @(#)e_acos.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_acos(x) 15b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Method : 16b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * acos(x) = pi/2 - ieee_asin(x) 17b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * acos(-x) = pi/2 + ieee_asin(x) 18b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * For |x|<=0.5 19b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 20b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * For x>0.5 21b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * acos(x) = pi/2 - (pi/2 - 2asin(ieee_sqrt((1-x)/2))) 22b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = 2asin(ieee_sqrt((1-x)/2)) 23b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=ieee_sqrt(z) 24b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = 2f + (2c + 2s*z*R(z)) 25b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 26b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * for f so that f+c ~ ieee_sqrt(z). 27b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * For x<-0.5 28b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * acos(x) = pi - 2asin(ieee_sqrt((1-|x|)/2)) 29b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=ieee_sqrt(z) 30b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 31b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Special cases: 32b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * if x is NaN, return x itself; 33b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * if |x|>1, return NaN with invalid signal. 34b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * 35b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project * Function needed: sqrt 36b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project */ 37b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 38b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#include "fdlibm.h" 39b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 40b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 41b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic const double 42b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 43b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectstatic double 44b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 45b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectone= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 46b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectpi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 47b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectpio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ 48b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Projectpio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ 49b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectpS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 50b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectpS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 51b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectpS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 52b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectpS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 53b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectpS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 54b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectpS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 55b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectqS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 56b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectqS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 57b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectqS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 58b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source ProjectqS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 59b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project 60b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#ifdef __STDC__ 61b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_acos(double x) 62b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#else 63b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double __ieee754_acos(x) 64b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double x; 65b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project#endif 66b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project{ 67b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project double z,p,q,r,w,s,c,df; 68b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project int hx,ix; 69b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project hx = __HI(x); 70b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project ix = hx&0x7fffffff; 71b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix>=0x3ff00000) { /* |x| >= 1 */ 72b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */ 73b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(hx>0) return 0.0; /* ieee_acos(1) = 0 */ 74b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project else return pi+2.0*pio2_lo; /* ieee_acos(-1)= pi */ 75b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 76b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return (x-x)/(x-x); /* ieee_acos(|x|>1) is NaN */ 77b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 78b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<0x3fe00000) { /* |x| < 0.5 */ 79b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ 80b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = x*x; 81b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 82b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 83b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = p/q; 84b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return pio2_hi - (x - (pio2_lo-x*r)); 85b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else if (hx<0) { /* x < -0.5 */ 86b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = (one+x)*0.5; 87b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 88b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 89b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project s = ieee_sqrt(z); 90b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = p/q; 91b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = r*s-pio2_lo; 92b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return pi - 2.0*(s+w); 93b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } else { /* x > 0.5 */ 94b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project z = (one-x)*0.5; 95b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project s = ieee_sqrt(z); 96b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project df = s; 97b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project __LO(df) = 0; 98b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project c = (z-df*df)/(s+df); 99b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 100b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 101b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project r = p/q; 102b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project w = r*s+c; 103b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project return 2.0*(df+w); 104b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project } 105b07e1d9fd8d9e4e03698e0bd9bf77154c5390326The Android Open Source Project} 106