11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* @(#)e_acos.c 1.3 95/01/18 */ 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Developed at SunSoft, a Sun Microsystems, Inc. business. 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 14a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 15a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* __ieee754_acos(x) 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Method : 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * acos(x) = pi/2 - asin(x) 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * acos(-x) = pi/2 + asin(x) 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * For |x|<=0.5 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * For x>0.5 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = 2asin(sqrt((1-x)/2)) 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = 2f + (2c + 2s*z*R(z)) 281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * for f so that f+c ~ sqrt(z). 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * For x<-0.5 311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) 331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Special cases: 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * if x is NaN, return x itself; 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * if |x|>1, return NaN with invalid signal. 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Function needed: sqrt 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 41a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <float.h> 42a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectone= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectpi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 49a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughespio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ 50a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesstatic volatile double 51a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughespio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ 52a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesstatic const double 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectpS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectpS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectpS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectpS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectpS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectpS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectqS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectqS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectqS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectqS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdouble 651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project__ieee754_acos(double x) 661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double z,p,q,r,w,s,c,df; 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t hx,ix; 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_HIGH_WORD(hx,x); 701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix = hx&0x7fffffff; 711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>=0x3ff00000) { /* |x| >= 1 */ 721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u_int32_t lx; 731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_LOW_WORD(lx,x); 741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ 751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx>0) return 0.0; /* acos(1) = 0 */ 761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<0x3fe00000) { /* |x| < 0.5 */ 811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ 821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = x*x; 831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = p/q; 861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return pio2_hi - (x - (pio2_lo-x*r)); 871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else if (hx<0) { /* x < -0.5 */ 881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = (one+x)*0.5; 891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = sqrt(z); 921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = p/q; 931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project w = r*s-pio2_lo; 941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return pi - 2.0*(s+w); 951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { /* x > 0.5 */ 961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = (one-x)*0.5; 971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = sqrt(z); 981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project df = s; 991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_LOW_WORD(df,0); 1001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project c = (z-df*df)/(s+df); 1011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 1021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 1031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = p/q; 1041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project w = r*s+c; 1051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return 2.0*(df+w); 1061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 108a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 109a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#if LDBL_MANT_DIG == 53 110a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__weak_reference(acos, acosl); 111a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#endif 112