1141296Sdas 2141296Sdas/* @(#)e_acos.c 1.3 95/01/18 */ 32116Sjkh/* 42116Sjkh * ==================================================== 52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 62116Sjkh * 7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 82116Sjkh * Permission to use, copy, modify, and distribute this 9141296Sdas * software is freely granted, provided that this notice 102116Sjkh * is preserved. 112116Sjkh * ==================================================== 122116Sjkh */ 132116Sjkh 14176451Sdas#include <sys/cdefs.h> 15176451Sdas__FBSDID("$FreeBSD$"); 162116Sjkh 172116Sjkh/* __ieee754_acos(x) 18141296Sdas * Method : 192116Sjkh * acos(x) = pi/2 - asin(x) 202116Sjkh * acos(-x) = pi/2 + asin(x) 212116Sjkh * For |x|<=0.5 222116Sjkh * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 232116Sjkh * For x>0.5 242116Sjkh * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) 25141296Sdas * = 2asin(sqrt((1-x)/2)) 262116Sjkh * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) 272116Sjkh * = 2f + (2c + 2s*z*R(z)) 282116Sjkh * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 292116Sjkh * for f so that f+c ~ sqrt(z). 302116Sjkh * For x<-0.5 312116Sjkh * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) 322116Sjkh * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) 332116Sjkh * 342116Sjkh * Special cases: 352116Sjkh * if x is NaN, return x itself; 362116Sjkh * if |x|>1, return NaN with invalid signal. 372116Sjkh * 38141296Sdas * Function needed: sqrt 392116Sjkh */ 402116Sjkh 41181074Sdas#include <float.h> 42181074Sdas 432116Sjkh#include "math.h" 442116Sjkh#include "math_private.h" 452116Sjkh 468870Srgrimesstatic const double 472116Sjkhone= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 482116Sjkhpi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 49181062Sdaspio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ 50181062Sdasstatic volatile double 51181062Sdaspio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ 52181062Sdasstatic const double 532116SjkhpS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 542116SjkhpS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 552116SjkhpS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 562116SjkhpS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 572116SjkhpS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 582116SjkhpS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 592116SjkhqS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 602116SjkhqS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 612116SjkhqS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 622116SjkhqS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 632116Sjkh 6497407Salfreddouble 65117912Speter__ieee754_acos(double x) 662116Sjkh{ 672116Sjkh double z,p,q,r,w,s,c,df; 682116Sjkh int32_t hx,ix; 692116Sjkh GET_HIGH_WORD(hx,x); 702116Sjkh ix = hx&0x7fffffff; 712116Sjkh if(ix>=0x3ff00000) { /* |x| >= 1 */ 722116Sjkh u_int32_t lx; 732116Sjkh GET_LOW_WORD(lx,x); 742116Sjkh if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ 752116Sjkh if(hx>0) return 0.0; /* acos(1) = 0 */ 762116Sjkh else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 772116Sjkh } 782116Sjkh return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 792116Sjkh } 802116Sjkh if(ix<0x3fe00000) { /* |x| < 0.5 */ 812116Sjkh if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ 822116Sjkh z = x*x; 832116Sjkh p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 842116Sjkh q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 852116Sjkh r = p/q; 862116Sjkh return pio2_hi - (x - (pio2_lo-x*r)); 872116Sjkh } else if (hx<0) { /* x < -0.5 */ 882116Sjkh z = (one+x)*0.5; 892116Sjkh p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 902116Sjkh q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 91141296Sdas s = sqrt(z); 922116Sjkh r = p/q; 932116Sjkh w = r*s-pio2_lo; 942116Sjkh return pi - 2.0*(s+w); 952116Sjkh } else { /* x > 0.5 */ 962116Sjkh z = (one-x)*0.5; 97141296Sdas s = sqrt(z); 982116Sjkh df = s; 992116Sjkh SET_LOW_WORD(df,0); 1002116Sjkh c = (z-df*df)/(s+df); 1012116Sjkh p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 1022116Sjkh q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 1032116Sjkh r = p/q; 1042116Sjkh w = r*s+c; 1052116Sjkh return 2.0*(df+w); 1062116Sjkh } 1072116Sjkh} 108181074Sdas 109181074Sdas#if LDBL_MANT_DIG == 53 110181074Sdas__weak_reference(acos, acosl); 111181074Sdas#endif 112