e_acos.c revision 302408
18729Sserb 29330Slana/* @(#)e_acos.c 1.3 95/01/18 */ 38729Sserb/* 48729Sserb * ==================================================== 58729Sserb * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 68729Sserb * 78729Sserb * Developed at SunSoft, a Sun Microsystems, Inc. business. 88729Sserb * Permission to use, copy, modify, and distribute this 98729Sserb * software is freely granted, provided that this notice 108729Sserb * is preserved. 118729Sserb * ==================================================== 128729Sserb */ 138729Sserb 148729Sserb#include <sys/cdefs.h> 158729Sserb__FBSDID("$FreeBSD: stable/11/lib/msun/src/e_acos.c 181074 2008-07-31 22:41:26Z das $"); 168729Sserb 178729Sserb/* __ieee754_acos(x) 188729Sserb * Method : 198729Sserb * acos(x) = pi/2 - asin(x) 208729Sserb * acos(-x) = pi/2 + asin(x) 218729Sserb * For |x|<=0.5 228729Sserb * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) 238729Sserb * For x>0.5 240Sduke * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) 250Sduke * = 2asin(sqrt((1-x)/2)) 260Sduke * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) 270Sduke * = 2f + (2c + 2s*z*R(z)) 280Sduke * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term 290Sduke * for f so that f+c ~ sqrt(z). 300Sduke * For x<-0.5 310Sduke * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) 320Sduke * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) 330Sduke * 340Sduke * Special cases: 350Sduke * if x is NaN, return x itself; 360Sduke * if |x|>1, return NaN with invalid signal. 370Sduke * 380Sduke * Function needed: sqrt 390Sduke */ 400Sduke 410Sduke#include <float.h> 420Sduke 430Sduke#include "math.h" 440Sduke#include "math_private.h" 450Sduke 460Sdukestatic const double 470Sdukeone= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 480Sdukepi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ 490Sdukepio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ 500Sdukestatic volatile double 510Sdukepio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ 520Sdukestatic const double 530SdukepS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ 540SdukepS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ 550SdukepS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ 560SdukepS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ 570SdukepS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ 580SdukepS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ 590SdukeqS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ 600SdukeqS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ 610SdukeqS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ 620SdukeqS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ 630Sduke 640Sdukedouble 650Sduke__ieee754_acos(double x) 660Sduke{ 670Sduke double z,p,q,r,w,s,c,df; 680Sduke int32_t hx,ix; 690Sduke GET_HIGH_WORD(hx,x); 700Sduke ix = hx&0x7fffffff; 710Sduke if(ix>=0x3ff00000) { /* |x| >= 1 */ 720Sduke u_int32_t lx; 730Sduke GET_LOW_WORD(lx,x); 740Sduke if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ 750Sduke if(hx>0) return 0.0; /* acos(1) = 0 */ 760Sduke else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 770Sduke } 780Sduke return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 790Sduke } 800Sduke if(ix<0x3fe00000) { /* |x| < 0.5 */ 810Sduke if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ 820Sduke z = x*x; 830Sduke p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 840Sduke q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 850Sduke r = p/q; 860Sduke return pio2_hi - (x - (pio2_lo-x*r)); 870Sduke } else if (hx<0) { /* x < -0.5 */ 880Sduke z = (one+x)*0.5; 890Sduke p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 900Sduke q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 910Sduke s = sqrt(z); 920Sduke r = p/q; 930Sduke w = r*s-pio2_lo; 940Sduke return pi - 2.0*(s+w); 950Sduke } else { /* x > 0.5 */ 960Sduke z = (one-x)*0.5; 970Sduke s = sqrt(z); 980Sduke df = s; 990Sduke SET_LOW_WORD(df,0); 1000Sduke c = (z-df*df)/(s+df); 1010Sduke p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); 1020Sduke q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); 1030Sduke r = p/q; 1040Sduke w = r*s+c; 1050Sduke return 2.0*(df+w); 1060Sduke } 1070Sduke} 1080Sduke 1090Sduke#if LDBL_MANT_DIG == 53 1100Sduke__weak_reference(acos, acosl); 1110Sduke#endif 1120Sduke