1181074Sdas 2181074Sdas/* @(#)e_acos.c 1.3 95/01/18 */ 3181074Sdas/* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */ 4181074Sdas/* 5181074Sdas * ==================================================== 6181074Sdas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7181074Sdas * 8181074Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 9181074Sdas * Permission to use, copy, modify, and distribute this 10181074Sdas * software is freely granted, provided that this notice 11181074Sdas * is preserved. 12181074Sdas * ==================================================== 13181074Sdas */ 14181074Sdas 15181074Sdas#include <sys/cdefs.h> 16181074Sdas__FBSDID("$FreeBSD$"); 17181074Sdas 18181074Sdas/* 19181074Sdas * See comments in e_acos.c. 20181074Sdas * Converted to long double by David Schultz <das@FreeBSD.ORG>. 21181074Sdas */ 22181074Sdas 23181074Sdas#include <float.h> 24181074Sdas 25181074Sdas#include "invtrig.h" 26181074Sdas#include "math.h" 27181074Sdas#include "math_private.h" 28181074Sdas 29181074Sdasstatic const long double 30181152Sdasone= 1.00000000000000000000e+00; 31181152Sdas 32181152Sdas#ifdef __i386__ 33181152Sdas/* XXX Work around the fact that gcc truncates long double constants on i386 */ 34181152Sdasstatic volatile double 35181152Sdaspi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 36181152Sdaspi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 37181152Sdas#define pi ((long double)pi1 + pi2) 38181152Sdas#else 39181152Sdasstatic const long double 40181074Sdaspi = 3.14159265358979323846264338327950280e+00L; 41181152Sdas#endif 42181152Sdas 43181074Sdaslong double 44181074Sdasacosl(long double x) 45181074Sdas{ 46181074Sdas union IEEEl2bits u; 47181074Sdas long double z,p,q,r,w,s,c,df; 48181074Sdas int16_t expsign, expt; 49181074Sdas u.e = x; 50181074Sdas expsign = u.xbits.expsign; 51181074Sdas expt = expsign & 0x7fff; 52181074Sdas if(expt >= BIAS) { /* |x| >= 1 */ 53181074Sdas if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) { 54181074Sdas if (expsign>0) return 0.0; /* acos(1) = 0 */ 55181074Sdas else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 56181074Sdas } 57181074Sdas return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 58181074Sdas } 59181074Sdas if(expt<BIAS-1) { /* |x| < 0.5 */ 60181074Sdas if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/ 61181074Sdas z = x*x; 62181074Sdas p = P(z); 63181074Sdas q = Q(z); 64181074Sdas r = p/q; 65181074Sdas return pio2_hi - (x - (pio2_lo-x*r)); 66181074Sdas } else if (expsign<0) { /* x < -0.5 */ 67181074Sdas z = (one+x)*0.5; 68181074Sdas p = P(z); 69181074Sdas q = Q(z); 70181074Sdas s = sqrtl(z); 71181074Sdas r = p/q; 72181074Sdas w = r*s-pio2_lo; 73181074Sdas return pi - 2.0*(s+w); 74181074Sdas } else { /* x > 0.5 */ 75181074Sdas z = (one-x)*0.5; 76181074Sdas s = sqrtl(z); 77181074Sdas u.e = s; 78181074Sdas u.bits.manl = 0; 79181074Sdas df = u.e; 80181074Sdas c = (z-df*df)/(s+df); 81181074Sdas p = P(z); 82181074Sdas q = Q(z); 83181074Sdas r = p/q; 84181074Sdas w = r*s+c; 85181074Sdas return 2.0*(df+w); 86181074Sdas } 87181074Sdas} 88