1 /* $OpenBSD: e_acosl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */ 2 /* @(#)e_acos.c 1.3 95/01/18 */ 3 /* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */ 4 /* 5 * ==================================================== 6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7 * 8 * Developed at SunSoft, a Sun Microsystems, Inc. business. 9 * Permission to use, copy, modify, and distribute this 10 * software is freely granted, provided that this notice 11 * is preserved. 12 * ==================================================== 13 */ 14 15 /* 16 * See comments in e_acos.c. 17 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 18 * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>. 19 */ 20 21 #include <float.h> 22 #include <math.h> 23 24 #include "invtrig.h" 25 #include "math_private.h" 26 27 #ifdef EXT_IMPLICIT_NBIT 28 #define LDBL_NBIT 0 29 #else /* EXT_IMPLICIT_NBIT */ 30 #define LDBL_NBIT 0x80000000 31 #endif /* EXT_IMPLICIT_NBIT */ 32 33 static const long double 34 one= 1.00000000000000000000e+00; 35 36 #if defined(__amd64__) || defined(__i386__) 37 /* XXX Work around the fact that gcc truncates long double constants on i386 */ 38 static volatile double 39 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 40 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 41 #define pi ((long double)pi1 + pi2) 42 #else 43 static const long double 44 pi = 3.14159265358979323846264338327950280e+00L; 45 #endif 46 47 long double 48 acosl(long double x) 49 { 50 union { 51 long double e; 52 struct ieee_ext bits; 53 } u; 54 long double z,p,q,r,w,s,c,df; 55 int16_t expsign, expt; 56 u.e = x; 57 expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp; 58 expt = expsign & 0x7fff; 59 if(expt >= BIAS) { /* |x| >= 1 */ 60 if(expt==BIAS && ((u.bits.ext_frach&~LDBL_NBIT) 61 #ifdef EXT_FRACHMBITS 62 | u.bits.ext_frachm 63 #endif /* EXT_FRACHMBITS */ 64 #ifdef EXT_FRACLMBITS 65 | u.bits.ext_fraclm 66 #endif /* EXT_FRACLMBITS */ 67 | u.bits.ext_fracl)==0) { 68 if (expsign>0) return 0.0; /* acos(1) = 0 */ 69 else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 70 } 71 return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 72 } 73 if(expt<BIAS-1) { /* |x| < 0.5 */ 74 if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/ 75 z = x*x; 76 p = P(z); 77 q = Q(z); 78 r = p/q; 79 return pio2_hi - (x - (pio2_lo-x*r)); 80 } else if (expsign<0) { /* x < -0.5 */ 81 z = (one+x)*0.5; 82 p = P(z); 83 q = Q(z); 84 s = sqrtl(z); 85 r = p/q; 86 w = r*s-pio2_lo; 87 return pi - 2.0*(s+w); 88 } else { /* x > 0.5 */ 89 z = (one-x)*0.5; 90 s = sqrtl(z); 91 u.e = s; 92 u.bits.ext_fracl = 0; 93 #ifdef EXT_FRACLMBITS 94 u.bits.ext_fraclm = 0; 95 #endif /* EXT_FRACLMBITS */ 96 df = u.e; 97 c = (z-df*df)/(s+df); 98 p = P(z); 99 q = Q(z); 100 r = p/q; 101 w = r*s+c; 102 return 2.0*(df+w); 103 } 104 } 105