1 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 #include <sys/cdefs.h> 16 __FBSDID("$FreeBSD$"); 17 18 /* 19 * See comments in e_acos.c. 20 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 21 */ 22 23 #include <float.h> 24 25 #include "invtrig.h" 26 #include "math.h" 27 #include "math_private.h" 28 29 static const long double 30 one= 1.00000000000000000000e+00; 31 32 #ifdef __i386__ 33 /* XXX Work around the fact that gcc truncates long double constants on i386 */ 34 static volatile double 35 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 36 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 37 #define pi ((long double)pi1 + pi2) 38 #else 39 static const long double 40 pi = 3.14159265358979323846264338327950280e+00L; 41 #endif 42 43 long double 44 acosl(long double x) 45 { 46 union IEEEl2bits u; 47 long double z,p,q,r,w,s,c,df; 48 int16_t expsign, expt; 49 u.e = x; 50 expsign = u.xbits.expsign; 51 expt = expsign & 0x7fff; 52 if(expt >= BIAS) { /* |x| >= 1 */ 53 if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) { 54 if (expsign>0) return 0.0; /* acos(1) = 0 */ 55 else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 56 } 57 return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 58 } 59 if(expt<BIAS-1) { /* |x| < 0.5 */ 60 if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/ 61 z = x*x; 62 p = P(z); 63 q = Q(z); 64 r = p/q; 65 return pio2_hi - (x - (pio2_lo-x*r)); 66 } else if (expsign<0) { /* x < -0.5 */ 67 z = (one+x)*0.5; 68 p = P(z); 69 q = Q(z); 70 s = sqrtl(z); 71 r = p/q; 72 w = r*s-pio2_lo; 73 return pi - 2.0*(s+w); 74 } else { /* x > 0.5 */ 75 z = (one-x)*0.5; 76 s = sqrtl(z); 77 u.e = s; 78 u.bits.manl = 0; 79 df = u.e; 80 c = (z-df*df)/(s+df); 81 p = P(z); 82 q = Q(z); 83 r = p/q; 84 w = r*s+c; 85 return 2.0*(df+w); 86 } 87 } 88