1 2 /* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 #include <sys/cdefs.h> 15 /* 16 * See comments in e_acos.c. 17 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 18 */ 19 20 #include <float.h> 21 22 #include "invtrig.h" 23 #include "math.h" 24 #include "math_private.h" 25 26 static const long double 27 one= 1.00000000000000000000e+00; 28 29 #ifdef __i386__ 30 /* XXX Work around the fact that gcc truncates long double constants on i386 */ 31 static volatile double 32 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 33 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 34 #define pi ((long double)pi1 + pi2) 35 #else 36 static const long double 37 pi = 3.14159265358979323846264338327950280e+00L; 38 #endif 39 40 long double 41 acosl(long double x) 42 { 43 union IEEEl2bits u; 44 long double z,p,q,r,w,s,c,df; 45 int16_t expsign, expt; 46 u.e = x; 47 expsign = u.xbits.expsign; 48 expt = expsign & 0x7fff; 49 if(expt >= BIAS) { /* |x| >= 1 */ 50 if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) { 51 if (expsign>0) return 0.0; /* acos(1) = 0 */ 52 else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 53 } 54 return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 55 } 56 if(expt<BIAS-1) { /* |x| < 0.5 */ 57 if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/ 58 z = x*x; 59 p = P(z); 60 q = Q(z); 61 r = p/q; 62 return pio2_hi - (x - (pio2_lo-x*r)); 63 } else if (expsign<0) { /* x < -0.5 */ 64 z = (one+x)*0.5; 65 p = P(z); 66 q = Q(z); 67 s = sqrtl(z); 68 r = p/q; 69 w = r*s-pio2_lo; 70 return pi - 2.0*(s+w); 71 } else { /* x > 0.5 */ 72 z = (one-x)*0.5; 73 s = sqrtl(z); 74 u.e = s; 75 u.bits.manl = 0; 76 df = u.e; 77 c = (z-df*df)/(s+df); 78 p = P(z); 79 q = Q(z); 80 r = p/q; 81 w = r*s+c; 82 return 2.0*(df+w); 83 } 84 } 85