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 /* 15 * See comments in e_acos.c. 16 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 17 */ 18 19 #include <float.h> 20 21 #include "invtrig.h" 22 #include "math.h" 23 #include "math_private.h" 24 25 static const long double 26 one= 1.00000000000000000000e+00; 27 28 #ifdef __i386__ 29 /* XXX Work around the fact that gcc truncates long double constants on i386 */ 30 static volatile double 31 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */ 32 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */ 33 #define pi ((long double)pi1 + pi2) 34 #else 35 static const long double 36 pi = 3.14159265358979323846264338327950280e+00L; 37 #endif 38 39 long double 40 acosl(long double x) 41 { 42 union IEEEl2bits u; 43 long double z,p,q,r,w,s,c,df; 44 int16_t expsign, expt; 45 u.e = x; 46 expsign = u.xbits.expsign; 47 expt = expsign & 0x7fff; 48 if(expt >= BIAS) { /* |x| >= 1 */ 49 if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) { 50 if (expsign>0) return 0.0; /* acos(1) = 0 */ 51 else return pi+2.0*pio2_lo; /* acos(-1)= pi */ 52 } 53 return (x-x)/(x-x); /* acos(|x|>1) is NaN */ 54 } 55 if(expt<BIAS-1) { /* |x| < 0.5 */ 56 if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/ 57 z = x*x; 58 p = P(z); 59 q = Q(z); 60 r = p/q; 61 return pio2_hi - (x - (pio2_lo-x*r)); 62 } else if (expsign<0) { /* x < -0.5 */ 63 z = (one+x)*0.5; 64 p = P(z); 65 q = Q(z); 66 s = sqrtl(z); 67 r = p/q; 68 w = r*s-pio2_lo; 69 return pi - 2.0*(s+w); 70 } else { /* x > 0.5 */ 71 z = (one-x)*0.5; 72 s = sqrtl(z); 73 u.e = s; 74 u.bits.manl = 0; 75 df = u.e; 76 c = (z-df*df)/(s+df); 77 p = P(z); 78 q = Q(z); 79 r = p/q; 80 w = r*s+c; 81 return 2.0*(df+w); 82 } 83 } 84