1 2 /* FreeBSD: head/lib/msun/src/e_asin.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_asin.c. 17 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 18 */ 19 20 #include "namespace.h" 21 #include <float.h> 22 #include <machine/ieee.h> 23 24 #include "math.h" 25 #include "math_private.h" 26 27 __weak_alias(asinl, _asinl) 28 29 #ifdef __HAVE_LONG_DOUBLE 30 31 #if LDBL_MANT_DIG == 64 32 #include "../ld80/invtrig.h" 33 #elif LDBL_MANT_DIG == 113 34 #include "../ld128/invtrig.h" 35 #else 36 #error "Unsupported long double format" 37 #endif 38 39 #ifdef LDBL_IMPLICIT_NBIT 40 #define LDBL_NBIT 0 41 #endif 42 43 static const long double 44 one = 1.00000000000000000000e+00, 45 huge = 1.000e+300; 46 47 long double 48 asinl(long double x) 49 { 50 union ieee_ext_u u; 51 long double t=0.0,w,p,q,c,r,s; 52 int16_t expsign, expt; 53 u.extu_ld = x; 54 expsign = GET_EXPSIGN(&u); 55 expt = expsign & 0x7fff; 56 if(expt >= BIAS) { /* |x|>= 1 */ 57 if(expt==BIAS && ((u.extu_frach&~LDBL_NBIT)|u.extu_fracl)==0) 58 /* asin(1)=+-pi/2 with inexact */ 59 return x*pio2_hi+x*pio2_lo; 60 return (x-x)/(x-x); /* asin(|x|>1) is NaN */ 61 } else if (expt<BIAS-1) { /* |x|<0.5 */ 62 if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */ 63 if(huge+x>one) return x;/* return x with inexact if x!=0*/ 64 } 65 t = x*x; 66 p = P(t); 67 q = Q(t); 68 w = p/q; 69 return x+x*w; 70 } 71 /* 1> |x|>= 0.5 */ 72 w = one-fabsl(x); 73 t = w*0.5; 74 p = P(t); 75 q = Q(t); 76 s = sqrtl(t); 77 if(u.extu_frach>=THRESH) { /* if |x| is close to 1 */ 78 w = p/q; 79 t = pio2_hi-(2.0*(s+s*w)-pio2_lo); 80 } else { 81 u.extu_ld = s; 82 u.extu_fracl = 0; 83 w = u.extu_ld; 84 c = (t-w*w)/(s+w); 85 r = p/q; 86 p = 2.0*s*r-(pio2_lo-2.0*c); 87 q = pio4_hi-2.0*w; 88 t = pio4_hi-(p-q); 89 } 90 if(expsign>0) return t; else return -t; 91 } 92 #else 93 long double 94 asinl(long double x) 95 { 96 return asin(x); 97 } 98 #endif 99