| Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 1 | |
| 2 | /* @(#)e_asin.c 1.3 95/01/18 */ |
| 3 | /* FreeBSD: head/lib/msun/src/e_asin.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_asin.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 | huge = 1.000e+300; |
| 32 | |
| 33 | long double |
| 34 | asinl(long double x) |
| 35 | { |
| 36 | union IEEEl2bits u; |
| 37 | long double t=0.0,w,p,q,c,r,s; |
| 38 | int16_t expsign, expt; |
| 39 | u.e = x; |
| 40 | expsign = u.xbits.expsign; |
| 41 | expt = expsign & 0x7fff; |
| 42 | if(expt >= BIAS) { /* |x|>= 1 */ |
| 43 | if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) |
| 44 | /* asin(1)=+-pi/2 with inexact */ |
| 45 | return x*pio2_hi+x*pio2_lo; |
| 46 | return (x-x)/(x-x); /* asin(|x|>1) is NaN */ |
| 47 | } else if (expt<BIAS-1) { /* |x|<0.5 */ |
| 48 | if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */ |
| 49 | if(huge+x>one) return x;/* return x with inexact if x!=0*/ |
| 50 | } |
| 51 | t = x*x; |
| 52 | p = P(t); |
| 53 | q = Q(t); |
| 54 | w = p/q; |
| 55 | return x+x*w; |
| 56 | } |
| 57 | /* 1> |x|>= 0.5 */ |
| 58 | w = one-fabsl(x); |
| 59 | t = w*0.5; |
| 60 | p = P(t); |
| 61 | q = Q(t); |
| 62 | s = sqrtl(t); |
| 63 | if(u.bits.manh>=THRESH) { /* if |x| is close to 1 */ |
| 64 | w = p/q; |
| 65 | t = pio2_hi-(2.0*(s+s*w)-pio2_lo); |
| 66 | } else { |
| 67 | u.e = s; |
| 68 | u.bits.manl = 0; |
| 69 | w = u.e; |
| 70 | c = (t-w*w)/(s+w); |
| 71 | r = p/q; |
| 72 | p = 2.0*s*r-(pio2_lo-2.0*c); |
| 73 | q = pio4_hi-2.0*w; |
| 74 | t = pio4_hi-(p-q); |
| 75 | } |
| 76 | if(expsign>0) return t; else return -t; |
| 77 | } |