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/* $OpenBSD: e_asinl.c,v 1.2 2016/09/12 19:47:02 guenther Exp $ */ |
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/* @(#)e_asin.c 1.3 95/01/18 */ |
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/* FreeBSD: head/lib/msun/src/e_asin.c 176451 2008-02-22 02:30:36Z das */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunSoft, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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/* |
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* See comments in e_asin.c. |
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* Converted to long double by David Schultz <das@FreeBSD.ORG>. |
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* Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>. |
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*/ |
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#include <float.h> |
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#include <math.h> |
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#include "invtrig.h" |
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#include "math_private.h" |
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#ifdef EXT_IMPLICIT_NBIT |
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#define LDBL_NBIT 0 |
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#else /* EXT_IMPLICIT_NBIT */ |
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#define LDBL_NBIT 0x80000000 |
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#endif /* EXT_IMPLICIT_NBIT */ |
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static const long double |
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one = 1.00000000000000000000e+00, |
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huge = 1.000e+300; |
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long double |
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asinl(long double x) |
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{ |
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union { |
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long double e; |
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struct ieee_ext bits; |
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} u; |
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long double t=0.0,w,p,q,c,r,s; |
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int16_t expsign, expt; |
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u.e = x; |
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expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp; |
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expt = expsign & 0x7fff; |
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if(expt >= BIAS) { /* |x|>= 1 */ |
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if(expt==BIAS && ((u.bits.ext_frach&~LDBL_NBIT) |
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#ifdef EXT_FRACHMBITS |
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| u.bits.ext_frachm |
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#endif /* EXT_FRACHMBITS */ |
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#ifdef EXT_FRACLMBITS |
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| u.bits.ext_fraclm |
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#endif /* EXT_FRACLMBITS */ |
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| u.bits.ext_fracl)==0) |
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/* asin(1)=+-pi/2 with inexact */ |
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return x*pio2_hi+x*pio2_lo; |
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return (x-x)/(x-x); /* asin(|x|>1) is NaN */ |
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} else if (expt<BIAS-1) { /* |x|<0.5 */ |
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if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */ |
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if(huge+x>one) return x;/* return x with inexact if x!=0*/ |
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} |
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t = x*x; |
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p = P(t); |
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q = Q(t); |
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w = p/q; |
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return x+x*w; |
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} |
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/* 1> |x|>= 0.5 */ |
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w = one-fabsl(x); |
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t = w*0.5; |
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p = P(t); |
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q = Q(t); |
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s = sqrtl(t); |
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#ifdef EXT_FRACHMBITS |
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if((((uint64_t)u.bits.ext_frach << EXT_FRACHMBITS) |
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| u.bits.ext_frachm) >= THRESH) { |
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/* if |x| is close to 1 */ |
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#else /* EXT_FRACHMBITS */ |
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if(u.bits.ext_frach>=THRESH) { /* if |x| is close to 1 */ |
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#endif /* EXT_FRACHMBITS */ |
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w = p/q; |
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t = pio2_hi-(2.0*(s+s*w)-pio2_lo); |
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} else { |
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u.e = s; |
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u.bits.ext_fracl = 0; |
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#ifdef EXT_FRACLMBITS |
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u.bits.ext_fraclm = 0; |
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#endif /* EXT_FRACLMBITS */ |
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w = u.e; |
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c = (t-w*w)/(s+w); |
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r = p/q; |
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p = 2.0*s*r-(pio2_lo-2.0*c); |
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q = pio4_hi-2.0*w; |
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t = pio4_hi-(p-q); |
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} |
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if(expsign>0) return t; else return -t; |
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} |
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DEF_STD(asinl); |