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153 lines
4.7 KiB
C
153 lines
4.7 KiB
C
/*
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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 SunPro, 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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Long double expansions are
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Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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and are incorporated herein by permission of the author. The author
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reserves the right to distribute this material elsewhere under different
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copying permissions. These modifications are distributed here under
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the following terms:
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, see
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<http://www.gnu.org/licenses/>. */
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/* __ieee754_asin(x)
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* Method :
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* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
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* we approximate asin(x) on [0,0.5] by
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* asin(x) = x + x*x^2*R(x^2)
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*
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* For x in [0.5,1]
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* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
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* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
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* then for x>0.98
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
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* For x<=0.98, let pio4_hi = pio2_hi/2, then
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* f = hi part of s;
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* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
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* and
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* asin(x) = pi/2 - 2*(s+s*z*R(z))
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* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
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* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
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*
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* Special cases:
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* if x is NaN, return x itself;
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* if |x|>1, return NaN with invalid signal.
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*
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*/
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#include <math.h>
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#include <math_private.h>
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static const long double
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one = 1.0L,
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huge = 1.0e+4932L,
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pio2_hi = 1.5707963267948966192021943710788178805159986950457096099853515625L,
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pio2_lo = 2.9127320560933561582586004641843300502121E-20L,
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pio4_hi = 7.8539816339744830960109718553940894025800E-1L,
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/* coefficient for R(x^2) */
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/* asin(x) = x + x^3 pS(x^2) / qS(x^2)
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0 <= x <= 0.5
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peak relative error 1.9e-21 */
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pS0 = -1.008714657938491626019651170502036851607E1L,
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pS1 = 2.331460313214179572063441834101394865259E1L,
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pS2 = -1.863169762159016144159202387315381830227E1L,
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pS3 = 5.930399351579141771077475766877674661747E0L,
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pS4 = -6.121291917696920296944056882932695185001E-1L,
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pS5 = 3.776934006243367487161248678019350338383E-3L,
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qS0 = -6.052287947630949712886794360635592886517E1L,
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qS1 = 1.671229145571899593737596543114258558503E2L,
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qS2 = -1.707840117062586426144397688315411324388E2L,
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qS3 = 7.870295154902110425886636075950077640623E1L,
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qS4 = -1.568433562487314651121702982333303458814E1L;
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/* 1.000000000000000000000000000000000000000E0 */
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long double
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__ieee754_asinl (long double x)
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{
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long double t, w, p, q, c, r, s;
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int32_t ix;
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u_int32_t se, i0, i1, k;
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GET_LDOUBLE_WORDS (se, i0, i1, x);
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ix = se & 0x7fff;
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ix = (ix << 16) | (i0 >> 16);
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if (ix >= 0x3fff8000)
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{ /* |x|>= 1 */
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if (ix == 0x3fff8000 && ((i0 - 0x80000000) | i1) == 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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}
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else if (ix < 0x3ffe8000)
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{ /* |x|<0.5 */
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if (ix < 0x3fde8000)
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{ /* if |x| < 2**-33 */
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if (huge + x > one)
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return x; /* return x with inexact if x!=0 */
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}
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else
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{
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t = x * x;
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p =
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t * (pS0 +
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t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
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q = qS0 + t * (qS1 + t * (qS2 + t * (qS3 + t * (qS4 + t))));
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w = p / q;
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return x + x * w;
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}
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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 = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5)))));
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q = qS0 + t * (qS1 + t * (qS2 + t * (qS3 + t * (qS4 + t))));
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s = __ieee754_sqrtl (t);
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if (ix >= 0x3ffef999)
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{ /* if |x| > 0.975 */
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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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}
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else
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{
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GET_LDOUBLE_WORDS (k, i0, i1, s);
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i1 = 0;
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SET_LDOUBLE_WORDS (w,k,i0,i1);
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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 ((se & 0x8000) == 0)
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return t;
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else
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return -t;
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}
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strong_alias (__ieee754_asinl, __asinl_finite)
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