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ec0ce0d3be
Similar to various other bugs in this area, some asin implementations do not raise the underflow exception for subnormal arguments, when the result is tiny and inexact. This patch forces the exception in a similar way to previous fixes. Tested for x86_64, x86, powerpc and mips64. [BZ #16351] * sysdeps/i386/fpu/e_asin.S (dbl_min): New object. (MO): New macro. (__ieee754_asin): Force underflow exception for results with small absolute value. * sysdeps/i386/fpu/e_asinf.S (flt_min): New object. (MO): New macro. (__ieee754_asinf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/dbl-64/e_asin.c: Include <float.h> and <math.h>. (__ieee754_asin): Force underflow exception for results with small absolute value. * sysdeps/ieee754/flt-32/e_asinf.c: Include <float.h>. (__ieee754_asinf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128/e_asinl.c: Include <float.h>. (__ieee754_asinl): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128ibm/e_asinl.c: Include <float.h>. (__ieee754_asinl): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-96/e_asinl.c: Include <float.h>. (__ieee754_asinl): Force underflow exception for results with small absolute value. * sysdeps/x86_64/fpu/multiarch/e_asin.c [HAVE_FMA4_SUPPORT]: Include <math.h>. * math/auto-libm-test-in: Do not mark underflow exceptions as possibly missing for bug 16351. * math/auto-libm-test-out: Regenerated.
254 lines
7.2 KiB
C
254 lines
7.2 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 the
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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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* Between .5 and .625 the approximation is
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* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
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* For x in [0.625,1]
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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 <float.h>
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#include <math.h>
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#include <math_private.h>
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long double sqrtl (long double);
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static const long double
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one = 1.0L,
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huge = 1.0e+300L,
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pio2_hi = 1.5707963267948966192313216916397514420986L,
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pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
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pio4_hi = 7.8539816339744830961566084581987569936977E-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-35 */
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pS0 = -8.358099012470680544198472400254596543711E2L,
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pS1 = 3.674973957689619490312782828051860366493E3L,
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pS2 = -6.730729094812979665807581609853656623219E3L,
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pS3 = 6.643843795209060298375552684423454077633E3L,
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pS4 = -3.817341990928606692235481812252049415993E3L,
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pS5 = 1.284635388402653715636722822195716476156E3L,
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pS6 = -2.410736125231549204856567737329112037867E2L,
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pS7 = 2.219191969382402856557594215833622156220E1L,
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pS8 = -7.249056260830627156600112195061001036533E-1L,
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pS9 = 1.055923570937755300061509030361395604448E-3L,
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qS0 = -5.014859407482408326519083440151745519205E3L,
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qS1 = 2.430653047950480068881028451580393430537E4L,
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qS2 = -4.997904737193653607449250593976069726962E4L,
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qS3 = 5.675712336110456923807959930107347511086E4L,
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qS4 = -3.881523118339661268482937768522572588022E4L,
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qS5 = 1.634202194895541569749717032234510811216E4L,
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qS6 = -4.151452662440709301601820849901296953752E3L,
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qS7 = 5.956050864057192019085175976175695342168E2L,
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qS8 = -4.175375777334867025769346564600396877176E1L,
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/* 1.000000000000000000000000000000000000000E0 */
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/* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
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-0.0625 <= x <= 0.0625
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peak relative error 3.3e-35 */
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rS0 = -5.619049346208901520945464704848780243887E0L,
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rS1 = 4.460504162777731472539175700169871920352E1L,
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rS2 = -1.317669505315409261479577040530751477488E2L,
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rS3 = 1.626532582423661989632442410808596009227E2L,
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rS4 = -3.144806644195158614904369445440583873264E1L,
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rS5 = -9.806674443470740708765165604769099559553E1L,
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rS6 = 5.708468492052010816555762842394927806920E1L,
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rS7 = 1.396540499232262112248553357962639431922E1L,
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rS8 = -1.126243289311910363001762058295832610344E1L,
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rS9 = -4.956179821329901954211277873774472383512E-1L,
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rS10 = 3.313227657082367169241333738391762525780E-1L,
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sS0 = -4.645814742084009935700221277307007679325E0L,
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sS1 = 3.879074822457694323970438316317961918430E1L,
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sS2 = -1.221986588013474694623973554726201001066E2L,
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sS3 = 1.658821150347718105012079876756201905822E2L,
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sS4 = -4.804379630977558197953176474426239748977E1L,
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sS5 = -1.004296417397316948114344573811562952793E2L,
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sS6 = 7.530281592861320234941101403870010111138E1L,
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sS7 = 1.270735595411673647119592092304357226607E1L,
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sS8 = -1.815144839646376500705105967064792930282E1L,
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sS9 = -7.821597334910963922204235247786840828217E-2L,
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/* 1.000000000000000000000000000000000000000E0 */
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asinr5625 = 5.9740641664535021430381036628424864397707E-1L;
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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 a, t, w, p, q, c, r, s;
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int flag;
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if (__glibc_unlikely (__isnanl (x)))
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return x + x;
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flag = 0;
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a = __builtin_fabsl (x);
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if (a == 1.0L) /* |x|>= 1 */
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return x * pio2_hi + x * pio2_lo; /* asin(1)=+-pi/2 with inexact */
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else if (a >= 1.0L)
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return (x - x) / (x - x); /* asin(|x|>1) is NaN */
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else if (a < 0.5L)
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{
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if (a < 6.938893903907228e-18L) /* |x| < 2**-57 */
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{
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if (fabsl (x) < LDBL_MIN)
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{
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long double force_underflow = x * x;
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math_force_eval (force_underflow);
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}
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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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/* Mark to use pS, qS later on. */
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flag = 1;
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}
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}
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else if (a < 0.625L)
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{
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t = a - 0.5625;
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p = ((((((((((rS10 * t
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+ rS9) * t
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+ rS8) * t
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+ rS7) * t
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+ rS6) * t
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+ rS5) * t
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+ rS4) * t
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+ rS3) * t
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+ rS2) * t
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+ rS1) * t
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+ rS0) * t;
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q = ((((((((( t
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+ sS9) * t
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+ sS8) * t
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+ sS7) * t
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+ sS6) * t
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+ sS5) * t
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+ sS4) * t
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+ sS3) * t
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+ sS2) * t
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+ sS1) * t
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+ sS0;
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t = asinr5625 + p / q;
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if (x > 0.0L)
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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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else
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{
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/* 1 > |x| >= 0.625 */
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w = one - a;
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t = w * 0.5;
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}
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p = (((((((((pS9 * t
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+ pS8) * t
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+ pS7) * t
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+ pS6) * t
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+ pS5) * t
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+ pS4) * t
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+ pS3) * t
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+ pS2) * t
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+ pS1) * t
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+ pS0) * t;
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q = (((((((( t
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+ qS8) * t
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+ qS7) * t
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+ qS6) * t
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+ qS5) * t
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+ qS4) * t
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+ qS3) * t
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+ qS2) * t
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+ qS1) * t
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+ qS0;
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if (flag) /* 2^-57 < |x| < 0.5 */
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{
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w = p / q;
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return x + x * w;
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}
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s = __ieee754_sqrtl (t);
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if (a > 0.975L)
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{
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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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w = ldbl_high (s);
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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 (x > 0.0L)
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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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