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fded7ed684
The ldbl-128 and ldbl-128ibm implementations of asinl produce uninitialized variable warnings with -Wuninitialized because the code for small arguments in fact always returns but the compiler cannot see this and instead sees that a variable would be uninitialized if the "if (huge + x > one)" conditional used to force the "inexact" exception were false. All the code in libm trying to force "inexact" for functions that are not exactly defined is suspect and should be removed at some point given that we now have a clear definition of the accuracy goals for libm functions which, following C99/C11, does not require anything about "inexact" for most functions (likewise, the multi-precision code that tries to give correctly-rounded results, very slowly, for functions for which the goals clearly do not include correct rounding, if the faster paths are accurate enough). However, for now this patch simply changes the code to use math_force_eval, rather than "if", to ensure the evaluation of the inexact computation. Tested for powerpc and mips64. * sysdeps/ieee754/ldbl-128/e_asinl.c (__ieee754_asinl): Don't use a conditional in forcing "inexact". * sysdeps/ieee754/ldbl-128ibm/e_asinl.c (__ieee754_asinl): Likewise.
264 lines
7.6 KiB
C
264 lines
7.6 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+4932L,
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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 t, w, p, q, c, r, s;
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int32_t ix, sign, flag;
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ieee854_long_double_shape_type u;
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flag = 0;
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u.value = x;
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sign = u.parts32.w0;
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ix = sign & 0x7fffffff;
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u.parts32.w0 = ix; /* |x| */
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if (ix >= 0x3fff0000) /* |x|>= 1 */
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{
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if (ix == 0x3fff0000
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&& (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 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 < 0x3ffe0000) /* |x| < 0.5 */
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{
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if (ix < 0x3fc60000) /* |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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long double force_inexact = huge + x;
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math_force_eval (force_inexact);
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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 (ix < 0x3ffe4000) /* 0.625 */
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{
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t = u.value - 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 ((sign & 0x80000000) == 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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else
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{
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/* 1 > |x| >= 0.625 */
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w = one - u.value;
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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 (ix >= 0x3ffef333) /* |x| > 0.975 */
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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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u.value = s;
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u.parts32.w3 = 0;
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u.parts32.w2 = 0;
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w = u.value;
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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 ((sign & 0x80000000) == 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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