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authorZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
committerZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
commit5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch)
tree4470480d904b65cf14ca524f96f79eca818c3eaf /sysdeps/ieee754/ldbl-128ibm/e_asinl.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
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Prepare for radical source tree reorganization.zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage directory, REORG.TODO, except for files that will certainly still exist in their current form at top level when we're done (COPYING, COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which are moved to the new directory OldChangeLogs, instead), and the generated file INSTALL (which is just deleted; in the new order, there will be no generated files checked into version control).
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diff --git a/sysdeps/ieee754/ldbl-128ibm/e_asinl.c b/sysdeps/ieee754/ldbl-128ibm/e_asinl.c
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--- a/sysdeps/ieee754/ldbl-128ibm/e_asinl.c
+++ /dev/null
@@ -1,250 +0,0 @@
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
- Long double expansions are
- Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
- and are incorporated herein by permission of the author. The author
- reserves the right to distribute this material elsewhere under different
- copying permissions. These modifications are distributed here under the
- following terms:
-
- This library is free software; you can redistribute it and/or
- modify it under the terms of the GNU Lesser General Public
- License as published by the Free Software Foundation; either
- version 2.1 of the License, or (at your option) any later version.
-
- This library is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- Lesser General Public License for more details.
-
- You should have received a copy of the GNU Lesser General Public
- License along with this library; if not, see
- <http://www.gnu.org/licenses/>. */
-
-/* __ieee754_asin(x)
- * Method :
- * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
- * we approximate asin(x) on [0,0.5] by
- * asin(x) = x + x*x^2*R(x^2)
- * Between .5 and .625 the approximation is
- * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
- * For x in [0.625,1]
- * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
- * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
- * then for x>0.98
- * asin(x) = pi/2 - 2*(s+s*z*R(z))
- * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
- * For x<=0.98, let pio4_hi = pio2_hi/2, then
- * f = hi part of s;
- * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
- * and
- * asin(x) = pi/2 - 2*(s+s*z*R(z))
- * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
- * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
- *
- * Special cases:
- * if x is NaN, return x itself;
- * if |x|>1, return NaN with invalid signal.
- *
- */
-
-
-#include <float.h>
-#include <math.h>
-#include <math_private.h>
-long double sqrtl (long double);
-
-static const long double
- one = 1.0L,
- huge = 1.0e+300L,
- pio2_hi = 1.5707963267948966192313216916397514420986L,
- pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
- pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
-
- /* coefficient for R(x^2) */
-
- /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
- 0 <= x <= 0.5
- peak relative error 1.9e-35 */
- pS0 = -8.358099012470680544198472400254596543711E2L,
- pS1 = 3.674973957689619490312782828051860366493E3L,
- pS2 = -6.730729094812979665807581609853656623219E3L,
- pS3 = 6.643843795209060298375552684423454077633E3L,
- pS4 = -3.817341990928606692235481812252049415993E3L,
- pS5 = 1.284635388402653715636722822195716476156E3L,
- pS6 = -2.410736125231549204856567737329112037867E2L,
- pS7 = 2.219191969382402856557594215833622156220E1L,
- pS8 = -7.249056260830627156600112195061001036533E-1L,
- pS9 = 1.055923570937755300061509030361395604448E-3L,
-
- qS0 = -5.014859407482408326519083440151745519205E3L,
- qS1 = 2.430653047950480068881028451580393430537E4L,
- qS2 = -4.997904737193653607449250593976069726962E4L,
- qS3 = 5.675712336110456923807959930107347511086E4L,
- qS4 = -3.881523118339661268482937768522572588022E4L,
- qS5 = 1.634202194895541569749717032234510811216E4L,
- qS6 = -4.151452662440709301601820849901296953752E3L,
- qS7 = 5.956050864057192019085175976175695342168E2L,
- qS8 = -4.175375777334867025769346564600396877176E1L,
- /* 1.000000000000000000000000000000000000000E0 */
-
- /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
- -0.0625 <= x <= 0.0625
- peak relative error 3.3e-35 */
- rS0 = -5.619049346208901520945464704848780243887E0L,
- rS1 = 4.460504162777731472539175700169871920352E1L,
- rS2 = -1.317669505315409261479577040530751477488E2L,
- rS3 = 1.626532582423661989632442410808596009227E2L,
- rS4 = -3.144806644195158614904369445440583873264E1L,
- rS5 = -9.806674443470740708765165604769099559553E1L,
- rS6 = 5.708468492052010816555762842394927806920E1L,
- rS7 = 1.396540499232262112248553357962639431922E1L,
- rS8 = -1.126243289311910363001762058295832610344E1L,
- rS9 = -4.956179821329901954211277873774472383512E-1L,
- rS10 = 3.313227657082367169241333738391762525780E-1L,
-
- sS0 = -4.645814742084009935700221277307007679325E0L,
- sS1 = 3.879074822457694323970438316317961918430E1L,
- sS2 = -1.221986588013474694623973554726201001066E2L,
- sS3 = 1.658821150347718105012079876756201905822E2L,
- sS4 = -4.804379630977558197953176474426239748977E1L,
- sS5 = -1.004296417397316948114344573811562952793E2L,
- sS6 = 7.530281592861320234941101403870010111138E1L,
- sS7 = 1.270735595411673647119592092304357226607E1L,
- sS8 = -1.815144839646376500705105967064792930282E1L,
- sS9 = -7.821597334910963922204235247786840828217E-2L,
- /* 1.000000000000000000000000000000000000000E0 */
-
- asinr5625 = 5.9740641664535021430381036628424864397707E-1L;
-
-
-
-long double
-__ieee754_asinl (long double x)
-{
- long double a, t, w, p, q, c, r, s;
- int flag;
-
- if (__glibc_unlikely (isnan (x)))
- return x + x;
- flag = 0;
- a = __builtin_fabsl (x);
- if (a == 1.0L) /* |x|>= 1 */
- return x * pio2_hi + x * pio2_lo; /* asin(1)=+-pi/2 with inexact */
- else if (a >= 1.0L)
- return (x - x) / (x - x); /* asin(|x|>1) is NaN */
- else if (a < 0.5L)
- {
- if (a < 6.938893903907228e-18L) /* |x| < 2**-57 */
- {
- math_check_force_underflow (x);
- long double force_inexact = huge + x;
- math_force_eval (force_inexact);
- return x; /* return x with inexact if x!=0 */
- }
- else
- {
- t = x * x;
- /* Mark to use pS, qS later on. */
- flag = 1;
- }
- }
- else if (a < 0.625L)
- {
- t = a - 0.5625;
- p = ((((((((((rS10 * t
- + rS9) * t
- + rS8) * t
- + rS7) * t
- + rS6) * t
- + rS5) * t
- + rS4) * t
- + rS3) * t
- + rS2) * t
- + rS1) * t
- + rS0) * t;
-
- q = ((((((((( t
- + sS9) * t
- + sS8) * t
- + sS7) * t
- + sS6) * t
- + sS5) * t
- + sS4) * t
- + sS3) * t
- + sS2) * t
- + sS1) * t
- + sS0;
- t = asinr5625 + p / q;
- if (x > 0.0L)
- return t;
- else
- return -t;
- }
- else
- {
- /* 1 > |x| >= 0.625 */
- w = one - a;
- t = w * 0.5;
- }
-
- p = (((((((((pS9 * t
- + pS8) * t
- + pS7) * t
- + pS6) * t
- + pS5) * t
- + pS4) * t
- + pS3) * t
- + pS2) * t
- + pS1) * t
- + pS0) * t;
-
- q = (((((((( t
- + qS8) * t
- + qS7) * t
- + qS6) * t
- + qS5) * t
- + qS4) * t
- + qS3) * t
- + qS2) * t
- + qS1) * t
- + qS0;
-
- if (flag) /* 2^-57 < |x| < 0.5 */
- {
- w = p / q;
- return x + x * w;
- }
-
- s = __ieee754_sqrtl (t);
- if (a > 0.975L)
- {
- w = p / q;
- t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
- }
- else
- {
- w = ldbl_high (s);
- c = (t - w * w) / (s + w);
- r = p / q;
- p = 2.0 * s * r - (pio2_lo - 2.0 * c);
- q = pio4_hi - 2.0 * w;
- t = pio4_hi - (p - q);
- }
-
- if (x > 0.0L)
- return t;
- else
- return -t;
-}
-strong_alias (__ieee754_asinl, __asinl_finite)