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diff --git a/sysdeps/ieee754/ldbl-128ibm/e_acosl.c b/sysdeps/ieee754/ldbl-128ibm/e_acosl.c
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-/*
- * ====================================================
- * 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, write to the Free Software
- Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
-
-/* __ieee754_acosl(x)
- * Method :
- * acos(x) = pi/2 - asin(x)
- * acos(-x) = pi/2 + asin(x)
- * For |x| <= 0.375
- * acos(x) = pi/2 - asin(x)
- * Between .375 and .5 the approximation is
- * acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x)
- * Between .5 and .625 the approximation is
- * acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
- * For x > 0.625,
- * acos(x) = 2 asin(sqrt((1-x)/2))
- * computed with an extended precision square root in the leading term.
- * For x < -0.625
- * acos(x) = pi - 2 asin(sqrt((1-|x|)/2))
- *
- * Special cases:
- * if x is NaN, return x itself;
- * if |x|>1, return NaN with invalid signal.
- *
- * Functions needed: __ieee754_sqrtl.
- */
-
-#include "math.h"
-#include "math_private.h"
-
-#ifdef __STDC__
-static const long double
-#else
-static long double
-#endif
- one = 1.0L,
- pio2_hi = 1.5707963267948966192313216916397514420986L,
- pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
-
- /* acos(0.5625 + x) = acos(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 */
-
- acosr5625 = 9.7338991014954640492751132535550279812151E-1L,
- pimacosr5625 = 2.1682027434402468335351320579240000860757E0L,
-
- /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x)
- -0.0625 <= x <= 0.0625
- peak relative error 2.1e-35 */
-
- P0 = 2.177690192235413635229046633751390484892E0L,
- P1 = -2.848698225706605746657192566166142909573E1L,
- P2 = 1.040076477655245590871244795403659880304E2L,
- P3 = -1.400087608918906358323551402881238180553E2L,
- P4 = 2.221047917671449176051896400503615543757E1L,
- P5 = 9.643714856395587663736110523917499638702E1L,
- P6 = -5.158406639829833829027457284942389079196E1L,
- P7 = -1.578651828337585944715290382181219741813E1L,
- P8 = 1.093632715903802870546857764647931045906E1L,
- P9 = 5.448925479898460003048760932274085300103E-1L,
- P10 = -3.315886001095605268470690485170092986337E-1L,
- Q0 = -1.958219113487162405143608843774587557016E0L,
- Q1 = 2.614577866876185080678907676023269360520E1L,
- Q2 = -9.990858606464150981009763389881793660938E1L,
- Q3 = 1.443958741356995763628660823395334281596E2L,
- Q4 = -3.206441012484232867657763518369723873129E1L,
- Q5 = -1.048560885341833443564920145642588991492E2L,
- Q6 = 6.745883931909770880159915641984874746358E1L,
- Q7 = 1.806809656342804436118449982647641392951E1L,
- Q8 = -1.770150690652438294290020775359580915464E1L,
- Q9 = -5.659156469628629327045433069052560211164E-1L,
- /* 1.000000000000000000000000000000000000000E0 */
-
- acosr4375 = 1.1179797320499710475919903296900511518755E0L,
- pimacosr4375 = 2.0236129215398221908706530535894517323217E0L,
-
- /* 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 */
-
-#ifdef __STDC__
-long double
-__ieee754_acosl (long double x)
-#else
-long double
-__ieee754_acosl (x)
- long double x;
-#endif
-{
- long double z, r, w, p, q, s, t, f2;
- int32_t ix, sign;
- ieee854_long_double_shape_type u;
-
- u.value = x;
- sign = u.parts32.w0;
- ix = sign & 0x7fffffff;
- u.parts32.w0 = ix; /* |x| */
- if (ix >= 0x3ff00000) /* |x| >= 1 */
- {
- if (ix == 0x3ff00000
- && (u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.w3) == 0)
- { /* |x| == 1 */
- if ((sign & 0x80000000) == 0)
- return 0.0; /* acos(1) = 0 */
- else
- return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */
- }
- return (x - x) / (x - x); /* acos(|x| > 1) is NaN */
- }
- else if (ix < 0x3fe00000) /* |x| < 0.5 */
- {
- if (ix < 0x3c600000) /* |x| < 2**-57 */
- return pio2_hi + pio2_lo;
- if (ix < 0x3fde0000) /* |x| < .4375 */
- {
- /* Arcsine of x. */
- z = x * x;
- p = (((((((((pS9 * z
- + pS8) * z
- + pS7) * z
- + pS6) * z
- + pS5) * z
- + pS4) * z
- + pS3) * z
- + pS2) * z
- + pS1) * z
- + pS0) * z;
- q = (((((((( z
- + qS8) * z
- + qS7) * z
- + qS6) * z
- + qS5) * z
- + qS4) * z
- + qS3) * z
- + qS2) * z
- + qS1) * z
- + qS0;
- r = x + x * p / q;
- z = pio2_hi - (r - pio2_lo);
- return z;
- }
- /* .4375 <= |x| < .5 */
- t = u.value - 0.4375L;
- p = ((((((((((P10 * t
- + P9) * t
- + P8) * t
- + P7) * t
- + P6) * t
- + P5) * t
- + P4) * t
- + P3) * t
- + P2) * t
- + P1) * t
- + P0) * t;
-
- q = (((((((((t
- + Q9) * t
- + Q8) * t
- + Q7) * t
- + Q6) * t
- + Q5) * t
- + Q4) * t
- + Q3) * t
- + Q2) * t
- + Q1) * t
- + Q0;
- r = p / q;
- if (sign & 0x80000000)
- r = pimacosr4375 - r;
- else
- r = acosr4375 + r;
- return r;
- }
- else if (ix < 0x3fe40000) /* |x| < 0.625 */
- {
- t = u.value - 0.5625L;
- 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;
- if (sign & 0x80000000)
- r = pimacosr5625 - p / q;
- else
- r = acosr5625 + p / q;
- return r;
- }
- else
- { /* |x| >= .625 */
- z = (one - u.value) * 0.5;
- s = __ieee754_sqrtl (z);
- /* Compute an extended precision square root from
- the Newton iteration s -> 0.5 * (s + z / s).
- The change w from s to the improved value is
- w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s.
- Express s = f1 + f2 where f1 * f1 is exactly representable.
- w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
- s + w has extended precision. */
- u.value = s;
- u.parts32.w2 = 0;
- u.parts32.w3 = 0;
- f2 = s - u.value;
- w = z - u.value * u.value;
- w = w - 2.0 * u.value * f2;
- w = w - f2 * f2;
- w = w / (2.0 * s);
- /* Arcsine of s. */
- p = (((((((((pS9 * z
- + pS8) * z
- + pS7) * z
- + pS6) * z
- + pS5) * z
- + pS4) * z
- + pS3) * z
- + pS2) * z
- + pS1) * z
- + pS0) * z;
- q = (((((((( z
- + qS8) * z
- + qS7) * z
- + qS6) * z
- + qS5) * z
- + qS4) * z
- + qS3) * z
- + qS2) * z
- + qS1) * z
- + qS0;
- r = s + (w + s * p / q);
-
- if (sign & 0x80000000)
- w = pio2_hi + (pio2_lo - r);
- else
- w = r;
- return 2.0 * w;
- }
-}