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Diffstat (limited to 'sysdeps/ieee754/ldbl-128/e_asinl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/e_asinl.c | 258 |
1 files changed, 0 insertions, 258 deletions
diff --git a/sysdeps/ieee754/ldbl-128/e_asinl.c b/sysdeps/ieee754/ldbl-128/e_asinl.c deleted file mode 100644 index 1edf1c05a1..0000000000 --- a/sysdeps/ieee754/ldbl-128/e_asinl.c +++ /dev/null @@ -1,258 +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> - -static const _Float128 - one = 1, - huge = L(1.0e+4932), - pio2_hi = L(1.5707963267948966192313216916397514420986), - pio2_lo = L(4.3359050650618905123985220130216759843812E-35), - pio4_hi = L(7.8539816339744830961566084581987569936977E-1), - - /* 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 = L(-8.358099012470680544198472400254596543711E2), - pS1 = L(3.674973957689619490312782828051860366493E3), - pS2 = L(-6.730729094812979665807581609853656623219E3), - pS3 = L(6.643843795209060298375552684423454077633E3), - pS4 = L(-3.817341990928606692235481812252049415993E3), - pS5 = L(1.284635388402653715636722822195716476156E3), - pS6 = L(-2.410736125231549204856567737329112037867E2), - pS7 = L(2.219191969382402856557594215833622156220E1), - pS8 = L(-7.249056260830627156600112195061001036533E-1), - pS9 = L(1.055923570937755300061509030361395604448E-3), - - qS0 = L(-5.014859407482408326519083440151745519205E3), - qS1 = L(2.430653047950480068881028451580393430537E4), - qS2 = L(-4.997904737193653607449250593976069726962E4), - qS3 = L(5.675712336110456923807959930107347511086E4), - qS4 = L(-3.881523118339661268482937768522572588022E4), - qS5 = L(1.634202194895541569749717032234510811216E4), - qS6 = L(-4.151452662440709301601820849901296953752E3), - qS7 = L(5.956050864057192019085175976175695342168E2), - qS8 = L(-4.175375777334867025769346564600396877176E1), - /* 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 = L(-5.619049346208901520945464704848780243887E0), - rS1 = L(4.460504162777731472539175700169871920352E1), - rS2 = L(-1.317669505315409261479577040530751477488E2), - rS3 = L(1.626532582423661989632442410808596009227E2), - rS4 = L(-3.144806644195158614904369445440583873264E1), - rS5 = L(-9.806674443470740708765165604769099559553E1), - rS6 = L(5.708468492052010816555762842394927806920E1), - rS7 = L(1.396540499232262112248553357962639431922E1), - rS8 = L(-1.126243289311910363001762058295832610344E1), - rS9 = L(-4.956179821329901954211277873774472383512E-1), - rS10 = L(3.313227657082367169241333738391762525780E-1), - - sS0 = L(-4.645814742084009935700221277307007679325E0), - sS1 = L(3.879074822457694323970438316317961918430E1), - sS2 = L(-1.221986588013474694623973554726201001066E2), - sS3 = L(1.658821150347718105012079876756201905822E2), - sS4 = L(-4.804379630977558197953176474426239748977E1), - sS5 = L(-1.004296417397316948114344573811562952793E2), - sS6 = L(7.530281592861320234941101403870010111138E1), - sS7 = L(1.270735595411673647119592092304357226607E1), - sS8 = L(-1.815144839646376500705105967064792930282E1), - sS9 = L(-7.821597334910963922204235247786840828217E-2), - /* 1.000000000000000000000000000000000000000E0 */ - - asinr5625 = L(5.9740641664535021430381036628424864397707E-1); - - - -_Float128 -__ieee754_asinl (_Float128 x) -{ - _Float128 t, w, p, q, c, r, s; - int32_t ix, sign, flag; - ieee854_long_double_shape_type u; - - flag = 0; - u.value = x; - sign = u.parts32.w0; - ix = sign & 0x7fffffff; - u.parts32.w0 = ix; /* |x| */ - if (ix >= 0x3fff0000) /* |x|>= 1 */ - { - if (ix == 0x3fff0000 - && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) - /* asin(1)=+-pi/2 with inexact */ - return x * pio2_hi + x * pio2_lo; - return (x - x) / (x - x); /* asin(|x|>1) is NaN */ - } - else if (ix < 0x3ffe0000) /* |x| < 0.5 */ - { - if (ix < 0x3fc60000) /* |x| < 2**-57 */ - { - math_check_force_underflow (x); - _Float128 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 (ix < 0x3ffe4000) /* 0.625 */ - { - t = u.value - 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 ((sign & 0x80000000) == 0) - return t; - else - return -t; - } - else - { - /* 1 > |x| >= 0.625 */ - w = one - u.value; - 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 (ix >= 0x3ffef333) /* |x| > 0.975 */ - { - w = p / q; - t = pio2_hi - (2.0 * (s + s * w) - pio2_lo); - } - else - { - u.value = s; - u.parts32.w3 = 0; - u.parts32.w2 = 0; - w = u.value; - 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 ((sign & 0x80000000) == 0) - return t; - else - return -t; -} -strong_alias (__ieee754_asinl, __asinl_finite) |