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Diffstat (limited to 'sysdeps/ieee754/ldbl-96/e_asinl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/e_asinl.c | 157 |
1 files changed, 0 insertions, 157 deletions
diff --git a/sysdeps/ieee754/ldbl-96/e_asinl.c b/sysdeps/ieee754/ldbl-96/e_asinl.c deleted file mode 100644 index f52b931459..0000000000 --- a/sysdeps/ieee754/ldbl-96/e_asinl.c +++ /dev/null @@ -1,157 +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) - * - * For x in [0.5,1] - * 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 long double - one = 1.0L, - huge = 1.0e+4932L, - pio2_hi = 0x1.921fb54442d1846ap+0L, /* pi/2 rounded to nearest to 64 - bits. */ - pio2_lo = -0x7.6733ae8fe47c65d8p-68L, /* pi/2 - pio2_hi rounded to - nearest to 64 bits. */ - pio4_hi = 0xc.90fdaa22168c235p-4L, /* pi/4 rounded to nearest to 64 - bits. */ - - /* 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-21 */ - pS0 = -1.008714657938491626019651170502036851607E1L, - pS1 = 2.331460313214179572063441834101394865259E1L, - pS2 = -1.863169762159016144159202387315381830227E1L, - pS3 = 5.930399351579141771077475766877674661747E0L, - pS4 = -6.121291917696920296944056882932695185001E-1L, - pS5 = 3.776934006243367487161248678019350338383E-3L, - - qS0 = -6.052287947630949712886794360635592886517E1L, - qS1 = 1.671229145571899593737596543114258558503E2L, - qS2 = -1.707840117062586426144397688315411324388E2L, - qS3 = 7.870295154902110425886636075950077640623E1L, - qS4 = -1.568433562487314651121702982333303458814E1L; - /* 1.000000000000000000000000000000000000000E0 */ - -long double -__ieee754_asinl (long double x) -{ - long double t, w, p, q, c, r, s; - int32_t ix; - u_int32_t se, i0, i1, k; - - GET_LDOUBLE_WORDS (se, i0, i1, x); - ix = se & 0x7fff; - ix = (ix << 16) | (i0 >> 16); - if (ix >= 0x3fff8000) - { /* |x|>= 1 */ - if (ix == 0x3fff8000 && ((i0 - 0x80000000) | i1) == 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 < 0x3ffe8000) - { /* |x|<0.5 */ - if (ix < 0x3fde8000) - { /* if |x| < 2**-33 */ - math_check_force_underflow (x); - if (huge + x > one) - return x; /* return x with inexact if x!=0 */ - } - else - { - t = x * x; - p = - t * (pS0 + - t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5))))); - q = qS0 + t * (qS1 + t * (qS2 + t * (qS3 + t * (qS4 + t)))); - w = p / q; - return x + x * w; - } - } - /* 1> |x|>= 0.5 */ - w = one - fabsl (x); - t = w * 0.5; - p = t * (pS0 + t * (pS1 + t * (pS2 + t * (pS3 + t * (pS4 + t * pS5))))); - q = qS0 + t * (qS1 + t * (qS2 + t * (qS3 + t * (qS4 + t)))); - s = __ieee754_sqrtl (t); - if (ix >= 0x3ffef999) - { /* if |x| > 0.975 */ - w = p / q; - t = pio2_hi - (2.0 * (s + s * w) - pio2_lo); - } - else - { - GET_LDOUBLE_WORDS (k, i0, i1, s); - i1 = 0; - SET_LDOUBLE_WORDS (w,k,i0,i1); - 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 ((se & 0x8000) == 0) - return t; - else - return -t; -} -strong_alias (__ieee754_asinl, __asinl_finite) |