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- /* e_sinhl.c -- long double version of e_sinh.c.
- * Conversion to long double by Ulrich Drepper,
- * Cygnus Support, drepper@cygnus.com.
- */
- /*
- * ====================================================
- * 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.
- * ====================================================
- */
- /* Changes for 128-bit long double 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/>. */
- /* sinhq(x)
- * Method :
- * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
- * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
- * 2.
- * E + E/(E+1)
- * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1q(x)
- * 2
- *
- * 25 <= x <= lnovft : sinhl(x) := expq(x)/2
- * lnovft <= x <= ln2ovft: sinhl(x) := expq(x/2)/2 * expq(x/2)
- * ln2ovft < x : sinhl(x) := x*shuge (overflow)
- *
- * Special cases:
- * sinhl(x) is |x| if x is +INF, -INF, or NaN.
- * only sinhl(0)=0 is exact for finite x.
- */
- #include "quadmath-imp.h"
- static const __float128 one = 1.0, shuge = 1.0e4931Q,
- ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
- __float128
- sinhq (__float128 x)
- {
- __float128 t, w, h;
- uint32_t jx, ix;
- ieee854_float128 u;
- /* Words of |x|. */
- u.value = x;
- jx = u.words32.w0;
- ix = jx & 0x7fffffff;
- /* x is INF or NaN */
- if (ix >= 0x7fff0000)
- return x + x;
- h = 0.5;
- if (jx & 0x80000000)
- h = -h;
- /* Absolute value of x. */
- u.words32.w0 = ix;
- /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
- if (ix <= 0x40044000)
- {
- if (ix < 0x3fc60000) /* |x| < 2^-57 */
- {
- math_check_force_underflow (x);
- if (shuge + x > one)
- return x; /* sinh(tiny) = tiny with inexact */
- }
- t = expm1q (u.value);
- if (ix < 0x3fff0000)
- return h * (2.0 * t - t * t / (t + one));
- return h * (t + t / (t + one));
- }
- /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
- if (ix <= 0x400c62e3) /* 11356.375 */
- return h * expq (u.value);
- /* |x| in [log(maxdouble), overflowthreshold]
- Overflow threshold is log(2 * maxdouble). */
- if (u.value <= ovf_thresh)
- {
- w = expq (0.5 * u.value);
- t = h * w;
- return t * w;
- }
- /* |x| > overflowthreshold, sinhl(x) overflow */
- return x * shuge;
- }
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