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authorupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
committerupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
commit554fd8c5195424bdbcabf5de30fdc183aba391bd (patch)
tree976dc5ab7fddf506dadce60ae936f43f58787092 /libquadmath/math/sinhq.c
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diff --git a/libquadmath/math/sinhq.c b/libquadmath/math/sinhq.c
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+/* e_sinhl.c -- __float128 version of e_sinh.c.
+ * Conversion to __float128 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 __float128 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_sinhl(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=expm1l(x)
+ * 2
+ *
+ * 25 <= x <= lnovft : sinhl(x) := expl(x)/2
+ * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(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 = 0.5Q;
+ 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 */
+ if (shuge + x > one)
+ return x; /* sinh(tiny) = tiny with inexact */
+ t = expm1q (u.value);
+ if (ix < 0x3fff0000)
+ return h * (2.0Q * 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 (0.5Q * u.value);
+ t = h * w;
+ return t * w;
+ }
+
+ /* |x| > overflowthreshold, sinhl(x) overflow */
+ return x * shuge;
+}