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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/coshq.c
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diff --git a/libquadmath/math/coshq.c b/libquadmath/math/coshq.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.
+ * ====================================================
+ */
+
+/* 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_coshl(x)
+ * Method :
+ * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
+ * 1. Replace x by |x| (coshl(x) = coshl(-x)).
+ * 2.
+ * [ exp(x) - 1 ]^2
+ * 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
+ * 2*exp(x)
+ *
+ * exp(x) + 1/exp(x)
+ * ln2/2 <= x <= 22 : coshl(x) := -------------------
+ * 2
+ * 22 <= x <= lnovft : coshl(x) := expl(x)/2
+ * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
+ * ln2ovft < x : coshl(x) := huge*huge (overflow)
+ *
+ * Special cases:
+ * coshl(x) is |x| if x is +INF, -INF, or NaN.
+ * only coshl(0)=1 is exact for finite x.
+ */
+
+#include "quadmath-imp.h"
+
+static const __float128 one = 1.0Q, half = 0.5Q, huge = 1.0e4900Q,
+ ovf_thresh = 1.1357216553474703894801348310092223067821E4Q;
+
+__float128
+coshq (__float128 x)
+{
+ __float128 t, w;
+ int32_t ex;
+ ieee854_float128 u;
+
+ u.value = x;
+ ex = u.words32.w0 & 0x7fffffff;
+
+ /* Absolute value of x. */
+ u.words32.w0 = ex;
+
+ /* x is INF or NaN */
+ if (ex >= 0x7fff0000)
+ return x * x;
+
+ /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
+ if (ex < 0x3ffd62e4) /* 0.3465728759765625 */
+ {
+ t = expm1q (u.value);
+ w = one + t;
+ if (ex < 0x3fb80000) /* |x| < 2^-116 */
+ return w; /* cosh(tiny) = 1 */
+
+ return one + (t * t) / (w + w);
+ }
+
+ /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
+ if (ex < 0x40044000)
+ {
+ t = expq (u.value);
+ return half * t + half / t;
+ }
+
+ /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
+ if (ex <= 0x400c62e3) /* 11356.375 */
+ return half * expq (u.value);
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ if (u.value <= ovf_thresh)
+ {
+ w = expq (half * u.value);
+ t = half * w;
+ return t * w;
+ }
+
+ /* |x| > overflowthresold, cosh(x) overflow */
+ return huge * huge;
+}