| /* |
| * ==================================================== |
| * 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, 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 "math.h" |
| #include "math_private.h" |
| |
| #ifdef __STDC__ |
| static const long double one = 1.0, half = 0.5, huge = 1.0e4900L, |
| ovf_thresh = 1.1357216553474703894801348310092223067821E4L; |
| #else |
| static long double one = 1.0, half = 0.5, huge = 1.0e4900L, |
| ovf_thresh = 1.1357216553474703894801348310092223067821E4L; |
| #endif |
| |
| #ifdef __STDC__ |
| long double |
| __ieee754_coshl (long double x) |
| #else |
| long double |
| __ieee754_coshl (x) |
| long double x; |
| #endif |
| { |
| long double t, w; |
| int32_t ex; |
| ieee854_long_double_shape_type u; |
| |
| u.value = x; |
| ex = u.parts32.w0 & 0x7fffffff; |
| |
| /* Absolute value of x. */ |
| u.parts32.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 = __expm1l (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 = __ieee754_expl (u.value); |
| return half * t + half / t; |
| } |
| |
| /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ |
| if (ex <= 0x400c62e3) /* 11356.375 */ |
| return half * __ieee754_expl (u.value); |
| |
| /* |x| in [log(maxdouble), overflowthresold] */ |
| if (u.value <= ovf_thresh) |
| { |
| w = __ieee754_expl (half * u.value); |
| t = half * w; |
| return t * w; |
| } |
| |
| /* |x| > overflowthresold, cosh(x) overflow */ |
| return huge * huge; |
| } |
