1/* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12/* Changes for 128-bit __float128 are 13 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> 14 and are incorporated herein by permission of the author. The author 15 reserves the right to distribute this material elsewhere under different 16 copying permissions. These modifications are distributed here under 17 the following terms: 18 19 This library is free software; you can redistribute it and/or 20 modify it under the terms of the GNU Lesser General Public 21 License as published by the Free Software Foundation; either 22 version 2.1 of the License, or (at your option) any later version. 23 24 This library is distributed in the hope that it will be useful, 25 but WITHOUT ANY WARRANTY; without even the implied warranty of 26 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 27 Lesser General Public License for more details. 28 29 You should have received a copy of the GNU Lesser General Public 30 License along with this library; if not, write to the Free Software 31 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ 32 33/* coshq(x) 34 * Method : 35 * mathematically coshq(x) if defined to be (exp(x)+exp(-x))/2 36 * 1. Replace x by |x| (coshq(x) = coshq(-x)). 37 * 2. 38 * [ exp(x) - 1 ]^2 39 * 0 <= x <= ln2/2 : coshq(x) := 1 + ------------------- 40 * 2*exp(x) 41 * 42 * exp(x) + 1/exp(x) 43 * ln2/2 <= x <= 22 : coshq(x) := ------------------- 44 * 2 45 * 22 <= x <= lnovft : coshq(x) := expq(x)/2 46 * lnovft <= x <= ln2ovft: coshq(x) := expq(x/2)/2 * expq(x/2) 47 * ln2ovft < x : coshq(x) := huge*huge (overflow) 48 * 49 * Special cases: 50 * coshq(x) is |x| if x is +INF, -INF, or NaN. 51 * only coshq(0)=1 is exact for finite x. 52 */ 53 54#include "quadmath-imp.h" 55 56static const __float128 one = 1.0Q, half = 0.5Q, huge = 1.0e4900Q, 57 ovf_thresh = 1.1357216553474703894801348310092223067821E4Q; 58 59__float128 60coshq (__float128 x) 61{ 62 __float128 t, w; 63 int32_t ex; 64 ieee854_float128 u; 65 66 u.value = x; 67 ex = u.words32.w0 & 0x7fffffff; 68 69 /* Absolute value of x. */ 70 u.words32.w0 = ex; 71 72 /* x is INF or NaN */ 73 if (ex >= 0x7fff0000) 74 return x * x; 75 76 /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expq(|x|)) */ 77 if (ex < 0x3ffd62e4) /* 0.3465728759765625 */ 78 { 79 t = expm1q (u.value); 80 w = one + t; 81 if (ex < 0x3fb80000) /* |x| < 2^-116 */ 82 return w; /* cosh(tiny) = 1 */ 83 84 return one + (t * t) / (w + w); 85 } 86 87 /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ 88 if (ex < 0x40044000) 89 { 90 t = expq (u.value); 91 return half * t + half / t; 92 } 93 94 /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ 95 if (ex <= 0x400c62e3) /* 11356.375 */ 96 return half * expq (u.value); 97 98 /* |x| in [log(maxdouble), overflowthresold] */ 99 if (u.value <= ovf_thresh) 100 { 101 w = expq (half * u.value); 102 t = half * w; 103 return t * w; 104 } 105 106 /* |x| > overflowthresold, cosh(x) overflow */ 107 return huge * huge; 108} 109