1 /* e_sinhl.c -- long double version of e_sinh.c. 2 * Conversion to long double by Ulrich Drepper, 3 * Cygnus Support, drepper@cygnus.com. 4 */ 5 6 /* 7 * ==================================================== 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 9 * 10 * Developed at SunPro, a Sun Microsystems, Inc. business. 11 * Permission to use, copy, modify, and distribute this 12 * software is freely granted, provided that this notice 13 * is preserved. 14 * ==================================================== 15 */ 16 17 /* Changes for 128-bit long double are 18 Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> 19 and are incorporated herein by permission of the author. The author 20 reserves the right to distribute this material elsewhere under different 21 copying permissions. These modifications are distributed here under 22 the following terms: 23 24 This library is free software; you can redistribute it and/or 25 modify it under the terms of the GNU Lesser General Public 26 License as published by the Free Software Foundation; either 27 version 2.1 of the License, or (at your option) any later version. 28 29 This library is distributed in the hope that it will be useful, 30 but WITHOUT ANY WARRANTY; without even the implied warranty of 31 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 32 Lesser General Public License for more details. 33 34 You should have received a copy of the GNU Lesser General Public 35 License along with this library; if not, see 36 <http://www.gnu.org/licenses/>. */ 37 38 /* sinhq(x) 39 * Method : 40 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 41 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)). 42 * 2. 43 * E + E/(E+1) 44 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1q(x) 45 * 2 46 * 47 * 25 <= x <= lnovft : sinhl(x) := expq(x)/2 48 * lnovft <= x <= ln2ovft: sinhl(x) := expq(x/2)/2 * expq(x/2) 49 * ln2ovft < x : sinhl(x) := x*shuge (overflow) 50 * 51 * Special cases: 52 * sinhl(x) is |x| if x is +INF, -INF, or NaN. 53 * only sinhl(0)=0 is exact for finite x. 54 */ 55 56 #include "quadmath-imp.h" 57 58 static const __float128 one = 1.0, shuge = 1.0e4931Q, 59 ovf_thresh = 1.1357216553474703894801348310092223067821E4Q; 60 61 __float128 62 sinhq (__float128 x) 63 { 64 __float128 t, w, h; 65 uint32_t jx, ix; 66 ieee854_float128 u; 67 68 /* Words of |x|. */ 69 u.value = x; 70 jx = u.words32.w0; 71 ix = jx & 0x7fffffff; 72 73 /* x is INF or NaN */ 74 if (ix >= 0x7fff0000) 75 return x + x; 76 77 h = 0.5; 78 if (jx & 0x80000000) 79 h = -h; 80 81 /* Absolute value of x. */ 82 u.words32.w0 = ix; 83 84 /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */ 85 if (ix <= 0x40044000) 86 { 87 if (ix < 0x3fc60000) /* |x| < 2^-57 */ 88 { 89 math_check_force_underflow (x); 90 if (shuge + x > one) 91 return x; /* sinh(tiny) = tiny with inexact */ 92 } 93 t = expm1q (u.value); 94 if (ix < 0x3fff0000) 95 return h * (2.0 * t - t * t / (t + one)); 96 return h * (t + t / (t + one)); 97 } 98 99 /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */ 100 if (ix <= 0x400c62e3) /* 11356.375 */ 101 return h * expq (u.value); 102 103 /* |x| in [log(maxdouble), overflowthreshold] 104 Overflow threshold is log(2 * maxdouble). */ 105 if (u.value <= ovf_thresh) 106 { 107 w = expq (0.5 * u.value); 108 t = h * w; 109 return t * w; 110 } 111 112 /* |x| > overflowthreshold, sinhl(x) overflow */ 113 return x * shuge; 114 } 115