1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #pragma weak __coshl = coshl 31 32 #include "libm.h" 33 #include "longdouble.h" 34 35 36 /* 37 * coshl(X) 38 * RETURN THE HYPERBOLIC COSINE OF X 39 * 40 * Method : 41 * 1. Replace x by |x| (coshl(x) = coshl(-x)). 42 * 2. 43 * [ expl(x) - 1 ]^2 44 * 0 <= x <= 0.3465 : coshl(x) := 1 + ------------------- 45 * 2*expl(x) 46 * 47 * expl(x) + 1/expl(x) 48 * 0.3465 <= x <= thresh : coshl(x) := ------------------- 49 * 2 50 * thresh <= x <= lnovft : coshl(x) := expl(x)/2 51 * lnovft <= x < INF : coshl(x) := scalbnl(expl(x-1024*ln2),1023) 52 * 53 * here 54 * thr1 a number that is near one half of ln2. 55 * thr2 a number such that 56 * expl(thresh)+expl(-thresh)=expl(thresh) 57 * lnovft: logrithm of the overflow threshold 58 * = MEP1*ln2 chopped to machine precision. 59 * ME maximum exponent 60 * MEP1 maximum exponent plus 1 61 * 62 * Special cases: 63 * coshl(x) is |x| if x is +INF, -INF, or NaN. 64 * only coshl(0)=1 is exact for finite x. 65 */ 66 67 #define ME 16383 68 #define MEP1 16384 69 #define LNOVFT 1.135652340629414394949193107797076342845e+4L 70 /* last 32 bits of LN2HI is zero */ 71 #define LN2HI 6.931471805599453094172319547495844850203e-0001L 72 #define LN2LO 1.667085920830552208890449330400379754169e-0025L 73 #define THR1 0.3465L 74 #define THR2 45.L 75 76 static const long double 77 half = 0.5L, 78 tinyl = 7.5e-37L, 79 one = 1.0L, 80 ln2hi = LN2HI, 81 ln2lo = LN2LO, 82 lnovftL = LNOVFT, 83 thr1 = THR1, 84 thr2 = THR2; 85 86 long double 87 coshl(long double x) { 88 long double t, w; 89 90 w = fabsl(x); 91 if (!finitel(w)) 92 return (w + w); /* x is INF or NaN */ 93 if (w < thr1) { 94 t = w < tinyl ? w : expm1l(w); 95 w = one + t; 96 if (w != one) 97 w = one + (t * t) / (w + w); 98 return (w); 99 } else if (w < thr2) { 100 t = expl(w); 101 return (half * (t + one / t)); 102 } else if (w <= lnovftL) 103 return (half * expl(w)); 104 else { 105 return (scalbnl(expl((w - MEP1 * ln2hi) - MEP1 * ln2lo), ME)); 106 } 107 } 108