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 acosh = __acosh 31 32 /* INDENT OFF */ 33 /* acosh(x) 34 * Method : 35 * Based on 36 * acosh(x) = log [ x + sqrt(x*x-1) ] 37 * we have 38 * acosh(x) := log(x)+ln2, if x is large; else 39 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x > 2; else 40 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t = x-1. 41 * 42 * Special cases: 43 * acosh(x) is NaN with signal if x < 1. 44 * acosh(NaN) is NaN without signal. 45 */ 46 /* INDENT ON */ 47 48 #include "libm_synonyms.h" /* __acosh, __log, __log1p */ 49 #include "libm_protos.h" /* _SVID_libm_error */ 50 #include "libm_macros.h" 51 #include <math.h> 52 53 static const double 54 one = 1.0, 55 ln2 = 6.93147180559945286227e-01; /* 3FE62E42, FEFA39EF */ 56 57 double 58 acosh(double x) { 59 double t; 60 int hx; 61 62 hx = ((int *) &x)[HIWORD]; 63 if (hx < 0x3ff00000) { /* x < 1 */ 64 if (isnan(x)) 65 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 66 return hx >= 0xfff80000 ? x : (x - x) / (x - x); 67 /* assumes sparc-like QNaN */ 68 #else 69 return (x - x) / (x - x); 70 #endif 71 else 72 return _SVID_libm_err(x, x, 29); 73 } 74 else if (hx >= 0x41b00000) { /* x > 2**28 */ 75 if (hx >= 0x7ff00000) { /* x is inf of NaN */ 76 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 77 return hx >= 0x7ff80000 ? x : x + x; 78 /* assumes sparc-like QNaN */ 79 #else 80 return x + x; 81 #endif 82 } 83 else /* acosh(huge)=log(2x) */ 84 return log(x) + ln2; 85 } 86 else if (((hx - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) { 87 return 0.0; /* acosh(1) = 0 */ 88 } 89 else if (hx > 0x40000000) { /* 2**28 > x > 2 */ 90 t = x * x; 91 return log(2.0 * x - one / (x + sqrt(t - one))); 92 } 93 else { /* 1 < x < 2 */ 94 t = x - one; 95 return log1p(t + sqrt(2.0 * t + t * t)); 96 } 97 }