125c28e83SPiotr Jasiukajtis /* 225c28e83SPiotr Jasiukajtis * CDDL HEADER START 325c28e83SPiotr Jasiukajtis * 425c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the 525c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License"). 625c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License. 725c28e83SPiotr Jasiukajtis * 825c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 925c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing. 1025c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions 1125c28e83SPiotr Jasiukajtis * and limitations under the License. 1225c28e83SPiotr Jasiukajtis * 1325c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each 1425c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 1525c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the 1625c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying 1725c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner] 1825c28e83SPiotr Jasiukajtis * 1925c28e83SPiotr Jasiukajtis * CDDL HEADER END 2025c28e83SPiotr Jasiukajtis */ 2125c28e83SPiotr Jasiukajtis 2225c28e83SPiotr Jasiukajtis /* 2325c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 2425c28e83SPiotr Jasiukajtis */ 2525c28e83SPiotr Jasiukajtis /* 2625c28e83SPiotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 2725c28e83SPiotr Jasiukajtis * Use is subject to license terms. 2825c28e83SPiotr Jasiukajtis */ 2925c28e83SPiotr Jasiukajtis 30*ddc0e0b5SRichard Lowe #pragma weak __acosh = acosh 3125c28e83SPiotr Jasiukajtis 3225c28e83SPiotr Jasiukajtis /* INDENT OFF */ 3325c28e83SPiotr Jasiukajtis /* 3425c28e83SPiotr Jasiukajtis * acosh(x) 3525c28e83SPiotr Jasiukajtis * Method : 3625c28e83SPiotr Jasiukajtis * Based on 3725c28e83SPiotr Jasiukajtis * acosh(x) = log [ x + sqrt(x*x-1) ] 3825c28e83SPiotr Jasiukajtis * we have 3925c28e83SPiotr Jasiukajtis * acosh(x) := log(x)+ln2, if x is large; else 4025c28e83SPiotr Jasiukajtis * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x > 2; else 4125c28e83SPiotr Jasiukajtis * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t = x-1. 4225c28e83SPiotr Jasiukajtis * 4325c28e83SPiotr Jasiukajtis * Special cases: 4425c28e83SPiotr Jasiukajtis * acosh(x) is NaN with signal if x < 1. 4525c28e83SPiotr Jasiukajtis * acosh(NaN) is NaN without signal. 4625c28e83SPiotr Jasiukajtis */ 4725c28e83SPiotr Jasiukajtis /* INDENT ON */ 4825c28e83SPiotr Jasiukajtis 4925c28e83SPiotr Jasiukajtis #include "libm_protos.h" /* _SVID_libm_error */ 5025c28e83SPiotr Jasiukajtis #include "libm_macros.h" 5125c28e83SPiotr Jasiukajtis #include <math.h> 5225c28e83SPiotr Jasiukajtis 5325c28e83SPiotr Jasiukajtis static const double 5425c28e83SPiotr Jasiukajtis one = 1.0, 5525c28e83SPiotr Jasiukajtis ln2 = 6.93147180559945286227e-01; /* 3FE62E42, FEFA39EF */ 5625c28e83SPiotr Jasiukajtis 5725c28e83SPiotr Jasiukajtis double 5825c28e83SPiotr Jasiukajtis acosh(double x) { 5925c28e83SPiotr Jasiukajtis double t; 6025c28e83SPiotr Jasiukajtis int hx; 6125c28e83SPiotr Jasiukajtis 6225c28e83SPiotr Jasiukajtis hx = ((int *) &x)[HIWORD]; 6325c28e83SPiotr Jasiukajtis if (hx < 0x3ff00000) { /* x < 1 */ 6425c28e83SPiotr Jasiukajtis if (isnan(x)) 6525c28e83SPiotr Jasiukajtis #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 6625c28e83SPiotr Jasiukajtis return (hx >= 0xfff80000 ? x : (x - x) / (x - x)); 6725c28e83SPiotr Jasiukajtis /* assumes sparc-like QNaN */ 6825c28e83SPiotr Jasiukajtis #else 6925c28e83SPiotr Jasiukajtis return (x - x) / (x - x); 7025c28e83SPiotr Jasiukajtis #endif 7125c28e83SPiotr Jasiukajtis else 7225c28e83SPiotr Jasiukajtis return (_SVID_libm_err(x, x, 29)); 7325c28e83SPiotr Jasiukajtis } else if (hx >= 0x41b00000) { 7425c28e83SPiotr Jasiukajtis /* x > 2**28 */ 7525c28e83SPiotr Jasiukajtis if (hx >= 0x7ff00000) { /* x is inf of NaN */ 7625c28e83SPiotr Jasiukajtis #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 7725c28e83SPiotr Jasiukajtis return (hx >= 0x7ff80000 ? x : x + x); 7825c28e83SPiotr Jasiukajtis /* assumes sparc-like QNaN */ 7925c28e83SPiotr Jasiukajtis #else 8025c28e83SPiotr Jasiukajtis return (x + x); 8125c28e83SPiotr Jasiukajtis #endif 8225c28e83SPiotr Jasiukajtis } else /* acosh(huge)=log(2x) */ 8325c28e83SPiotr Jasiukajtis return (log(x) + ln2); 8425c28e83SPiotr Jasiukajtis } else if (((hx - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) { 8525c28e83SPiotr Jasiukajtis return (0.0); /* acosh(1) = 0 */ 8625c28e83SPiotr Jasiukajtis } else if (hx > 0x40000000) { 8725c28e83SPiotr Jasiukajtis /* 2**28 > x > 2 */ 8825c28e83SPiotr Jasiukajtis t = x * x; 8925c28e83SPiotr Jasiukajtis return (log(2.0 * x - one / (x + sqrt(t - one)))); 9025c28e83SPiotr Jasiukajtis } else { 9125c28e83SPiotr Jasiukajtis /* 1 < x < 2 */ 9225c28e83SPiotr Jasiukajtis t = x - one; 9325c28e83SPiotr Jasiukajtis return (log1p(t + sqrt(2.0 * t + t * t))); 9425c28e83SPiotr Jasiukajtis } 9525c28e83SPiotr Jasiukajtis } 96