2 /* @(#)e_acosh.c 1.3 95/01/18 */
3 /* $FreeBSD: head/lib/msun/src/e_acosh.c 251599 2013-06-10 06:04:58Z das $ */
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
12 * ====================================================
19 * acosh(x) = log [ x + sqrt(x*x-1) ]
21 * acosh(x) := log(x)+ln2, if x is large; else
22 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
23 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26 * acosh(x) is NaN with signal if x<1.
27 * acosh(NaN) is NaN without signal.
33 #include "math_private.h"
37 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
40 __ieee754_acosh(double x)
45 EXTRACT_WORDS(hx,lx,x);
46 if(hx<0x3ff00000) { /* x < 1 */
48 } else if(hx >=0x41b00000) { /* x > 2**28 */
49 if(hx >=0x7ff00000) { /* x is inf of NaN */
52 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
53 } else if(((hx-0x3ff00000)|lx)==0) {
54 return 0.0; /* acosh(1) = 0 */
55 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
57 return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
60 return log1p(t+sqrt(2.0*t+t*t));
64 #if LDBL_MANT_DIG == 53
65 __weak_reference(acosh, acoshl);