1 /* origin: FreeBSD /usr/src/lib/msun/src/e_acosh.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
16 * acosh(x) = log [ x + sqrt(x*x-1) ]
18 * acosh(x) := log(x)+ln2, if x is large; else
19 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
20 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
23 * acosh(x) is NaN with signal if x<1.
24 * acosh(NaN) is NaN without signal.
31 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
33 double acosh(double x)
39 EXTRACT_WORDS(hx, lx, x);
40 if (hx < 0x3ff00000) { /* x < 1 */
42 } else if (hx >= 0x41b00000) { /* x > 2**28 */
43 if (hx >= 0x7ff00000) /* x is inf of NaN */
45 return log(x) + ln2; /* acosh(huge) = log(2x) */
46 } else if ((hx-0x3ff00000 | lx) == 0) {
47 return 0.0; /* acosh(1) = 0 */
48 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
50 return log(2.0*x - one/(x+sqrt(t-one)));
51 } else { /* 1 < x < 2 */
53 return log1p(t + sqrt(2.0*t+t*t));