1 /* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_acoshl.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
15 * acoshl(x) = logl [ x + sqrtl(x*x-1) ]
17 * acoshl(x) := logl(x)+ln2, if x is large; else
18 * acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
19 * acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
22 * acoshl(x) is NaN with signal if x<1.
23 * acoshl(NaN) is NaN without signal.
28 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
29 long double acoshl(long double x)
33 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
34 static const long double
36 ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
38 long double acoshl(long double x)
43 GET_LDOUBLE_WORDS(se, i0, i1, x);
44 if (se < 0x3fff || se & 0x8000) { /* x < 1 */
46 } else if (se >= 0x401d) { /* x > 2**30 */
47 if (se >= 0x7fff) /* x is inf or NaN */
49 return logl(x) + ln2; /* acoshl(huge) = logl(2x) */
50 } else if (((se-0x3fff)|i0|i1) == 0) {
51 return 0.0; /* acosh(1) = 0 */
52 } else if (se > 0x4000) { /* x > 2 */
54 return logl(2.0*x - one/(x + sqrtl(t - one)));
58 return log1pl(t + sqrtl(2.0*t + t*t));