1 /* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_asinhl.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 * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
17 * asinhl(x) := x if 1+x*x=1,
18 * := signl(x)*(logl(x)+ln2)) for large |x|, else
19 * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
20 * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
25 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
26 long double asinhl(long double x)
30 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
31 static const long double
32 one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
33 ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
34 huge = 1.000000000000000000e+4900L;
36 long double asinhl(long double x)
41 GET_LDOUBLE_EXP(hx, x);
44 return x + x; /* x is inf or NaN */
45 if (ix < 0x3fde) { /* |x| < 2**-34 */
46 /* return x, raise inexact if x != 0 */
50 if (ix > 0x4020) { /* |x| > 2**34 */
51 w = logl(fabsl(x)) + ln2;
52 } else if (ix > 0x4000) { /* 2**34 > |x| > 2.0 */
54 w = logl(2.0*t + one/(sqrtl(x*x + one) + t));
55 } else { /* 2.0 > |x| > 2**-28 */
57 w =log1pl(fabsl(x) + t/(one + sqrtl(one + t)));