| 1 | /* s_asinhl.c -- long double version of s_asinh.c. |
| 2 | * Conversion to long double by Ulrich Drepper, |
| 3 | * Cygnus Support, drepper@cygnus.com. |
| 4 | */ |
| 5 | |
| 6 | /* |
| 7 | * ==================================================== |
| 8 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 9 | * |
| 10 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 11 | * Permission to use, copy, modify, and distribute this |
| 12 | * software is freely granted, provided that this notice |
| 13 | * is preserved. |
| 14 | * ==================================================== |
| 15 | */ |
| 16 | |
| 17 | #if defined(LIBM_SCCS) && !defined(lint) |
| 18 | static char rcsid[] = "$NetBSD: $" ; |
| 19 | #endif |
| 20 | |
| 21 | /* asinhl(x) |
| 22 | * Method : |
| 23 | * Based on |
| 24 | * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] |
| 25 | * we have |
| 26 | * asinhl(x) := x if 1+x*x=1, |
| 27 | * := signl(x)*(logl(x)+ln2)) for large |x|, else |
| 28 | * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else |
| 29 | * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) |
| 30 | */ |
| 31 | |
| 32 | #include <float.h> |
| 33 | #include <math.h> |
| 34 | #include <math_private.h> |
| 35 | #include <math-underflow.h> |
| 36 | #include <libm-alias-ldouble.h> |
| 37 | |
| 38 | static const _Float128 |
| 39 | one = 1, |
| 40 | ln2 = L(6.931471805599453094172321214581765681e-1), |
| 41 | huge = L(1.0e+4900); |
| 42 | |
| 43 | _Float128 |
| 44 | __asinhl (_Float128 x) |
| 45 | { |
| 46 | _Float128 t, w; |
| 47 | int32_t ix, sign; |
| 48 | ieee854_long_double_shape_type u; |
| 49 | |
| 50 | u.value = x; |
| 51 | sign = u.parts32.w0; |
| 52 | ix = sign & 0x7fffffff; |
| 53 | if (ix == 0x7fff0000) |
| 54 | return x + x; /* x is inf or NaN */ |
| 55 | if (ix < 0x3fc70000) |
| 56 | { /* |x| < 2^ -56 */ |
| 57 | math_check_force_underflow (x); |
| 58 | if (huge + x > one) |
| 59 | return x; /* return x inexact except 0 */ |
| 60 | } |
| 61 | u.parts32.w0 = ix; |
| 62 | if (ix > 0x40350000) |
| 63 | { /* |x| > 2 ^ 54 */ |
| 64 | w = __ieee754_logl (u.value) + ln2; |
| 65 | } |
| 66 | else if (ix >0x40000000) |
| 67 | { /* 2^ 54 > |x| > 2.0 */ |
| 68 | t = u.value; |
| 69 | w = __ieee754_logl (2.0 * t + one / (sqrtl (x * x + one) + t)); |
| 70 | } |
| 71 | else |
| 72 | { /* 2.0 > |x| > 2 ^ -56 */ |
| 73 | t = x * x; |
| 74 | w = __log1pl (u.value + t / (one + sqrtl (one + t))); |
| 75 | } |
| 76 | if (sign & 0x80000000) |
| 77 | return -w; |
| 78 | else |
| 79 | return w; |
| 80 | } |
| 81 | libm_alias_ldouble (__asinh, asinh) |
| 82 | |