| /* Optimized for 64-bit by Ulrich Drepper <drepper@gmail.com>, 2012 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| /* __ieee754_acosh(x) |
| * Method : |
| * Based on |
| * acosh(x) = log [ x + sqrt(x*x-1) ] |
| * we have |
| * acosh(x) := log(x)+ln2, if x is large; else |
| * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
| * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
| * |
| * Special cases: |
| * acosh(x) is NaN with signal if x<1. |
| * acosh(NaN) is NaN without signal. |
| */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| |
| static const double |
| one = 1.0, |
| ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
| |
| double |
| __ieee754_acosh (double x) |
| { |
| int64_t hx; |
| EXTRACT_WORDS64 (hx, x); |
| |
| if (hx > INT64_C (0x4000000000000000)) |
| { |
| if (__builtin_expect (hx >= INT64_C (0x41b0000000000000), 0)) |
| { |
| /* x > 2**28 */ |
| if (hx >= INT64_C (0x7ff0000000000000)) |
| /* x is inf of NaN */ |
| return x + x; |
| else |
| return __ieee754_log (x) + ln2;/* acosh(huge)=log(2x) */ |
| } |
| |
| /* 2**28 > x > 2 */ |
| double t = x * x; |
| return __ieee754_log (2.0 * x - one / (x + __ieee754_sqrt (t - one))); |
| } |
| else if (__builtin_expect (hx > INT64_C (0x3ff0000000000000), 1)) |
| { |
| /* 1<x<2 */ |
| double t = x - one; |
| return __log1p (t + __ieee754_sqrt (2.0 * t + t * t)); |
| } |
| else if (__builtin_expect (hx == INT64_C (0x3ff0000000000000), 1)) |
| return 0.0; /* acosh(1) = 0 */ |
| else /* x < 1 */ |
| return (x - x) / (x - x); |
| } |
| strong_alias (__ieee754_acosh, __acosh_finite) |
