/* origin: FreeBSD /usr/src/lib/msun/src/e_acosh.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== * */ /* 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 "libm.h" static const double one = 1.0, ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ double acosh(double x) { double t; int32_t hx; uint32_t lx; EXTRACT_WORDS(hx, lx, x); if (hx < 0x3ff00000) { /* x < 1 */ return (x-x)/(x-x); } else if (hx >= 0x41b00000) { /* x > 2**28 */ if (hx >= 0x7ff00000) /* x is inf of NaN */ return x+x; return log(x) + ln2; /* acosh(huge) = log(2x) */ } else if ((hx-0x3ff00000 | lx) == 0) { return 0.0; /* acosh(1) = 0 */ } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ t = x*x; return log(2.0*x - one/(x+sqrt(t-one))); } else { /* 1 < x < 2 */ t = x-one; return log1p(t + sqrt(2.0*t+t*t)); } }