/* * ==================================================== * 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) { double t; int32_t hx; u_int32_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; } else return __ieee754_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 __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one))); } else { /* 1<x<2 */ t = x-one; return log1p(t+sqrt(2.0*t+t*t)); } } /* * wrapper acosh(x) */ #ifndef _IEEE_LIBM double acosh(double x) { double z = __ieee754_acosh(x); if (_LIB_VERSION == _IEEE_ || isnan(x)) return z; if (x < 1.0) return __kernel_standard(x, x, 29); /* acosh(x<1) */ return z; } #else strong_alias(__ieee754_acosh, acosh) #endif libm_hidden_def(acosh)