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- /*
- * ====================================================
- * 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));
- }
- }
- strong_alias(__ieee754_acosh, acosh)
- libm_hidden_def(acosh)
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