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Annotation of src/lib/libm/src/e_acosh.c, Revision 1.1.1.1

1.1       jtc         1:
                      2: /* @(#)e_acosh.c 5.1 93/09/24 */
                      3: /*
                      4:  * ====================================================
                      5:  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
                      6:  *
                      7:  * Developed at SunPro, a Sun Microsystems, Inc. business.
                      8:  * Permission to use, copy, modify, and distribute this
                      9:  * software is freely granted, provided that this notice
                     10:  * is preserved.
                     11:  * ====================================================
                     12:  *
                     13:  */
                     14:
                     15: /* __ieee754_acosh(x)
                     16:  * Method :
                     17:  *     Based on
                     18:  *             acosh(x) = log [ x + sqrt(x*x-1) ]
                     19:  *     we have
                     20:  *             acosh(x) := log(x)+ln2, if x is large; else
                     21:  *             acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
                     22:  *             acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
                     23:  *
                     24:  * Special cases:
                     25:  *     acosh(x) is NaN with signal if x<1.
                     26:  *     acosh(NaN) is NaN without signal.
                     27:  */
                     28:
                     29: #include "fdlibm.h"
                     30:
                     31: #ifdef __STDC__
                     32: static const double
                     33: #else
                     34: static double
                     35: #endif
                     36: one    = 1.0,
                     37: ln2    = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
                     38:
                     39: #ifdef __STDC__
                     40:        double __ieee754_acosh(double x)
                     41: #else
                     42:        double __ieee754_acosh(x)
                     43:        double x;
                     44: #endif
                     45: {
                     46:        double t;
                     47:        int n0,hx;
                     48:        n0 = ((*(int*)&one)>>29)^1;
                     49:        hx = *(n0+(int*)&x);
                     50:        if(hx<0x3ff00000) {             /* x < 1 */
                     51:            return (x-x)/(x-x);
                     52:        } else if(hx >=0x41b00000) {    /* x > 2**28 */
                     53:            if(hx >=0x7ff00000) {       /* x is inf of NaN */
                     54:                return x+x;
                     55:            } else
                     56:                return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */
                     57:        } else if(((hx-0x3ff00000)|*(1-n0+(int*)&x))==0) {
                     58:            return 0.0;                 /* acosh(1) = 0 */
                     59:        } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
                     60:            t=x*x;
                     61:            return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
                     62:        } else {                        /* 1<x<2 */
                     63:            t = x-one;
                     64:            return log1p(t+sqrt(2.0*t+t*t));
                     65:        }
                     66: }