contrib/openbsd_libm/src/e_acosh.c

   1 /* @(#)e_acosh.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 /* acosh(x)
  14  * Method :
  15  *      Based on
  16  *              acosh(x) = log [ x + sqrt(x*x-1) ]
  17  *      we have
  18  *              acosh(x) := log(x)+ln2, if x is large; else
  19  *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
  20  *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
  21  *
  22  * Special cases:
  23  *      acosh(x) is NaN with signal if x<1.
  24  *      acosh(NaN) is NaN without signal.
  25  */
  26
  27 #include <float.h>
  28 #include <math.h>
  29
  30 #include "math_private.h"
  31
  32 static const double
  33 one     = 1.0,
  34 ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
  35
  36 double
  37 acosh(double x)
  38 {
  39         double t;
  40         int32_t hx;
  41         u_int32_t lx;
  42         EXTRACT_WORDS(hx,lx,x);
  43         if(hx<0x3ff00000) {             /* x < 1 */
  44             return (x-x)/(x-x);
  45         } else if(hx >=0x41b00000) {    /* x > 2**28 */
  46             if(hx >=0x7ff00000) {       /* x is inf of NaN */
  47                 return x+x;
  48             } else
  49                 return log(x)+ln2;      /* acosh(huge)=log(2x) */
  50         } else if(((hx-0x3ff00000)|lx)==0) {
  51             return 0.0;                 /* acosh(1) = 0 */
  52         } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
  53             t=x*x;
  54             return log(2.0*x-one/(x+sqrt(t-one)));
  55         } else {                        /* 1<x<2 */
  56             t = x-one;
  57             return log1p(t+sqrt(2.0*t+t*t));
  58         }
  59 }
  60
  61 #if     LDBL_MANT_DIG == DBL_MANT_DIG
  62 __strong_alias(acoshl, acosh);
  63 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */