sysdeps/ieee754/ldbl-128ibm/e_acoshl.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 /* __ieee754_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 <math.h>
  28 #include <math_private.h>
  29
  30 static const long double
  31 one     = 1.0L,
  32 ln2     = 6.93147180559945286227e-01L;  /* 0x3FE62E42, 0xFEFA39EF */
  33
  34 long double
  35 __ieee754_acoshl(long double x)
  36 {
  37         long double t;
  38         int64_t hx;
  39         u_int64_t lx;
  40         GET_LDOUBLE_WORDS64(hx,lx,x);
  41         if(hx<0x3ff0000000000000LL) {           /* x < 1 */
  42             return (x-x)/(x-x);
  43         } else if(hx >=0x41b0000000000000LL) {  /* x > 2**28 */
  44             if(hx >=0x7ff0000000000000LL) {     /* x is inf of NaN */
  45                 return x+x;
  46             } else
  47                 return __ieee754_logl(x)+ln2;   /* acosh(huge)=log(2x) */
  48         } else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) {
  49             return 0.0;                 /* acosh(1) = 0 */
  50         } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
  51             t=x*x;
  52             return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
  53         } else {                        /* 1<x<2 */
  54             t = x-one;
  55             return __log1p(t+__ieee754_sqrtl(2.0*t+t*t));
  56         }
  57 }
  58 strong_alias (__ieee754_acoshl, __acoshl_finite)