toolchain/gcc/newlib/libm/math/e_acosh.c

   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 #ifndef _DOUBLE_IS_32BITS
  32
  33 #ifdef __STDC__
  34 static const double
  35 #else
  36 static double
  37 #endif
  38 one     = 1.0,
  39 ln2     = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
  40
  41 #ifdef __STDC__
  42         double __ieee754_acosh(double x)
  43 #else
  44         double __ieee754_acosh(x)
  45         double x;
  46 #endif
  47 {
  48         double t;
  49         __int32_t hx;
  50         __uint32_t lx;
  51         EXTRACT_WORDS(hx,lx,x);
  52         if(hx<0x3ff00000) {             /* x < 1 */
  53             return (x-x)/(x-x);
  54         } else if(hx >=0x41b00000) {    /* x > 2**28 */
  55             if(hx >=0x7ff00000) {       /* x is inf of NaN */
  56                 return x+x;
  57             } else
  58                 return __ieee754_log(x)+ln2;    /* acosh(huge)=log(2x) */
  59         } else if(((hx-0x3ff00000)|lx)==0) {
  60             return 0.0;                 /* acosh(1) = 0 */
  61         } else if (hx > 0x40000000) {   /* 2**28 > x > 2 */
  62             t=x*x;
  63             return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
  64         } else {                        /* 1<x<2 */
  65             t = x-one;
  66             return log1p(t+__ieee754_sqrt(2.0*t+t*t));
  67         }
  68 }
  69
  70 #endif /* defined(_DOUBLE_IS_32BITS) */