libquadmath/math/acoshq.c

   1 /* acoshq.c -- __float128 version of e_acosh.c.
   2  * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 /* acoshq(x)
  17  * Method :
  18  *      Based on
  19  *              acoshl(x) = logl [ x + sqrtl(x*x-1) ]
  20  *      we have
  21  *              acoshl(x) := logl(x)+ln2,       if x is large; else
  22  *              acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
  23  *              acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
  24  *
  25  * Special cases:
  26  *      acoshl(x) is NaN with signal if x<1.
  27  *      acoshl(NaN) is NaN without signal.
  28  */
  29
  30 #include "quadmath-imp.h"
  31
  32 static const __float128
  33 one     = 1.0Q,
  34 ln2     = 0.6931471805599453094172321214581766Q;
  35
  36 __float128
  37 acoshq (__float128 x)
  38 {
  39         __float128 t;
  40         uint64_t lx;
  41         int64_t hx;
  42         GET_FLT128_WORDS64(hx,lx,x);
  43         if(hx<0x3fff000000000000LL) {           /* x < 1 */
  44             return (x-x)/(x-x);
  45         } else if(hx >=0x4035000000000000LL) {  /* x > 2**54 */
  46             if(hx >=0x7fff000000000000LL) {     /* x is inf of NaN */
  47                 return x+x;
  48             } else
  49                 return logq(x)+ln2;     /* acoshl(huge)=logl(2x) */
  50         } else if(((hx-0x3fff000000000000LL)|lx)==0) {
  51             return 0.0Q;                        /* acosh(1) = 0 */
  52         } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */
  53             t=x*x;
  54             return logq(2.0Q*x-one/(x+sqrtq(t-one)));
  55         } else {                        /* 1<x<2 */
  56             t = x-one;
  57             return log1pq(t+sqrtq(2.0Q*t+t*t));
  58         }
  59 }