text: /* @(#)e_acosh.c 5.1 93/09/24 */
  /*
   * ====================================================
   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   *
   * Developed at SunPro, a Sun Microsystems, Inc. business.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
  
  /* acoshl(x)
   * Method :
   *	Based on
   *		acoshl(x) = logl [ x + sqrtl(x*x-1) ]
   *	we have
   *		acoshl(x) := logl(x)+ln2,	if x is large; else
   *		acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
   *		acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
   *
   * Special cases:
   *	acoshl(x) is NaN with signal if x<1.
   *	acoshl(NaN) is NaN without signal.
   */
  
  #include <openlibm_math.h>
  
  #include "math_private.h"
  
  static const long double
  one	= 1.0,
  ln2	= 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
  
  long double
  acoshl(long double x)
  {
  	long double t;
  	u_int32_t se,i0,i1;
  	GET_LDOUBLE_WORDS(se,i0,i1,x);
  	if(se<0x3fff || se & 0x8000) {	/* x < 1 */
  	    return (x-x)/(x-x);
  	} else if(se >=0x401d) {	/* x > 2**30 */
  	    if(se >=0x7fff) {		/* x is inf of NaN */
  		return x+x;
  	    } else
  		return logl(x)+ln2;	/* acoshl(huge)=logl(2x) */
  	} else if(((se-0x3fff)|i0|i1)==0) {
  	    return 0.0;			/* acosh(1) = 0 */
  	} else if (se > 0x4000) {	/* 2**28 > x > 2 */
  	    t=x*x;
  	    return logl(2.0*x-one/(x+sqrtl(t-one)));
  	} else {			/* 1<x<2 */
  	    t = x-one;
  	    return log1pl(t+sqrtl(2.0*t+t*t));
  	}
  }
  