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  #include <libm-alias-finite.h>
      30  
      31  static const long double
      32  one	= 1.0L,
      33  ln2	= M_LN2l;
      34  
      35  long double
      36  __ieee754_acoshl(long double x)
      37  {
      38  	long double t;
      39  	int64_t hx;
      40  	uint64_t lx;
      41  	double xhi, xlo;
      42  
      43  	ldbl_unpack (x, &xhi, &xlo);
      44  	EXTRACT_WORDS64 (hx, xhi);
      45  	EXTRACT_WORDS64 (lx, xlo);
      46  	if(hx<0x3ff0000000000000LL) {		/* x < 1 */
      47  	    return (x-x)/(x-x);
      48  	} else if(hx >=0x4370000000000000LL) {	/* x >= 2**56 */
      49  	    if(hx >=0x7ff0000000000000LL) {	/* x is inf of NaN */
      50  		return x+x;
      51  	    } else
      52  		return __ieee754_logl(x)+ln2;	/* acosh(huge)=log(2x) */
      53  	} else if (((hx-0x3ff0000000000000LL)|(lx&0x7fffffffffffffffLL))==0) {
      54  	    return 0.0;			/* acosh(1) = 0 */
      55  	} else if (hx > 0x4000000000000000LL) {	/* 2**56 > x > 2 */
      56  	    t=x*x;
      57  	    return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one)));
      58  	} else {			/* 1<x<2 */
      59  	    t = x-one;
      60  	    return __log1pl(t+sqrtl(2.0*t+t*t));
      61  	}
      62  }
      63  libm_alias_finite (__ieee754_acoshl, __acoshl)