1  /* e_acoshl.c -- long double version of e_acosh.c.
       2   */
       3  
       4  /*
       5   * ====================================================
       6   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       7   *
       8   * Developed at SunPro, a Sun Microsystems, Inc. business.
       9   * Permission to use, copy, modify, and distribute this
      10   * software is freely granted, provided that this notice
      11   * is preserved.
      12   * ====================================================
      13   */
      14  
      15  /* __ieee754_acoshl(x)
      16   * Method :
      17   *	Based on
      18   *		acoshl(x) = logl [ x + sqrtl(x*x-1) ]
      19   *	we have
      20   *		acoshl(x) := logl(x)+ln2,	if x is large; else
      21   *		acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
      22   *		acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
      23   *
      24   * Special cases:
      25   *	acoshl(x) is NaN with signal if x<1.
      26   *	acoshl(NaN) is NaN without signal.
      27   */
      28  
      29  #include <math.h>
      30  #include <math_private.h>
      31  #include <libm-alias-finite.h>
      32  
      33  static const _Float128
      34  one	= 1.0,
      35  ln2	= L(0.6931471805599453094172321214581766);
      36  
      37  _Float128
      38  __ieee754_acoshl(_Float128 x)
      39  {
      40  	_Float128 t;
      41  	uint64_t lx;
      42  	int64_t hx;
      43  	GET_LDOUBLE_WORDS64(hx,lx,x);
      44  	if(hx<0x3fff000000000000LL) {		/* x < 1 */
      45  	    return (x-x)/(x-x);
      46  	} else if(hx >=0x4035000000000000LL) {	/* x > 2**54 */
      47  	    if(hx >=0x7fff000000000000LL) {	/* x is inf of NaN */
      48  		return x+x;
      49  	    } else
      50  		return __ieee754_logl(x)+ln2;	/* acoshl(huge)=logl(2x) */
      51  	} else if(((hx-0x3fff000000000000LL)|lx)==0) {
      52  	    return 0;			/* acosh(1) = 0 */
      53  	} else if (hx > 0x4000000000000000LL) {	/* 2**28 > x > 2 */
      54  	    t=x*x;
      55  	    return __ieee754_logl(2*x-one/(x+sqrtl(t-one)));
      56  	} else {			/* 1<x<2 */
      57  	    t = x-one;
      58  	    return __log1pl(t+sqrtl(2*t+t*t));
      59  	}
      60  }
      61  libm_alias_finite (__ieee754_acoshl, __acoshl)