1  /* e_acoshl.c -- long double 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) = logq [ x + sqrtq(x*x-1) ]
      20   *	we have
      21   *		acoshl(x) := logq(x)+ln2,	if x is large; else
      22   *		acoshl(x) := logq(2x-1/(sqrtq(x*x-1)+x)) if x>2; else
      23   *		acoshl(x) := log1pq(t+sqrtq(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	= 1.0,
      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)=logq(2x) */
      50  	} else if(((hx-0x3fff000000000000LL)|lx)==0) {
      51  	    return 0;			/* acosh(1) = 0 */
      52  	} else if (hx > 0x4000000000000000LL) {	/* 2**28 > x > 2 */
      53  	    t=x*x;
      54  	    return logq(2*x-one/(x+sqrtq(t-one)));
      55  	} else {			/* 1<x<2 */
      56  	    t = x-one;
      57  	    return log1pq(t+sqrtq(2*t+t*t));
      58  	}
      59  }