kc3-lang/libquadmath/math/acoshq.c

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• Hash : 4f659ab9
  Author : Thomas de Grivel
  Date : 2025-11-02T19:33:45
  

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• math/acoshq.c

• /* e_acoshl.c -- long double version of e_acosh.c.
   * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
   */
  
  /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  /* acoshq(x)
   * Method :
   *	Based on
   *		acoshl(x) = logq [ x + sqrtq(x*x-1) ]
   *	we have
   *		acoshl(x) := logq(x)+ln2,	if x is large; else
   *		acoshl(x) := logq(2x-1/(sqrtq(x*x-1)+x)) if x>2; else
   *		acoshl(x) := log1pq(t+sqrtq(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 "quadmath-imp.h"
  
  static const __float128
  one	= 1.0,
  ln2	= 0.6931471805599453094172321214581766Q;
  
  __float128
  acoshq(__float128 x)
  {
  	__float128 t;
  	uint64_t lx;
  	int64_t hx;
  	GET_FLT128_WORDS64(hx,lx,x);
  	if(hx<0x3fff000000000000LL) {		/* x < 1 */
  	    return (x-x)/(x-x);
  	} else if(hx >=0x4035000000000000LL) {	/* x > 2**54 */
  	    if(hx >=0x7fff000000000000LL) {	/* x is inf of NaN */
  		return x+x;
  	    } else
  		return logq(x)+ln2;	/* acoshl(huge)=logq(2x) */
  	} else if(((hx-0x3fff000000000000LL)|lx)==0) {
  	    return 0;			/* acosh(1) = 0 */
  	} else if (hx > 0x4000000000000000LL) {	/* 2**28 > x > 2 */
  	    t=x*x;
  	    return logq(2*x-one/(x+sqrtq(t-one)));
  	} else {			/* 1<x<2 */
  	    t = x-one;
  	    return log1pq(t+sqrtq(2*t+t*t));
  	}
  }
  

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