glibc/sysdeps/ieee754/dbl-64/e_cosh.c

/* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */
/*
 * ====================================================
 * 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.
 * ====================================================
 */

/* __ieee754_cosh(x)
 * Method :
 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
 *	1. Replace x by |x| (cosh(x) = cosh(-x)).
 *	2.
 *							[ exp(x) - 1 ]^2
 *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
 *							   2*exp(x)
 *
 *						  exp(x) +  1/exp(x)
 *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
 *							  2
 *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2
 *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
 *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
 *
 * Special cases:
 *	cosh(x) is |x| if x is +INF, -INF, or NaN.
 *	only cosh(0)=1 is exact for finite x.
 */

#include <math.h>
#include <math-narrow-eval.h>
#include <math_private.h>
#include <libm-alias-finite.h>

static const double one = 1.0, half = 0.5, huge = 1.0e300;

double
__ieee754_cosh (double x)
{
  double t, w;
  int32_t ix;
  uint32_t lx;

  /* High word of |x|. */
  GET_HIGH_WORD (ix, x);
  ix &= 0x7fffffff;

  /* |x| in [0,22] */
  if (ix < 0x40360000)
    {
      /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
      if (ix < 0x3fd62e43)
	{
	  if (ix < 0x3c800000)
	    return one;                                   /* cosh(tiny) = 1 */
	  t = __expm1 (fabs (x));
	  w = one + t;
	  return one + (t * t) / (w + w);
	}

      /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
      t = __ieee754_exp (fabs (x));
      return half * t + half / t;
    }

  /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
  if (ix < 0x40862e42)
    return half * __ieee754_exp (fabs (x));

  /* |x| in [log(maxdouble), overflowthresold] */
  GET_LOW_WORD (lx, x);
  if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (uint32_t) 0x8fb9f87d)))
    {
      w = __ieee754_exp (half * fabs (x));
      t = half * w;
      return t * w;
    }

  /* x is INF or NaN */
  if (ix >= 0x7ff00000)
    return x * x;

  /* |x| > overflowthresold, cosh(x) overflow */
  return math_narrow_eval (huge * huge);
}
libm_alias_finite (__ieee754_cosh, __cosh)