/* @(#)e_sinh.c 5.1 93/09/24 */

/*

 * ====================================================

 * 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.

 * ====================================================

 */

#if defined(LIBM_SCCS) && !defined(lint)

static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";

#endif

/* __ieee754_sinh(x)

 * Method :

 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2

 *	1. Replace x by |x| (sinh(-x) = -sinh(x)).

 *	2.

 *						    E + E/(E+1)

 *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)

 *							2

 *

 *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2

 *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)

 *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)

 *

 * Special cases:

 *	sinh(x) is |x| if x is +INF, -INF, or NaN.

 *	only sinh(0)=0 is exact for finite x.

 */

#include <float.h>

#include <math.h>

#include <math-narrow-eval.h>

#include <math_private.h>

#include <math-underflow.h>

static const double one = 1.0, shuge = 1.0e307;

double

__ieee754_sinh (double x)

{

  double t, w, h;

  int32_t ix, jx;

  uint32_t lx;

  /* High word of |x|. */

  GET_HIGH_WORD (jx, x);

  ix = jx & 0x7fffffff;

  /* x is INF or NaN */

  if (__glibc_unlikely (ix >= 0x7ff00000))

    return x + x;

  h = 0.5;

  if (jx < 0)

    h = -h;

  /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */

  if (ix < 0x40360000)                  /* |x|<22 */

    {

      if (__glibc_unlikely (ix < 0x3e300000)) {            /* |x|<2**-28 */

	math_check_force_underflow (x);

	if (shuge + x > one)

	  return x;

	/* sinh(tiny) = tiny with inexact */

      }

      t = __expm1 (fabs (x));

      if (ix < 0x3ff00000)

	return h * (2.0 * t - t * t / (t + one));

      return h * (t + t / (t + one));

    }

  /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */

  if (ix < 0x40862e42)

    return h * __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 (0.5 * fabs (x));

      t = h * w;

      return t * w;

    }

  /* |x| > overflowthresold, sinh(x) overflow */

  return math_narrow_eval (x * shuge);

}

strong_alias (__ieee754_sinh, __sinh_finite)