1  /* @(#)e_sinh.c 5.1 93/09/24 */
       2  /*
       3   * ====================================================
       4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       5   *
       6   * Developed at SunPro, a Sun Microsystems, Inc. business.
       7   * Permission to use, copy, modify, and distribute this
       8   * software is freely granted, provided that this notice
       9   * is preserved.
      10   * ====================================================
      11   */
      12  
      13  #if defined(LIBM_SCCS) && !defined(lint)
      14  static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
      15  #endif
      16  
      17  /* __ieee754_sinh(x)
      18   * Method :
      19   * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
      20   *	1. Replace x by |x| (sinh(-x) = -sinh(x)).
      21   *	2.
      22   *						    E + E/(E+1)
      23   *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
      24   *							2
      25   *
      26   *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2
      27   *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
      28   *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
      29   *
      30   * Special cases:
      31   *	sinh(x) is |x| if x is +INF, -INF, or NaN.
      32   *	only sinh(0)=0 is exact for finite x.
      33   */
      34  
      35  #include <float.h>
      36  #include <math.h>
      37  #include <math-narrow-eval.h>
      38  #include <math_private.h>
      39  #include <math-underflow.h>
      40  #include <libm-alias-finite.h>
      41  
      42  static const double one = 1.0, shuge = 1.0e307;
      43  
      44  double
      45  __ieee754_sinh (double x)
      46  {
      47    double t, w, h;
      48    int32_t ix, jx;
      49    uint32_t lx;
      50  
      51    /* High word of |x|. */
      52    GET_HIGH_WORD (jx, x);
      53    ix = jx & 0x7fffffff;
      54  
      55    /* x is INF or NaN */
      56    if (__glibc_unlikely (ix >= 0x7ff00000))
      57      return x + x;
      58  
      59    h = 0.5;
      60    if (jx < 0)
      61      h = -h;
      62    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
      63    if (ix < 0x40360000)                  /* |x|<22 */
      64      {
      65        if (__glibc_unlikely (ix < 0x3e300000)) {            /* |x|<2**-28 */
      66  	math_check_force_underflow (x);
      67  	if (shuge + x > one)
      68  	  return x;
      69  	/* sinh(tiny) = tiny with inexact */
      70        }
      71        t = __expm1 (fabs (x));
      72        if (ix < 0x3ff00000)
      73  	return h * (2.0 * t - t * t / (t + one));
      74        return h * (t + t / (t + one));
      75      }
      76  
      77    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
      78    if (ix < 0x40862e42)
      79      return h * __ieee754_exp (fabs (x));
      80  
      81    /* |x| in [log(maxdouble), overflowthresold] */
      82    GET_LOW_WORD (lx, x);
      83    if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (uint32_t) 0x8fb9f87d)))
      84      {
      85        w = __ieee754_exp (0.5 * fabs (x));
      86        t = h * w;
      87        return t * w;
      88      }
      89  
      90    /* |x| > overflowthresold, sinh(x) overflow */
      91    return math_narrow_eval (x * shuge);
      92  }
      93  libm_alias_finite (__ieee754_sinh, __sinh)