1  /*
       2   * ====================================================
       3   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       4   *
       5   * Developed at SunPro, a Sun Microsystems, Inc. business.
       6   * Permission to use, copy, modify, and distribute this
       7   * software is freely granted, provided that this notice
       8   * is preserved.
       9   * ====================================================
      10   */
      11  
      12  
      13  /* __ieee754_sinh(x)
      14   * Method :
      15   * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
      16   *	1. Replace x by |x| (sinh(-x) = -sinh(x)).
      17   *	2.
      18   *						    E + E/(E+1)
      19   *	    0        <= x <= 40     :  sinh(x) := --------------, E=expm1(x)
      20   *							2
      21   *
      22   *	    40       <= x <= lnovft :  sinh(x) := exp(x)/2
      23   *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
      24   *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
      25   *
      26   * Special cases:
      27   *	sinh(x) is |x| if x is +INF, -INF, or NaN.
      28   *	only sinh(0)=0 is exact for finite x.
      29   */
      30  
      31  #include <float.h>
      32  #include <math.h>
      33  #include <math_private.h>
      34  #include <math-underflow.h>
      35  #include <libm-alias-finite.h>
      36  
      37  static const long double one = 1.0, shuge = 1.0e307;
      38  
      39  long double
      40  __ieee754_sinhl(long double x)
      41  {
      42  	long double t,w,h;
      43  	int64_t ix,jx;
      44  	double xhi;
      45  
      46      /* High word of |x|. */
      47  	xhi = ldbl_high (x);
      48  	EXTRACT_WORDS64 (jx, xhi);
      49  	ix = jx&0x7fffffffffffffffLL;
      50  
      51      /* x is INF or NaN */
      52  	if(ix>=0x7ff0000000000000LL) return x+x;
      53  
      54  	h = 0.5;
      55  	if (jx<0) h = -h;
      56      /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
      57  	if (ix < 0x4044000000000000LL) {	/* |x|<40 */
      58  	    if (ix<0x3c90000000000000LL) {	/* |x|<2**-54 */
      59  		math_check_force_underflow (x);
      60  		if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
      61  	    }
      62  	    t = __expm1l(fabsl(x));
      63  	    if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
      64  	    w = t/(t+one);
      65  	    return h*(t+w);
      66  	}
      67  
      68      /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
      69  	if (ix < 0x40862e42fefa39efLL)  return h*__ieee754_expl(fabsl(x));
      70  
      71      /* |x| in [log(maxdouble), overflowthresold] */
      72  	if (ix <= 0x408633ce8fb9f87eLL) {
      73  	    w = __ieee754_expl(0.5*fabsl(x));
      74  	    t = h*w;
      75  	    return t*w;
      76  	}
      77  
      78      /* |x| > overflowthresold, sinh(x) overflow */
      79  	return x*shuge;
      80  }
      81  libm_alias_finite (__ieee754_sinhl, __sinhl)