contrib/openbsd_libm/src/e_sinh.c

   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 /* 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 <= 22     :  sinh(x) := --------------, E=expm1(x)
  20  *                                                      2
  21  *
  22  *          22       <= 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
  34 #include "math_private.h"
  35
  36 static const double one = 1.0, shuge = 1.0e307;
  37
  38 double
  39 sinh(double x)
  40 {
  41         double t,w,h;
  42         int32_t ix,jx;
  43         u_int32_t lx;
  44
  45     /* High word of |x|. */
  46         GET_HIGH_WORD(jx,x);
  47         ix = jx&0x7fffffff;
  48
  49     /* x is INF or NaN */
  50         if(ix>=0x7ff00000) return x+x;
  51
  52         h = 0.5;
  53         if (jx<0) h = -h;
  54     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
  55         if (ix < 0x40360000) {          /* |x|<22 */
  56             if (ix<0x3e300000)          /* |x|<2**-28 */
  57                 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
  58             t = expm1(fabs(x));
  59             if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
  60             return h*(t+t/(t+one));
  61         }
  62
  63     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
  64         if (ix < 0x40862E42)  return h*exp(fabs(x));
  65
  66     /* |x| in [log(maxdouble), overflowthresold] */
  67         GET_LOW_WORD(lx,x);
  68         if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  69             w = exp(0.5*fabs(x));
  70             t = h*w;
  71             return t*w;
  72         }
  73
  74     /* |x| > overflowthresold, sinh(x) overflow */
  75         return x*shuge;
  76 }
  77
  78 #if     LDBL_MANT_DIG == DBL_MANT_DIG
  79 __strong_alias(sinhl, sinh);
  80 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */