libm/e_sinh.c

   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 /* __ieee754_sinh(x)
  13  * Method :
  14  * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
  15  *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
  16  *      2.
  17  *                                                  E + E/(E+1)
  18  *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
  19  *                                                      2
  20  *
  21  *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
  22  *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
  23  *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
  24  *
  25  * Special cases:
  26  *      sinh(x) is |x| if x is +INF, -INF, or NaN.
  27  *      only sinh(0)=0 is exact for finite x.
  28  */
  29
  30 #include "math.h"
  31 #include "math_private.h"
  32
  33 static const double one = 1.0, shuge = 1.0e307;
  34
  35 double __ieee754_sinh(double x)
  36 {
  37         double t,w,h;
  38         int32_t ix,jx;
  39         u_int32_t lx;
  40
  41     /* High word of |x|. */
  42         GET_HIGH_WORD(jx,x);
  43         ix = jx&0x7fffffff;
  44
  45     /* x is INF or NaN */
  46         if(ix>=0x7ff00000) return x+x;
  47
  48         h = 0.5;
  49         if (jx<0) h = -h;
  50     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
  51         if (ix < 0x40360000) {          /* |x|<22 */
  52             if (ix<0x3e300000)          /* |x|<2**-28 */
  53                 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
  54             t = expm1(fabs(x));
  55             if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
  56             return h*(t+t/(t+one));
  57         }
  58
  59     /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
  60         if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
  61
  62     /* |x| in [log(maxdouble), overflowthresold] */
  63         GET_LOW_WORD(lx,x);
  64         if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
  65             w = __ieee754_exp(0.5*fabs(x));
  66             t = h*w;
  67             return t*w;
  68         }
  69
  70     /* |x| > overflowthresold, sinh(x) overflow */
  71         return x*shuge;
  72 }
  73
  74 /*
  75  * wrapper sinh(x)
  76  */
  77 #ifndef _IEEE_LIBM
  78 double sinh(double x)
  79 {
  80         double z = __ieee754_sinh(x);
  81         if (_LIB_VERSION == _IEEE_)
  82                 return z;
  83         if (!isfinite(z) && isfinite(x))
  84                 return __kernel_standard(x, x, 25); /* sinh overflow */
  85         return z;
  86 }
  87 #else
  88 strong_alias(__ieee754_sinh, sinh)
  89 #endif
  90 libm_hidden_def(sinh)