sysdeps/ieee754/ldbl-128ibm/e_sinhl.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
  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 <math.h>
  32 #include <math_private.h>
  33
  34 static const long double one = 1.0, shuge = 1.0e307;
  35
  36 long double
  37 __ieee754_sinhl(long double x)
  38 {
  39         long double t,w,h;
  40         int64_t ix,jx;
  41         double xhi;
  42
  43     /* High word of |x|. */
  44         xhi = ldbl_high (x);
  45         EXTRACT_WORDS64 (jx, xhi);
  46         ix = jx&0x7fffffffffffffffLL;
  47
  48     /* x is INF or NaN */
  49         if(ix>=0x7ff0000000000000LL) return x+x;
  50
  51         h = 0.5;
  52         if (jx<0) h = -h;
  53     /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
  54         if (ix < 0x4044000000000000LL) {        /* |x|<40 */
  55             if (ix<0x3e20000000000000LL)        /* |x|<2**-29 */
  56                 if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
  57             t = __expm1l(fabsl(x));
  58             if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
  59             w = t/(t+one);
  60             return h*(t+w);
  61         }
  62
  63     /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
  64         if (ix < 0x40862e42fefa39efLL)  return h*__ieee754_expl(fabsl(x));
  65
  66     /* |x| in [log(maxdouble), overflowthresold] */
  67         if (ix <= 0x408633ce8fb9f87dLL) {
  68             w = __ieee754_expl(0.5*fabsl(x));
  69             t = h*w;
  70             return t*w;
  71         }
  72
  73     /* |x| > overflowthresold, sinh(x) overflow */
  74         return x*shuge;
  75 }
  76 strong_alias (__ieee754_sinhl, __sinhl_finite)