math: sinh.c cleanup similar to the cosh one

[musl] / src / math / sinh.c

diff --git a/src/math/sinh.c b/src/math/sinh.c
index 0c67ba3..47e36bf 100644 (file)
--- a/src/math/sinh.c
+++ b/src/math/sinh.c
@@ -1,71 +1,39 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_sinh.c */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunSoft, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-/* sinh(x)
- * Method :
- * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
- *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
- *      2.
- *                                                  E + E/(E+1)
- *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
- *                                                      2
- *
- *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
- *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
- *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
- *
- * Special cases:
- *      sinh(x) is |x| if x is +INF, -INF, or NaN.
- *      only sinh(0)=0 is exact for finite x.
- */
-
 #include "libm.h"
 
-static const double huge = 1.0e307;
-
+/* sinh(x) = (exp(x) - 1/exp(x))/2
+ *         = (exp(x)-1 + (exp(x)-1)/exp(x))/2
+ *         = x + x^3/6 + o(x^5)
+ */
 double sinh(double x)
 {
-       double t, h;
-       int32_t ix, jx;
-
-       /* High word of |x|. */
-       GET_HIGH_WORD(jx, x);
-       ix = jx & 0x7fffffff;
-
-       /* x is INF or NaN */
-       if (ix >= 0x7ff00000)
-               return x + x;
+       union {double f; uint64_t i;} u = {.f = x};
+       uint32_t w;
+       double t, h, absx;
 
        h = 0.5;
-       if (jx < 0) h = -h;
-       /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
-       if (ix < 0x40360000) {  /* |x|<22 */
-               if (ix < 0x3e300000)  /* |x|<2**-28 */
-                       /* raise inexact, return x */
-                       if (huge+x > 1.0)
+       if (u.i >> 63)
+               h = -h;
+       /* |x| */
+       u.i &= (uint64_t)-1/2;
+       absx = u.f;
+       w = u.i >> 32;
+
+       /* |x| < log(DBL_MAX) */
+       if (w < 0x40862e42) {
+               t = expm1(absx);
+               if (w < 0x3ff00000) {
+                       if (w < 0x3ff00000 - (26<<20))
+                               /* note: inexact is raised by expm1 */
+                               /* note: this branch avoids underflow */
                                return x;
-               t = expm1(fabs(x));
-               if (ix < 0x3ff00000)
-                       return h*(2.0*t - t*t/(t+1.0));
-               return h*(t + t/(t+1.0));
+                       return h*(2*t - t*t/(t+1));
+               }
+               /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
+               return h*(t + t/(t+1));
        }
 
-       /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
-       if (ix < 0x40862E42)
-               return h*exp(fabs(x));
-
-       /* |x| in [log(maxdouble), overflowthresold] */
-       if (ix <= 0x408633CE)
-               return h * 2.0 * __expo2(fabs(x)); /* h is for sign only */
-
-       /* |x| > overflowthresold, sinh(x) overflow */
-       return x*huge;
+       /* |x| > log(DBL_MAX) or nan */
+       /* note: the result is stored to handle overflow */
+       t = 2*h*__expo2(absx);
+       return t;
 }