math: sinh.c cleanup similar to the cosh one

comments are kept in the double version of the function

1 files changed, 29 insertions, 61 deletions

diff --git a/src/math/sinh.c b/src/math/sinh.c
index 0c67ba39..47e36bfa 100644
--- 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;
 }