X-Git-Url: http://nsz.repo.hu/git/?a=blobdiff_plain;f=src%2Fmath%2Fcosh.c;h=100f8231d8829604b9e293491a9abb1774b4b29a;hb=c6383b7b10303457306932584fc23f24b5153a81;hp=a1f7dbc7bed86e52c692a9f190f10b45fec47ca1;hpb=634c3a63027aa4a693b64fae0e2f6e1635558e93;p=musl

diff --git a/src/math/cosh.c b/src/math/cosh.c
index a1f7dbc7..100f8231 100644
--- a/src/math/cosh.c
+++ b/src/math/cosh.c
@@ -1,74 +1,40 @@
-/* origin: FreeBSD /usr/src/lib/msun/src/e_cosh.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.
- * ====================================================
- */
-/* cosh(x)
- * Method :
- * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
- *      1. Replace x by |x| (cosh(x) = cosh(-x)).
- *      2.
- *                                                      [ exp(x) - 1 ]^2
- *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
- *                                                         2*exp(x)
- *
- *                                                exp(x) +  1/exp(x)
- *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
- *                                                        2
- *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
- *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
- *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
- *
- * Special cases:
- *      cosh(x) is |x| if x is +INF, -INF, or NaN.
- *      only cosh(0)=1 is exact for finite x.
- */
-
 #include "libm.h"
 
-static const double huge = 1.0e300;
-
+/* cosh(x) = (exp(x) + 1/exp(x))/2
+ *         = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
+ *         = 1 + x*x/2 + o(x^4)
+ */
 double cosh(double x)
 {
-	double t, w;
-	int32_t ix;
-
-	GET_HIGH_WORD(ix, x);
-	ix &= 0x7fffffff;
-
-	/* x is INF or NaN */
-	if (ix >= 0x7ff00000)
-		return x*x;
-
-	/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
-	if (ix < 0x3fd62e43) {
-		t = expm1(fabs(x));
-		w = 1.0+t;
-		if (ix < 0x3c800000)
-			return w;  /* cosh(tiny) = 1 */
-		return 1.0 + (t*t)/(w+w);
+	union {double f; uint64_t i;} u = {.f = x};
+	uint32_t w;
+	double t;
+
+	/* |x| */
+	u.i &= (uint64_t)-1/2;
+	x = u.f;
+	w = u.i >> 32;
+
+	/* |x| < log(2) */
+	if (w < 0x3fe62e42) {
+		if (w < 0x3ff00000 - (26<<20)) {
+			/* raise inexact if x!=0 */
+			FORCE_EVAL(x + 0x1p120f);
+			return 1;
+		}
+		t = expm1(x);
+		return 1 + t*t/(2*(1+t));
 	}
 
-	/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|))/2; */
-	if (ix < 0x40360000) {
-		t = exp(fabs(x));
-		return 0.5*t + 0.5/t;
+	/* |x| < log(DBL_MAX) */
+	if (w < 0x40862e42) {
+		t = exp(x);
+		/* note: if x>log(0x1p26) then the 1/t is not needed */
+		return 0.5*(t + 1/t);
 	}
 
-	/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
-	if (ix < 0x40862E42)
-		return 0.5*exp(fabs(x));
-
-	/* |x| in [log(maxdouble), overflowthresold] */
-	if (ix <= 0x408633CE)
-		return __expo2(fabs(x));
-
-	/* |x| > overflowthresold, cosh(x) overflow */
-	return huge*huge;
+	/* |x| > log(DBL_MAX) or nan */
+	/* note: the result is stored to handle overflow */
+	t = __expo2(x);
+	return t;
 }