summaryrefslogtreecommitdiff
path: root/src/math/cosh.c
diff options
context:
space:
mode:
authorRich Felker <dalias@aerifal.cx>2012-03-13 01:17:53 -0400
committerRich Felker <dalias@aerifal.cx>2012-03-13 01:17:53 -0400
commitb69f695acedd4ce2798ef9ea28d834ceccc789bd (patch)
treeeafd98b9b75160210f3295ac074d699f863d958e /src/math/cosh.c
parentd46cf2e14cc4df7cc75e77d7009fcb6df1f48a33 (diff)
downloadmusl-b69f695acedd4ce2798ef9ea28d834ceccc789bd.tar.gz
first commit of the new libm!
thanks to the hard work of Szabolcs Nagy (nsz), identifying the best (from correctness and license standpoint) implementations from freebsd and openbsd and cleaning them up! musl should now fully support c99 float and long double math functions, and has near-complete complex math support. tgmath should also work (fully on gcc-compatible compilers, and mostly on any c99 compiler). based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from nsz's libm git repo, with some additions (dummy versions of a few missing long double complex functions, etc.) by me. various cleanups still need to be made, including re-adding (if they're correct) some asm functions that were dropped.
Diffstat (limited to 'src/math/cosh.c')
-rw-r--r--src/math/cosh.c74
1 files changed, 74 insertions, 0 deletions
diff --git a/src/math/cosh.c b/src/math/cosh.c
new file mode 100644
index 00000000..5f38b276
--- /dev/null
+++ b/src/math/cosh.c
@@ -0,0 +1,74 @@
+/* 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 one = 1.0, half = 0.5, huge = 1.0e300;
+
+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 = one+t;
+ if (ix < 0x3c800000)
+ return w; /* cosh(tiny) = 1 */
+ return one + (t*t)/(w+w);
+ }
+
+ /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|))/2; */
+ if (ix < 0x40360000) {
+ t = exp(fabs(x));
+ return half*t + half/t;
+ }
+
+ /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
+ if (ix < 0x40862E42)
+ return half*exp(fabs(x));
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ if (ix <= 0x408633CE)
+ return __expo2(fabs(x));
+
+ /* |x| > overflowthresold, cosh(x) overflow */
+ return huge*huge;
+}