initial check-in, version 0.5.0 v0.5.0

1 files changed, 82 insertions, 0 deletions

diff --git a/src/math/e_cosh.c b/src/math/e_cosh.c
new file mode 100644
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+
+/* @(#)e_cosh.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * 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 <math.h>
+#include "math_private.h"
+
+static const double one = 1.0, half=0.5, huge = 1.0e300;
+
+double
+cosh(double x)
+{
+        double t,w;
+        int32_t ix;
+        uint32_t lx;
+
+    /* High word of |x|. */
+        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] */
+        GET_LOW_WORD(lx,x);
+        if (ix<0x408633CE ||
+              ((ix==0x408633ce)&&(lx<=(uint32_t)0x8fb9f87d))) {
+            w = exp(half*fabs(x));
+            t = half*w;
+            return t*w;
+        }
+
+    /* |x| > overflowthresold, cosh(x) overflow */
+        return huge*huge;
+}