math: finished cosh.c cleanup

[musl] / src / math / cosh.c

diff --git a/src/math/cosh.c b/src/math/cosh.c
index 2fcdea8..100f823 100644 (file)
--- a/src/math/cosh.c
+++ b/src/math/cosh.c
@@ -1,71 +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) := inf (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"
 
+/* 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)
 {
        union {double f; uint64_t i;} u = {.f = x};
-       uint32_t ix;
+       uint32_t w;
        double t;
 
        /* |x| */
        u.i &= (uint64_t)-1/2;
        x = u.f;
-       ix = u.i >> 32;
+       w = u.i >> 32;
 
-       /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
-       if (ix < 0x3fd62e43) {
-               t = expm1(x);
-               if (ix < 0x3c800000)
+       /* |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) {
+       /* |x| < log(DBL_MAX) */
+       if (w < 0x40862e42) {
                t = exp(x);
-               return 0.5*t + 0.5/t;
+               /* 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(x);
-
-       /* |x| in [log(maxdouble), overflowthresold] */
-       if (ix <= 0x408633ce)
-               return __expo2(x);
-
-       /* overflow (or nan) */
-       x *= 0x1p1023;
-       return x;
+       /* |x| > log(DBL_MAX) or nan */
+       /* note: the result is stored to handle overflow */
+       t = __expo2(x);
+       return t;
 }