Merged revisions 76861 via svnmerge from

svn+ssh://pythondev@svn.python.org/python/trunk

........
  r76861 | mark.dickinson | 2009-12-16 20:13:40 +0000 (Wed, 16 Dec 2009) | 3 lines

  Issue #3366: Add expm1 function to math module.  Thanks Eric Smith for
  testing on Windows.
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Modules/_math.c

@@ -0,0 +1,31 @@
+/* Definitions of some C99 math library functions, for those platforms
+   that don't implement these functions already. */
+
+#include <float.h>
+#include <math.h>
+
+/* Mathematically, expm1(x) = exp(x) - 1.  The expm1 function is designed
+   to avoid the significant loss of precision that arises from direct
+   evaluation of the expression exp(x) - 1, for x near 0. */
+
+double
+_Py_expm1(double x)
+{
+    /* For abs(x) >= log(2), it's safe to evaluate exp(x) - 1 directly; this
+       also works fine for infinities and nans.
+
+       For smaller x, we can use a method due to Kahan that achieves close to
+       full accuracy.
+    */
+
+    if (fabs(x) < 0.7) {
+        double u;
+        u = exp(x);
+        if (u == 1.0)
+            return x;
+        else
+            return (u - 1.0) * x / log(u);
+    }
+    else
+        return exp(x) - 1.0;
+}