Test from one of Kahan's articles

"Why is Floating-Point Computation so Hard to Debug when it Goes Wrong?"

This is a MUCH better example than massive rounding errors as in calculatepi.test

diff --git a/src/tests/wrongr.cpp b/src/tests/wrongr.cpp
new file mode 100644 (file)
index 0000000..a7f5ec0
--- /dev/null
+++ b/src/tests/wrongr.cpp
@@ -0,0 +1,35 @@
+#include "main.h"
+#include <cmath>
+
+using namespace IPDF;
+/**
+ * Example from Kahan's "Why is Floating-Point Computation so Hard to Debug when it Goes Wrong?"
+ * Published on Kahan's website, March 2007  http://www.cs.berkeley.edu/~wkahan/WrongR.pdf
+ * In this example we compute h(x) = |x| ... except it is not!
+ * Note that the errors are NOT due to catastrophic cancellation (no subtraction) or division (no division) or accumulated rounding (only 128 operations)
+ * http://www.cs.berkeley.edu/~wkahan/WrongR.pdf
+ */
+
+Real h(Real x)
+{
+       Real y = abs(x);
+       for (int k = 0; k < 128; ++k)
+       {
+               y = sqrt(y);
+       }
+       Real w = y;
+       for (int k = 0; k < 128; ++k)
+       {
+               w = w*w;
+       }
+       return w;
+}
+
+int main(int argc, char ** argv)
+{
+       for (Real x = -2; x < 2; x+=1e-3)
+       {
+               printf("%lf\t%lf\t%lf\n", x, Float(h(x)), abs(Float(x)));
+       }
+       return 0;
+}