From: Sam Moore <matches@ucc.asn.au>
Date: Thu, 1 May 2014 16:21:11 +0000 (+0800)
Subject: Test from one of Kahan's articles
X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=commitdiff_plain;h=b95fd30aafb3f47d2bfc8aa8f75600db4fdb995c;hp=e6e138e8baad2dda39cecbb35557710f2a550398

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
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;
+}