gallivm: Import the code to compute the minimax polynomials.

It's quite a pain to remember the details after a while, and it is quite
likely we'll want to use this again, either for different polynomial
orders or different functions, so commit it here.

diff --git a/src/gallium/auxiliary/gallivm/f.cpp b/src/gallium/auxiliary/gallivm/f.cpp
new file mode 100644 (file)
index 0000000..5eb09c0
--- /dev/null
+++ b/src/gallium/auxiliary/gallivm/f.cpp
@@ -0,0 +1,85 @@
+/**************************************************************************
+ *
+ * (C) Copyright VMware, Inc 2010.
+ * (C) Copyright John Maddock 2006.
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0. (See accompanying file
+ * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ *
+ **************************************************************************/
+
+
+/*
+ * This file allows to compute the minimax polynomial coefficients we use
+ * for fast exp2/log2.
+ *
+ * How to use this source:
+ *
+ * - Download and abuild the NTL library from
+ *   http://shoup.net/ntl/download.html
+ *
+ * - Download boost source code matching to your distro. 
+ *
+ * - Goto libs/math/minimax and replace f.cpp with this file.
+ *
+ * - Build as
+ *
+ *   g++ -o minimax -I /path/to/ntl/include main.cpp f.cpp /path/to/ntl/src/ntl.a -lboost_math_tr1
+ *
+ * - Run as 
+ *
+ *    ./minimax
+ *
+ * - For example, to compute exp2 5th order polynomial between [0, 1] do:
+ *
+ *    variant 1
+ *    range 0 1
+ *    order 5 0
+ *    steps 200
+ *    info
+ *
+ * - For more info see
+ * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
+ */
+
+#define L22
+#include <boost/math/bindings/rr.hpp>
+#include <boost/math/tools/polynomial.hpp>
+
+#include <cmath>
+
+
+boost::math::ntl::RR f(const boost::math::ntl::RR& x, int variant)
+{
+   static const boost::math::ntl::RR tiny = boost::math::tools::min_value<boost::math::ntl::RR>() * 64;
+   
+   switch(variant)
+   {
+   case 0:
+      // log2(x)/(x - 1)
+      return log(x)/log(2.0)/(x - 1.0);
+
+   case 1:
+      // exp2(x)
+      return exp(x*log(2.0));
+   }
+
+   return 0;
+}
+
+
+void show_extra(
+   const boost::math::tools::polynomial<boost::math::ntl::RR>& n, 
+   const boost::math::tools::polynomial<boost::math::ntl::RR>& d, 
+   const boost::math::ntl::RR& x_offset, 
+   const boost::math::ntl::RR& y_offset, 
+   int variant)
+{
+   switch(variant)
+   {
+   default:
+      // do nothing here...
+      ;
+   }
+}
+