First draft of cstdfloat example

example/cstdfloat_example.cpp

@@ -0,0 +1,94 @@
+//  Copyright John Maddock 2014
+//  Copyright Christopher Kormanyos 2014.
+//  Copyright Paul A. Bristow 2014.
+
+//  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)
+
+/* 
+
+/*[cstdfloat_example_1
+`This example shows use of a specified-width floating-point typedef
+to evaluate a moderately complex math function using
+[@http://en.wikipedia.org/wiki/Double-precision_floating-point_format IEEE754 64-bit double-precision].
+about 15 decimal digits `std::numeric_limits<boost::float64_t>::digits10`,
+(but never exceeding 17 decimal digits `std::numeric_limits<boost::float64_t>::max_digits10`).
+
+The Jahnke Emden lambda function is described at
+
+Weisstein, Eric W. "Lambda Function." From MathWorld--A Wolfram Web Resource. 
+http://mathworld.wolfram.com/LambdaFunction.html
+
+E. Jahnke and F. Emde, "Tables of Functions with Formulae and Curves,"
+Dover, New York, 4th ed., (1945), pp. 180-188.
+
+//] [/cstdfloat_example_1]
+*/
+
+#include <cmath>
+#include <iostream>
+
+#include <boost/cstdfloat.hpp>
+#include <boost/math/special_functions.hpp>
+
+boost::float64_t jahnke_emden_lambda(boost::float64_t v, boost::float64_t x)
+{
+  const boost::float64_t gamma_v_plus_one = boost::math::tgamma(v + 1);
+  const boost::float64_t x_half_pow_v     = std::pow(x /2, v);
+
+  return gamma_v_plus_one * boost::math::cyl_bessel_j(x, v) / x_half_pow_v;
+}
+
+int main()
+{
+/*[cstdfloat_example_2
+`To ensure that all possibly significant digits including trailing zeros are shown.
+*/
+  std::cout.precision(std::numeric_limits<boost::float64_t>::max_digits10);
+  std::cout.setf(std::ios::showpoint); // show all significant trailing zeros.
+  try
+  { // Always use try'n'catch blocks to ensure any error messages are available.
+
+    // Evaluate a sample of the lambda function:
+  boost::float64_t v = 1.;
+  boost::float64_t x = 1.;
+  
+  std::cout << jahnke_emden_lambda(v, x) << std::endl; // 0.88010117148986700
+//] [/cstdfloat_example_2]
+
+  for (int i = 0; i < 10; i++)
+  {
+    std::cout << std::setprecision(2) << boost::float64_t(i) << ' ' 
+      << std::setprecision(std::numeric_limits<boost::float64_t>::max_digits10)
+      << jahnke_emden_lambda(boost::float64_t(i), v) << std::endl; // 
+  }
+
+  }
+  catch (std::exception ex)
+  {
+    std::cout << "Thrown exception " << ex.what() << std::endl;
+  }
+
+} // int main()
+
+/*
+[cstdfloat_output
+
+  1.0000000000000000
+  0.88010117148986700
+  0.00 0.00000000000000000
+  1.0 0.88010117148986700
+  2.0 4.6137984620549854
+  3.0 16.274830009244948
+  4.0 -25.360637961042869
+  5.0 -1257.9038883512258
+  6.0 -12749.592182518225
+  7.0 -3020.9830849309396
+  8.0 2421897.6013183575
+  9.0 45577595.449204892
+
+] [/cstdfloat_output]
+
+
+*/