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244 lines
9.2 KiB
C++
244 lines
9.2 KiB
C++
// Copyright John Maddock 2014
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// Copyright Christopher Kormanyos 2014.
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// Copyright Paul A. Bristow 2014.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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/*[cstdfloat_example_1
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`This example shows use of a specified-width floating-point typedef
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to evaluate a moderately complex math function using
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[@http://en.wikipedia.org/wiki/Double-precision_floating-point_format IEEE754 64-bit double-precision].
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about 15 decimal digits `std::numeric_limits<boost::float64_t>::digits10`,
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(but never exceeding 17 decimal digits `std::numeric_limits<boost::float64_t>::max_digits10`).
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The Jahnke Emden lambda function is described at
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Weisstein, Eric W. "Lambda Function." From MathWorld--A Wolfram Web Resource.
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http://mathworld.wolfram.com/LambdaFunction.html
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E. Jahnke and F. Emde, "Tables of Functions with Formulae and Curves,"
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Dover, New York, 4th ed., (1945), pp. 180-188.
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//] [/cstdfloat_example_1]
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*/
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#include <cmath>
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#include <iostream>
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#include <boost/cstdfloat.hpp>
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#include <boost/math/special_functions.hpp>
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/*!
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Function max_digits10
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Returns maximum number of possibly significant decimal digits for a floating-point type FPT,
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even for older compilers/standard libraries that
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lack support for std::numeric_limits<FPT>::max_digits10,
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when the Kahan formula is used instead.
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Also provides the correct result for Visual Studio 2010 where the value provided for float is wrong.
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*/
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namespace boost
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{
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template <typename FPT>
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int max_digits10()
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{
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// Since max_digits10 is not defined (or wrong) on older systems, define a local max_digits10.
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// Usage: int m = max_digits10<boost::float64_t>();
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const int m =
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#if (defined BOOST_NO_CXX11_NUMERIC_LIMITS) || (_MSC_VER == 1600) // is wrongly 8 not 9 for VS2010.
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2 + std::numeric_limits<FPT>::digits * 3010/10000;
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#else
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std::numeric_limits<FPT>::max_digits10;
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#endif
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return m;
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}
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} // namespace boost
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boost::float64_t jahnke_emden_lambda(boost::float64_t v, boost::float64_t x)
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{
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const boost::float64_t gamma_v_plus_one = boost::math::tgamma(v + 1);
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const boost::float64_t x_half_pow_v = std::pow(x /2, v);
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return gamma_v_plus_one * boost::math::cyl_bessel_j(x, v) / x_half_pow_v;
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}
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int main()
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{
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std::cout.setf(std::ios::showpoint); // show all significant trailing zeros.
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long double p = 1.L;
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//std::cout.precision(std::numeric_limits<long double>::digits10);
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std::cout << "pi = " << p << std::endl;
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/*[cstdfloat_example_2
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`To ensure that all possibly significant digits including trailing zeros are shown.
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*/
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std::cout.precision(std::numeric_limits<boost::float64_t>::max_digits10);
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try
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{ // Always use try'n'catch blocks to ensure any error messages are available.
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// Evaluate a sample of the lambda function:
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boost::float64_t v = 1.;
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boost::float64_t x = 1.;
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std::cout << jahnke_emden_lambda(v, x) << std::endl; // 0.88010117148986700
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//] [/cstdfloat_example_2]
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for (int i = 0; i < 10; i++)
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{
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std::cout << std::setprecision(2) << boost::float64_t(i) << ' '
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<< std::setprecision(std::numeric_limits<boost::float64_t>::max_digits10)
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<< jahnke_emden_lambda(boost::float64_t(i), v) << std::endl; //
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}
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std::cout << "Floating-point type long double is available." << std::endl;
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std::cout << " std::numeric_limits<long double>::digits10 == "
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<< std::numeric_limits<long double>::digits10 << std::endl;
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std::cout << " std::numeric_limits<long double>::max_digits10 == "
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<< std::numeric_limits<long double>::max_digits10 << std::endl; // 21
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long double p = boost::math::constants::pi<double>();
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std::cout.precision(std::numeric_limits<long double>::digits10);
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std::cout << "pi = " << p << std::endl;
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// http://www.boost.org/doc/libs/1_54_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/float128.html
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#ifdef BOOST_FLOAT16_C
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std::cout << "Floating-point type boost::float16_t is available." << std::endl;
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#else
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std::cout << "Floating-point type boost::float16_t is NOT available." << std::endl;
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#endif
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#ifdef BOOST_FLOAT32_C
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std::cout << "Floating-point type boost::float32_t is available." << std::endl;
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std::cout << " std::numeric_limits<boost::float32_t>::digits10 == "
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<< std::numeric_limits<boost::float32_t>::digits10 << std::endl;
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std::cout << " std::numeric_limits<boost::float32_t>::max_digits10 == "
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<< std::numeric_limits<boost::float32_t>::max_digits10 << std::endl;
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#else
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std::cout << "Floating-point type boost::float32_t is NOT available." << std::endl;
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#endif
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#ifdef BOOST_FLOAT64_C
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std::cout << "Floating-point type boost::float64_t is available." << std::endl;
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std::cout << " std::numeric_limits<boost::float64_t>::digits10 == "
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<< std::numeric_limits<boost::float64_t>::digits10 << std::endl;
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std::cout << " std::numeric_limits<boost::float64_t>::max_digits10 == "
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<< std::numeric_limits<boost::float64_t>::max_digits10 << std::endl;
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#else
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std::cout << "Floating-point type boost::float64_t is NOT available." << std::endl;
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#endif
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#ifdef BOOST_FLOAT80_C
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std::cout << "Floating-point type boost::float80_t is available." << std::endl;
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std::cout << " std::numeric_limits<boost::float80_t>::digits10 == "
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<< std::numeric_limits<boost::float80_t>::digits10 << std::endl;
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std::cout << " std::numeric_limits<boost::float80_t>::max_digits10 == "
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<< std::numeric_limits<boost::float80_t>::max_digits10 << std::endl;
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#else
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std::cout << "Floating-point type boost::float80_t is NOT available." << std::endl;
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#endif
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#ifdef BOOST_FLOAT128_C
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std::cout << "Floating-point type boost::float128_t is available." << std::endl;
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std::cout << " std::numeric_limits<boost::float128_t>::digits10 == "
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<< std::numeric_limits<boost::float128_t>::digits10 << std::endl;
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std::cout << " std::numeric_limits<boost::float128_t>::max_digits10 == "
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<< std::numeric_limits<boost::float128_t>::max_digits10 << std::endl;
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#else
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std::cout << "Floating-point type boost::float128_t is NOT available." << std::endl;
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#endif
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// Show some constants that depend on the available type.
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#ifdef BOOST_FLOAT16_C
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std::cout.precision(boost::max_digits10<boost::float16_t>()); // Show all significant decimal digits,
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std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
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std::cout << "BOOST_FLOAT16_C(123.456789012345678901234567890) = "
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<< BOOST_FLOAT16_C(123.456789012345678901234567890) << std::endl;
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// BOOST_FLOAT16_C(123.456789012345678901234567890) = 123.45678901234568
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#endif
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#ifdef BOOST_FLOAT32_C
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std::cout.precision(boost::max_digits10<boost::float32_t>()); // Show all significant decimal digits,
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std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
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std::cout << "BOOST_FLOAT32_C(123.456789012345678901234567890) = "
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<< BOOST_FLOAT32_C(123.456789012345678901234567890) << std::endl;
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// BOOST_FLOAT32_C(123.456789012345678901234567890) = 123.456787
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#endif
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#ifdef BOOST_FLOAT64_C
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std::cout.precision(boost::max_digits10<boost::float64_t>()); // Show all significant decimal digits,
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std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
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std::cout << "BOOST_FLOAT64_C(123.456789012345678901234567890) = "
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<< BOOST_FLOAT64_C(123.456789012345678901234567890) << std::endl;
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// BOOST_FLOAT64_C(123.456789012345678901234567890) = 123.45678901234568
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#endif
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#ifdef BOOST_FLOAT80_C
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std::cout.precision(boost::max_digits10<boost::float80_t>()); // Show all significant decimal digits,
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std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
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std::cout << "BOOST_FLOAT80_C(123.456789012345678901234567890) = "
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<< BOOST_FLOAT80_C(123.456789012345678901234567890) << std::endl;
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// BOOST_FLOAT80_C(123.456789012345678901234567890) = 123.456789012345678901234567890000000000000000
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#endif
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#ifdef BOOST_FLOAT128_C
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std::cout.precision(boost::max_digits10<boost::float128_t>()); // Show all significant decimal digits,
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std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
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std::cout << "BOOST_FLOAT128_C(123.456789012345678901234567890) = "
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<< BOOST_FLOAT128_C(123.456789012345678901234567890) << std::endl;
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// BOOST_FLOAT128_C(123.456789012345678901234567890) = 123.456789012345678901234567890000000000000000000
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#endif
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}
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catch (std::exception ex)
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{
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std::cout << "Thrown exception " << ex.what() << std::endl;
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}
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} // int main()
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/*
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[cstdfloat_output
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0.88010117148986700
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0.00 0.00000000000000000
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1.0 0.88010117148986700
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2.0 4.6137984620549872
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3.0 16.274830009244951
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4.0 -25.360637961042869
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5.0 -1257.9038883512264
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6.0 -12749.592182518225
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7.0 -3020.9830849309437
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8.0 2421897.6013183584
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9.0 45577595.449204877
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Floating-point type boost::float16_t is NOT available.
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Floating-point type boost::float32_t is available.
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std::numeric_limits<boost::float32_t>::digits10 == 6
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std::numeric_limits<boost::float32_t>::max_digits10 == 9
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Floating-point type boost::float64_t is available.
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std::numeric_limits<boost::float64_t>::digits10 == 15
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std::numeric_limits<boost::float64_t>::max_digits10 == 17
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Floating-point type boost::float80_t is NOT available.
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Floating-point type boost::float128_t is NOT available.
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BOOST_FLOAT32_C(123.456789012345678901234567890) = 123.456787
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BOOST_FLOAT64_C(123.456789012345678901234567890) = 123.45678901234568
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] [/cstdfloat_output]
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*/
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