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diff --git a/src/boost/libs/math/example/cstdfloat_example.cpp b/src/boost/libs/math/example/cstdfloat_example.cpp
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+// Copyright John Maddock 2014
+// Copyright Christopher Kormanyos 2014.
+// Copyright Paul A. Bristow 2016.
+
+// 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)
+
+// Contains Quickbook snippets as C++ comments - do not remove.
+
+/*
+`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. Emden, "Tables of Functions with Formulae and Curves,"
+Dover, New York, 4th ed., (1945), pages 180-188.
+
+*/
+
+//[cstdfloat_example_1
+#include <boost/cstdfloat.hpp> // For float_64_t, float128_t. Must be first include!
+#include <cmath> // for pow function.
+#include <boost/math/special_functions.hpp> // For gamma function.
+//] [/cstdfloat_example_1]
+#include <boost/type_traits/is_same.hpp>
+
+#include <iostream>
+
+/*!
+Function max_digits10
+Returns maximum number of possibly significant decimal digits for a floating-point type FPT,
+even for older compilers/standard libraries that
+lack support for std::numeric_limits<FPT>::max_digits10,
+when the Kahan formula 2 + binary_digits * 0.3010 is used instead.
+Also provides the correct result for Visual Studio 2010
+(where the value 8 provided for float is wrong).
+*/
+namespace boost
+{
+template <typename FPT>
+const int max_digits10()
+{
+// Since max_digits10 is not defined (or wrong) on older systems, define a local max_digits10.
+ // Usage: int m = max_digits10<boost::float64_t>();
+ const int m =
+#if (defined BOOST_NO_CXX11_NUMERIC_LIMITS) || (_MSC_VER == 1600) // is wrongly 8 not 9 for VS2010.
+ 2 + std::numeric_limits<FPT>::digits * 3010/10000;
+#else
+ std::numeric_limits<FPT>::max_digits10;
+#endif
+ return m;
+}
+} // namespace boost
+
+//`Define the Jahnke-Emden_lambda function.
+//[cstdfloat_example_2
+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;
+}
+//] [/cstdfloat_example_2]
+
+int main()
+{
+ std::cout.setf(std::ios::showpoint); // show all significant trailing zeros.
+
+ long double p = 1.L;
+ //std::cout.precision(std::numeric_limits<long double>::digits10);
+
+ std::cout << "pi = " << p << std::endl;
+
+//[cstdfloat_example_3
+//`Ensure that all possibly significant digits (17) including trailing zeros are shown.
+
+ std::cout.precision(std::numeric_limits<boost::float64_t>::max_digits10);
+ std::cout.setf(std::ios::showpoint); // Show trailing zeros.
+
+ try
+ { // Always use try'n'catch blocks to ensure any error messages are displayed.
+
+ // Evaluate and display an evaluation of the Jahnke-Emden 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_3]
+
+ // We can show some evaluations with various precisions:
+ { // float64_t
+ 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; //
+ }
+ }
+ { // floatmax_t = the maximum available on this platform.
+ for (int i = 0; i < 10; i++)
+ {
+ std::cout << std::setprecision(2) << boost::floatmax_t(i) << ' '
+ << std::setprecision(std::numeric_limits<boost::floatmax_t>::max_digits10)
+ << jahnke_emden_lambda(boost::floatmax_t(i), v) << std::endl; //
+ }
+ }
+ // Show the precision of long double (this might be 64, 80 or 128 bits).
+ std::cout << "Floating-point type long double is available with:" << std::endl;
+ std::cout << " std::numeric_limits<long double>::digits10 == "
+ << std::numeric_limits<long double>::digits10 << std::endl; // 18
+ std::cout << " std::numeric_limits<long double>::max_digits10 == "
+ << std::numeric_limits<long double>::max_digits10 << std::endl; // 21
+ long double p = boost::math::constants::pi<double>();
+ std::cout.precision(std::numeric_limits<long double>::digits10);
+ std::cout << "pi = " << p << std::endl;
+
+//[cstdfloat_constant_2
+//`These allow floating-point [*constants of at least the specified width] to be declared:
+
+ // Declare Archimedes' constant using float32_t with approximately 7 decimal digits of precision.
+ static const boost::float32_t pi = BOOST_FLOAT32_C(3.1415926536);
+
+ // Declare the Euler-gamma constant with approximately 15 decimal digits of precision.
+ static const boost::float64_t euler =
+ BOOST_FLOAT64_C(0.57721566490153286060651209008240243104216);
+
+ // Declare the Golden Ratio constant with the maximum decimal digits of precision that the platform supports.
+ static const boost::floatmax_t golden_ratio =
+ BOOST_FLOATMAX_C(1.61803398874989484820458683436563811772);
+//] [/cstdfloat_constant_2]
+
+// http://www.boost.org/doc/libs/1_55_0/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/float128.html
+//[cstdfloat_constant_1
+// Display the constant pi to the maximum available precision.
+ boost::floatmax_t pi_max = boost::math::constants::pi<boost::floatmax_t>();
+ std::cout.precision(std::numeric_limits<boost::floatmax_t>::digits10);
+ std::cout << "Most precise pi = " << pi_max << std::endl;
+// If floatmax_t is float_128_t, then
+// Most precise pi = 3.141592653589793238462643383279503
+//] [/cstdfloat_constant_1]
+
+// Test all the floating-point precisions in turn, and if they are available
+// then display how many decimal digits of precision.
+#ifdef BOOST_FLOAT16_C
+ std::cout << "Floating-point type boost::float16_t is available." << std::endl;
+#else
+ std::cout << "Floating-point type boost::float16_t is NOT available." << std::endl;
+#endif
+
+#ifdef BOOST_FLOAT32_C
+ std::cout << "Floating-point type boost::float32_t is available." << std::endl;
+ std::cout << " std::numeric_limits<boost::float32_t>::digits10 == "
+ << std::numeric_limits<boost::float32_t>::digits10 << std::endl;
+ std::cout << " std::numeric_limits<boost::float32_t>::max_digits10 == "
+ << std::numeric_limits<boost::float32_t>::max_digits10 << std::endl;
+#else
+ std::cout << "Floating-point type boost::float32_t is NOT available." << std::endl;
+#endif
+
+#ifdef BOOST_FLOAT64_C
+ std::cout << "Floating-point type boost::float64_t is available." << std::endl;
+ std::cout << " std::numeric_limits<boost::float64_t>::digits10 == "
+ << std::numeric_limits<boost::float64_t>::digits10 << std::endl;
+ std::cout << " std::numeric_limits<boost::float64_t>::max_digits10 == "
+ << std::numeric_limits<boost::float64_t>::max_digits10 << std::endl;
+#else
+ std::cout << "Floating-point type boost::float64_t is NOT available." << std::endl;
+#endif
+
+#ifdef BOOST_FLOAT80_C
+ std::cout << "Floating-point type boost::float80_t is available." << std::endl;
+ std::cout << " std::numeric_limits<boost::float80_t>::digits10 == "
+ << std::numeric_limits<boost::float80_t>::digits10 << std::endl;
+ std::cout << " std::numeric_limits<boost::float80_t>::max_digits10 == "
+ << std::numeric_limits<boost::float80_t>::max_digits10 << std::endl;
+#else
+ std::cout << "Floating-point type boost::float80_t is NOT available." << std::endl;
+#endif
+
+#ifdef BOOST_FLOAT128_C
+ std::cout << "Floating-point type boost::float128_t is available." << std::endl;
+ std::cout << " std::numeric_limits<boost::float128_t>::digits10 == "
+ << std::numeric_limits<boost::float128_t>::digits10 << std::endl;
+ std::cout << " std::numeric_limits<boost::float128_t>::max_digits10 == "
+ << std::numeric_limits<boost::float128_t>::max_digits10 << std::endl;
+#else
+ std::cout << "Floating-point type boost::float128_t is NOT available." << std::endl;
+#endif
+
+// Show some constants at a precision depending on the available type(s).
+#ifdef BOOST_FLOAT16_C
+ std::cout.precision(boost::max_digits10<boost::float16_t>()); // Show all significant decimal digits,
+ std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
+
+ std::cout << "BOOST_FLOAT16_C(123.456789012345678901234567890) = "
+ << BOOST_FLOAT16_C(123.456789012345678901234567890) << std::endl;
+ // BOOST_FLOAT16_C(123.456789012345678901234567890) = 123.45678901234568
+#endif
+
+//[floatmax_widths_1
+#ifdef BOOST_FLOAT32_C
+ std::cout.precision(boost::max_digits10<boost::float32_t>()); // Show all significant decimal digits,
+ std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
+ std::cout << "BOOST_FLOAT32_C(123.4567890123456789012345678901234567890) = "
+ << BOOST_FLOAT32_C(123.4567890123456789012345678901234567890) << std::endl;
+ // BOOST_FLOAT32_C(123.4567890123456789012345678901234567890) = 123.456787
+#endif
+//] [/floatmax_widths_1]
+
+#ifdef BOOST_FLOAT64_C
+ std::cout.precision(boost::max_digits10<boost::float64_t>()); // Show all significant decimal digits,
+ std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
+ std::cout << "BOOST_FLOAT64_C(123.4567890123456789012345678901234567890) = "
+ << BOOST_FLOAT64_C(123.4567890123456789012345678901234567890) << std::endl;
+ // BOOST_FLOAT64_C(123.4567890123456789012345678901234567890) = 123.45678901234568
+#endif
+
+#ifdef BOOST_FLOAT80_C
+ std::cout.precision(boost::max_digits10<boost::float80_t>()); // Show all significant decimal digits,
+ std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
+ std::cout << "BOOST_FLOAT80_C(123.4567890123456789012345678901234567890) = "
+ << BOOST_FLOAT80_C(123.4567890123456789012345678901234567890) << std::endl;
+ // BOOST_FLOAT80_C(123.4567890123456789012345678901234567890) = 123.456789012345678903
+#endif
+
+#ifdef BOOST_FLOAT128_C
+ std::cout.precision(boost::max_digits10<boost::float128_t>()); // Show all significant decimal digits,
+ std::cout.setf(std::ios::showpoint); // including all significant trailing zeros.
+ std::cout << "BOOST_FLOAT128_C(123.4567890123456789012345678901234567890) = "
+ << BOOST_FLOAT128_C(123.4567890123456789012345678901234567890) << std::endl;
+ // BOOST_FLOAT128_C(123.4567890123456789012345678901234567890) = 123.456789012345678901234567890123453
+#endif
+
+/*
+//[floatmax_widths_2
+BOOST_FLOAT32_C(123.4567890123456789012345678901234567890) = 123.456787
+BOOST_FLOAT64_C(123.4567890123456789012345678901234567890) = 123.45678901234568
+BOOST_FLOAT80_C(123.4567890123456789012345678901234567890) = 123.456789012345678903
+BOOST_FLOAT128_C(123.4567890123456789012345678901234567890) = 123.456789012345678901234567890123453
+//] [/floatmax_widths_2]
+*/
+
+// Display the precisions available for floatmax_t
+
+#ifdef BOOST_FLOATMAX_C
+ BOOST_ASSERT(std::numeric_limits<boost::floatmax_t>::is_specialized == true);
+ BOOST_ASSERT(std::numeric_limits<boost::floatmax_t>::is_iec559 == true);
+ BOOST_ASSERT(BOOST_FLOATMAX_C(0.) == 0);
+
+ std::cout << "floatmax_t " << std::numeric_limits<boost::floatmax_t>::digits << " bits\n" // 113
+ << std::numeric_limits<boost::floatmax_t>::digits10 << " decimal digits\n" // 34
+ << std::numeric_limits<boost::floatmax_t>::max_digits10 << " max_digits\n" // 36
+ << std::numeric_limits<boost::floatmax_t>::radix << " radix\n"
+ << std::endl;
+
+ int significand_bits = std::numeric_limits<boost::floatmax_t>::digits;
+ int exponent_max = std::numeric_limits<boost::floatmax_t>::max_exponent;
+ int exponent_min = std::numeric_limits<boost::floatmax_t>::min_exponent;
+ int exponent_bits = 1 + static_cast<int>(std::log2(std::numeric_limits<boost::floatmax_t>::max_exponent));
+ int sign_bits = std::numeric_limits<boost::floatmax_t>::is_signed;
+
+ std::cout << "significand_bits (including one implicit bit)" << significand_bits
+ << ", exponent_bits " << exponent_bits
+ << ", sign_bits " << sign_bits << std::endl;
+
+ // One can compute the total number of bits in the floatmax_t,
+ // but probably not at compile time.
+
+ std::cout << "bits = " << significand_bits + exponent_bits + sign_bits -1 << std::endl;
+ // -1 to take account of the implicit bit that is not part of the physical layout.
+
+ // One can compare typedefs (but, of course, only those that are defined for the platform in use.)
+ std::cout.setf(std::ios::boolalpha);
+ std::cout << "double, double: " << std::is_same<double, double>::value << std::endl;
+ bool b = boost::is_same<boost::floatmax_t, boost::float64_t>::value;
+ std::cout << "boost::is_same<boost::floatmax_t, boost::float64_t>::value; " << b << std::endl;
+ std::cout << "floatmax_t, float64_t: "
+ << std::is_same<boost::floatmax_t, boost::float64_t>::value << std::endl;
+
+/*`So the simplest way of obtaining the total number of bits in the floatmax_t
+is to infer it from the std::numeric_limits<>::digits value.
+This is possible because the type, must be a IEEE754 layout. */
+//[floatmax_1
+ const int fpbits =
+ (std::numeric_limits<boost::floatmax_t>::digits == 113) ? 128 :
+ (std::numeric_limits<boost::floatmax_t>::digits == 64) ? 80 :
+ (std::numeric_limits<boost::floatmax_t>::digits == 53) ? 64 :
+ (std::numeric_limits<boost::floatmax_t>::digits == 24) ? 32 :
+ (std::numeric_limits<boost::floatmax_t>::digits == 11) ? 16 :
+ 0; // Unknown - not IEEE754 format.
+ std::cout << fpbits << " bits." << std::endl;
+//] [/floatmax_1]
+#endif
+
+ }
+ catch (std::exception ex)
+ { // Display details about why any exceptions are thrown.
+ std::cout << "Thrown exception " << ex.what() << std::endl;
+ }
+
+} // int main()
+
+/*
+[cstdfloat_output
+
+GCC 4.8.1 with quadmath
+
+ pi = 1.00000
+ 0.88010117148986700
+ 0.0 0.0000000000000000
+ 1.0 0.88010117148986700
+ 2.0 4.6137984620549872
+ 3.0 16.274830009244951
+ 4.0 -25.360637961042869
+ 5.0 -1257.9038883512264
+ 6.0 -12749.592182518225
+ 7.0 -3020.9830849309437
+ 8.0 2421897.6013183584
+ 9.0 45577595.449204877
+ 0.0 0.00000000000000000000000000000000000
+ 1.0 0.880101171489866995756301548681221902
+ 2.0 4.61379846205498722611082484945654869
+ 3.0 16.2748300092449511566883302293717861
+ 4.0 -25.3606379610428689375112298876047134
+ 5.0 -1257.90388835122644195507746189832687
+ 6.0 -12749.5921825182249449426308274269104
+ 7.0 -3020.98308493094373261556029319763184
+ 8.0 2421897.60131835844367742538452148438
+ 9.0 45577595.4492048770189285278320312500
+ Floating-point type long double is available with:
+ std::numeric_limits<long double>::digits10 == 18
+ std::numeric_limits<long double>::max_digits10 == 21
+ pi = 3.14159265358979312
+ Most precise pi = 3.141592653589793238462643383279503
+ Floating-point type boost::float16_t is NOT available.
+ Floating-point type boost::float32_t is available.
+ std::numeric_limits<boost::float32_t>::digits10 == 6
+ std::numeric_limits<boost::float32_t>::max_digits10 == 9
+ Floating-point type boost::float64_t is available.
+ std::numeric_limits<boost::float64_t>::digits10 == 15
+ std::numeric_limits<boost::float64_t>::max_digits10 == 17
+ Floating-point type boost::float80_t is available.
+ std::numeric_limits<boost::float80_t>::digits10 == 18
+ std::numeric_limits<boost::float80_t>::max_digits10 == 21
+ Floating-point type boost::float128_t is available.
+ std::numeric_limits<boost::float128_t>::digits10 == 34
+ std::numeric_limits<boost::float128_t>::max_digits10 == 36
+ BOOST_FLOAT32_C(123.4567890123456789012345678901234567890) = 123.456787
+ BOOST_FLOAT64_C(123.4567890123456789012345678901234567890) = 123.45678901234568
+ BOOST_FLOAT80_C(123.4567890123456789012345678901234567890) = 123.456789012345678903
+ BOOST_FLOAT128_C(123.4567890123456789012345678901234567890) = 123.456789012345678901234567890123453
+ floatmax_t 113 bits
+ 34 decimal digits
+ 36 max_digits
+ 2 radix
+
+ significand_bits (including one implicit bit)113, exponent_bits 15, sign_bits 1
+ bits = 128
+ double, double: true
+ boost::is_same<boost::floatmax_t, boost::float64_t>::value; false
+ floatmax_t, float64_t: false
+ 128 bits.
+
+ RUN SUCCESSFUL (total time: 53ms)
+
+GCC 6.1.1
+
+pi = 1.00000
+0.88010117148986700
+0.0 0.0000000000000000
+1.0 0.88010117148986700
+2.0 4.6137984620549872
+3.0 16.274830009244951
+4.0 -25.360637961042869
+5.0 -1257.9038883512264
+6.0 -12749.592182518225
+7.0 -3020.9830849309437
+8.0 2421897.6013183584
+9.0 45577595.449204877
+0.0 0.00000000000000000000000000000000000
+1.0 0.880101171489866995756301548681221902
+2.0 4.61379846205498722611082484945654869
+3.0 16.2748300092449511566883302293717861
+4.0 -25.3606379610428689375112298876047134
+5.0 -1257.90388835122644195507746189832687
+6.0 -12749.5921825182249449426308274269104
+7.0 -3020.98308493094373261556029319763184
+8.0 2421897.60131835844367742538452148438
+9.0 45577595.4492048770189285278320312500
+Floating-point type long double is available with:
+ std::numeric_limits<long double>::digits10 == 18
+ std::numeric_limits<long double>::max_digits10 == 21
+pi = 3.14159265358979312
+Most precise pi = 3.14159265358979323846264338327950
+Floating-point type boost::float16_t is NOT available.
+Floating-point type boost::float32_t is available.
+ std::numeric_limits<boost::float32_t>::digits10 == 6
+ std::numeric_limits<boost::float32_t>::max_digits10 == 9
+Floating-point type boost::float64_t is available.
+ std::numeric_limits<boost::float64_t>::digits10 == 15
+ std::numeric_limits<boost::float64_t>::max_digits10 == 17
+Floating-point type boost::float80_t is available.
+ std::numeric_limits<boost::float80_t>::digits10 == 18
+ std::numeric_limits<boost::float80_t>::max_digits10 == 21
+Floating-point type boost::float128_t is available.
+ std::numeric_limits<boost::float128_t>::digits10 == 33
+ std::numeric_limits<boost::float128_t>::max_digits10 == 36
+BOOST_FLOAT32_C(123.4567890123456789012345678901234567890) = 123.456787
+BOOST_FLOAT64_C(123.4567890123456789012345678901234567890) = 123.45678901234568
+BOOST_FLOAT80_C(123.4567890123456789012345678901234567890) = 123.456789012345678903
+BOOST_FLOAT128_C(123.4567890123456789012345678901234567890) = 123.456789012345678901234567890123453
+floatmax_t 113 bits
+33 decimal digits
+36 max_digits
+2 radix
+
+significand_bits (including one implicit bit)113, exponent_bits 15, sign_bits 1
+bits = 128
+double, double: true
+boost::is_same<boost::floatmax_t, boost::float64_t>::value; false
+floatmax_t, float64_t: false
+128 bits.
+
+
+ MSVC 2013 64-bit
+
+ 1> pi = 1.00000
+ 1> 0.88010117148986700
+ 1> 0.00 0.00000000000000000
+ 1> 1.0 0.88010117148986700
+ 1> 2.0 4.6137984620549854
+ 1> 3.0 16.274830009244948
+ 1> 4.0 -25.360637961042869
+ 1> 5.0 -1257.9038883512258
+ 1> 6.0 -12749.592182518225
+ 1> 7.0 -3020.9830849309396
+ 1> 8.0 2421897.6013183575
+ 1> 9.0 45577595.449204892
+ 1> 0.00 0.00000000000000000
+ 1> 1.0 0.88010117148986700
+ 1> 2.0 4.6137984620549854
+ 1> 3.0 16.274830009244948
+ 1> 4.0 -25.360637961042869
+ 1> 5.0 -1257.9038883512258
+ 1> 6.0 -12749.592182518225
+ 1> 7.0 -3020.9830849309396
+ 1> 8.0 2421897.6013183575
+ 1> 9.0 45577595.449204892
+ 1> Floating-point type long double is available with:
+ 1> std::numeric_limits<long double>::digits10 == 15
+ 1> std::numeric_limits<long double>::max_digits10 == 17
+ 1> pi = 3.14159265358979
+ 1> Most precise pi = 3.14159265358979
+ 1> Floating-point type boost::float16_t is NOT available.
+ 1> Floating-point type boost::float32_t is available.
+ 1> std::numeric_limits<boost::float32_t>::digits10 == 6
+ 1> std::numeric_limits<boost::float32_t>::max_digits10 == 9
+ 1> Floating-point type boost::float64_t is available.
+ 1> std::numeric_limits<boost::float64_t>::digits10 == 15
+ 1> std::numeric_limits<boost::float64_t>::max_digits10 == 17
+ 1> Floating-point type boost::float80_t is NOT available.
+ 1> Floating-point type boost::float128_t is NOT available.
+ 1> BOOST_FLOAT32_C(123.4567890123456789012345678901234567890) = 123.456787
+ 1> BOOST_FLOAT64_C(123.4567890123456789012345678901234567890) = 123.45678901234568
+ 1> floatmax_t 53 bits
+ 1> 15 decimal digits
+ 1> 17 max_digits
+ 1> 2 radix
+ 1>
+ 1> significand_bits (including one implicit bit)53, exponent_bits 11, sign_bits 1
+ 1> bits = 64
+ 1> double, double: true
+ 1> boost::is_same<boost::floatmax_t, boost::float64_t>::value; true
+ 1> floatmax_t, float64_t: true
+ 1> 64 bits.
+] [/cstdfloat_output]
+
+
+*/
+
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-21 12:31:11 +0000