int main(int
#ifdef BOOST_FLOAT128_C
argc
#endif
, char*[])
{
#ifdef BOOST_FLOAT128_C
if(argc > 1000)
instantiate(BOOST_FLOAT128_C(1.23));
#endif
}
static boost::math::cstdfloat::detail::float_internal128_t denorm_min () { return BOOST_FLOAT128_C(0.0); }
static boost::math::cstdfloat::detail::float_internal128_t signaling_NaN() { return BOOST_FLOAT128_C(0.0); }
static boost::math::cstdfloat::detail::float_internal128_t quiet_NaN () { return ::BOOST_CSTDFLOAT_FLOAT128_SQRT(BOOST_FLOAT128_C(-1.0)); }
static boost::math::cstdfloat::detail::float_internal128_t infinity () { return BOOST_FLOAT128_C(1.0) / BOOST_FLOAT128_C(0.0); }
static boost::math::cstdfloat::detail::float_internal128_t round_error() { return BOOST_FLOAT128_C(0.5); }
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()