mirror of
https://github.com/boostorg/multiprecision.git
synced 2026-01-19 16:32:12 +00:00
55bf069621
* Update Jamfile.v2 * Update introduction.qbk * Update tutorial.qbk * Update tutorial_cpp_int.qbk * Update tutorial_gmp_int.qbk * Update tutorial_tommath.qbk * Update integer_examples.cpp * Update tutorial_cpp_bin_float.qbk * Update tutorial_cpp_dec_float.qbk * Update tutorial_gmp_float.qbk * Update tutorial_mpfr_float.qbk * Update tutorial_float128.qbk * Update tutorial_float_builtin_ctor.qbk * Update big_seventh.cpp * Update tutorial_float_eg.qbk * Update floating_point_examples.cpp * Update mpfr_precision.cpp * Update gauss_laguerre_quadrature.cpp * Update tutorial_interval_mpfi.qbk * Update tutorial_cpp_complex.qbk * Update tutorial_mpc_complex.qbk * Update tutorial_float128_complex.qbk * Update tutorial_complex_adaptor.qbk * Update tutorial_rational.qbk * Update tutorial_tommath_rational.qbk * Update tutorial_logged_adaptor.qbk * Update tutorial_debug_adaptor.qbk * Update tutorial_visualizers.qbk * Update tutorial_fwd.qbk * Update tutorial_conversions.qbk * Update tutorial_random.qbk * Update random_snips.cpp * Update tutorial_constexpr.qbk * Update tutorial_import_export.qbk * Update cpp_int_import_export.cpp * Update tutorial_mixed_precision.qbk * Update tutorial_variable_precision.qbk * Update scoped_precision_example.cpp * Update tutorial_numeric_limits.qbk * Update tutorial_numeric_limits.qbk * Update numeric_limits_snips.cpp * Update numeric_limits_snips.cpp * Update tutorial_numeric_limits.qbk * Update numeric_limits_snips.cpp * Update numeric_limits_snips.cpp * Update tutorial_io.qbk * Update reference_number.qbk * Update reference_cpp_bin_float.qbk * Update reference_cpp_double_fp_backend.qbk * Update reference_internal_support.qbk * Update reference_backend_requirements.qbk * Update performance.qbk * Update performance_overhead.qbk * Update performance_real_world.qbk * Update performance_integer_real_world.qbk * Update performance_rational_real_world.qbk * Update reference_number.qbk * Update tutorial_numeric_limits.qbk * Update reference_backend_requirements.qbk
100 lines
5.0 KiB
Plaintext
100 lines
5.0 KiB
Plaintext
[/
|
|
Copyright 2011 - 2020 John Maddock.
|
|
Copyright 2013 - 2019 Paul A. Bristow.
|
|
Copyright 2013 Christopher Kormanyos.
|
|
|
|
Distributed under 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).
|
|
]
|
|
|
|
[section:mpfr_float mpfr_float]
|
|
|
|
`#include <boost/multiprecision/mpfr.hpp>`
|
|
|
|
namespace boost{ namespace multiprecision{
|
|
|
|
enum mpfr_allocation_type
|
|
{
|
|
allocate_stack,
|
|
allocate_dynamic
|
|
};
|
|
|
|
template <unsigned Digits10, mpfr_allocation_type AllocateType = allocate_dynamic>
|
|
class mpfr_float_backend;
|
|
|
|
typedef number<mpfr_float_backend<50> > mpfr_float_50;
|
|
typedef number<mpfr_float_backend<100> > mpfr_float_100;
|
|
typedef number<mpfr_float_backend<500> > mpfr_float_500;
|
|
typedef number<mpfr_float_backend<1000> > mpfr_float_1000;
|
|
typedef number<mpfr_float_backend<0> > mpfr_float;
|
|
|
|
typedef number<mpfr_float_backend<50, allocate_stack> > static_mpfr_float_50;
|
|
typedef number<mpfr_float_backend<100, allocate_stack> > static_mpfr_float_100;
|
|
|
|
}} // namespaces
|
|
|
|
The `mpfr_float_backend` type is used in conjunction with `number`: It acts as a thin wrapper around the [mpfr] `mpfr_t`
|
|
to provide an real-number type that is a drop-in replacement for the native C++ floating-point types, but with
|
|
much greater precision.
|
|
|
|
Type `mpfr_float_backend` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or
|
|
at variable precision by setting the template argument to zero. The typedefs mpfr_float_50, mpfr_float_100,
|
|
mpfr_float_500, mpfr_float_1000 provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision
|
|
respectively. The typedef mpfr_float provides a variable precision type whose precision can be controlled via the
|
|
`number`s member functions.
|
|
|
|
In addition the second template parameter lets you choose between dynamic allocation (the default,
|
|
and uses MPFR's normal allocation routines),
|
|
or stack allocation (where all the memory required for the underlying data types is stored
|
|
within `mpfr_float_backend`). The latter option can result in significantly faster code, at the
|
|
expense of growing the size of `mpfr_float_backend`. It can only be used at ['fixed precision], and
|
|
should only be used for lower digit counts. Note that we can not guarantee that using `allocate_stack`
|
|
won't cause any calls to `mpfr`'s allocation routines, as `mpfr` may call these inside its own code.
|
|
The following table gives an idea of the performance tradeoff's at 50 decimal digits
|
|
precision[footnote Compiled with VC++10 and /Ox, with MPFR-3.0.0 and MPIR-2.3.0]:
|
|
|
|
[table
|
|
[[Type][Bessel function evaluation, relative times]]
|
|
[[`number<mpfr_float_backend<50, allocate_static>, et_on>`][1.0 (5.5s)]]
|
|
[[`number<mpfr_float_backend<50, allocate_static>, et_off>`][1.05 (5.8s)]]
|
|
[[`number<mpfr_float_backend<50, allocate_dynamic>, et_on>`][1.05 (5.8s)]]
|
|
[[`number<mpfr_float_backend<50, allocate_dynamic>, et_off>`][1.16 (6.4s)]]
|
|
]
|
|
|
|
[note This type only provides `numeric_limits` support when the precision is fixed at compile time.]
|
|
|
|
As well as the usual conversions from arithmetic and string types, instances of `number<mpfr_float_backend<N> >` are
|
|
copy constructible and assignable from:
|
|
|
|
* The [gmp] native types `mpf_t`, `mpz_t`, `mpq_t`.
|
|
* The [mpfr] native type `mpfr_t`.
|
|
* The `number` wrappers around those types: `number<mpfr_float_backend<M> >`, `number<mpf_float<M> >`, `number<gmp_int>`, `number<gmp_rational>`.
|
|
|
|
It's also possible to access the underlying `mpfr_t` via the data() member function of `mpfr_float_backend`.
|
|
|
|
Things you should know when using this type:
|
|
|
|
* A default constructed `mpfr_float_backend` is set to zero (['Note that this is [*not] the default [mpfr] behavior]).
|
|
* All operations use round to nearest.
|
|
* No changes are made to [gmp] or [mpfr] global settings, so this type can coexist with existing
|
|
[mpfr] or [gmp] code.
|
|
* The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32.
|
|
* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move-aware.
|
|
* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted
|
|
as a valid floating-point number.
|
|
* Division by zero results in an infinity.
|
|
* When using the variable precision type `mpfr_float`, then copy construction and assignment ['copies the precision
|
|
of the source variable]. Likewise move construction and assignment.
|
|
* When constructing the variable precision type `mpfr_float` you can specify two arguments to the constructor - the first
|
|
is the value to assign to the variable, the second is an unsigned integer specifying the precision in decimal places. The
|
|
`assign` member function similarly has a 2-argument overload taking the value to assign and the precision. You can use this
|
|
to preserve the precision of the target variable using the somewhat arcane: `a.assign(b, a.precision())`, which assigns `b` to `a`
|
|
but preserves the precision of `a`.
|
|
|
|
[h5 [mpfr] example:]
|
|
|
|
[mpfr_eg]
|
|
|
|
[endsect] [/section:mpfr_float mpfr_float]
|