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81 lines
4.0 KiB
Plaintext
81 lines
4.0 KiB
Plaintext
[/
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Copyright 2011 - 2020 John Maddock.
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Copyright 2013 - 2019 Paul A. Bristow.
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Copyright 2013 Christopher Kormanyos.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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[section:mpc_complex mpc_complex]
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`#include <boost/multiprecision/mpc.hpp>`
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namespace boost{ namespace multiprecision{
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template <unsigned Digits10>
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class mpc_complex_backend;
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typedef number<mpc_complex_backend<50> > mpc_complex_50;
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typedef number<mpc_complex_backend<100> > mpc_complex_100;
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typedef number<mpc_complex_backend<500> > mpc_complex_500;
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typedef number<mpc_complex_backend<1000> > mpc_complex_1000;
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typedef number<mpc_complex_backend<0> > mpc_complex;
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}} // namespaces
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The `mpc_complex_backend` type is used in conjunction with `number`: It acts as a thin wrapper around the [mpc] `mpc_t`
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to provide a real-number type that is a drop-in replacement for `std::complex`, but with
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much greater precision.
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Type `mpc_complex_backend` can be used at fixed precision by specifying a non-zero `Digits10` template parameter, or
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at variable precision by setting the template argument to zero. The typedefs mpc_complex_50, mpc_complex_100,
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mpc_complex_500, mpc_complex_1000 provide complex types at 50, 100, 500 and 1000 decimal digits precision
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respectively. The typedef mpc_complex provides a variable precision type whose precision can be controlled via the
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`number`s member functions.
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The `mpc` backend should allow use of the same syntax as the C++ standard library complex type.
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When using this backend, remember to link with the flags `-lmpc -lmpfr -lgmp`.
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As well as the usual conversions from arithmetic and string types, instances of `number<mpc_complex_backend<N> >` are
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copy constructible and assignable from:
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* The [gmp] native types `mpf_t`, `mpz_t`, `mpq_t`.
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* The [mpfr] native type `mpfr_t`.
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* The [mpc] native type `mpc_t`.
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* The `number` wrappers around those types: `number<mpfr_float_backend<M> >`, `number<mpf_float<M> >`, `number<gmp_int>`, `number<gmp_rational>`.
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It's also possible to access the underlying `mpc_t` via the `data()` member function of `mpfr_float_backend`.
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Things you should know when using this type:
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* A default constructed `mpc_complex_backend` is set to zero (['Note that this is [*not] the default [mpc] behavior]).
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* All operations use round to nearest.
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* No changes are made to [mpc], [gmp] or [mpfr] global settings, so this type can coexist with existing
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[mpc], [mpfr] or [gmp] code.
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* The code can equally use [mpir] in place of [gmp] - indeed that is the preferred option on Win32.
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* This backend supports rvalue-references and is move-aware, making instantiations of `number` on this backend move aware.
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* Conversion from a string results in a `std::runtime_error` being thrown if the string can not be interpreted
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as a valid complex number.
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* Division by zero results in a complex-infinity.
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* Unlike `std::complex`, you can not use `reinterpret_cast` to treat this type as an array of the underlying floating point type.
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* Unlike `std::complex`, there are no literals for imaginary values.
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* When using the variable precision type `mpc_complex`, then copy construction and assignment ['copies the precision
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of the source variable]. Likewise move construction and assignment.
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* When constructing the variable precision type `mpc_complex` you can specify two arguments to the constructor - the first
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is the value to assign to the variable, the second is an unsigned integer specifying the precision in decimal places. The
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`assign` member function similarly has a 2-argument overload taking the value to assign and the precision. You can use this
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to preserve the precision of the target variable using the somewhat arcane: `a.assign(b, a.precision())`, which assigns `b` to `a`
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but preserves the precision of `a`.
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[h5 [mpc] example:]
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[mpc_eg]
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Which produces the output (for the multiprecision type):
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[mpc_out]
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[endsect] [/section:mpc_complex mpc_complex]
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