multiprecision/doc/tutorial_cpp_bin_float.qbk

[/
  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:cpp_bin_float cpp_bin_float]

`#include <boost/multiprecision/cpp_bin_float.hpp>`

   namespace boost{ namespace multiprecision{

   enum digit_base_type
   {
      digit_base_2 = 2,
      digit_base_10 = 10
   };

   template <unsigned Digits, digit_base_type base = digit_base_10, class Allocator = void, class Exponent = int, ExponentMin = 0, ExponentMax = 0>
   class cpp_bin_float;

   typedef number<cpp_bin_float<50> > cpp_bin_float_50;
   typedef number<cpp_bin_float<100> > cpp_bin_float_100;

   typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, std::int16_t, -126, 127>, et_off>         cpp_bin_float_single;
   typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, std::int16_t, -1022, 1023>, et_off>       cpp_bin_float_double;
   typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, std::int16_t, -16382, 16383>, et_off>     cpp_bin_float_double_extended;
   typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, std::int16_t, -16382, 16383>, et_off>    cpp_bin_float_quad;
   typedef number<backends::cpp_bin_float<237, backends::digit_base_2, void, std::int32_t, -262142, 262143>, et_off>  cpp_bin_float_oct;

   }} // namespaces

The `cpp_bin_float` back-end is used in conjunction with `number`: It acts as an entirely C++ (header only and dependency free)
floating-point number type that is a drop-in replacement for the native C++ floating-point types, but with
much greater precision.

Type `cpp_bin_float` can be used at fixed precision by specifying a non-zero `Digits` template parameter.
The typedefs `cpp_bin_float_50` and `cpp_bin_float_100` provide arithmetic types at 50 and 100 decimal digits precision
respectively.

Optionally, you can specify whether the precision is specified in decimal digits or binary bits - for example
to declare a `cpp_bin_float` with exactly the same precision as `double` one would use
`number<cpp_bin_float<53, digit_base_2> >`.  The typedefs `cpp_bin_float_single`, `cpp_bin_float_double`,
`cpp_bin_float_quad`, `cpp_bin_float_oct` and `cpp_bin_float_double_extended` provide
software analogues of the IEEE single, double, quad and octuple float data types, plus the Intel-extended-double type respectively.
Note that while these types are functionally equivalent to the native IEEE types, they do not have the same size
or bit-layout as true IEEE compatible types.

Normally `cpp_bin_float` allocates no memory: all of the space required for its digits is allocated
directly within the class.  As a result care should be taken not to use the class with too high a digit count
as stack space requirements can grow out of control.  If that represents a problem then providing an allocator
as a template parameter causes `cpp_bin_float` to dynamically allocate the memory it needs: this
significantly reduces the size of `cpp_bin_float` and increases the viable upper limit on the number of digits
at the expense of performance.  However, please bear in mind that arithmetic operations rapidly become ['very] expensive
as the digit count grows: the current implementation really isn't optimized or designed for large digit counts.
Note that since the actual type of the objects allocated
is completely opaque, the suggestion would be to use an allocator with `void` `value_type`, for example:
`number<cpp_bin_float<1000, digit_base_10, std::allocator<void> > >`.

The final template parameters determine the type and range of the exponent: parameter `Exponent` can be
any signed integer type, but note that `MinExponent` and `MaxExponent` can not go right up to the limits
of the `Exponent` type as there has to be a little extra headroom for internal calculations.  You will
get a compile time error if this is the case.  In addition if MinExponent or MaxExponent are zero, then
the library will choose suitable values that are as large as possible given the constraints of the type
and need for extra headroom for internal calculations.

There is full standard library and `numeric_limits` support available for this type.

Things you should know when using this type:

* Default constructed `cpp_bin_float`s have a value of zero.
* The radix of this type is 2, even when the precision is specified as decimal digits.
* The type supports both infinities and NaNs.  An infinity is generated whenever the result would overflow,
and a NaN is generated for any mathematically undefined operation.
* There is a `std::numeric_limits` specialisation for this type.
* Any `number` instantiated on this type is convertible to any other `number` instantiated on this type -
for example you can convert from `number<cpp_bin_float<50> >` to `number<cpp_bin_float<SomeOtherValue> >`.
Narrowing conversions round to nearest and are `explicit`.
* 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.
* All arithmetic operations are correctly rounded to nearest.  String conversions and the `sqrt` function
are also correctly rounded, but transcendental functions (sin, cos, pow, exp etc.) are not.

[h5 cpp_bin_float example:]

[cpp_bin_float_eg]

[endsect]