123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249 |
- [book Standardized Floating-Point typedefs for C and C++
- [quickbook 1.7]
- [copyright 2014 Christopher Kormanyos, John Maddock, Paul A. Bristow]
- [license
- 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])
- ]
- [authors [Kormanyos, Christopher], [Maddock, John], [Bristow, Paul A.] ]
- [last-revision $Date$]
- [/version 1.8.3]
- ]
- [template tr1[] [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf Technical Report on C++ Library Extensions]]
- [template C99[] [@http://www.open-std.org/JTC1/SC22/WG14/www/docs/n1256.pdf C99 Standard ISO/IEC 9899:1999]]
- [def __gsl [@http://www.gnu.org/software/gsl/ GSL-1.9]]
- [def __glibc [@http://www.gnu.org/software/libc/ GNU C Lib]]
- [def __hpc [@http://docs.hp.com/en/B9106-90010/index.html HP-UX C Library]]
- [def __cephes [@http://www.netlib.org/cephes/ Cephes]]
- [def __NTL [@http://www.shoup.net/ntl/ NTL A Library for doing Number Theory]]
- [def __NTL_RR [@http://shoup.net/ntl/doc/RR.txt NTL::RR]]
- [def __NTL_quad_float [@http://shoup.net/ntl/doc/quad_float.txt NTL::quad_float]]
- [def __MPFR [@http://www.mpfr.org/ GNU MPFR library]]
- [def __GMP [@http://gmplib.org/ GNU Multiple Precision Arithmetic Library]]
- [def __multiprecision [@http://www.boost.org/doc/libs/1_53_0_beta1/libs/multiprecision/doc/html/index.html Boost.Multiprecision]]
- [def __cpp_dec_float [@http://www.boost.org/doc/libs/1_53_0_beta1/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/cpp_dec_float.html cpp_dec_float]]
- [def __R [@http://www.r-project.org/ The R Project for Statistical Computing]]
- [def __godfrey [link godfrey Godfrey]]
- [def __pugh [link pugh Pugh]]
- [def __NaN [@http://en.wikipedia.org/wiki/NaN NaN]]
- [def __errno [@http://en.wikipedia.org/wiki/Errno `::errno`]]
- [def __Mathworld [@http://mathworld.wolfram.com Wolfram MathWorld]]
- [def __Mathematica [@http://www.wolfram.com/products/mathematica/index.html Wolfram Mathematica]]
- [def __WolframAlpha [@http://www.wolframalpha.com/ Wolfram Alpha]]
- [def __TOMS748 [@http://portal.acm.org/citation.cfm?id=210111 TOMS Algorithm 748: enclosing zeros of continuous functions]]
- [def __TOMS910 [@http://portal.acm.org/citation.cfm?id=1916469 TOMS Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations]]
- [def __why_complements [link why_complements why complements?]]
- [def __complements [link math_toolkit.stat_tut.overview.complements complements]]
- [def __performance [link perf performance]]
- [def __building [link math_toolkit.building building libraries]]
- [def __e_float [@http://calgo.acm.org/910.zip e_float (TOMS Algorithm 910)]]
- [def __Abramowitz_Stegun M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, NBS (1964)]
- [def __DMLF [@http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]]
- [def __IEEE754 [@http://en.wikipedia.org/wiki/IEEE_floating_point IEEE_floating_point]]
- [def __N3626 [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2013/n3626.pdf N3626]]
- [def __N1703 [@http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1703.pdf N1703]]
- [/ Some composite templates]
- [template super[x]'''<superscript>'''[x]'''</superscript>''']
- [template sub[x]'''<subscript>'''[x]'''</subscript>''']
- [template floor[x]'''⌊'''[x]'''⌋''']
- [template floorlr[x][lfloor][x][rfloor]]
- [template ceil[x] '''⌈'''[x]'''⌉''']
- [/template header_file[file] [@../../../../[file] [file]]]
- [note A printer-friendly PDF version of this manual is also available.]
- [section:overview Overview]
- The header `<boost/cstdfloat.hpp>` provides optional standardized
- floating-point `typedef`s having specified widths.
- These are useful for writing portable code because they
- should behave identically on all platforms.
- All `typedef`s are in `namespace boost`.
- The `typedef`s include `float16_t, float32_t, float64_t, float128_t`,
- their corresponding least and fast types,
- and the corresponding maximum-width type.
- The `typedef`s are based on underlying built-in types
- such as `float`, `double`, or `long double`, or based on other compiler-specific
- non-standardized types such as `__float128`.
- The underlying types of these typedef's must conform with
- the corresponding specifications of binary16, binary32, binary64,
- and binary128 in __IEEE754 floating-point format
- [@http://en.wikipedia.org/wiki/IEEE_floating_point].
- The typedef's are based on __N3626
- proposed for a new C++14 standard header `<cstdfloat>` and
- __N1703 proposed for a new C language standard header `<stdfloat.h>`.
- The 128-bit floating-point type, of great interest in scientific and
- numeric programming, is not required in the boost header,
- and may not be supplied for all platforms/compilers, because compiler
- support for a 128-bit floating-point type is not mandated by either
- the C standard or the C++ standard.
- The following code uses `<boost/cstdfloat.hpp>` in combination with
- `<boost/math/special_functions.hpp>` to compute a simplified
- version of the Jahnke-Emden-Lambda function. Here, we use
- a floating-point type with exactly 64 bits (i.e., `float64_t`).
- If we were to use, for instance, built-in `double`,
- then there would be no guarantee that the code would
- behave identically on all platforms. With `float64_t` from
- `<boost/cstdfloat.hpp>`, however, this is very likely.
- Using `float64_t`, we know that
- this code is portable and uses a floating-point type
- with approximately 15 decimal digits of precision.
- #include <cmath>
- #include <boost/cstdfloat.hpp>
- #include <boost/math/special_functions.hpp>
- 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;
- }
- See `cstdfloat_test.cpp` for a more detailed test program.
- [endsect] [/section:overview Overview]
- [section:rationale Rationale]
- The implementation of `<boost/cstdfloat.hpp>` is designed to utilize `<float.h>`,
- defined in the 1989 C standard. The preprocessor is used to query certain
- preprocessor definitions in `<float.h>` such as FLT_MAX, DBL_MAX, etc.
- Based on the results of these queries, an attempt is made to automatically
- detect the presence of built-in floating-point types having specified widths.
- An unequivocal test regarding conformance with __IEEE754 (IEC599) based on
- [@ http://en.cppreference.com/w/cpp/types/numeric_limits/is_iec559 `std::numeric_limits<>::is_iec559`]
- is performed with `BOOST_STATIC_ASSERT`.
- The header `<boost/cstdfloat.hpp>` makes the standardized floating-point
- `typedef`s safely available in `namespace boost` without placing any names
- in `namespace std`. The intention is to complement rather than compete
- with a potential future C++ Standard Library that may contain these `typedef`s.
- Should some future C++ standard include `<stdfloat.h>` and `<cstdfloat>`,
- then `<boost/cstdfloat.hpp>` will continue to function, but will become redundant
- and may be safely deprecated.
- Because `<boost/cstdfloat.hpp>` is a boost header, its name conforms to the
- boost header naming conventions, not the C++ Standard Library header
- naming conventions.
- [note
- <boost/cstdfloat.hpp> [*cannot synthesize or create
- a `typedef` if the underlying type is not provided by the compiler].
- For example, if a compiler does not have an underlying floating-point
- type with 128 bits (highly sought-after in scientific and numeric programming),
- then `float128_t` and its corresponding least and fast types are not
- provided by `<boost/cstdfloat.hpp`>.]
- [warning
- As an implementation artifact, certain C macro names from `<float.h>`
- may possibly be visible to users of `<boost/cstdfloat.hpp>`.
- Don't rely on using these macros; they are not part of any Boost-specified interface.
- Use `std::numeric_limits<>` for floating-point ranges, etc. instead.]
- [endsect] [/section:rationale Rationale]
- [section:exact_typdefs Exact-Width Floating-Point `typedef`s]
- The `typedef float#_t`, with # replaced by the width, designates a
- floating-point type of exactly # bits. For example `float32_t` denotes
- a single-precision floating-point type with approximately
- 7 decimal digits of precision (equivalent to binary32 in __IEEE754).
- Floating-point types specified in C and C++ are allowed to have
- implementation-specific widths and formats.
- However, if a platform supports underlying floating-point types
- (conformant with __IEEE754) with widths of 16, 32, 64, 128 bits,
- or any combination thereof,
- then `<boost/cstdfloat.hpp>` does provide the corresponding `typedef`s
- `float16_t, float32_t, float64_t, float128_t,`
- their corresponding least and fast types,
- and the corresponding maximum-width type
- The absence of `float128_t` is indicated by the macro `BOOST_NO_FLOAT128_T`.
- [endsect] [/section:exact_typdefs Exact-Width Floating-Point `typedef`s]
- [section:fastest_typdefs Fastest minimum-width floating-point `typedef`s]
- The `typedef float_least#_t`, with # replaced by the width, designates a
- floating-point type with a [*width of at least # bits], such that no
- floating-point type with lesser size has at least the specified width.
- Thus, `float_least32_t` denotes the smallest floating-point type with
- a width of at least 32 bits.
- Minimum-width floating-point types are provided for all existing
- exact-width floating-point types on a given platform.
- For example, if a platfrom supports `float32_t` and `float64_t`,
- then `float_least32_t` and `float_least64_t` will also be supported, etc.
- [endsect] [/section:fastest_typdefs Fastest minimum-width floating-point `typedef`s]
- [section:fastest_typdefs Fastest minimum-width floating-point `typedef`s]
- The typedef `float_fast#_t`, with # replaced by the width, designates
- the [*fastest] floating-point type with a width of at least # bits.
- There is no absolute guarantee that these types are the fastest for all purposes.
- In any case, however, they satisfy the precision and width requirements.
- Fastest minimum-width floating-point types are provided for all existing
- exact-width floating-point types on a given platform.
- For example, if a platform supports `float32_t` and `float64_t`,
- then `float_fast32_t` and `float_fast64_t` will also be supported, etc.
- [endsect] [/section:fastest_typdefs Fastest minimum-width floating-point `typedef`s]
- [section:greatest_typdefs Greatest-width floating-point typedef]
- The `typedef floatmax_t` designates a floating-point type capable of representing
- any value of any floating-point type in a given platform.
- The greatest-width typedef is provided for all platforms.
- [endsect] [/section:greatest_typdefs Greatest-width floating-point typedef]
- [section:macros Floating-Point Constant Macros]
- All macros of the type `BOOST_FLOAT16_C, BOOST_FLOAT32_C, BOOST_FLOAT64_C,
- BOOST_FLOAT128_C, BOOST_FLOATMAX_C` are always defined after inclusion of
- `<boost/cstdfloat.hpp>`. These allow floating-point constants of at
- least the specified width to be declared.
- For example:
- #include <boost/cstdfloat.hpp>
- // Declare Pythagoras' constant 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 34 decimal digits of precision.
- static const boost::float128_t euler = BOOST_FLOAT128_C(0.57721566490153286060651209008240243104216);
- [endsect] [/section:macros Floating-Point Constant Macros]
- [/ cstdfloat.qbk
- Copyright 2014 Christopher Kormanyos, John Maddock and Paul A. Bristow.
- 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).
- ]
|