| [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). |
| ] |
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