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diff --git a/libs/math/tools/doc/cstdfloat.qbk b/libs/math/tools/doc/cstdfloat.qbk new file mode 100644 index 000000000..5d9b2fd78 --- /dev/null +++ b/libs/math/tools/doc/cstdfloat.qbk @@ -0,0 +1,249 @@ +[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). +] + + + + |