diff --git a/doc/integer.qbk b/doc/integer.qbk index 75042f2..8136f0d 100644 --- a/doc/integer.qbk +++ b/doc/integer.qbk @@ -2,7 +2,6 @@ [quickbook 1.6] [compatibility-mode 1.5] [copyright 2001-2009 Beman Dawes, Daryle Walker, Gennaro Prota, John Maddock] - [purpose Integer Type Selection] [license Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at @@ -17,13 +16,13 @@ [section:overview Overview] Boost.Integer provides integer type support, particularly helpful in generic programming. -It provides the means to select an integer type based upon its properties, like the number of bits or +It provides the means to select an integer type based upon its properties, like the number of bits or the maximum supported value, as well as compile-time bit mask selection. There is a derivative of -std::numeric_limits that provides integral constant expressions for `min` and `max`. -Finally, it provides two compile-time algorithms: determining the highest power of two in a +std::numeric_limits that provides integral constant expressions for `min` and `max`. +Finally, it provides two compile-time algorithms: determining the highest power of two in a compile-time value; and computing min and max of constant expressions. -[table +[table [[Component][Header][Purpose]] [ [Forward Declarations.] @@ -38,8 +37,8 @@ compile-time value; and computing min and max of constant expressions. [ [[link boost_integer.integer Integer Type Selection].] [[^[@../../../../boost/integer.hpp ]]] - [Templates for integer type selection based on properties such as maximum value or number of bits: - Use to select the type of an integer when some property such as maximum value or number of bits is known. + [Templates for integer type selection based on properties such as maximum value or number of bits: + Use to select the type of an integer when some property such as maximum value or number of bits is known. Useful for generic programming. ] ] [ @@ -50,21 +49,33 @@ compile-time value; and computing min and max of constant expressions. [ [[link boost_integer.mask Integer Masks].] [[^[@../../../../boost/integer/integer_mask.hpp ]]] - [Templates for the selection of integer masks, single or lowest group, based on the number of bits: + [Templates for the selection of integer masks, single or lowest group, based on the number of bits: Use to select a particular mask when the bit position(s) are based on a compile-time variable. Useful for generic programming. ] ] [ [[link boost_integer.log2 Compile time log2 Calculation].] [[^[@../../../../boost/integer/static_log2.hpp ]]] - [Template for finding the highest power of two in a number: + [Template for finding the highest power of two in a number: Use to find the bit-size/range based on a maximum value. Useful for generic programming. ] ] [ [[link boost_integer.minmax Compile time min/max calculation].] [[^[@../../../../boost/integer/static_min_max.hpp ]]] - [Templates for finding the extrema of two numbers: + [Templates for finding the extrema of two numbers: Use to find a bound based on a minimum or maximum value. Useful for generic programming. ] ] + [ + [[link boost_integer.extended_euclidean Extended Euclidean algorithm].] + [[^[@../../../../boost/integer/extended_euclidean.hpp ]]] + [Solves /mx + ny = gcd(x,y)/ for /x/ and /y/.] + ] + [ + [[link boost_integer.mod_inverse Modular multiplicative inverse].] + [[^[@../../../../boost/integer/mod_inverse.hpp ]]] + [Given /a/ and /m/, solves /ax/ = 1 mod /m/ for /x/.] + ] + + ] [endsect] @@ -75,7 +86,7 @@ compile-time value; and computing min and max of constant expressions. The C++ Standard Library header supplies a class template `numeric_limits<>` with specializations for each fundamental type. -For integer types, the interesting members of `std::numeric_limits<>` are: +For integer types, the interesting members of `std::numeric_limits<>` are: static const bool is_specialized; // Will be true for integer types. static T min() throw(); // Smallest representable value. @@ -85,13 +96,13 @@ For integer types, the interesting members of `std::numeric_limits<>` are: static const bool is_signed; // True if the type is signed. static const bool is_integer; // Will be true for all integer types. -For many uses, these are sufficient. -But min() and max() are problematical because they are not constant expressions (std::5.19), -yet some usages require constant expressions. +For many uses, these are sufficient. +But min() and max() are problematical because they are not constant expressions (std::5.19), +yet some usages require constant expressions. -The template class [^integer_traits] addresses this problem. +The template class [^integer_traits] addresses this problem. -[endsect] +[endsect] [section Synopsis] @@ -110,33 +121,33 @@ The template class [^integer_traits] addresses this problem. }; } -[endsect] +[endsect] [section Description] -Template class [^integer_traits] is derived from [^std::numeric_limits]. The primary specialization adds the single -[^bool] member [^is_integral] with the compile-time constant value [^false]. -However, for all integral types [^T] (std::3.9.1/7 [basic.fundamental]), there are specializations -provided with the following compile-time constants defined: +Template class [^integer_traits] is derived from [^std::numeric_limits]. The primary specialization adds the single +[^bool] member [^is_integral] with the compile-time constant value [^false]. +However, for all integral types [^T] (std::3.9.1/7 [basic.fundamental]), there are specializations +provided with the following compile-time constants defined: -[table +[table [[member][type][value]] [[[^is_integral]][bool][[^true]]] [[[^const_min]][[^T]][equivalent to [^std::numeric_limits::min()]]] [[[^const_max]][[^T]][equivalent to [^std::numeric_limits::max()]]] ] -Note: The /is_integral/ flag is provided, because a user-defined integer class should specialize -[^std::numeric_limits<>::is_integer = true], while compile-time constants -[^const_min] and [^const_max] are not provided for that user-defined class, unless boost::integer_traits is also specialized. +Note: The /is_integral/ flag is provided, because a user-defined integer class should specialize +[^std::numeric_limits<>::is_integer = true], while compile-time constants +[^const_min] and [^const_max] are not provided for that user-defined class, unless boost::integer_traits is also specialized. -[endsect] +[endsect] [section Test Program] -The program [^[@../../test/integer_traits_test.cpp integer_traits_test.cpp]] exercises the [^integer_traits] class. +The program [^[@../../test/integer_traits_test.cpp integer_traits_test.cpp]] exercises the [^integer_traits] class. -[endsect] +[endsect] [section Acknowledgements] @@ -147,8 +158,8 @@ Beman Dawes, Ed Brey, Steve Cleary, and Nathan Myers discussed the integer trait [section:integer Integer Type Selection] -The [@../../../../boost/integer.hpp ] type selection templates allow -integer types to be selected based on desired characteristics such as number of bits or maximum value. +The [@../../../../boost/integer.hpp ] type selection templates allow +integer types to be selected based on desired characteristics such as number of bits or maximum value. This facility is particularly useful for solving generic programming problems. [section:synopsis Synopsis] @@ -164,7 +175,7 @@ This facility is particularly useful for solving generic programming problems. // signed template - struct int_t + struct int_t { /* Member exact may or may not be defined depending upon Bits */ typedef ``['implementation-defined-type]`` exact; @@ -174,7 +185,7 @@ This facility is particularly useful for solving generic programming problems. // unsigned template - struct uint_t + struct uint_t { /* Member exact may or may not be defined depending upon Bits */ typedef ``['implementation-defined-type]`` exact; @@ -184,14 +195,14 @@ This facility is particularly useful for solving generic programming problems. // signed template - struct int_max_value_t + struct int_max_value_t { typedef ``['implementation-defined-type]`` least; typedef int_fast_t::fast fast; }; template - struct int_min_value_t + struct int_min_value_t { typedef ``['implementation-defined-type]`` least; typedef int_fast_t::fast fast; @@ -199,7 +210,7 @@ This facility is particularly useful for solving generic programming problems. // unsigned template - struct uint_value_t + struct uint_value_t { typedef ``['implementation-defined-type]`` least; typedef int_fast_t::fast fast; @@ -210,25 +221,25 @@ This facility is particularly useful for solving generic programming problems. [section:easiest Easiest-to-Manipulate Types] -The [^int_fast_t] class template maps its input type to the next-largest type that the processor -can manipulate the easiest, or to itself if the input type is already an easy-to-manipulate type. -For instance, processing a bunch of [^char] objects may go faster if they were converted to [^int] objects before processing. -The input type, passed as the only template parameter, must be a built-in integral type, except [^bool]. -Unsigned integral types can be used, as well as signed integral types. +The [^int_fast_t] class template maps its input type to the next-largest type that the processor +can manipulate the easiest, or to itself if the input type is already an easy-to-manipulate type. +For instance, processing a bunch of [^char] objects may go faster if they were converted to [^int] objects before processing. +The input type, passed as the only template parameter, must be a built-in integral type, except [^bool]. +Unsigned integral types can be used, as well as signed integral types. The output type is given as the nested type [^fast]. -[*Implementation Notes:] -By default, the output type is identical to the input type. Eventually, this code's implementation should -be customized for each platform to give accurate mappings between the built-in types and the easiest-to-manipulate +[*Implementation Notes:] +By default, the output type is identical to the input type. Eventually, this code's implementation should +be customized for each platform to give accurate mappings between the built-in types and the easiest-to-manipulate built-in types. Also, there is no guarantee that the output type actually is easier to manipulate than the input type. [endsect] [section:sized Sized Types] -The [^int_t], [^uint_t], [^int_max_value_t], [^int_min_value_t], and [^uint_value_t] class templates find -the most appropiate built-in integral type for the given template parameter. This type is given by the -nested type [^least]. The easiest-to-manipulate version of that type is given by the nested type [^fast]. +The [^int_t], [^uint_t], [^int_max_value_t], [^int_min_value_t], and [^uint_value_t] class templates find +the most appropiate built-in integral type for the given template parameter. This type is given by the +nested type [^least]. The easiest-to-manipulate version of that type is given by the nested type [^fast]. The following table describes each template's criteria. [table Criteria for the Sized Type Class Templates @@ -237,60 +248,60 @@ The following table describes each template's criteria. ] [ [[^boost::int_t::least]] - [The smallest, built-in, signed integral type with at least /N/ bits, including the sign bit. - The parameter should be a positive number. A compile-time error results if the parameter is + [The smallest, built-in, signed integral type with at least /N/ bits, including the sign bit. + The parameter should be a positive number. A compile-time error results if the parameter is larger than the number of bits in the largest integer type.] ] [ [[^boost::int_t::fast]] - [The easiest-to-manipulate, built-in, signed integral type with at least /N/ bits, including the sign bit. - The parameter should be a positive number. A compile-time error results if the parameter is + [The easiest-to-manipulate, built-in, signed integral type with at least /N/ bits, including the sign bit. + The parameter should be a positive number. A compile-time error results if the parameter is larger than the number of bits in the largest integer type.] ] [ [[^boost::int_t::exact]] - [A built-in, signed integral type with exactly /N/ bits, including the sign bit. + [A built-in, signed integral type with exactly /N/ bits, including the sign bit. The parameter should be a positive number. Note that the member /exact/ is defined [*only] if there exists a type with exactly /N/ bits.] ] [ [[^boost::uint_t::least]] - [The smallest, built-in, unsigned integral type with at least /N/ bits. - The parameter should be a positive number. A compile-time error results if the + [The smallest, built-in, unsigned integral type with at least /N/ bits. + The parameter should be a positive number. A compile-time error results if the parameter is larger than the number of bits in the largest integer type.] ] [ [[^boost::uint_t::fast]] - [The easiest-to-manipulate, built-in, unsigned integral type with at least /N/ bits. - The parameter should be a positive number. A compile-time error results if the + [The easiest-to-manipulate, built-in, unsigned integral type with at least /N/ bits. + The parameter should be a positive number. A compile-time error results if the parameter is larger than the number of bits in the largest integer type.] ] [ [[^boost::uint_t::exact]] - [A built-in, unsigned integral type with exactly /N/ bits. - The parameter should be a positive number. A compile-time error results if the - parameter is larger than the number of bits in the largest integer type. + [A built-in, unsigned integral type with exactly /N/ bits. + The parameter should be a positive number. A compile-time error results if the + parameter is larger than the number of bits in the largest integer type. Note that the member /exact/ is defined [*only] if there exists a type with exactly N bits.] ] [ [[^boost::int_max_value_t::last]] - [The smallest, built-in, signed integral type that can hold all the values in the inclusive range ['0 - V]. + [The smallest, built-in, signed integral type that can hold all the values in the inclusive range ['0 - V]. The parameter should be a positive number.] ] [ [[^boost::int_max_value_t::fast]] - [The easiest-to-manipulate, built-in, signed integral type that can hold all the values in the inclusive range ['0 - V]. + [The easiest-to-manipulate, built-in, signed integral type that can hold all the values in the inclusive range ['0 - V]. The parameter should be a positive number.] ] [ [[^boost::int_min_value_t::least]] - [The smallest, built-in, signed integral type that can hold all the values in the inclusive range ['V - 0]. + [The smallest, built-in, signed integral type that can hold all the values in the inclusive range ['V - 0]. The parameter should be a negative number.] ] [ [[^boost::int_min_value_t::fast]] - [The easiest-to-manipulate, built-in, signed integral type that can hold all the values in the inclusive range ['V - 0]. + [The easiest-to-manipulate, built-in, signed integral type that can hold all the values in the inclusive range ['V - 0]. The parameter should be a negative number.] ] [ @@ -317,10 +328,10 @@ The following table describes each template's criteria. { boost::int_t<24>::least my_var; // my_var has at least 24-bits //... - // This one is guarenteed not to be truncated: + // This one is guaranteed not to be truncated: boost::int_max_value_t<1000>::least my1000 = 1000; //... - // This one is guarenteed not to be truncated, and as fast + // This one is guaranteed not to be truncated, and as fast // to manipulate as possible, its size may be greater than // that of my1000: boost::int_max_value_t<1000>::fast my_fast1000 = 1000; @@ -330,7 +341,7 @@ The following table describes each template's criteria. [section Demonstration Program] -The program [@../../test/integer_test.cpp integer_test.cpp] is a simplistic demonstration of the results from instantiating +The program [@../../test/integer_test.cpp integer_test.cpp] is a simplistic demonstration of the results from instantiating various examples of the sized type class templates. [endsect] @@ -347,31 +358,32 @@ The rationale for the design of the templates in this header includes: [section Alternative] -If the number of bits required is known beforehand, it may be more appropriate to use the types supplied +If the number of bits required is known beforehand, it may be more appropriate to use the types supplied in [@../../../../boost/cstdint.hpp ]. [endsect] [section Credits] -The author of most of the Boost integer type choosing templates is -[@http://www.boost.org/people/beman_dawes.html Beman Dawes]. -He gives thanks to Valentin Bonnard and [@http://www.boost.org/people/kevlin_henney.htm Kevlin Henney] -for sharing their designs for similar templates. +The author of most of the Boost integer type choosing templates is +[@http://www.boost.org/people/beman_dawes.html Beman Dawes]. +He gives thanks to Valentin Bonnard and [@http://www.boost.org/people/kevlin_henney.htm Kevlin Henney] +for sharing their designs for similar templates. [@http://www.boost.org/people/daryle_walker.html Daryle Walker] designed the value-based sized templates. [endsect] [endsect] [include gcd/math-gcd.qbk] - +[include modular_arithmetic/extended_euclidean.qbk] +[include modular_arithmetic/mod_inverse.qbk] [section:mask Integer Masks] [section Overview] -The class templates in [@../../../../boost/integer/integer_mask.hpp ] -provide bit masks for a certain bit position or a contiguous-bit pack of a certain size. +The class templates in [@../../../../boost/integer/integer_mask.hpp ] +provide bit masks for a certain bit position or a contiguous-bit pack of a certain size. The types of the masking constants come from the [link boost_integer.integer integer type selection templates] header. [endsect] @@ -411,14 +423,14 @@ The types of the masking constants come from the [link boost_integer.integer int } // namespace boost -[endsect] +[endsect] [section Single Bit-Mask Class Template] -The [^boost::high_bit_mask_t] class template provides constants for bit masks representing the bit at a -certain position. The masks are equivalent to the value 2[super Bit], where [^Bit] is the template parameter. -The bit position must be a nonnegative number from zero to ['Max], where Max is one less than the -number of bits supported by the largest unsigned built-in integral type. The following table describes +The [^boost::high_bit_mask_t] class template provides constants for bit masks representing the bit at a +certain position. The masks are equivalent to the value 2[super Bit], where [^Bit] is the template parameter. +The bit position must be a nonnegative number from zero to ['Max], where Max is one less than the +number of bits supported by the largest unsigned built-in integral type. The following table describes the members of an instantiation of [^high_bit_mask_t]. [table Members of the `boost::high_bit_mask_t` Class Template @@ -430,14 +442,14 @@ the members of an instantiation of [^high_bit_mask_t]. [[[^bit_position]][The value of the template parameter, in case its needed from a renamed instantiation of the class template.]] ] -[endsect] +[endsect] [section Group Bit-Mask Class Template] -The [^boost::low_bits_mask_t] class template provides constants for bit masks -equivalent to the value (2[super Bits] - 1), where [^Bits] is the template parameter. -The parameter [^Bits] must be a non-negative integer from -zero to ['Max], where Max is the number of bits supported by the largest, unsigned, built-in integral type. +The [^boost::low_bits_mask_t] class template provides constants for bit masks +equivalent to the value (2[super Bits] - 1), where [^Bits] is the template parameter. +The parameter [^Bits] must be a non-negative integer from +zero to ['Max], where Max is the number of bits supported by the largest, unsigned, built-in integral type. The following table describes the members of [^low_bits_mask_t]. [table Members of the [^boost::low_bits_mask_t] Class Template @@ -453,7 +465,7 @@ The following table describes the members of [^low_bits_mask_t]. [section Implementation Notes] -When [^Bits] is the exact size of a built-in unsigned type, the implementation has to change to +When [^Bits] is the exact size of a built-in unsigned type, the implementation has to change to prevent undefined behavior. Therefore, there are specializations of [^low_bits_mask_t] at those bit counts. [endsect] @@ -479,23 +491,23 @@ prevent undefined behavior. Therefore, there are specializations of [^low_bits_m //... } -[endsect] +[endsect] [section Demonstration Program] -The program [@../../test/integer_mask_test.cpp integer_mask_test.cpp] is a simplistic demonstration of the +The program [@../../test/integer_mask_test.cpp integer_mask_test.cpp] is a simplistic demonstration of the results from instantiating various examples of the bit mask class templates. -[endsect] +[endsect] [section Rationale] -The class templates in this header are an extension of the [link boost_integer.integer integer type selection class templates]. -The new class templates provide the same sized types, but also convenient masks to use when extracting the -highest or all the significant bits when the containing built-in type contains more bits. +The class templates in this header are an extension of the [link boost_integer.integer integer type selection class templates]. +The new class templates provide the same sized types, but also convenient masks to use when extracting the +highest or all the significant bits when the containing built-in type contains more bits. This prevents contamination of values by the higher, unused bits. -[endsect] +[endsect] [section Credits] @@ -506,7 +518,7 @@ The author of the Boost bit mask class templates is [@http://www.boost.org/peopl [section:log2 Compile Time log2 Calculation] -The class template in [@../../../../boost/integer/static_log2.hpp ] +The class template in [@../../../../boost/integer/static_log2.hpp ] determines the position of the highest bit in a given value. This facility is useful for solving generic programming problems. [section Synopsis] @@ -533,47 +545,47 @@ determines the position of the highest bit in a given value. This facility is us } // namespace boost -[endsect] +[endsect] [section Usage] -The [^boost::static_log2] class template takes one template parameter, a value of type -[^static_log2_argument_type]. The template only defines one member, [^value], which gives the +The [^boost::static_log2] class template takes one template parameter, a value of type +[^static_log2_argument_type]. The template only defines one member, [^value], which gives the truncated, base-two logarithm of the template argument. -Since the logarithm of zero, for any base, is undefined, there is a specialization of [^static_log2] -for a template argument of zero. This specialization has no members, so an attempt to use the base-two +Since the logarithm of zero, for any base, is undefined, there is a specialization of [^static_log2] +for a template argument of zero. This specialization has no members, so an attempt to use the base-two logarithm of zero results in a compile-time error. -Note: +Note: * [^static_log2_argument_type] is an ['unsigned integer type] (C++ standard, 3.9.1p3). * [^static_log2_result_type] is an ['integer type] (C++ standard, 3.9.1p7). -[endsect] +[endsect] [section Demonstration Program] -The program [@../../test/static_log2_test.cpp static_log2_test.cpp] is a simplistic +The program [@../../test/static_log2_test.cpp static_log2_test.cpp] is a simplistic demonstration of the results from instantiating various examples of the binary logarithm class template. [endsect] [section Rationale] -The base-two (binary) logarithm, abbreviated lb, function is occasionally used to give order-estimates -of computer algorithms. The truncated logarithm can be considered the highest power-of-two in a value, -which corresponds to the value's highest set bit (for binary integers). Sometimes the highest-bit position +The base-two (binary) logarithm, abbreviated lb, function is occasionally used to give order-estimates +of computer algorithms. The truncated logarithm can be considered the highest power-of-two in a value, +which corresponds to the value's highest set bit (for binary integers). Sometimes the highest-bit position could be used in generic programming, which requires the position to be available statically (['i.e.] at compile-time). -[endsect] +[endsect] [section Credits] -The original version of the Boost binary logarithm class template was -written by [@http://www.boost.org/people/daryle_walker.html Daryle Walker] and then -enhanced by Giovanni Bajo with support for compilers without partial template specialization. -The current version was suggested, together with a reference implementation, by Vesa Karvonen. +The original version of the Boost binary logarithm class template was +written by [@http://www.boost.org/people/daryle_walker.html Daryle Walker] and then +enhanced by Giovanni Bajo with support for compilers without partial template specialization. +The current version was suggested, together with a reference implementation, by Vesa Karvonen. Gennaro Prota wrote the actual source file. [endsect] @@ -581,15 +593,15 @@ Gennaro Prota wrote the actual source file. [section:minmax Compile time min/max calculation] -The class templates in [@../../../../boost/integer/static_min_max.hpp ] -provide a compile-time evaluation of the minimum or maximum of two integers. These facilities are useful +The class templates in [@../../../../boost/integer/static_min_max.hpp ] +provide a compile-time evaluation of the minimum or maximum of two integers. These facilities are useful for generic programming problems. [section Synopsis] namespace boost { - + typedef ``['implementation-defined]`` static_min_max_signed_type; typedef ``['implementation-defined]`` static_min_max_unsigned_type; @@ -607,15 +619,15 @@ for generic programming problems. } -[endsect] +[endsect] [section Usage] -The four class templates provide the combinations for finding the minimum or maximum of two [^signed] or -[^unsigned] ([^long]) parameters, /Value1/ and /Value2/, at compile-time. Each template has a single static data member, +The four class templates provide the combinations for finding the minimum or maximum of two [^signed] or +[^unsigned] ([^long]) parameters, /Value1/ and /Value2/, at compile-time. Each template has a single static data member, [^value], which is set to the respective minimum or maximum of the template's parameters. -[endsect] +[endsect] [section Example] @@ -653,14 +665,14 @@ The four class templates provide the combinations for finding the minimum or max [section Demonstration Program] -The program [@../../test/static_min_max_test.cpp static_min_max_test.cpp] is a simplistic demonstration of +The program [@../../test/static_min_max_test.cpp static_min_max_test.cpp] is a simplistic demonstration of various comparisons using the compile-time extrema class templates. -[endsect] +[endsect] [section Rationale] -Sometimes the minimum or maximum of several values needs to be found for later compile-time processing, +Sometimes the minimum or maximum of several values needs to be found for later compile-time processing, ['e.g.] for a bound for another class template. [endsect] @@ -682,23 +694,23 @@ The author of the Boost compile-time extrema class templates is [@http://www.boo [h4 1.42.0] * Reverted Trunk to release branch state (i.e. a "known good state"). -* Fixed issues: [@https://svn.boost.org/trac/boost/ticket/653 653], -[@https://svn.boost.org/trac/boost/ticket/3084 3084], -[@https://svn.boost.org/trac/boost/ticket/3177 3177], -[@https://svn.boost.org/trac/boost/ticket/3180 3180], -[@https://svn.boost.org/trac/boost/ticket/3548 3568], -[@https://svn.boost.org/trac/boost/ticket/3657 3657], +* Fixed issues: [@https://svn.boost.org/trac/boost/ticket/653 653], +[@https://svn.boost.org/trac/boost/ticket/3084 3084], +[@https://svn.boost.org/trac/boost/ticket/3177 3177], +[@https://svn.boost.org/trac/boost/ticket/3180 3180], +[@https://svn.boost.org/trac/boost/ticket/3548 3568], +[@https://svn.boost.org/trac/boost/ticket/3657 3657], [@https://svn.boost.org/trac/boost/ticket/2134 2134]. -* Added long long support to [^boost::static_log2], [^boost::static_signed_min], [^boost::static_signed_max], +* Added long long support to [^boost::static_log2], [^boost::static_signed_min], [^boost::static_signed_max], [^boost::static_unsigned_min][^boost::static_unsigned_max], when available. -* The argument type and the result type of [^boost::static_signed_min] etc are now typedef'd. -Formerly, they were hardcoded as [^unsigned long] and [^int] respectively. Please, use the +* The argument type and the result type of [^boost::static_signed_min] etc are now typedef'd. +Formerly, they were hardcoded as [^unsigned long] and [^int] respectively. Please, use the provided typedefs in new code (and update old code as soon as possible). [h4 1.32.0] -* The argument type and the result type of [^boost::static_log2] are now typedef'd. -Formerly, they were hardcoded as [^unsigned long] and [^int] respectively. Please, use the +* The argument type and the result type of [^boost::static_log2] are now typedef'd. +Formerly, they were hardcoded as [^unsigned long] and [^int] respectively. Please, use the provided typedefs in new code (and update old code as soon as possible). [endsect] diff --git a/doc/modular_arithmetic/mod_inverse.qbk b/doc/modular_arithmetic/mod_inverse.qbk index 0cb0bf5..2f3e66e 100644 --- a/doc/modular_arithmetic/mod_inverse.qbk +++ b/doc/modular_arithmetic/mod_inverse.qbk @@ -14,7 +14,7 @@ A fast algorithm for computing modular multiplicative inverses based on the exte namespace boost { namespace integer { template - boost::optional mod_inverse(Z a, Z p); + boost::optional mod_inverse(Z a, Z m); }} @@ -22,7 +22,7 @@ A fast algorithm for computing modular multiplicative inverses based on the exte [section Usage] -Multiplicative modular inverses exist if and only if /a/ and /p/ are coprime. +Multiplicative modular inverses exist if and only if /a/ and /m/ are coprime. So for example auto x = mod_inverse(2, 5);