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504 lines
23 KiB
C++
504 lines
23 KiB
C++
#pragma once
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#include <boost/mpl/bool.hpp>
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#include <boost/mpl/int.hpp>
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#include <boost/mpl/if.hpp>
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#include <boost/mpl/and.hpp>
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#include <boost/mpl/or.hpp>
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#include <boost/mpl/not.hpp>
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#include <boost/mpl/greater.hpp>
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#include <boost/mpl/min_max.hpp>
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#include <boost/mpl/equal_to.hpp>
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#include <boost/mpl/comparison.hpp>
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#include <DB/Core/Types.h>
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#include <tuple>
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namespace DB
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{
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/** Позволяет получить тип результата применения функций +, -, *, /, %, div (целочисленное деление).
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* Правила отличаются от используемых в C++.
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*/
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namespace NumberTraits
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{
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using Unsigned = boost::mpl::false_ ;
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using Signed = boost::mpl::true_ ;
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using Integer = boost::mpl::false_ ;
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using Floating = boost::mpl::true_ ;
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using Bits0 = boost::mpl::int_<0> ;
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using Bits8 = boost::mpl::int_<8> ;
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using Bits16 = boost::mpl::int_<16> ;
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using Bits32 = boost::mpl::int_<32> ;
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using Bits64 = boost::mpl::int_<64> ;
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using BitsTooMany = boost::mpl::int_<1024>;
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struct Error {};
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template <typename T> struct Next;
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template <> struct Next<Bits0> { using Type = Bits0; };
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template <> struct Next<Bits8> { using Type = Bits16; };
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template <> struct Next<Bits16> { using Type = Bits32; };
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template <> struct Next<Bits32> { using Type = Bits64; };
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template <> struct Next<Bits64> { using Type = Bits64; };
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template <typename T> struct ExactNext { using Type = typename Next<T>::Type; };
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template <> struct ExactNext<Bits64> { using Type = BitsTooMany; };
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template <typename T> struct Traits;
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template <> struct Traits<void> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits0 Bits; };
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template <> struct Traits<UInt8> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits8 Bits; };
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template <> struct Traits<UInt16> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits16 Bits; };
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template <> struct Traits<UInt32> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits32 Bits; };
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template <> struct Traits<UInt64> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits64 Bits; };
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template <> struct Traits<Int8> { typedef Signed Sign; typedef Integer Floatness; typedef Bits8 Bits; };
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template <> struct Traits<Int16> { typedef Signed Sign; typedef Integer Floatness; typedef Bits16 Bits; };
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template <> struct Traits<Int32> { typedef Signed Sign; typedef Integer Floatness; typedef Bits32 Bits; };
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template <> struct Traits<Int64> { typedef Signed Sign; typedef Integer Floatness; typedef Bits64 Bits; };
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template <> struct Traits<Float32> { typedef Signed Sign; typedef Floating Floatness; typedef Bits32 Bits; };
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template <> struct Traits<Float64> { typedef Signed Sign; typedef Floating Floatness; typedef Bits64 Bits; };
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template <typename Sign, typename Floatness, typename Bits> struct Construct;
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template <> struct Construct<Unsigned, Integer, Bits0> { using Type = void ; };
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template <> struct Construct<Unsigned, Floating, Bits0> { using Type = void ; };
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template <> struct Construct<Signed, Integer, Bits0> { using Type = void ; };
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template <> struct Construct<Signed, Floating, Bits0> { using Type = void ; };
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template <> struct Construct<Unsigned, Integer, Bits8> { using Type = UInt8 ; };
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template <> struct Construct<Unsigned, Integer, Bits16> { using Type = UInt16 ; };
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template <> struct Construct<Unsigned, Integer, Bits32> { using Type = UInt32 ; };
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template <> struct Construct<Unsigned, Integer, Bits64> { using Type = UInt64 ; };
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template <> struct Construct<Unsigned, Floating, Bits8> { using Type = Float32 ; };
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template <> struct Construct<Unsigned, Floating, Bits16> { using Type = Float32 ; };
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template <> struct Construct<Unsigned, Floating, Bits32> { using Type = Float32 ; };
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template <> struct Construct<Unsigned, Floating, Bits64> { using Type = Float64 ; };
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template <> struct Construct<Signed, Integer, Bits8> { using Type = Int8 ; };
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template <> struct Construct<Signed, Integer, Bits16> { using Type = Int16 ; };
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template <> struct Construct<Signed, Integer, Bits32> { using Type = Int32 ; };
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template <> struct Construct<Signed, Integer, Bits64> { using Type = Int64 ; };
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template <> struct Construct<Signed, Floating, Bits8> { using Type = Float32 ; };
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template <> struct Construct<Signed, Floating, Bits16> { using Type = Float32 ; };
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template <> struct Construct<Signed, Floating, Bits32> { using Type = Float32 ; };
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template <> struct Construct<Signed, Floating, Bits64> { using Type = Float64 ; };
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template <typename Sign, typename Floatness> struct Construct<Sign, Floatness, BitsTooMany> { using Type = Error; };
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template <typename T>
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inline bool isErrorType()
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{
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return false;
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}
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template <>
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inline bool isErrorType<Error>()
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{
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return true;
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}
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/** Результат сложения или умножения вычисляется по следующим правилам:
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* - если один из аргументов с плавающей запятой, то результат - с плавающей запятой, иначе - целый;
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* - если одно из аргументов со знаком, то результат - со знаком, иначе - без знака;
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* - результат содержит больше бит (не только значащих), чем максимум в аргументах
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* (например, UInt8 + Int32 = Int64).
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*/
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template <typename A, typename B> struct ResultOfAdditionMultiplication
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{
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typedef typename Construct<
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typename boost::mpl::or_<typename Traits<A>::Sign, typename Traits<B>::Sign>::type,
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typename boost::mpl::or_<typename Traits<A>::Floatness, typename Traits<B>::Floatness>::type,
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typename Next<typename boost::mpl::max<typename Traits<A>::Bits, typename Traits<B>::Bits>::type>::Type>::Type Type;
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};
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template <typename A, typename B> struct ResultOfSubtraction
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{
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typedef typename Construct<
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Signed,
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typename boost::mpl::or_<typename Traits<A>::Floatness, typename Traits<B>::Floatness>::type,
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typename Next<typename boost::mpl::max<typename Traits<A>::Bits, typename Traits<B>::Bits>::type>::Type>::Type Type;
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};
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/** При делении всегда получается число с плавающей запятой.
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*/
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template <typename A, typename B> struct ResultOfFloatingPointDivision
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{
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using Type = Float64;
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};
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/** При целочисленном делении получается число, битность которого равна делимому.
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*/
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template <typename A, typename B> struct ResultOfIntegerDivision
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{
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typedef typename Construct<
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typename boost::mpl::or_<typename Traits<A>::Sign, typename Traits<B>::Sign>::type,
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typename boost::mpl::or_<typename Traits<A>::Floatness, typename Traits<B>::Floatness>::type,
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typename Traits<A>::Bits>::Type Type;
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};
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/** При взятии остатка получается число, битность которого равна делителю.
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*/
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template <typename A, typename B> struct ResultOfModulo
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{
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typedef typename Construct<
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typename boost::mpl::or_<typename Traits<A>::Sign, typename Traits<B>::Sign>::type,
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Integer,
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typename Traits<B>::Bits>::Type Type;
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};
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template <typename A> struct ResultOfNegate
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{
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typedef typename Construct<
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Signed,
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typename Traits<A>::Floatness,
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typename boost::mpl::if_<
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typename Traits<A>::Sign,
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typename Traits<A>::Bits,
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typename Next<typename Traits<A>::Bits>::Type>::type>::Type Type;
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};
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template <typename A> struct ResultOfAbs
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{
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typedef typename Construct<
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Unsigned,
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typename Traits<A>::Floatness,
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typename Traits <A>::Bits>::Type Type;
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};
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/** При побитовых операциях получается целое число, битность которого равна максимальной из битностей аргументов.
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*/
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template <typename A, typename B> struct ResultOfBit
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{
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typedef typename Construct<
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typename boost::mpl::or_<typename Traits<A>::Sign, typename Traits<B>::Sign>::type,
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Integer,
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typename boost::mpl::max<
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typename boost::mpl::if_<
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typename Traits<A>::Floatness,
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Bits64,
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typename Traits<A>::Bits>::type,
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typename boost::mpl::if_<
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typename Traits<B>::Floatness,
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Bits64,
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typename Traits<B>::Bits>::type>::type>::Type Type;
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};
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template <typename A> struct ResultOfBitNot
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{
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typedef typename Construct<
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typename Traits<A>::Sign,
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Integer,
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typename Traits<A>::Bits>::Type Type;
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};
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/** Приведение типов для функции if:
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* 1) void, Type -> Type
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* 2) UInt<x>, UInt<y> -> UInt<max(x,y)>
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* 3) Int<x>, Int<y> -> Int<max(x,y)>
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* 4) Float<x>, Float<y> -> Float<max(x, y)>
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* 5) UInt<x>, Int<y> -> Int<max(x*2, y)>
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* 6) Float<x>, [U]Int<y> -> Float<max(x, y*2)>
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* 7) UInt64 , Int<x> -> Error
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* 8) Float<x>, [U]Int64 -> Error
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*/
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template <typename A, typename B>
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struct ResultOfIf
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{
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typedef
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/// 1)
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typename boost::mpl::if_<
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typename boost::mpl::equal_to<typename Traits<A>::Bits, Bits0>::type,
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B,
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typename boost::mpl::if_<
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typename boost::mpl::equal_to<typename Traits<B>::Bits, Bits0>::type,
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A,
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/// 4) и 6)
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typename boost::mpl::if_<
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typename boost::mpl::or_<
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typename Traits<A>::Floatness,
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typename Traits<B>::Floatness>::type,
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typename Construct<
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Signed,
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Floating,
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typename boost::mpl::max< /// Этот максимум нужен только потому что if_ всегда вычисляет все аргументы.
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typename boost::mpl::max<
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typename boost::mpl::if_<
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typename Traits<A>::Floatness,
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typename Traits<A>::Bits,
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typename ExactNext<typename Traits<A>::Bits>::Type>::type,
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typename boost::mpl::if_<
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typename Traits<B>::Floatness,
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typename Traits<B>::Bits,
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typename ExactNext<typename Traits<B>::Bits>::Type>::type>::type,
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Bits32>::type>::Type,
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/// 2) и 3)
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typename boost::mpl::if_<
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typename boost::mpl::equal_to<
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typename Traits<A>::Sign,
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typename Traits<B>::Sign>::type,
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typename boost::mpl::if_<
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typename boost::mpl::less<
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typename Traits<A>::Bits,
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typename Traits<B>::Bits>::type,
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B,
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A>::type,
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/// 5)
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typename Construct<
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Signed,
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Integer,
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typename boost::mpl::max<
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typename boost::mpl::if_<
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typename Traits<A>::Sign,
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typename Traits<A>::Bits,
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typename ExactNext<typename Traits<A>::Bits>::Type>::type,
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typename boost::mpl::if_<
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typename Traits<B>::Sign,
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typename Traits<B>::Bits,
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typename ExactNext<typename Traits<B>::Bits>::Type>::type>::type>::Type>::type>::type>::type>::type Type;
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};
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/** Перед применением оператора % и побитовых операций, операнды приводятся к целым числам. */
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template <typename A> struct ToInteger
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{
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typedef typename Construct<
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typename Traits<A>::Sign,
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Integer,
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typename boost::mpl::if_<
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typename Traits<A>::Floatness,
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Bits64,
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typename Traits<A>::Bits>::type>::Type Type;
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};
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/// Notes on type composition.
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///
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/// I. Problem statement.
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///
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/// Type composition with ResultOfIf is not associative. Example:
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/// (Int8 x UInt32) x Float32 = Int64 x Float32 = Error;
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/// Int8 x (UInt32 x Float32) = Int8 x Float64 = Float64.
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/// In order to sort out this issue, we design a slightly improved version
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/// of ResultOfIf.
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///
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/// II. A more rigorous approach to ResultOfIf.
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///
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/// First we represent the set of types:
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/// T = {Void,Int8,Int16,Int32,Int64,UInt8,UInt16,UInt32,UInt64,Float32,Float64}
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/// as a poset P with the partial order being such that for any t1,t2 ∈ T,
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/// t1 < t2 if and only if the domain of values of t1 is included in the domain
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/// of values of t2.
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///
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/// For each type t ∈ T, we define C(t) as the set of chains of the poset P whose
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/// unique minimal element is T.
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///
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/// Now for any two types t1,t2 ∈ T, we define the poset C(t1,t2) as the intersection
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/// C(t1) ∩ C(t2).
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///
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/// Denote K(t1,t2) as the unique antichain of C(t1,t2) in which each element minimally
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/// represents both t1 and t2. It is important to keep in mind that t1 and t2 are
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/// *not* comparable.
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///
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/// For the most part, K(t1,t2) coincides with the result of the application of
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/// ResultOfIf to t1 and t2. Nevertheless, for some particular combinations of t1
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/// and t2, the map K returns one of the following two antichains: {Int32,Float32},
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/// {Int64,Float64}.
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///
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/// From these observations, we conclude that the type system T and the composition
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/// law ResultOfIf are not powerful enough to represent all the combinations of
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/// elements of T. That is the reason why ResultOfIf is not associative.
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///
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/// III. Extending ResultOfIf.
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///
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/// Let's embed T into a larger set E of "enriched types" such that:
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/// 1. E ⊂ TxT;
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/// 2. for each t ∈ T, (T,Void) ∈ E.
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/// 3. (Int32,Float32) ∈ E
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/// 4. (Int64,Float64) ∈ E.
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///
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/// E represents the image A of the map K, a set of antichains, as a set of types.
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///
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/// Consider the canonical injection ψ : T x T ----> E x E and the natural bijection
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/// φ : A ----> E.
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/// Then there exists a unique map K' : E x E ----> E, that makes the diagram below
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/// commutative:
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///
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/// K
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/// T x T ----> A
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/// | |
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/// | ψ | φ
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/// ↓ L ↓
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/// E x E ----> E
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///
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/// L is exactly the same map as K, the sole difference being that L takes as
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/// parameters extended types that map to ordinary ones.
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///
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/// Finally we extend the map L. To this end, we complete the type composition table
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/// with the new types (Int32,Float32) and (Int64,Float64) appearing on either
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/// the left-hand side or the right-hand side. This extended map is called
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/// TypeProduct in the implementation. TypeProduct is both commutative and associative.
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///
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/// IV. Usage.
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///
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/// When we need to compose ordinary types, the following is to be performed:
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/// 1. embed each type into its counterpart in E with EmbedType;
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/// 2. compose the resulting enriched types with TypeProduct;
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/// 3. return the first component of the result with ToOrdinaryType, which means
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/// that, given an extended type e = (p,q) ∈ E, we return the ordinary type p ∈ T.
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///
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/// The result is the type we are looking for.
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///
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/// V. Example.
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///
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/// Suppose we need to compose, as in the problem statement, the types Int8,
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/// UInt32, and Float32. The corresponding embedded types are:
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/// (Int8,Void), (UInt32,Void), (Float32,Void).
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///
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/// By computing (Int8 x UInt32) x Float32, we get:
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///
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/// TypeProduct(TypeProduct((Int8,Void),(UInt32,Void)), (Float32,Void))
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/// = TypeProduct((Int64,Float64), (Float32,Void))
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/// = (Float64,void)
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/// Thus, (Int8 x UInt32) x Float32 = Float64.
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///
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/// By computing Int8 x (UInt32 x Float32), we get:
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///
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/// TypeProduct((Int8,Void), TypeProduct((UInt32,Void), (Float32,Void)))
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/// = TypeProduct((Int8,Void), (Float64,Void))
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/// = (Float64,void)
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/// Thus, Int8 x (UInt32 x Float32) = Float64.
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///
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namespace Enriched
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{
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/// Definitions of enriched types.
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using Void = std::tuple<void, void>;
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using Int8 = std::tuple<DB::Int8, void>;
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using Int16 = std::tuple<DB::Int16, void>;
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using Int32 = std::tuple<DB::Int32, void>;
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using Int64 = std::tuple<DB::Int64, void>;
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using UInt8 = std::tuple<DB::UInt8, void>;
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using UInt16 = std::tuple<DB::UInt16, void>;
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using UInt32 = std::tuple<DB::UInt32, void>;
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using UInt64 = std::tuple<DB::UInt64, void>;
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using Float32 = std::tuple<DB::Float32, void>;
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using Float64 = std::tuple<DB::Float64, void>;
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using IntFloat32 = std::tuple<DB::Int32, DB::Float32>;
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using IntFloat64 = std::tuple<DB::Int64, DB::Float64>;
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}
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/// Embed an ordinary type into the corresponding enriched type.
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template <typename T>
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struct EmbedType;
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template <> struct EmbedType<void> { using Type = Enriched::Void; };
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template <> struct EmbedType<Int8> { using Type = Enriched::Int8; };
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template <> struct EmbedType<Int16> { using Type = Enriched::Int16; };
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template <> struct EmbedType<Int32> { using Type = Enriched::Int32; };
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template <> struct EmbedType<Int64> { using Type = Enriched::Int64; };
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template <> struct EmbedType<UInt8> { using Type = Enriched::UInt8; };
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template <> struct EmbedType<UInt16> { using Type = Enriched::UInt16; };
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template <> struct EmbedType<UInt32> { using Type = Enriched::UInt32; };
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template <> struct EmbedType<UInt64> { using Type = Enriched::UInt64; };
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template <> struct EmbedType<Float32> { using Type = Enriched::Float32; };
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template <> struct EmbedType<Float64> { using Type = Enriched::Float64; };
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/// Get an ordinary type from an enriched type.
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template <typename TType>
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struct ToOrdinaryType
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{
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using Type = typename std::tuple_element<0, TType>::type;
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};
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/// Get an ordinary type from an enriched type.
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/// Error case.
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template <>
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struct ToOrdinaryType<Error>
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{
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using Type = Error;
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};
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/// Compute the product of two enriched numeric types.
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template <typename T1, typename T2>
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struct TypeProduct
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{
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using Type = Error;
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};
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/// Compute the product of two enriched numeric types.
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/// Case when both of the source types and the resulting type map to ordinary types.
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template <typename A, typename B>
|
||
struct TypeProduct<std::tuple<A, void>, std::tuple<B, void> >
|
||
{
|
||
private:
|
||
using Result = typename NumberTraits::ResultOfIf<A, B>::Type;
|
||
|
||
public:
|
||
using Type = typename std::conditional<
|
||
std::is_same<Result, Error>::value,
|
||
Error,
|
||
std::tuple<Result, void>
|
||
>::type;
|
||
};
|
||
|
||
/// Compute the product of two enriched numeric types.
|
||
/// Case when a source type or the resulting type does not map to any ordinary type.
|
||
template <> struct TypeProduct<Enriched::Int8, Enriched::UInt16> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::UInt16, Enriched::Int8> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::Int8, Enriched::UInt32> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::UInt32, Enriched::Int8> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::Int16, Enriched::UInt16> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::UInt16, Enriched::Int16> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::Int16, Enriched::UInt32> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::UInt32, Enriched::Int16> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::Int32, Enriched::UInt32> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::UInt32, Enriched::Int32> { using Type = Enriched::IntFloat64; };
|
||
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::Int8> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::Int8, Enriched::IntFloat32> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::Int16> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::Int16, Enriched::IntFloat32> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::Int32> { using Type = Enriched::Int32; };
|
||
template <> struct TypeProduct<Enriched::Int32, Enriched::IntFloat32> { using Type = Enriched::Int32; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::Int64> { using Type = Enriched::Int64; };
|
||
template <> struct TypeProduct<Enriched::Int64, Enriched::IntFloat32> { using Type = Enriched::Int64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::Float32> { using Type = Enriched::Float32; };
|
||
template <> struct TypeProduct<Enriched::Float32, Enriched::IntFloat32> { using Type = Enriched::Float32; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::Float64> { using Type = Enriched::Float64; };
|
||
template <> struct TypeProduct<Enriched::Float64, Enriched::IntFloat32> { using Type = Enriched::Float64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::UInt8> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::UInt8, Enriched::IntFloat32> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::UInt16> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::UInt16, Enriched::IntFloat32> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::UInt32> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::UInt32, Enriched::IntFloat32> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::IntFloat32> { using Type = Enriched::IntFloat32; };
|
||
template <> struct TypeProduct<Enriched::IntFloat32, Enriched::IntFloat64> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::IntFloat32> { using Type = Enriched::IntFloat64; };
|
||
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::Int8> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::Int8, Enriched::IntFloat64> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::Int16> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::Int16, Enriched::IntFloat64> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::Int32> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::Int32, Enriched::IntFloat64> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::Int64> { using Type = Enriched::Int64; };
|
||
template <> struct TypeProduct<Enriched::Int64, Enriched::IntFloat64> { using Type = Enriched::Int64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::Float32> { using Type = Enriched::Float64; };
|
||
template <> struct TypeProduct<Enriched::Float32, Enriched::IntFloat64> { using Type = Enriched::Float64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::Float64> { using Type = Enriched::Float64; };
|
||
template <> struct TypeProduct<Enriched::Float64, Enriched::IntFloat64> { using Type = Enriched::Float64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::UInt8> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::UInt8, Enriched::IntFloat64> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::UInt16> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::UInt16, Enriched::IntFloat64> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::UInt32> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::UInt32, Enriched::IntFloat64> { using Type = Enriched::IntFloat64; };
|
||
template <> struct TypeProduct<Enriched::IntFloat64, Enriched::IntFloat64> { using Type = Enriched::IntFloat64; };
|
||
|
||
}
|
||
|
||
}
|