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656 lines
27 KiB
C++
656 lines
27 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 HasNull = boost::mpl::true_;
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using HasNoNull = boost::mpl::false_;
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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, typename Nullability>
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struct AddNullability;
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template <typename T>
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struct AddNullability<T, HasNull>
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{
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using Type = Nullable<T>;
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};
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template <typename T>
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struct AddNullability<T, HasNoNull>
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{
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using Type = T;
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};
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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 <typename T>
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struct Traits<Nullable<T>>
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{
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using Sign = typename Traits<T>::Sign;
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using Floatness = typename Traits<T>::Floatness;
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using Bits = typename Traits<T>::Bits;
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using Nullity = HasNull;
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};
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template <> struct Traits<void> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits0 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<Null> : Traits<Nullable<void>> {};
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template <> struct Traits<UInt8> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits8 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<UInt16> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits16 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<UInt32> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits32 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<UInt64> { typedef Unsigned Sign; typedef Integer Floatness; typedef Bits64 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<Int8> { typedef Signed Sign; typedef Integer Floatness; typedef Bits8 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<Int16> { typedef Signed Sign; typedef Integer Floatness; typedef Bits16 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<Int32> { typedef Signed Sign; typedef Integer Floatness; typedef Bits32 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<Int64> { typedef Signed Sign; typedef Integer Floatness; typedef Bits64 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<Float32> { typedef Signed Sign; typedef Floating Floatness; typedef Bits32 Bits; typedef HasNoNull Nullity; };
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template <> struct Traits<Float64> { typedef Signed Sign; typedef Floating Floatness; typedef Bits64 Bits; typedef HasNoNull Nullity; };
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template <typename Sign, typename Floatness, typename Bits, typename Nullity> struct Construct;
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template <typename Sign, typename Floatness, typename Bits>
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struct Construct<Sign, Floatness, Bits, HasNull>
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{
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using Type = Nullable<typename Construct<Sign, Floatness, Bits, HasNoNull>::Type>;
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};
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template <> struct Construct<Unsigned, Integer, Bits0, HasNull> { using Type = Null; };
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template <> struct Construct<Unsigned, Floating, Bits0, HasNull> { using Type = Null; };
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template <> struct Construct<Signed, Integer, Bits0, HasNull> { using Type = Null; };
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template <> struct Construct<Signed, Floating, Bits0, HasNull> { using Type = Null; };
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template <typename Sign, typename Floatness>
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struct Construct<Sign, Floatness, BitsTooMany, HasNull>
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{
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using Type = Error;
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};
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template <typename Sign, typename Floatness>
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struct Construct<Sign, Floatness, BitsTooMany, HasNoNull>
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{
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using Type = Error;
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};
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template <> struct Construct<Unsigned, Integer, Bits0, HasNoNull> { using Type = void; };
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template <> struct Construct<Unsigned, Floating, Bits0, HasNoNull> { using Type = void; };
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template <> struct Construct<Signed, Integer, Bits0, HasNoNull> { using Type = void; };
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template <> struct Construct<Signed, Floating, Bits0, HasNoNull> { using Type = void; };
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template <> struct Construct<Unsigned, Integer, Bits8, HasNoNull> { using Type = UInt8 ; };
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template <> struct Construct<Unsigned, Integer, Bits16, HasNoNull> { using Type = UInt16 ; };
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template <> struct Construct<Unsigned, Integer, Bits32, HasNoNull> { using Type = UInt32 ; };
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template <> struct Construct<Unsigned, Integer, Bits64, HasNoNull> { using Type = UInt64 ; };
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template <> struct Construct<Unsigned, Floating, Bits8, HasNoNull> { using Type = Float32 ; };
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template <> struct Construct<Unsigned, Floating, Bits16, HasNoNull> { using Type = Float32 ; };
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template <> struct Construct<Unsigned, Floating, Bits32, HasNoNull> { using Type = Float32 ; };
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template <> struct Construct<Unsigned, Floating, Bits64, HasNoNull> { using Type = Float64 ; };
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template <> struct Construct<Signed, Integer, Bits8, HasNoNull> { using Type = Int8 ; };
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template <> struct Construct<Signed, Integer, Bits16, HasNoNull> { using Type = Int16 ; };
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template <> struct Construct<Signed, Integer, Bits32, HasNoNull> { using Type = Int32 ; };
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template <> struct Construct<Signed, Integer, Bits64, HasNoNull> { using Type = Int64 ; };
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template <> struct Construct<Signed, Floating, Bits8, HasNoNull> { using Type = Float32 ; };
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template <> struct Construct<Signed, Floating, Bits16, HasNoNull> { using Type = Float32 ; };
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template <> struct Construct<Signed, Floating, Bits32, HasNoNull> { using Type = Float32 ; };
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template <> struct Construct<Signed, Floating, Bits64, HasNoNull> { using Type = Float64 ; };
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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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/// Returns the type A augmented with nullity = nullity(A) | nullity(B)
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template <typename A, typename B>
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struct UpdateNullity
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{
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using Type = typename Construct<
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typename Traits<A>::Sign,
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typename Traits<A>::Floatness,
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typename Traits<A>::Bits,
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typename boost::mpl::or_<typename Traits<A>::Nullity, typename Traits<B>::Nullity>::type
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>::Type;
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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,
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typename boost::mpl::or_<typename Traits<A>::Nullity, typename Traits<B>::Nullity>::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,
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typename boost::mpl::or_<typename Traits<A>::Nullity, typename Traits<B>::Nullity>::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,
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typename boost::mpl::or_<typename Traits<A>::Nullity, typename Traits<B>::Nullity>::type>::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,
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typename boost::mpl::or_<typename Traits<A>::Nullity, typename Traits<B>::Nullity>::type>::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,
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typename Traits<A>::Nullity>::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,
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typename Traits<A>::Nullity>::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,
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typename boost::mpl::or_<typename Traits<A>::Nullity, typename Traits<B>::Nullity>::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,
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typename Traits<A>::Nullity>::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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typename UpdateNullity<B, A>::Type,
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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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typename UpdateNullity<A, B>::Type,
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/// 4) and 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,
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typename boost::mpl::or_<typename Traits<A>::Nullity, typename Traits<B>::Nullity>::type>::Type,
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/// 2) and 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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typename UpdateNullity<B, A>::Type,
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typename UpdateNullity<A, B>::Type>::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,
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typename boost::mpl::or_<typename Traits<A>::Nullity, typename Traits<B>::Nullity>::type
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>::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,
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typename Traits<A>::Nullity
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>::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,
|
||
/// UInt32, and Float32. The corresponding embedded types are:
|
||
/// (Int8,Void), (UInt32,Void), (Float32,Void).
|
||
///
|
||
/// By computing (Int8 x UInt32) x Float32, we get:
|
||
///
|
||
/// TypeProduct(TypeProduct((Int8,Void),(UInt32,Void)), (Float32,Void))
|
||
/// = TypeProduct((Int64,Float64), (Float32,Void))
|
||
/// = (Float64,void)
|
||
/// Thus, (Int8 x UInt32) x Float32 = Float64.
|
||
///
|
||
/// By computing Int8 x (UInt32 x Float32), we get:
|
||
///
|
||
/// TypeProduct((Int8,Void), TypeProduct((UInt32,Void), (Float32,Void)))
|
||
/// = TypeProduct((Int8,Void), (Float64,Void))
|
||
/// = (Float64,void)
|
||
/// Thus, Int8 x (UInt32 x Float32) = Float64.
|
||
///
|
||
|
||
namespace Enriched
|
||
{
|
||
|
||
/// Definitions of enriched types.
|
||
template <typename Nullity> using Void = std::tuple<void, void, Nullity>;
|
||
template <typename Nullity> using Int8 = std::tuple<DB::Int8, void, Nullity>;
|
||
template <typename Nullity> using Int16 = std::tuple<DB::Int16, void, Nullity>;
|
||
template <typename Nullity> using Int32 = std::tuple<DB::Int32, void, Nullity>;
|
||
template <typename Nullity> using Int64 = std::tuple<DB::Int64, void, Nullity>;
|
||
template <typename Nullity> using UInt8 = std::tuple<DB::UInt8, void, Nullity>;
|
||
template <typename Nullity> using UInt16 = std::tuple<DB::UInt16, void, Nullity>;
|
||
template <typename Nullity> using UInt32 = std::tuple<DB::UInt32, void, Nullity>;
|
||
template <typename Nullity> using UInt64 = std::tuple<DB::UInt64, void, Nullity>;
|
||
template <typename Nullity> using Float32 = std::tuple<DB::Float32, void, Nullity>;
|
||
template <typename Nullity> using Float64 = std::tuple<DB::Float64, void, Nullity>;
|
||
template <typename Nullity> using IntFloat32 = std::tuple<DB::Int32, DB::Float32, Nullity>;
|
||
template <typename Nullity> using IntFloat64 = std::tuple<DB::Int64, DB::Float64, Nullity>;
|
||
|
||
}
|
||
|
||
/// Embed an ordinary type into the corresponding enriched type.
|
||
template <typename T>
|
||
struct EmbedType;
|
||
|
||
template <> struct EmbedType<Error> { using Type = Error; };
|
||
|
||
template <> struct EmbedType<void> { using Type = Enriched::Void<HasNoNull>; };
|
||
template <> struct EmbedType<Int8> { using Type = Enriched::Int8<HasNoNull>; };
|
||
template <> struct EmbedType<Int16> { using Type = Enriched::Int16<HasNoNull>; };
|
||
template <> struct EmbedType<Int32> { using Type = Enriched::Int32<HasNoNull>; };
|
||
template <> struct EmbedType<Int64> { using Type = Enriched::Int64<HasNoNull>; };
|
||
template <> struct EmbedType<UInt8> { using Type = Enriched::UInt8<HasNoNull>; };
|
||
template <> struct EmbedType<UInt16> { using Type = Enriched::UInt16<HasNoNull>; };
|
||
template <> struct EmbedType<UInt32> { using Type = Enriched::UInt32<HasNoNull>; };
|
||
template <> struct EmbedType<UInt64> { using Type = Enriched::UInt64<HasNoNull>; };
|
||
template <> struct EmbedType<Float32> { using Type = Enriched::Float32<HasNoNull>; };
|
||
template <> struct EmbedType<Float64> { using Type = Enriched::Float64<HasNoNull>; };
|
||
|
||
template <> struct EmbedType<Null> { using Type = Enriched::Void<HasNull>; };
|
||
template <> struct EmbedType<Nullable<Int8> > { using Type = Enriched::Int8<HasNull>; };
|
||
template <> struct EmbedType<Nullable<Int16> > { using Type = Enriched::Int16<HasNull>; };
|
||
template <> struct EmbedType<Nullable<Int32> > { using Type = Enriched::Int32<HasNull>; };
|
||
template <> struct EmbedType<Nullable<Int64> > { using Type = Enriched::Int64<HasNull>; };
|
||
template <> struct EmbedType<Nullable<UInt8> > { using Type = Enriched::UInt8<HasNull>; };
|
||
template <> struct EmbedType<Nullable<UInt16> > { using Type = Enriched::UInt16<HasNull>; };
|
||
template <> struct EmbedType<Nullable<UInt32> > { using Type = Enriched::UInt32<HasNull>; };
|
||
template <> struct EmbedType<Nullable<UInt64> > { using Type = Enriched::UInt64<HasNull>; };
|
||
template <> struct EmbedType<Nullable<Float32> > { using Type = Enriched::Float32<HasNull>; };
|
||
template <> struct EmbedType<Nullable<Float64> > { using Type = Enriched::Float64<HasNull>; };
|
||
|
||
/// Get an ordinary type from an enriched type.
|
||
template <typename TType>
|
||
struct ToOrdinaryType
|
||
{
|
||
using Type = typename std::conditional<
|
||
std::is_same<typename std::tuple_element<2, TType>::type, HasNoNull>::value,
|
||
typename std::tuple_element<0, TType>::type,
|
||
Nullable<typename std::tuple_element<0, TType>::type>
|
||
>::type;
|
||
};
|
||
|
||
/// Get an ordinary type from an enriched type.
|
||
/// Error case.
|
||
template <>
|
||
struct ToOrdinaryType<Error>
|
||
{
|
||
using Type = Error;
|
||
};
|
||
|
||
namespace
|
||
{
|
||
|
||
/// The following helper functions and structures are used for the TypeProduct implementation.
|
||
|
||
/// Check if two types are equal up to nullity.
|
||
template <typename T1, typename T2>
|
||
constexpr bool areSimilarTypes()
|
||
{
|
||
return std::is_same<
|
||
typename std::tuple_element<0, T1>::type,
|
||
typename std::tuple_element<0, T2>::type
|
||
>::value &&
|
||
std::is_same<
|
||
typename std::tuple_element<1, T1>::type,
|
||
typename std::tuple_element<1, T2>::type
|
||
>::value;
|
||
}
|
||
|
||
/// Check if a pair of types {A,B} equals a pair of types {A1,B1} up to nullity.
|
||
template <typename A, typename B, template <typename> class A1, template <typename> class B1>
|
||
constexpr bool areSimilarPairs()
|
||
{
|
||
/// NOTE: the use of HasNoNull here is a trick. It has no meaning.
|
||
return (areSimilarTypes<A, A1<HasNoNull>>() && areSimilarTypes<B, B1<HasNoNull>>()) ||
|
||
(areSimilarTypes<A, B1<HasNoNull>>() && areSimilarTypes<B, A1<HasNoNull>>());
|
||
}
|
||
|
||
/// Check if a pair of enriched types {A,B} that have straight mappings to ordinary
|
||
/// types must be processed in a special way.
|
||
template <typename A, typename B>
|
||
constexpr bool isExceptionalPair()
|
||
{
|
||
return areSimilarPairs<A, B, Enriched::Int8, Enriched::UInt16>() ||
|
||
areSimilarPairs<A, B, Enriched::Int8, Enriched::UInt32>() ||
|
||
areSimilarPairs<A, B, Enriched::Int16, Enriched::UInt16>() ||
|
||
areSimilarPairs<A, B, Enriched::Int16, Enriched::UInt32>() ||
|
||
areSimilarPairs<A, B, Enriched::Int32, Enriched::UInt32>();
|
||
}
|
||
|
||
/// Check if a pair of enriched types {A,B} is ordinary. Here "ordinary" means
|
||
/// that both types map to ordinary types and that they are not exceptional as
|
||
/// defined in the function above.
|
||
template <typename A, typename B>
|
||
constexpr bool isOrdinaryPair()
|
||
{
|
||
return std::is_same<typename std::tuple_element<1, A>::type, void>::value &&
|
||
std::is_same<typename std::tuple_element<1, B>::type, void>::value &&
|
||
!isExceptionalPair<A, B>();
|
||
}
|
||
|
||
/// Returns nullity(A) | nullity(B).
|
||
template <typename A, typename B>
|
||
struct CombinedNullity
|
||
{
|
||
private:
|
||
using NullityA = typename Traits<typename ToOrdinaryType<A>::Type>::Nullity;
|
||
using NullityB = typename Traits<typename ToOrdinaryType<B>::Type>::Nullity;
|
||
|
||
public:
|
||
using Type = typename boost::mpl::or_<NullityA, NullityB>::type;
|
||
};
|
||
|
||
}
|
||
|
||
/// Compute the product of two enriched numeric types.
|
||
/// This statement catches all the incorrect combinations.
|
||
template <typename T1, typename T2, typename Enable = void>
|
||
struct TypeProduct
|
||
{
|
||
using Type = Error;
|
||
};
|
||
|
||
/// Compute the product of two enriched numeric types.
|
||
/// Case when both these types are ordinary in the meaning defined above.
|
||
template <typename A, typename B>
|
||
struct TypeProduct<A, B, typename std::enable_if<isOrdinaryPair<A, B>()>::type>
|
||
{
|
||
private:
|
||
using Result = typename ResultOfIf<
|
||
typename ToOrdinaryType<A>::Type,
|
||
typename ToOrdinaryType<B>::Type
|
||
>::Type;
|
||
|
||
public:
|
||
using Type = typename EmbedType<Result>::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.
|
||
|
||
#define DEFINE_TYPE_PRODUCT_RULE(T1, T2, T3) \
|
||
template <typename A, typename B> \
|
||
struct TypeProduct< \
|
||
A, \
|
||
B, \
|
||
typename std::enable_if< \
|
||
!isOrdinaryPair<A, B>() && \
|
||
areSimilarPairs<A, B, T1, T2>() \
|
||
>::type> \
|
||
{ \
|
||
using Type = typename T3<typename CombinedNullity<A, B>::Type>; \
|
||
}
|
||
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::Int8, Enriched::UInt16, Enriched::IntFloat32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::Int8, Enriched::UInt32, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::Int16, Enriched::UInt16, Enriched::IntFloat32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::Int16, Enriched::UInt32, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::Int32, Enriched::UInt32, Enriched::IntFloat64);
|
||
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::Int8, Enriched::IntFloat32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::Int16, Enriched::IntFloat32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::Int32, Enriched::Int32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::Int64, Enriched::Int64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::Float32, Enriched::Float32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::Float64, Enriched::Float64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::UInt8, Enriched::IntFloat32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::UInt16, Enriched::IntFloat32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::UInt32, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::IntFloat32, Enriched::IntFloat32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::IntFloat64, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::Int8, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::Int16, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::Int32, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::Int64, Enriched::Int64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::Float32, Enriched::Float64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::Float64, Enriched::Float64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::UInt8, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::UInt16, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::UInt32, Enriched::IntFloat64);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::IntFloat64, Enriched::IntFloat64);
|
||
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat32, Enriched::Void, Enriched::IntFloat32);
|
||
DEFINE_TYPE_PRODUCT_RULE(Enriched::IntFloat64, Enriched::Void, Enriched::IntFloat64);
|
||
|
||
#undef DEFINE_TYPE_PRODUCT_RULE
|
||
|
||
}
|
||
|
||
}
|