926 lines
21 KiB
C++
926 lines
21 KiB
C++
#pragma once
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#include "CoreTypes.h"
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#include "Numeric/Bit.h"
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#include "Numeric/Limits.h"
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#include "Templates/Tuple.h"
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#include "TypeTraits/TypeTraits.h"
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#include "Miscellaneous/AssertionMacros.h"
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#include <cmath>
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NAMESPACE_REDCRAFT_BEGIN
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NAMESPACE_MODULE_BEGIN(Redcraft)
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NAMESPACE_MODULE_BEGIN(Utility)
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NAMESPACE_BEGIN(Math)
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NAMESPACE_PRIVATE_BEGIN
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template <CFloatingPoint T>
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struct TFloatingTypeTraits
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{
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static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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};
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template <>
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struct TFloatingTypeTraits<float>
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{
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// IEEE-754 single precision floating point format.
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// SEEEEEEE EMMMMMMM MMMMMMMM MMMMMMMM
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using FIntegralT = uint32;
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static constexpr int SignBits = 1;
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static constexpr int ExponentBits = 8;
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static constexpr int MantissaBits = 23;
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static_assert(SignBits + ExponentBits + MantissaBits == sizeof(float) * 8);
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static constexpr int ExponentBias = 127;
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static constexpr int SignShift = 31;
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static constexpr int ExponentShift = 23;
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static constexpr int MantissaShift = 0;
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static constexpr FIntegralT SignMask = 0x80000000;
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static constexpr FIntegralT ExponentMask = 0x7F800000;
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static constexpr FIntegralT MantissaMask = 0x007FFFFF;
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};
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template <>
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struct TFloatingTypeTraits<double>
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{
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// IEEE-754 double precision floating point format.
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// SEEEEEEE EEEEMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM
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using FIntegralT = uint64;
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static constexpr int SignBits = 1;
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static constexpr int ExponentBits = 11;
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static constexpr int MantissaBits = 52;
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static_assert(SignBits + ExponentBits + MantissaBits == sizeof(double) * 8);
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static constexpr int ExponentBias = 1023;
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static constexpr int SignShift = 63;
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static constexpr int ExponentShift = 52;
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static constexpr int MantissaShift = 0;
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static constexpr FIntegralT SignMask = 0x8000000000000000;
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static constexpr FIntegralT ExponentMask = 0x7FF0000000000000;
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static constexpr FIntegralT MantissaMask = 0x000FFFFFFFFFFFFF;
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};
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NAMESPACE_PRIVATE_END
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#define RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS(Concept, Func) \
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template <Concept T, Concept U> requires (CCommonType<T, U>) \
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FORCEINLINE constexpr auto Func(T A, U B) \
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{ \
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return Math::Func<TCommonType<T, U>>(A, B); \
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}
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#define RESOLVE_ARITHMETIC_AMBIGUITY_3_ARGS(Concept, Func) \
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template <Concept T, Concept U, Concept V> requires (CCommonType<T, U, V>) \
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FORCEINLINE constexpr auto Func(T A, U B, V C) \
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{ \
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return Math::Func<TCommonType<T, U, V>>(A, B, C); \
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}
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template <CArithmetic T>
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FORCEINLINE constexpr T IsWithin(T A, T MinValue, T MaxValue)
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{
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return A >= MinValue && A < MaxValue;
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}
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RESOLVE_ARITHMETIC_AMBIGUITY_3_ARGS(CArithmetic, IsWithin)
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template <CArithmetic T>
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FORCEINLINE constexpr T IsWithinInclusive(T A, T MinValue, T MaxValue)
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{
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return A >= MinValue && A <= MaxValue;
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}
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RESOLVE_ARITHMETIC_AMBIGUITY_3_ARGS(CArithmetic, IsWithinInclusive)
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template <CArithmetic T>
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FORCEINLINE constexpr T Trunc(T A)
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{
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if constexpr (CIntegral<T>) return A;
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else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::trunc(A);
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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template <CArithmetic T, CArithmetic U>
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FORCEINLINE constexpr T TruncTo(U A)
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{
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if constexpr (CIntegral<T> && CIntegral<U>) return A;
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else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::trunc(static_cast<float>(A));
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}
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else if constexpr (CIntegral<T>)
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{
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return static_cast<T>(A);
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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template <CArithmetic T>
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FORCEINLINE constexpr T Ceil(T A)
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{
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if constexpr (CIntegral<T>) return A;
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else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::ceil(A);
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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template <CArithmetic T, CArithmetic U>
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FORCEINLINE constexpr T CeilTo(U A)
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{
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if constexpr (CIntegral<T> && CIntegral<U>) return A;
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else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::ceil(static_cast<float>(A));
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}
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else if constexpr (CIntegral<T>)
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{
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T I = Math::TruncTo<T>(A);
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I += static_cast<U>(I) < A;
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return I;
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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template <CArithmetic T>
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FORCEINLINE constexpr T Floor(T A)
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{
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if constexpr (CIntegral<T>) return A;
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else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::floor(A);
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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template <CArithmetic T, CArithmetic U>
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FORCEINLINE constexpr T FloorTo(U A)
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{
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if constexpr (CIntegral<T> && CIntegral<U>) return A;
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else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::floor(static_cast<float>(A));
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}
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else if constexpr (CIntegral<T>)
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{
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T I = Math::TruncTo<T>(A);
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I -= static_cast<U>(I) > A;
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return I;
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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template <CArithmetic T>
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FORCEINLINE constexpr T Round(T A)
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{
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if constexpr (CIntegral<T>) return A;
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else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::round(A);
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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template <CArithmetic T, CArithmetic U>
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FORCEINLINE constexpr T RoundTo(U A)
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{
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if constexpr (CIntegral<T> && CIntegral<U>) return A;
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else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::round(static_cast<float>(A));
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}
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else if constexpr (CIntegral<T>)
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{
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return Math::FloorTo<T>(A + static_cast<U>(0.5));
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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template <CSigned T>
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FORCEINLINE constexpr T Abs(T A)
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{
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return A < 0 ? -A : A;
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}
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template <CUnsigned T>
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FORCEINLINE constexpr T Abs(T A)
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{
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return A;
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}
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template <CArithmetic T>
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FORCEINLINE constexpr T Sign(T A)
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{
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if (A == static_cast<T>(0)) return static_cast<T>( 0);
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if (A < static_cast<T>(0)) return static_cast<T>(-1);
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return static_cast<T>(1);
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}
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template <CArithmetic T, CArithmetic... Ts> requires (CCommonType<T, Ts...>)
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FORCEINLINE constexpr auto Min(T A, Ts... InOther)
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{
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if constexpr (sizeof...(Ts) == 0) return A;
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else
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{
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using FCommonT = TCommonType<T, Ts...>;
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FCommonT B = Math::Min(InOther...);
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return A < B ? A : B;
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}
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}
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template <CArithmetic T, CArithmetic... Ts> requires (CCommonType<T, Ts...>)
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FORCEINLINE constexpr auto Max(T A, Ts... InOther)
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{
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if constexpr (sizeof...(Ts) == 0) return A;
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else
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{
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using FCommonT = TCommonType<T, Ts...>;
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FCommonT B = Math::Max(InOther...);
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return A > B ? A : B;
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}
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}
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template <CArithmetic T, CArithmetic... Ts> requires (CCommonType<T, Ts...>)
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FORCEINLINE constexpr size_t MinIndex(T A, Ts... InOther)
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{
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if constexpr (sizeof...(Ts) == 0) return 0;
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else
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{
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size_t Index = Math::MinIndex(InOther...);
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bool bFlag;
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ForwardAsTuple(InOther...).Visit([&bFlag, A](auto B) { bFlag = A < B; }, Index);
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return bFlag ? 0 : Index + 1;
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}
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}
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template <CArithmetic T, CArithmetic... Ts> requires (CCommonType<T, Ts...>)
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FORCEINLINE constexpr size_t MaxIndex(T A, Ts... InOther)
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{
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if constexpr (sizeof...(Ts) == 0) return 0;
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else
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{
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size_t Index = Math::MaxIndex(InOther...);
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bool bFlag;
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ForwardAsTuple(InOther...).Visit([&bFlag, A](auto B) { bFlag = A > B; }, Index);
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return bFlag ? 0 : Index + 1;
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}
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}
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template <CIntegral T>
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FORCEINLINE constexpr auto Div(T A, T B)
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{
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checkf(B != 0, TEXT("Illegal divisor. It must not be zero."));
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struct { T Quotient; T Remainder; } Result;
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Result.Quotient = A / B;
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Result.Remainder = A % B;
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return Result;
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}
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template <CIntegral T>
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FORCEINLINE constexpr T DivAndCeil(T A, T B)
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{
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return (A + B - 1) / B;
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}
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template <CIntegral T>
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FORCEINLINE constexpr T DivAndFloor(T A, T B)
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{
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return A / B;
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}
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template <CIntegral T>
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FORCEINLINE constexpr T DivAndRound(T A, T B)
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{
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return A >= 0
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? (A + B / 2 ) / B
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: (A - B / 2 + 1) / B;
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}
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RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS(CIntegral, Div)
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template <CArithmetic T>
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FORCEINLINE constexpr bool IsNearlyEqual(T A, T B, T Epsilon = TNumericLimits<T>::Epsilon())
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{
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return Math::Abs<T>(A - B) <= Epsilon;
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}
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RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS(CArithmetic, IsNearlyEqual)
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RESOLVE_ARITHMETIC_AMBIGUITY_3_ARGS(CArithmetic, IsNearlyEqual)
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template <CArithmetic T>
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FORCEINLINE constexpr bool IsNearlyZero(T A, T Epsilon = TNumericLimits<T>::Epsilon())
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{
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return Math::Abs<T>(A) <= Epsilon;
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}
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RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS(CArithmetic, IsNearlyZero)
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template <CFloatingPoint T>
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FORCEINLINE constexpr T IsInfinity(T A)
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{
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using Traits = NAMESPACE_PRIVATE::TFloatingTypeTraits<T>;
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auto IntegralValue = Math::BitCast<typename Traits::FIntegralT>(A);
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return (IntegralValue & Traits::ExponentMask) == Traits::ExponentMask && (IntegralValue & Traits::MantissaMask) == 0;
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}
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template <CFloatingPoint T>
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FORCEINLINE constexpr T IsNaN(T A)
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{
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using Traits = NAMESPACE_PRIVATE::TFloatingTypeTraits<T>;
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auto IntegralValue = Math::BitCast<typename Traits::FIntegralT>(A);
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return (IntegralValue & Traits::ExponentMask) == Traits::ExponentMask && (IntegralValue & Traits::MantissaMask) != 0;
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}
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template <CFloatingPoint T>
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FORCEINLINE constexpr T IsNormal(T A)
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{
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using Traits = NAMESPACE_PRIVATE::TFloatingTypeTraits<T>;
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auto IntegralValue = Math::BitCast<typename Traits::FIntegralT>(A);
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return (IntegralValue & Traits::ExponentMask) != 0 && (IntegralValue & Traits::ExponentMask) != Traits::ExponentMask;
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}
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template <CFloatingPoint T>
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FORCEINLINE constexpr T IsDenorm(T A)
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{
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using Traits = NAMESPACE_PRIVATE::TFloatingTypeTraits<T>;
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auto IntegralValue = Math::BitCast<typename Traits::FIntegralT>(A);
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return (IntegralValue & Traits::ExponentMask) == 0 && (IntegralValue & Traits::MantissaMask) != 0;
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}
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template <CFloatingPoint T>
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FORCEINLINE constexpr bool IsNegative(T A)
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{
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using Traits = NAMESPACE_PRIVATE::TFloatingTypeTraits<T>;
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auto IntegralValue = Math::BitCast<typename Traits::FIntegralT>(A);
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return (IntegralValue & Traits::SignMask) >> Traits::SignShift;
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}
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template <CFloatingPoint T>
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FORCEINLINE constexpr uint Exponent(T A)
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{
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using Traits = NAMESPACE_PRIVATE::TFloatingTypeTraits<T>;
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auto IntegralValue = Math::BitCast<typename Traits::FIntegralT>(A);
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return ((IntegralValue & Traits::ExponentMask) >> Traits::ExponentShift) - Traits::ExponentBias;
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}
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template <CFloatingPoint T, CUnsignedIntegral U>
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FORCEINLINE constexpr T NaN(U Payload)
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{
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using Traits = NAMESPACE_PRIVATE::TFloatingTypeTraits<T>;
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checkf(Payload != 0, TEXT("Illegal payload. It must not be zero."));
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checkf(Payload < (static_cast<typename Traits::FIntegralT>(1) << Traits::MantissaBits), TEXT("Illegal payload. It must be less than 2^MantissaBits."));
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if (Payload == 0) return TNumericLimits<T>::QuietNaN();
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typename Traits::FIntegralT ValidPayload = Payload & Traits::MantissaMask;
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return Math::BitCast<T>(ValidPayload | Traits::ExponentMask);
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}
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template <CFloatingPoint T, CEnum U>
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FORCEINLINE constexpr T NaN(U Payload)
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{
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TUnderlyingType<U> IntegralValue = static_cast<TUnderlyingType<U>>(Payload);
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return Math::NaN<T>(IntegralValue);
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}
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template <CFloatingPoint T>
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FORCEINLINE constexpr auto NaNPayload(T A)
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{
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using Traits = NAMESPACE_PRIVATE::TFloatingTypeTraits<T>;
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auto IntegralValue = Math::BitCast<typename Traits::FIntegralT>(A);
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return IntegralValue & Traits::MantissaMask;
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}
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template <CEnum T, CFloatingPoint U>
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FORCEINLINE constexpr auto NaNPayload(U A)
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{
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return static_cast<T>(Math::NaNPayload(A));
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}
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template <CFloatingPoint T>
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FORCEINLINE constexpr T FMod(T A, T B)
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{
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if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::fmod(A, B);
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS(CFloatingPoint, FMod)
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template <CFloatingPoint T>
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FORCEINLINE constexpr T Remainder(T A, T B)
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{
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if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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return NAMESPACE_STD::remainder(A, B);
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return TNumericLimits<T>::QuietNaN();
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}
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RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS(CFloatingPoint, Remainder)
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template <CFloatingPoint T>
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FORCEINLINE constexpr auto RemQuo(T A, T B)
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{
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struct { int Quotient; T Remainder; } Result;
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if constexpr (CSameAs<T, float> || CSameAs<T, double>)
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{
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Result.Remainder = NAMESPACE_STD::remquo(A, B, &Result.Quotient);
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return Result;
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}
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else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
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return Result;
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}
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|
|
RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS(CFloatingPoint, RemQuo)
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr auto ModF(T A)
|
|
{
|
|
struct { T IntegralPart; T FractionalPart; } Result;
|
|
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
Result.FractionalPart = NAMESPACE_STD::modf(A, &Result.IntegralPart);
|
|
|
|
return Result;
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return Result;
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Exp(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::exp(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Exp2(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::exp2(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T ExpMinus1(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::expm1(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Log(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::log(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Log2(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::log2(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Log10(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::log10(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Log1Plus(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::log1p(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CArithmetic T>
|
|
FORCEINLINE constexpr T Square(T A)
|
|
{
|
|
return A * A;
|
|
}
|
|
|
|
template <CArithmetic T>
|
|
FORCEINLINE constexpr T Cube(T A)
|
|
{
|
|
return A * A * A;
|
|
}
|
|
|
|
template <CIntegral T>
|
|
FORCEINLINE constexpr T Pow(T A, T B)
|
|
{
|
|
if (B < 0)
|
|
{
|
|
checkf(false, TEXT("Illegal exponent. It must be greater than or equal to zero for integral."));
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
T Result = 1;
|
|
|
|
while (B != 0)
|
|
{
|
|
if (B & 1) Result *= A;
|
|
A *= A;
|
|
B >>= 1;
|
|
}
|
|
|
|
return Result;
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Pow(T A, T B)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::pow(A, B);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS(CFloatingPoint, Pow)
|
|
|
|
template <CIntegral T>
|
|
FORCEINLINE constexpr T Sqrt(T A)
|
|
{
|
|
if (A < 0)
|
|
{
|
|
checkf(false, TEXT("Illegal argument. It must be greater than or equal to zero."));
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
T X = A;
|
|
|
|
while (true)
|
|
{
|
|
T Y = (X + A / X) / 2;
|
|
|
|
if (Y >= X) return X;
|
|
|
|
X = Y;
|
|
}
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Sqrt(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::sqrt(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CIntegral T>
|
|
FORCEINLINE constexpr T Cbrt(T A)
|
|
{
|
|
if (A < 0) return -Math::Cbrt(-A);
|
|
|
|
T X = A;
|
|
|
|
while (true)
|
|
{
|
|
T Y = (X + A / (X * X)) / 2;
|
|
|
|
if (Y >= X) return X;
|
|
|
|
X = Y;
|
|
}
|
|
}
|
|
|
|
template <CFloatingPoint T>
|
|
FORCEINLINE constexpr T Cbrt(T A)
|
|
{
|
|
if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
return NAMESPACE_STD::cbrt(A);
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
template <CArithmetic T, CArithmetic... Ts> requires (CCommonType<T, Ts...>)
|
|
FORCEINLINE constexpr auto Sum(T A, Ts... InOther)
|
|
{
|
|
if constexpr (sizeof...(Ts) == 0) return A;
|
|
|
|
else
|
|
{
|
|
using FCommonT = TCommonType<T, Ts...>;
|
|
|
|
FCommonT Sum = A + Math::Sum(InOther...);
|
|
|
|
return Sum;
|
|
}
|
|
}
|
|
|
|
template <CArithmetic T, CArithmetic... Ts> requires (CCommonType<T, Ts...>)
|
|
FORCEINLINE constexpr auto SquaredSum(T A, Ts... InOther)
|
|
{
|
|
if constexpr (sizeof...(Ts) == 0) return Math::Square(A);
|
|
|
|
else
|
|
{
|
|
using FCommonT = TCommonType<T, Ts...>;
|
|
|
|
FCommonT Sum = A + Math::SquaredSum(InOther...);
|
|
|
|
return Sum;
|
|
}
|
|
}
|
|
|
|
template <CArithmetic T, CArithmetic... Ts> requires (CCommonType<T, Ts...>)
|
|
FORCEINLINE constexpr auto Avg(T A, Ts... InOther)
|
|
{
|
|
if constexpr (sizeof...(Ts) == 0) return A;
|
|
|
|
else
|
|
{
|
|
using FCommonT = TCommonType<T, Ts...>;
|
|
|
|
FCommonT Sum = A + Math::Sum(InOther...);
|
|
|
|
return Sum / (sizeof...(Ts) + 1);
|
|
}
|
|
}
|
|
|
|
template <CArithmetic T>
|
|
FORCEINLINE constexpr T Hypot(T A)
|
|
{
|
|
return Math::Abs(A);
|
|
}
|
|
|
|
template <CArithmetic T, CArithmetic U>
|
|
FORCEINLINE constexpr auto Hypot(T A, U B)
|
|
{
|
|
using FCommonT = TCommonType<T, U>;
|
|
|
|
if constexpr (CIntegral<FCommonT>) return static_cast<FCommonT>(Math::Sqrt(Math::Square(A) + Math::Square(B)));
|
|
|
|
else if constexpr (CSameAs<FCommonT, float> || CSameAs<FCommonT, double>)
|
|
{
|
|
return NAMESPACE_STD::hypot(static_cast<FCommonT>(A), static_cast<FCommonT>(B));
|
|
}
|
|
|
|
else static_assert(sizeof(FCommonT) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<FCommonT>::QuietNaN();
|
|
}
|
|
|
|
template <CArithmetic T, CArithmetic U, CArithmetic V>
|
|
FORCEINLINE constexpr auto Hypot(T A, U B, V C)
|
|
{
|
|
using FCommonT = TCommonType<T, U, V>;
|
|
|
|
if constexpr (CIntegral<FCommonT>) return static_cast<FCommonT>(Math::Sqrt(Math::SquaredSum(A, B, C)));
|
|
|
|
else if constexpr (CSameAs<FCommonT, float> || CSameAs<FCommonT, double>)
|
|
{
|
|
return NAMESPACE_STD::hypot(static_cast<FCommonT>(A), static_cast<FCommonT>(B), static_cast<FCommonT>(C));
|
|
}
|
|
|
|
else static_assert(sizeof(FCommonT) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<FCommonT>::QuietNaN();
|
|
}
|
|
|
|
template <CArithmetic... Ts> requires (CCommonType<Ts...>)
|
|
FORCEINLINE constexpr auto Hypot(Ts... InOther)
|
|
{
|
|
return Math::Sqrt(Math::SquaredSum(InOther...));
|
|
}
|
|
|
|
template <CArithmetic T>
|
|
FORCEINLINE constexpr T Clamp(T A, T MinValue, T MaxValue)
|
|
{
|
|
return Math::Min(Math::Max(A, MinValue), MaxValue);
|
|
}
|
|
|
|
RESOLVE_ARITHMETIC_AMBIGUITY_3_ARGS(CArithmetic, Clamp)
|
|
|
|
template <CArithmetic T>
|
|
FORCEINLINE constexpr T WrappingClamp(T A, T MinValue, T MaxValue)
|
|
{
|
|
if (MinValue > MaxValue)
|
|
{
|
|
checkf(false, TEXT("Illegal range. MinValue must be less than or equal to MaxValue."));
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
if (MinValue == MaxValue) return MinValue;
|
|
|
|
if constexpr (CSameAs<T, bool>) return A;
|
|
|
|
else if constexpr (CIntegral<T>)
|
|
{
|
|
using FUnsignedT = TMakeUnsigned<T>;
|
|
|
|
FUnsignedT Range = MaxValue - MinValue;
|
|
|
|
if (A < MinValue)
|
|
{
|
|
FUnsignedT Modulo = static_cast<FUnsignedT>(MinValue - A) % Range;
|
|
|
|
return Modulo != 0 ? MaxValue - Modulo : MinValue;
|
|
}
|
|
|
|
if (A > MaxValue)
|
|
{
|
|
FUnsignedT Modulo = static_cast<FUnsignedT>(A - MaxValue) % Range;
|
|
|
|
return Modulo != 0 ? MinValue + Modulo : MaxValue;
|
|
}
|
|
|
|
return A;
|
|
}
|
|
|
|
else if constexpr (CSameAs<T, float> || CSameAs<T, double>)
|
|
{
|
|
T Range = MaxValue - MinValue;
|
|
|
|
if (A < MinValue) return MaxValue - Math::FMod(MinValue - A, Range);
|
|
if (A > MaxValue) return MinValue + Math::FMod(A - MaxValue, Range);
|
|
|
|
return A;
|
|
}
|
|
|
|
else static_assert(sizeof(T) == -1, "Unsupported floating point type.");
|
|
|
|
return TNumericLimits<T>::QuietNaN();
|
|
}
|
|
|
|
RESOLVE_ARITHMETIC_AMBIGUITY_3_ARGS(CArithmetic, WrappingClamp)
|
|
|
|
#undef RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS
|
|
#undef RESOLVE_ARITHMETIC_AMBIGUITY_3_ARGS
|
|
|
|
NAMESPACE_END(Math)
|
|
|
|
NAMESPACE_MODULE_END(Utility)
|
|
NAMESPACE_MODULE_END(Redcraft)
|
|
NAMESPACE_REDCRAFT_END
|