feat(numeric): add basic and floating point manipulation functions and the corresponding testing
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@ -13,6 +13,7 @@ void TestNumeric()
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{
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TestLiteral();
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TestBit();
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TestMath();
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}
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void TestLiteral()
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@ -120,6 +121,54 @@ void TestBit()
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always_check(Math::RotateRight(0b00011101u8, -1) == 0b00111010u8);
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}
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void TestMath()
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{
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always_check(Math::Abs(-1) == 1);
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always_check(Math::Abs( 0) == 0);
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always_check(Math::Abs( 1) == 1);
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always_check(Math::Sign(-4) == -1);
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always_check(Math::Sign( 0) == 0);
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always_check(Math::Sign( 4) == 1);
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always_check(Math::Min(1, 2, 3, 4, 5) == 1);
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always_check(Math::Min(5, 4, 3, 2, 1) == 1);
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always_check(Math::Max(1, 2, 3, 4, 5) == 5);
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always_check(Math::Max(5, 4, 3, 2, 1) == 5);
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always_check(Math::IsNearlyEqual(4.0, 4.0));
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always_check(Math::IsNearlyZero(0.0));
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always_check(Math::IsInfinity( TNumericLimits<float32>::Infinity()));
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always_check(Math::IsInfinity(-TNumericLimits<float32>::Infinity()));
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always_check(Math::IsNaN( TNumericLimits<float32>::QuietNaN()));
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always_check(Math::IsNaN(-TNumericLimits<float32>::QuietNaN()));
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always_check(Math::IsNaN( TNumericLimits<float32>::SignalingNaN()));
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always_check(Math::IsNaN(-TNumericLimits<float32>::SignalingNaN()));
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always_check(Math::IsNaN(Math::NaN<float32>(4u)));
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always_check(Math::IsNormal(1.0e4));
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always_check(Math::IsNormal(1.0e8));
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always_check(!Math::IsNegative(+1.0));
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always_check(!Math::IsNegative(+0.0));
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always_check( Math::IsNegative(-0.0));
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always_check( Math::IsNegative(-1.0));
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always_check(Math::Exponent(1.0) == 0);
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always_check(Math::Exponent(2.0) == 1);
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always_check(Math::Exponent(4.0) == 2);
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always_check(Math::NaNPayload(Math::NaN<float32>(4u)) == 4u);
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enum class ETest : uint16 { A = 65535 };
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always_check(Math::NaNPayload<ETest>(Math::NaN<float32>(ETest::A)) == ETest::A);
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}
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NAMESPACE_END(Testing)
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NAMESPACE_MODULE_END(Utility)
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@ -21,7 +21,7 @@ FORCEINLINE constexpr T BitCast(const U& Value)
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template <CUnsignedIntegral T>
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FORCEINLINE constexpr T ByteSwap(T Value)
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{
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static_assert(sizeof(T) <= 16, "ByteSwap only works with T up to 128 bits.");
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static_assert(sizeof(T) <= 16, "ByteSwap only works with T up to 128 bits");
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if constexpr (sizeof(T) == 1) return Value;
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280
Redcraft.Utility/Source/Public/Numeric/Math.h
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280
Redcraft.Utility/Source/Public/Numeric/Math.h
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@ -0,0 +1,280 @@
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#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 "TypeTraits/TypeTraits.h"
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#include "Miscellaneous/AssertionMacros.h"
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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 <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 <CIntegral T>
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FORCEINLINE constexpr auto Div(T LHS, T RHS)
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{
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checkf(RHS != 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 = LHS / RHS;
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Result.Remainder = LHS % RHS;
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return Result;
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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 LHS, T RHS, T Epsilon = TNumericLimits<T>::Epsilon())
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{
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return Math::Abs<T>(LHS - RHS) <= 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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#undef RESOLVE_ARITHMETIC_AMBIGUITY_2_ARGS
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#undef RESOLVE_ARITHMETIC_AMBIGUITY_3_ARGS
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NAMESPACE_END(Math)
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NAMESPACE_MODULE_END(Utility)
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NAMESPACE_MODULE_END(Redcraft)
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NAMESPACE_REDCRAFT_END
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@ -5,3 +5,4 @@
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#include "Numeric/Limits.h"
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#include "Numeric/Numbers.h"
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#include "Numeric/Bit.h"
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#include "Numeric/Math.h"
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@ -11,6 +11,7 @@ NAMESPACE_BEGIN(Testing)
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REDCRAFTUTILITY_API void TestNumeric();
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REDCRAFTUTILITY_API void TestLiteral();
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REDCRAFTUTILITY_API void TestBit();
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REDCRAFTUTILITY_API void TestMath();
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NAMESPACE_END(Testing)
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