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499 lines
16 KiB
C++
499 lines
16 KiB
C++
#pragma once
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#include <cmath>
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#include <limits>
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#include "Defines.h"
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#include "Types.h"
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#include <Common/NaNUtils.h>
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#include <Common/UInt128.h>
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/** Preceptually-correct number comparisons.
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* Example: Int8(-1) != UInt8(255)
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*/
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namespace accurate
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{
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using DB::UInt64;
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/** Cases:
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1) Safe conversion (in case of default C++ operators)
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a) int vs any int
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b) uint vs any uint
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c) float vs any float
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2) int vs uint
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a) sizeof(int) <= sizeof(uint). Accurate comparison with MAX_INT tresholds
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b) sizeof(int) > sizeof(uint). Casting to int
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3) integral_type vs floating_type
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a) sizeof(integral_type) <= 4. Comparison via casting arguments to Float64
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b) sizeof(integral_type) == 8. Accurate comparison. Consider 3 sets of intervals:
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1) interval between adjacent floats less or equal 1
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2) interval between adjacent floats greater then 2
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3) float is outside [MIN_INT64; MAX_INT64]
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*/
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// Case 1. Is pair of floats or pair of ints or pair of uints
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template <typename A, typename B>
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constexpr bool is_safe_conversion = (std::is_floating_point_v<A> && std::is_floating_point_v<B>)
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|| (is_integral_v<A> && is_integral_v<B> && !(is_signed_v<A> ^ is_signed_v<B>))
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|| (std::is_same_v<A, DB::Int128> && std::is_same_v<B, DB::Int128>)
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|| (is_integral_v<A> && std::is_same_v<B, DB::Int128>)
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|| (std::is_same_v<A, DB::Int128> && is_integral_v<B>);
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template <typename A, typename B>
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using bool_if_safe_conversion = std::enable_if_t<is_safe_conversion<A, B>, bool>;
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template <typename A, typename B>
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using bool_if_not_safe_conversion = std::enable_if_t<!is_safe_conversion<A, B>, bool>;
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/// Case 2. Are params IntXX and UIntYY ?
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template <typename TInt, typename TUInt>
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constexpr bool is_any_int_vs_uint
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= is_integral_v<TInt> && is_integral_v<TUInt> && is_signed_v<TInt> && is_unsigned_v<TUInt>;
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// Case 2a. Are params IntXX and UIntYY and sizeof(IntXX) >= sizeof(UIntYY) (in such case will use accurate compare)
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template <typename TInt, typename TUInt>
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constexpr bool is_le_int_vs_uint = is_any_int_vs_uint<TInt, TUInt> && (sizeof(TInt) <= sizeof(TUInt));
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template <typename TInt, typename TUInt>
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using bool_if_le_int_vs_uint_t = std::enable_if_t<is_le_int_vs_uint<TInt, TUInt>, bool>;
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template <typename TInt, typename TUInt>
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inline bool_if_le_int_vs_uint_t<TInt, TUInt> greaterOpTmpl(TInt a, TUInt b)
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{
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return static_cast<TUInt>(a) > b && a >= 0 && b <= static_cast<TUInt>(std::numeric_limits<TInt>::max());
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}
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template <typename TUInt, typename TInt>
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inline bool_if_le_int_vs_uint_t<TInt, TUInt> greaterOpTmpl(TUInt a, TInt b)
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{
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return a > static_cast<TUInt>(b) || b < 0 || a > static_cast<TUInt>(std::numeric_limits<TInt>::max());
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}
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template <typename TInt, typename TUInt>
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inline bool_if_le_int_vs_uint_t<TInt, TUInt> equalsOpTmpl(TInt a, TUInt b)
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{
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return static_cast<TUInt>(a) == b && a >= 0 && b <= static_cast<TUInt>(std::numeric_limits<TInt>::max());
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}
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template <typename TUInt, typename TInt>
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inline bool_if_le_int_vs_uint_t<TInt, TUInt> equalsOpTmpl(TUInt a, TInt b)
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{
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return a == static_cast<TUInt>(b) && b >= 0 && a <= static_cast<TUInt>(std::numeric_limits<TInt>::max());
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}
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// Case 2b. Are params IntXX and UIntYY and sizeof(IntXX) > sizeof(UIntYY) (in such case will cast UIntYY to IntXX and compare)
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template <typename TInt, typename TUInt>
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constexpr bool is_gt_int_vs_uint = is_any_int_vs_uint<TInt, TUInt> && (sizeof(TInt) > sizeof(TUInt));
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template <typename TInt, typename TUInt>
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using bool_if_gt_int_vs_uint = std::enable_if_t<is_gt_int_vs_uint<TInt, TUInt>, bool>;
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template <typename TInt, typename TUInt>
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inline bool_if_gt_int_vs_uint<TInt, TUInt> greaterOpTmpl(TInt a, TUInt b)
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{
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return static_cast<TInt>(a) > static_cast<TInt>(b);
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}
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template <typename TInt, typename TUInt>
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inline bool_if_gt_int_vs_uint<TInt, TUInt> greaterOpTmpl(TUInt a, TInt b)
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{
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return static_cast<TInt>(a) > static_cast<TInt>(b);
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}
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template <typename TInt, typename TUInt>
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inline bool_if_gt_int_vs_uint<TInt, TUInt> equalsOpTmpl(TInt a, TUInt b)
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{
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return static_cast<TInt>(a) == static_cast<TInt>(b);
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}
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template <typename TInt, typename TUInt>
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inline bool_if_gt_int_vs_uint<TInt, TUInt> equalsOpTmpl(TUInt a, TInt b)
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{
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return static_cast<TInt>(a) == static_cast<TInt>(b);
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}
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// Case 3a. Comparison via conversion to double.
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template <typename TAInt, typename TAFloat>
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using bool_if_double_can_be_used
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= std::enable_if_t<is_integral_v<TAInt> && (sizeof(TAInt) <= 4) && std::is_floating_point_v<TAFloat>, bool>;
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template <typename TAInt, typename TAFloat>
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inline bool_if_double_can_be_used<TAInt, TAFloat> greaterOpTmpl(TAInt a, TAFloat b)
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{
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return static_cast<double>(a) > static_cast<double>(b);
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}
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template <typename TAInt, typename TAFloat>
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inline bool_if_double_can_be_used<TAInt, TAFloat> greaterOpTmpl(TAFloat a, TAInt b)
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{
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return static_cast<double>(a) > static_cast<double>(b);
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}
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template <typename TAInt, typename TAFloat>
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inline bool_if_double_can_be_used<TAInt, TAFloat> equalsOpTmpl(TAInt a, TAFloat b)
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{
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return static_cast<double>(a) == static_cast<double>(b);
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}
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template <typename TAInt, typename TAFloat>
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inline bool_if_double_can_be_used<TAInt, TAFloat> equalsOpTmpl(TAFloat a, TAInt b)
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{
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return static_cast<double>(a) == static_cast<double>(b);
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}
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/* Final realiztions */
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template <typename A, typename B>
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inline bool_if_not_safe_conversion<A, B> greaterOp(A a, B b)
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{
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return greaterOpTmpl(a, b);
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}
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template <typename A, typename B>
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inline bool_if_safe_conversion<A, B> greaterOp(A a, B b)
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{
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return a > b;
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}
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// Case 3b. 64-bit integers vs floats comparison.
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// See hint at https://github.com/JuliaLang/julia/issues/257 (but it doesn't work properly for -2**63)
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constexpr DB::Int64 MAX_INT64_WITH_EXACT_FLOAT64_REPR = 9007199254740992LL; // 2^53
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template <>
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inline bool greaterOp<DB::Float64, DB::Int64>(DB::Float64 f, DB::Int64 i)
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{
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if (-MAX_INT64_WITH_EXACT_FLOAT64_REPR <= i && i <= MAX_INT64_WITH_EXACT_FLOAT64_REPR)
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return f > static_cast<DB::Float64>(i);
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return (f >= static_cast<DB::Float64>(std::numeric_limits<DB::Int64>::max())) // rhs is 2**63 (not 2^63 - 1)
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|| (f > static_cast<DB::Float64>(std::numeric_limits<DB::Int64>::min()) && static_cast<DB::Int64>(f) > i);
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}
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template <>
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inline bool greaterOp<DB::Int64, DB::Float64>(DB::Int64 i, DB::Float64 f)
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{
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if (-MAX_INT64_WITH_EXACT_FLOAT64_REPR <= i && i <= MAX_INT64_WITH_EXACT_FLOAT64_REPR)
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return f < static_cast<DB::Float64>(i);
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return (f < static_cast<DB::Float64>(std::numeric_limits<DB::Int64>::min()))
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|| (f < static_cast<DB::Float64>(std::numeric_limits<DB::Int64>::max()) && i > static_cast<DB::Int64>(f));
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}
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template <>
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inline bool greaterOp<DB::Float64, DB::UInt64>(DB::Float64 f, DB::UInt64 u)
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{
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if (u <= static_cast<DB::UInt64>(MAX_INT64_WITH_EXACT_FLOAT64_REPR))
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return f > static_cast<DB::Float64>(u);
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return (f >= static_cast<DB::Float64>(std::numeric_limits<DB::UInt64>::max()))
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|| (f >= 0 && static_cast<DB::UInt64>(f) > u);
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}
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template <>
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inline bool greaterOp<DB::UInt64, DB::Float64>(DB::UInt64 u, DB::Float64 f)
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{
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if (u <= static_cast<DB::UInt64>(MAX_INT64_WITH_EXACT_FLOAT64_REPR))
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return static_cast<DB::Float64>(u) > f;
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return (f < 0)
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|| (f < static_cast<DB::Float64>(std::numeric_limits<DB::UInt64>::max()) && u > static_cast<UInt64>(f));
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}
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// Case 3b for float32
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template <>
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inline bool greaterOp<DB::Float32, DB::Int64>(DB::Float32 f, DB::Int64 i)
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{
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return greaterOp(static_cast<DB::Float64>(f), i);
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}
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template <>
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inline bool greaterOp<DB::Int64, DB::Float32>(DB::Int64 i, DB::Float32 f)
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{
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return greaterOp(i, static_cast<DB::Float64>(f));
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}
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template <>
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inline bool greaterOp<DB::Float32, DB::UInt64>(DB::Float32 f, DB::UInt64 u)
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{
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return greaterOp(static_cast<DB::Float64>(f), u);
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}
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template <>
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inline bool greaterOp<DB::UInt64, DB::Float32>(DB::UInt64 u, DB::Float32 f)
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{
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return greaterOp(u, static_cast<DB::Float64>(f));
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}
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template <>
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inline bool greaterOp<DB::Float64, DB::UInt128>(DB::Float64 f, DB::UInt128 u)
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{
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return u.low == 0 && greaterOp(f, u.high);
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}
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template <>
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inline bool greaterOp<DB::UInt128, DB::Float64>(DB::UInt128 u, DB::Float64 f)
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{
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return u.low != 0 || greaterOp(u.high, f);
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}
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template <>
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inline bool greaterOp<DB::Float32, DB::UInt128>(DB::Float32 f, DB::UInt128 u)
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{
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return greaterOp(static_cast<DB::Float64>(f), u);
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}
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template <>
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inline bool greaterOp<DB::UInt128, DB::Float32>(DB::UInt128 u, DB::Float32 f)
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{
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return greaterOp(u, static_cast<DB::Float64>(f));
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}
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template <typename A, typename B>
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inline bool_if_not_safe_conversion<A, B> equalsOp(A a, B b)
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{
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return equalsOpTmpl(a, b);
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}
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template <typename A, typename B>
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inline bool_if_safe_conversion<A, B> equalsOp(A a, B b)
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{
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using LargestType = std::conditional_t<sizeof(A) >= sizeof(B), A, B>;
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return static_cast<LargestType>(a) == static_cast<LargestType>(b);
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::Float64, DB::UInt64>(DB::Float64 f, DB::UInt64 u)
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{
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return static_cast<DB::UInt64>(f) == u && f == static_cast<DB::Float64>(u);
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::UInt64, DB::Float64>(DB::UInt64 u, DB::Float64 f)
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{
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return u == static_cast<DB::UInt64>(f) && static_cast<DB::Float64>(u) == f;
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::Float64, DB::Int64>(DB::Float64 f, DB::Int64 u)
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{
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return static_cast<DB::Int64>(f) == u && f == static_cast<DB::Float64>(u);
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::Int64, DB::Float64>(DB::Int64 u, DB::Float64 f)
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{
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return u == static_cast<DB::Int64>(f) && static_cast<DB::Float64>(u) == f;
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::Float32, DB::UInt64>(DB::Float32 f, DB::UInt64 u)
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{
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return static_cast<DB::UInt64>(f) == u && f == static_cast<DB::Float32>(u);
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::UInt64, DB::Float32>(DB::UInt64 u, DB::Float32 f)
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{
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return u == static_cast<DB::UInt64>(f) && static_cast<DB::Float32>(u) == f;
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::Float32, DB::Int64>(DB::Float32 f, DB::Int64 u)
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{
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return static_cast<DB::Int64>(f) == u && f == static_cast<DB::Float32>(u);
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::Int64, DB::Float32>(DB::Int64 u, DB::Float32 f)
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{
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return u == static_cast<DB::Int64>(f) && static_cast<DB::Float32>(u) == f;
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}
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template <>
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inline bool NO_SANITIZE_UNDEFINED equalsOp<DB::UInt128, DB::Float64>(DB::UInt128 u, DB::Float64 f)
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{
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return u.low == 0 && equalsOp(static_cast<UInt64>(u.high), f);
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}
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template <>
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inline bool equalsOp<DB::UInt128, DB::Float32>(DB::UInt128 u, DB::Float32 f)
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{
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return equalsOp(u, static_cast<DB::Float64>(f));
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}
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template <>
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inline bool equalsOp<DB::Float64, DB::UInt128>(DB::Float64 f, DB::UInt128 u)
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{
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return equalsOp(u, f);
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}
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template <>
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inline bool equalsOp<DB::Float32, DB::UInt128>(DB::Float32 f, DB::UInt128 u)
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{
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return equalsOp(static_cast<DB::Float64>(f), u);
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}
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inline bool NO_SANITIZE_UNDEFINED greaterOp(DB::Int128 i, DB::Float64 f)
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{
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static constexpr __int128 min_int128 = __int128(0x8000000000000000ll) << 64;
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static constexpr __int128 max_int128 = (__int128(0x7fffffffffffffffll) << 64) + 0xffffffffffffffffll;
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if (-MAX_INT64_WITH_EXACT_FLOAT64_REPR <= i && i <= MAX_INT64_WITH_EXACT_FLOAT64_REPR)
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return static_cast<DB::Float64>(i) > f;
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return (f < static_cast<DB::Float64>(min_int128))
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|| (f < static_cast<DB::Float64>(max_int128) && i > static_cast<DB::Int128>(f));
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}
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inline bool NO_SANITIZE_UNDEFINED greaterOp(DB::Float64 f, DB::Int128 i)
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{
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static constexpr __int128 min_int128 = __int128(0x8000000000000000ll) << 64;
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static constexpr __int128 max_int128 = (__int128(0x7fffffffffffffffll) << 64) + 0xffffffffffffffffll;
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if (-MAX_INT64_WITH_EXACT_FLOAT64_REPR <= i && i <= MAX_INT64_WITH_EXACT_FLOAT64_REPR)
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return f > static_cast<DB::Float64>(i);
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return (f >= static_cast<DB::Float64>(max_int128))
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|| (f > static_cast<DB::Float64>(min_int128) && static_cast<DB::Int128>(f) > i);
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}
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inline bool greaterOp(DB::Int128 i, DB::Float32 f) { return greaterOp(i, static_cast<DB::Float64>(f)); }
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inline bool greaterOp(DB::Float32 f, DB::Int128 i) { return greaterOp(static_cast<DB::Float64>(f), i); }
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inline bool NO_SANITIZE_UNDEFINED equalsOp(DB::Int128 i, DB::Float64 f) { return i == static_cast<DB::Int128>(f) && static_cast<DB::Float64>(i) == f; }
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inline bool NO_SANITIZE_UNDEFINED equalsOp(DB::Int128 i, DB::Float32 f) { return i == static_cast<DB::Int128>(f) && static_cast<DB::Float32>(i) == f; }
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inline bool equalsOp(DB::Float64 f, DB::Int128 i) { return equalsOp(i, f); }
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inline bool equalsOp(DB::Float32 f, DB::Int128 i) { return equalsOp(i, f); }
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template <typename A, typename B>
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inline bool_if_not_safe_conversion<A, B> notEqualsOp(A a, B b)
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{
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return !equalsOp(a, b);
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}
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template <typename A, typename B>
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inline bool_if_safe_conversion<A, B> notEqualsOp(A a, B b)
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{
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return a != b;
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}
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template <typename A, typename B>
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inline bool_if_not_safe_conversion<A, B> lessOp(A a, B b)
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{
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return greaterOp(b, a);
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}
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template <typename A, typename B>
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inline bool_if_safe_conversion<A, B> lessOp(A a, B b)
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{
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return a < b;
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}
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template <typename A, typename B>
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inline bool_if_not_safe_conversion<A, B> lessOrEqualsOp(A a, B b)
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{
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if (isNaN(a) || isNaN(b))
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return false;
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return !greaterOp(a, b);
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}
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template <typename A, typename B>
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inline bool_if_safe_conversion<A, B> lessOrEqualsOp(A a, B b)
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{
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return a <= b;
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}
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template <typename A, typename B>
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inline bool_if_not_safe_conversion<A, B> greaterOrEqualsOp(A a, B b)
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{
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if (isNaN(a) || isNaN(b))
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return false;
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return !greaterOp(b, a);
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}
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template <typename A, typename B>
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inline bool_if_safe_conversion<A, B> greaterOrEqualsOp(A a, B b)
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{
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return a >= b;
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}
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/// Converts numeric to an equal numeric of other type.
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template <typename From, typename To>
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inline bool NO_SANITIZE_UNDEFINED convertNumeric(From value, To & result)
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{
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/// If the type is actually the same it's not necessary to do any checks.
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if constexpr (std::is_same_v<From, To>)
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{
|
|
result = value;
|
|
return true;
|
|
}
|
|
|
|
/// Note that NaNs doesn't compare equal to anything, but they are still in range of any Float type.
|
|
if (isNaN(value) && std::is_floating_point_v<To>)
|
|
{
|
|
result = value;
|
|
return true;
|
|
}
|
|
|
|
result = static_cast<To>(value);
|
|
return equalsOp(value, result);
|
|
}
|
|
|
|
}
|
|
|
|
|
|
namespace DB
|
|
{
|
|
|
|
template <typename A, typename B> struct EqualsOp
|
|
{
|
|
/// An operation that gives the same result, if arguments are passed in reverse order.
|
|
using SymmetricOp = EqualsOp<B, A>;
|
|
|
|
static UInt8 apply(A a, B b) { return accurate::equalsOp(a, b); }
|
|
};
|
|
|
|
template <typename A, typename B> struct NotEqualsOp
|
|
{
|
|
using SymmetricOp = NotEqualsOp<B, A>;
|
|
static UInt8 apply(A a, B b) { return accurate::notEqualsOp(a, b); }
|
|
};
|
|
|
|
template <typename A, typename B> struct GreaterOp;
|
|
|
|
template <typename A, typename B> struct LessOp
|
|
{
|
|
using SymmetricOp = GreaterOp<B, A>;
|
|
static UInt8 apply(A a, B b) { return accurate::lessOp(a, b); }
|
|
};
|
|
|
|
template <typename A, typename B> struct GreaterOp
|
|
{
|
|
using SymmetricOp = LessOp<B, A>;
|
|
static UInt8 apply(A a, B b) { return accurate::greaterOp(a, b); }
|
|
};
|
|
|
|
template <typename A, typename B> struct GreaterOrEqualsOp;
|
|
|
|
template <typename A, typename B> struct LessOrEqualsOp
|
|
{
|
|
using SymmetricOp = GreaterOrEqualsOp<B, A>;
|
|
static UInt8 apply(A a, B b) { return accurate::lessOrEqualsOp(a, b); }
|
|
};
|
|
|
|
template <typename A, typename B> struct GreaterOrEqualsOp
|
|
{
|
|
using SymmetricOp = LessOrEqualsOp<B, A>;
|
|
static UInt8 apply(A a, B b) { return accurate::greaterOrEqualsOp(a, b); }
|
|
};
|
|
|
|
}
|