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review
This commit is contained in:
Artem Mustafin
parent
18c586be87
commit
ffa0f88292
@ -1,27 +1,237 @@
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#include <Functions/hilbertDecode.h>
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#include <Common/BitHelpers.h>
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#include <Functions/FunctionFactory.h>
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#include <Functions/FunctionSpaceFillingCurve.h>
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#include <Functions/PerformanceAdaptors.h>
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#include <limits>
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namespace DB
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{
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namespace HilbertDetails
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{
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template <UInt8 bit_step>
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class HilbertDecodeLookupTable
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{
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public:
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constexpr static UInt8 LOOKUP_TABLE[0] = {};
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};
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template <>
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class HilbertDecodeLookupTable<1>
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{
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public:
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constexpr static UInt8 LOOKUP_TABLE[16] = {
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4, 1, 3, 10,
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0, 6, 7, 13,
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15, 9, 8, 2,
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11, 14, 12, 5
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};
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};
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template <>
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class HilbertDecodeLookupTable<2>
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{
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public:
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constexpr static UInt8 LOOKUP_TABLE[64] = {
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0, 20, 21, 49, 18, 3, 7, 38,
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26, 11, 15, 46, 61, 41, 40, 12,
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16, 1, 5, 36, 8, 28, 29, 57,
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10, 30, 31, 59, 39, 54, 50, 19,
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47, 62, 58, 27, 55, 35, 34, 6,
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53, 33, 32, 4, 24, 9, 13, 44,
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63, 43, 42, 14, 45, 60, 56, 25,
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37, 52, 48, 17, 2, 22, 23, 51
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};
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};
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template <>
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class HilbertDecodeLookupTable<3>
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{
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public:
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constexpr static UInt8 LOOKUP_TABLE[256] = {
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64, 1, 9, 136, 16, 88, 89, 209, 18, 90, 91, 211, 139, 202, 194, 67,
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4, 76, 77, 197, 70, 7, 15, 142, 86, 23, 31, 158, 221, 149, 148, 28,
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36, 108, 109, 229, 102, 39, 47, 174, 118, 55, 63, 190, 253, 181, 180, 60,
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187, 250, 242, 115, 235, 163, 162, 42, 233, 161, 160, 40, 112, 49, 57, 184,
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0, 72, 73, 193, 66, 3, 11, 138, 82, 19, 27, 154, 217, 145, 144, 24,
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96, 33, 41, 168, 48, 120, 121, 241, 50, 122, 123, 243, 171, 234, 226, 99,
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100, 37, 45, 172, 52, 124, 125, 245, 54, 126, 127, 247, 175, 238, 230, 103,
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223, 151, 150, 30, 157, 220, 212, 85, 141, 204, 196, 69, 6, 78, 79, 199,
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255, 183, 182, 62, 189, 252, 244, 117, 173, 236, 228, 101, 38, 110, 111, 231,
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159, 222, 214, 87, 207, 135, 134, 14, 205, 133, 132, 12, 84, 21, 29, 156,
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155, 218, 210, 83, 203, 131, 130, 10, 201, 129, 128, 8, 80, 17, 25, 152,
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32, 104, 105, 225, 98, 35, 43, 170, 114, 51, 59, 186, 249, 177, 176, 56,
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191, 254, 246, 119, 239, 167, 166, 46, 237, 165, 164, 44, 116, 53, 61, 188,
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251, 179, 178, 58, 185, 248, 240, 113, 169, 232, 224, 97, 34, 106, 107, 227,
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219, 147, 146, 26, 153, 216, 208, 81, 137, 200, 192, 65, 2, 74, 75, 195,
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68, 5, 13, 140, 20, 92, 93, 213, 22, 94, 95, 215, 143, 206, 198, 71
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};
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};
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}
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template <UInt8 bit_step>
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class FunctionHilbertDecode2DWIthLookupTableImpl
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{
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static_assert(bit_step <= 3, "bit_step should not be more than 3 to fit in UInt8");
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public:
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static std::tuple<UInt64, UInt64> decode(UInt64 hilbert_code)
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{
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UInt64 x = 0;
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UInt64 y = 0;
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const auto leading_zeros_count = getLeadingZeroBits(hilbert_code);
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const auto used_bits = std::numeric_limits<UInt64>::digits - leading_zeros_count;
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auto [current_shift, state] = getInitialShiftAndState(used_bits);
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while (current_shift >= 0)
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{
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const UInt8 hilbert_bits = (hilbert_code >> current_shift) & HILBERT_MASK;
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const auto [x_bits, y_bits] = getCodeAndUpdateState(hilbert_bits, state);
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x |= (x_bits << (current_shift >> 1));
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y |= (y_bits << (current_shift >> 1));
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current_shift -= getHilbertShift(bit_step);
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}
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return {x, y};
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}
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private:
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// for bit_step = 3
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// LOOKUP_TABLE[SSHHHHHH] = SSXXXYYY
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// where SS - 2 bits for state, XXX - 3 bits of x, YYY - 3 bits of y
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// State is rotation of curve on every step, left/up/right/down - therefore 2 bits
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static std::pair<UInt64, UInt64> getCodeAndUpdateState(UInt8 hilbert_bits, UInt8& state)
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{
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const UInt8 table_index = state | hilbert_bits;
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const auto table_code = HilbertDetails::HilbertDecodeLookupTable<bit_step>::LOOKUP_TABLE[table_index];
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state = table_code & STATE_MASK;
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const UInt64 x_bits = (table_code & X_MASK) >> bit_step;
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const UInt64 y_bits = table_code & Y_MASK;
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return {x_bits, y_bits};
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}
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// hilbert code is double size of input values
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static constexpr UInt8 getHilbertShift(UInt8 shift)
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{
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return shift << 1;
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}
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static std::pair<Int8, UInt8> getInitialShiftAndState(UInt8 used_bits)
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{
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UInt8 iterations = used_bits / HILBERT_SHIFT;
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Int8 initial_shift = iterations * HILBERT_SHIFT;
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if (initial_shift < used_bits)
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{
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++iterations;
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}
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else
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{
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initial_shift -= HILBERT_SHIFT;
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}
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UInt8 state = iterations % 2 == 0 ? LEFT_STATE : DEFAULT_STATE;
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return {initial_shift, state};
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}
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constexpr static UInt8 STEP_MASK = (1 << bit_step) - 1;
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constexpr static UInt8 HILBERT_SHIFT = getHilbertShift(bit_step);
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constexpr static UInt8 HILBERT_MASK = (1 << HILBERT_SHIFT) - 1;
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constexpr static UInt8 STATE_MASK = 0b11 << HILBERT_SHIFT;
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constexpr static UInt8 Y_MASK = STEP_MASK;
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constexpr static UInt8 X_MASK = STEP_MASK << bit_step;
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constexpr static UInt8 LEFT_STATE = 0b01 << HILBERT_SHIFT;
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constexpr static UInt8 DEFAULT_STATE = bit_step % 2 == 0 ? LEFT_STATE : 0;
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};
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class FunctionHilbertDecode : public FunctionSpaceFillingCurveDecode<2, 0, 32>
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{
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public:
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static constexpr auto name = "hilbertDecode";
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static FunctionPtr create(ContextPtr)
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{
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return std::make_shared<FunctionHilbertDecode>();
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}
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String getName() const override { return name; }
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ColumnPtr executeImpl(const ColumnsWithTypeAndName & arguments, const DataTypePtr &, size_t input_rows_count) const override
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{
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size_t num_dimensions;
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const auto * col_const = typeid_cast<const ColumnConst *>(arguments[0].column.get());
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const auto * mask = typeid_cast<const ColumnTuple *>(col_const->getDataColumnPtr().get());
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if (mask)
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num_dimensions = mask->tupleSize();
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else
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num_dimensions = col_const->getUInt(0);
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auto non_const_arguments = arguments;
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non_const_arguments[1].column = non_const_arguments[1].column->convertToFullColumnIfConst();
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const ColumnPtr & col_code = non_const_arguments[1].column;
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Columns tuple_columns(num_dimensions);
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const auto shrink = [mask](const UInt64 value, const UInt8 column_id)
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{
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if (mask)
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return value >> mask->getColumn(column_id).getUInt(0);
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return value;
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};
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auto col0 = ColumnUInt64::create();
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auto & vec0 = col0->getData();
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vec0.resize(input_rows_count);
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if (num_dimensions == 1)
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{
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for (size_t i = 0; i < input_rows_count; i++)
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{
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vec0[i] = shrink(col_code->getUInt(i), 0);
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}
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tuple_columns[0] = std::move(col0);
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return ColumnTuple::create(tuple_columns);
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}
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auto col1 = ColumnUInt64::create();
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auto & vec1 = col1->getData();
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vec1.resize(input_rows_count);
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if (num_dimensions == 2)
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{
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for (size_t i = 0; i < input_rows_count; i++)
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{
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const auto res = FunctionHilbertDecode2DWIthLookupTableImpl<3>::decode(col_code->getUInt(i));
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vec0[i] = shrink(std::get<0>(res), 0);
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vec1[i] = shrink(std::get<1>(res), 1);
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}
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tuple_columns[0] = std::move(col0);
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tuple_columns[1] = std::move(col1);
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return ColumnTuple::create(tuple_columns);
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}
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return ColumnTuple::create(tuple_columns);
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}
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};
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REGISTER_FUNCTION(HilbertDecode)
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{
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factory.registerFunction<FunctionHilbertDecode>(FunctionDocumentation{
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.description=R"(
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Decodes Hilbert Curve code into the corresponding unsigned integer tuple
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Decodes a Hilbert curve index back into a tuple of unsigned integers, representing coordinates in multi-dimensional space.
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The function has two modes of operation:
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- Simple
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- Expanded
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Simple: accepts a resulting tuple size as a first argument and the code as a second argument.
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Simple Mode: Accepts the desired tuple size as the first argument (up to 2) and the Hilbert index as the second argument. This mode decodes the index into a tuple of the specified size.
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[example:simple]
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Will decode into: `(8, 0)`
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The resulting tuple size cannot be more than 2
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Expanded: accepts a range mask (tuple) as a first argument and the code as a second argument.
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Each number in mask configures the amount of bits that corresponding argument will be shifted right
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Expanded Mode: Takes a range mask (tuple) as the first argument and the Hilbert index as the second argument.
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Each number in the mask specifies the number of bits by which the corresponding decoded argument will be right-shifted, effectively scaling down the output values.
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[example:range_shrank]
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Note: see hilbertEncode() docs on why range change might be beneficial.
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Still limited to 2 numbers at most.
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@ -30,7 +240,7 @@ Hilbert code for one argument is always the argument itself (as a tuple).
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[example:identity]
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Produces: `(1)`
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You can shrink one argument too:
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A single argument with a tuple specifying bit shifts will be right-shifted accordingly.
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[example:identity_shrank]
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Produces: `(128)`
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@ -1,221 +0,0 @@
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#pragma once
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#include <Columns/ColumnConst.h>
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#include <Columns/ColumnTuple.h>
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#include <Columns/ColumnsNumber.h>
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#include <Common/BitHelpers.h>
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#include <Functions/FunctionSpaceFillingCurve.h>
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#include <Functions/IFunction.h>
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#include <Functions/PerformanceAdaptors.h>
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#include <limits>
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namespace DB
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{
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namespace HilbertDetails
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{
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template <UInt8 bit_step>
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class HilbertDecodeLookupTable
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{
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public:
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constexpr static UInt8 LOOKUP_TABLE[0] = {};
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};
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template <>
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class HilbertDecodeLookupTable<1>
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{
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public:
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constexpr static UInt8 LOOKUP_TABLE[16] = {
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4, 1, 3, 10,
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0, 6, 7, 13,
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15, 9, 8, 2,
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11, 14, 12, 5
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};
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};
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template <>
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class HilbertDecodeLookupTable<2>
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{
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public:
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constexpr static UInt8 LOOKUP_TABLE[64] = {
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0, 20, 21, 49, 18, 3, 7, 38,
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26, 11, 15, 46, 61, 41, 40, 12,
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16, 1, 5, 36, 8, 28, 29, 57,
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10, 30, 31, 59, 39, 54, 50, 19,
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47, 62, 58, 27, 55, 35, 34, 6,
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53, 33, 32, 4, 24, 9, 13, 44,
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63, 43, 42, 14, 45, 60, 56, 25,
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37, 52, 48, 17, 2, 22, 23, 51
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};
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};
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template <>
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class HilbertDecodeLookupTable<3>
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{
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public:
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constexpr static UInt8 LOOKUP_TABLE[256] = {
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64, 1, 9, 136, 16, 88, 89, 209, 18, 90, 91, 211, 139, 202, 194, 67,
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4, 76, 77, 197, 70, 7, 15, 142, 86, 23, 31, 158, 221, 149, 148, 28,
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36, 108, 109, 229, 102, 39, 47, 174, 118, 55, 63, 190, 253, 181, 180, 60,
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187, 250, 242, 115, 235, 163, 162, 42, 233, 161, 160, 40, 112, 49, 57, 184,
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0, 72, 73, 193, 66, 3, 11, 138, 82, 19, 27, 154, 217, 145, 144, 24,
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96, 33, 41, 168, 48, 120, 121, 241, 50, 122, 123, 243, 171, 234, 226, 99,
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100, 37, 45, 172, 52, 124, 125, 245, 54, 126, 127, 247, 175, 238, 230, 103,
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223, 151, 150, 30, 157, 220, 212, 85, 141, 204, 196, 69, 6, 78, 79, 199,
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255, 183, 182, 62, 189, 252, 244, 117, 173, 236, 228, 101, 38, 110, 111, 231,
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159, 222, 214, 87, 207, 135, 134, 14, 205, 133, 132, 12, 84, 21, 29, 156,
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155, 218, 210, 83, 203, 131, 130, 10, 201, 129, 128, 8, 80, 17, 25, 152,
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32, 104, 105, 225, 98, 35, 43, 170, 114, 51, 59, 186, 249, 177, 176, 56,
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191, 254, 246, 119, 239, 167, 166, 46, 237, 165, 164, 44, 116, 53, 61, 188,
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251, 179, 178, 58, 185, 248, 240, 113, 169, 232, 224, 97, 34, 106, 107, 227,
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219, 147, 146, 26, 153, 216, 208, 81, 137, 200, 192, 65, 2, 74, 75, 195,
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68, 5, 13, 140, 20, 92, 93, 213, 22, 94, 95, 215, 143, 206, 198, 71
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};
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};
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}
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template <UInt8 bit_step>
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class FunctionHilbertDecode2DWIthLookupTableImpl
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{
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static_assert(bit_step <= 3, "bit_step should not be more than 3 to fit in UInt8");
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public:
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static std::tuple<UInt64, UInt64> decode(UInt64 hilbert_code)
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{
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UInt64 x = 0;
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UInt64 y = 0;
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const auto leading_zeros_count = getLeadingZeroBits(hilbert_code);
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const auto used_bits = std::numeric_limits<UInt64>::digits - leading_zeros_count;
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auto [current_shift, state] = getInitialShiftAndState(used_bits);
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while (current_shift >= 0)
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{
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const UInt8 hilbert_bits = (hilbert_code >> current_shift) & HILBERT_MASK;
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const auto [x_bits, y_bits] = getCodeAndUpdateState(hilbert_bits, state);
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x |= (x_bits << (current_shift >> 1));
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y |= (y_bits << (current_shift >> 1));
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current_shift -= getHilbertShift(bit_step);
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}
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return {x, y};
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}
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private:
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// for bit_step = 3
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// LOOKUP_TABLE[SSHHHHHH] = SSXXXYYY
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// where SS - 2 bits for state, XXX - 3 bits of x, YYY - 3 bits of y
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// State is rotation of curve on every step, left/up/right/down - therefore 2 bits
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static std::pair<UInt64, UInt64> getCodeAndUpdateState(UInt8 hilbert_bits, UInt8& state)
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{
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const UInt8 table_index = state | hilbert_bits;
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const auto table_code = HilbertDetails::HilbertDecodeLookupTable<bit_step>::LOOKUP_TABLE[table_index];
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state = table_code & STATE_MASK;
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const UInt64 x_bits = (table_code & X_MASK) >> bit_step;
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const UInt64 y_bits = table_code & Y_MASK;
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return {x_bits, y_bits};
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}
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// hilbert code is double size of input values
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static constexpr UInt8 getHilbertShift(UInt8 shift)
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{
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return shift << 1;
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}
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static std::pair<Int8, UInt8> getInitialShiftAndState(UInt8 used_bits)
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{
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UInt8 iterations = used_bits / HILBERT_SHIFT;
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Int8 initial_shift = iterations * HILBERT_SHIFT;
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if (initial_shift < used_bits)
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{
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++iterations;
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}
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else
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{
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initial_shift -= HILBERT_SHIFT;
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}
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UInt8 state = iterations % 2 == 0 ? LEFT_STATE : DEFAULT_STATE;
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return {initial_shift, state};
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}
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constexpr static UInt8 STEP_MASK = (1 << bit_step) - 1;
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constexpr static UInt8 HILBERT_SHIFT = getHilbertShift(bit_step);
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constexpr static UInt8 HILBERT_MASK = (1 << HILBERT_SHIFT) - 1;
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constexpr static UInt8 STATE_MASK = 0b11 << HILBERT_SHIFT;
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constexpr static UInt8 Y_MASK = STEP_MASK;
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constexpr static UInt8 X_MASK = STEP_MASK << bit_step;
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constexpr static UInt8 LEFT_STATE = 0b01 << HILBERT_SHIFT;
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constexpr static UInt8 DEFAULT_STATE = bit_step % 2 == 0 ? LEFT_STATE : 0;
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};
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class FunctionHilbertDecode : public FunctionSpaceFillingCurveDecode<2, 0, 32>
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{
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public:
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static constexpr auto name = "hilbertDecode";
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static FunctionPtr create(ContextPtr)
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{
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return std::make_shared<FunctionHilbertDecode>();
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}
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String getName() const override { return name; }
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ColumnPtr executeImpl(const ColumnsWithTypeAndName & arguments, const DataTypePtr &, size_t input_rows_count) const override
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{
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size_t nd;
|
||||
const auto * col_const = typeid_cast<const ColumnConst *>(arguments[0].column.get());
|
||||
const auto * mask = typeid_cast<const ColumnTuple *>(col_const->getDataColumnPtr().get());
|
||||
if (mask)
|
||||
nd = mask->tupleSize();
|
||||
else
|
||||
nd = col_const->getUInt(0);
|
||||
auto non_const_arguments = arguments;
|
||||
non_const_arguments[1].column = non_const_arguments[1].column->convertToFullColumnIfConst();
|
||||
const ColumnPtr & col_code = non_const_arguments[1].column;
|
||||
Columns tuple_columns(nd);
|
||||
|
||||
const auto shrink = [mask](const UInt64 value, const UInt8 column_id)
|
||||
{
|
||||
if (mask)
|
||||
return value >> mask->getColumn(column_id).getUInt(0);
|
||||
return value;
|
||||
};
|
||||
|
||||
auto col0 = ColumnUInt64::create();
|
||||
auto & vec0 = col0->getData();
|
||||
vec0.resize(input_rows_count);
|
||||
|
||||
if (nd == 1)
|
||||
{
|
||||
for (size_t i = 0; i < input_rows_count; i++)
|
||||
{
|
||||
vec0[i] = shrink(col_code->getUInt(i), 0);
|
||||
}
|
||||
tuple_columns[0] = std::move(col0);
|
||||
return ColumnTuple::create(tuple_columns);
|
||||
}
|
||||
|
||||
auto col1 = ColumnUInt64::create();
|
||||
auto & vec1 = col1->getData();
|
||||
vec1.resize(input_rows_count);
|
||||
|
||||
if (nd == 2)
|
||||
{
|
||||
for (size_t i = 0; i < input_rows_count; i++)
|
||||
{
|
||||
const auto res = FunctionHilbertDecode2DWIthLookupTableImpl<3>::decode(col_code->getUInt(i));
|
||||
vec0[i] = shrink(std::get<0>(res), 0);
|
||||
vec1[i] = shrink(std::get<1>(res), 1);
|
||||
}
|
||||
tuple_columns[0] = std::move(col0);
|
||||
tuple_columns[1] = std::move(col1);
|
||||
return ColumnTuple::create(tuple_columns);
|
||||
}
|
||||
|
||||
return ColumnTuple::create(tuple_columns);
|
||||
}
|
||||
};
|
||||
|
||||
}
|
||||
@ -1,15 +1,238 @@
|
||||
#include <Functions/hilbertEncode.h>
|
||||
#include <Common/BitHelpers.h>
|
||||
#include <Functions/FunctionSpaceFillingCurve.h>
|
||||
#include <Functions/PerformanceAdaptors.h>
|
||||
#include <limits>
|
||||
#include <optional>
|
||||
#include <Functions/FunctionFactory.h>
|
||||
|
||||
|
||||
namespace DB
|
||||
{
|
||||
|
||||
namespace ErrorCodes
|
||||
{
|
||||
extern const int ILLEGAL_TYPE_OF_ARGUMENT;
|
||||
extern const int ARGUMENT_OUT_OF_BOUND;
|
||||
}
|
||||
|
||||
namespace HilbertDetails
|
||||
{
|
||||
|
||||
template <UInt8 bit_step>
|
||||
class HilbertEncodeLookupTable
|
||||
{
|
||||
public:
|
||||
constexpr static UInt8 LOOKUP_TABLE[0] = {};
|
||||
};
|
||||
|
||||
template <>
|
||||
class HilbertEncodeLookupTable<1>
|
||||
{
|
||||
public:
|
||||
constexpr static UInt8 LOOKUP_TABLE[16] = {
|
||||
4, 1, 11, 2,
|
||||
0, 15, 5, 6,
|
||||
10, 9, 3, 12,
|
||||
14, 7, 13, 8
|
||||
};
|
||||
};
|
||||
|
||||
template <>
|
||||
class HilbertEncodeLookupTable<2>
|
||||
{
|
||||
public:
|
||||
constexpr static UInt8 LOOKUP_TABLE[64] = {
|
||||
0, 51, 20, 5, 17, 18, 39, 6,
|
||||
46, 45, 24, 9, 15, 60, 43, 10,
|
||||
16, 1, 62, 31, 35, 2, 61, 44,
|
||||
4, 55, 8, 59, 21, 22, 25, 26,
|
||||
42, 41, 38, 37, 11, 56, 7, 52,
|
||||
28, 13, 50, 19, 47, 14, 49, 32,
|
||||
58, 27, 12, 63, 57, 40, 29, 30,
|
||||
54, 23, 34, 33, 53, 36, 3, 48
|
||||
};
|
||||
};
|
||||
|
||||
|
||||
template <>
|
||||
class HilbertEncodeLookupTable<3>
|
||||
{
|
||||
public:
|
||||
constexpr static UInt8 LOOKUP_TABLE[256] = {
|
||||
64, 1, 206, 79, 16, 211, 84, 21, 131, 2, 205, 140, 81, 82, 151, 22, 4,
|
||||
199, 8, 203, 158, 157, 88, 25, 69, 70, 73, 74, 31, 220, 155, 26, 186,
|
||||
185, 182, 181, 32, 227, 100, 37, 59, 248, 55, 244, 97, 98, 167, 38, 124,
|
||||
61, 242, 115, 174, 173, 104, 41, 191, 62, 241, 176, 47, 236, 171, 42, 0,
|
||||
195, 68, 5, 250, 123, 60, 255, 65, 66, 135, 6, 249, 184, 125, 126, 142,
|
||||
141, 72, 9, 246, 119, 178, 177, 15, 204, 139, 10, 245, 180, 51, 240, 80,
|
||||
17, 222, 95, 96, 33, 238, 111, 147, 18, 221, 156, 163, 34, 237, 172, 20,
|
||||
215, 24, 219, 36, 231, 40, 235, 85, 86, 89, 90, 101, 102, 105, 106, 170,
|
||||
169, 166, 165, 154, 153, 150, 149, 43, 232, 39, 228, 27, 216, 23, 212, 108,
|
||||
45, 226, 99, 92, 29, 210, 83, 175, 46, 225, 160, 159, 30, 209, 144, 48,
|
||||
243, 116, 53, 202, 75, 12, 207, 113, 114, 183, 54, 201, 136, 77, 78, 190,
|
||||
189, 120, 57, 198, 71, 130, 129, 63, 252, 187, 58, 197, 132, 3, 192, 234,
|
||||
107, 44, 239, 112, 49, 254, 127, 233, 168, 109, 110, 179, 50, 253, 188, 230,
|
||||
103, 162, 161, 52, 247, 56, 251, 229, 164, 35, 224, 117, 118, 121, 122, 218,
|
||||
91, 28, 223, 138, 137, 134, 133, 217, 152, 93, 94, 11, 200, 7, 196, 214,
|
||||
87, 146, 145, 76, 13, 194, 67, 213, 148, 19, 208, 143, 14, 193, 128,
|
||||
};
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
|
||||
template <UInt8 bit_step>
|
||||
class FunctionHilbertEncode2DWIthLookupTableImpl
|
||||
{
|
||||
static_assert(bit_step <= 3, "bit_step should not be more than 3 to fit in UInt8");
|
||||
public:
|
||||
static UInt64 encode(UInt64 x, UInt64 y)
|
||||
{
|
||||
UInt64 hilbert_code = 0;
|
||||
const auto leading_zeros_count = getLeadingZeroBits(x | y);
|
||||
const auto used_bits = std::numeric_limits<UInt64>::digits - leading_zeros_count;
|
||||
|
||||
auto [current_shift, state] = getInitialShiftAndState(used_bits);
|
||||
while (current_shift >= 0)
|
||||
{
|
||||
const UInt8 x_bits = (x >> current_shift) & STEP_MASK;
|
||||
const UInt8 y_bits = (y >> current_shift) & STEP_MASK;
|
||||
const auto hilbert_bits = getCodeAndUpdateState(x_bits, y_bits, state);
|
||||
hilbert_code |= (hilbert_bits << getHilbertShift(current_shift));
|
||||
current_shift -= bit_step;
|
||||
}
|
||||
|
||||
return hilbert_code;
|
||||
}
|
||||
|
||||
private:
|
||||
// for bit_step = 3
|
||||
// LOOKUP_TABLE[SSXXXYYY] = SSHHHHHH
|
||||
// where SS - 2 bits for state, XXX - 3 bits of x, YYY - 3 bits of y
|
||||
// State is rotation of curve on every step, left/up/right/down - therefore 2 bits
|
||||
static UInt64 getCodeAndUpdateState(UInt8 x_bits, UInt8 y_bits, UInt8& state)
|
||||
{
|
||||
const UInt8 table_index = state | (x_bits << bit_step) | y_bits;
|
||||
const auto table_code = HilbertDetails::HilbertEncodeLookupTable<bit_step>::LOOKUP_TABLE[table_index];
|
||||
state = table_code & STATE_MASK;
|
||||
return table_code & HILBERT_MASK;
|
||||
}
|
||||
|
||||
// hilbert code is double size of input values
|
||||
static constexpr UInt8 getHilbertShift(UInt8 shift)
|
||||
{
|
||||
return shift << 1;
|
||||
}
|
||||
|
||||
static std::pair<Int8, UInt8> getInitialShiftAndState(UInt8 used_bits)
|
||||
{
|
||||
UInt8 iterations = used_bits / bit_step;
|
||||
Int8 initial_shift = iterations * bit_step;
|
||||
if (initial_shift < used_bits)
|
||||
{
|
||||
++iterations;
|
||||
}
|
||||
else
|
||||
{
|
||||
initial_shift -= bit_step;
|
||||
}
|
||||
UInt8 state = iterations % 2 == 0 ? LEFT_STATE : DEFAULT_STATE;
|
||||
return {initial_shift, state};
|
||||
}
|
||||
|
||||
constexpr static UInt8 STEP_MASK = (1 << bit_step) - 1;
|
||||
constexpr static UInt8 HILBERT_SHIFT = getHilbertShift(bit_step);
|
||||
constexpr static UInt8 HILBERT_MASK = (1 << HILBERT_SHIFT) - 1;
|
||||
constexpr static UInt8 STATE_MASK = 0b11 << HILBERT_SHIFT;
|
||||
constexpr static UInt8 LEFT_STATE = 0b01 << HILBERT_SHIFT;
|
||||
constexpr static UInt8 DEFAULT_STATE = bit_step % 2 == 0 ? LEFT_STATE : 0;
|
||||
};
|
||||
|
||||
|
||||
class FunctionHilbertEncode : public FunctionSpaceFillingCurveEncode
|
||||
{
|
||||
public:
|
||||
static constexpr auto name = "hilbertEncode";
|
||||
static FunctionPtr create(ContextPtr)
|
||||
{
|
||||
return std::make_shared<FunctionHilbertEncode>();
|
||||
}
|
||||
|
||||
String getName() const override { return name; }
|
||||
|
||||
ColumnPtr executeImpl(const ColumnsWithTypeAndName & arguments, const DataTypePtr &, size_t input_rows_count) const override
|
||||
{
|
||||
size_t num_dimensions = arguments.size();
|
||||
size_t vector_start_index = 0;
|
||||
const auto * const_col = typeid_cast<const ColumnConst *>(arguments[0].column.get());
|
||||
const ColumnTuple * mask;
|
||||
if (const_col)
|
||||
mask = typeid_cast<const ColumnTuple *>(const_col->getDataColumnPtr().get());
|
||||
else
|
||||
mask = typeid_cast<const ColumnTuple *>(arguments[0].column.get());
|
||||
if (mask)
|
||||
{
|
||||
num_dimensions = mask->tupleSize();
|
||||
vector_start_index = 1;
|
||||
for (size_t i = 0; i < num_dimensions; i++)
|
||||
{
|
||||
auto ratio = mask->getColumn(i).getUInt(0);
|
||||
if (ratio > 32)
|
||||
throw Exception(ErrorCodes::ARGUMENT_OUT_OF_BOUND,
|
||||
"Illegal argument {} of function {}, should be a number in range 0-32",
|
||||
arguments[0].column->getName(), getName());
|
||||
}
|
||||
}
|
||||
|
||||
auto non_const_arguments = arguments;
|
||||
for (auto & argument : non_const_arguments)
|
||||
argument.column = argument.column->convertToFullColumnIfConst();
|
||||
|
||||
auto col_res = ColumnUInt64::create();
|
||||
ColumnUInt64::Container & vec_res = col_res->getData();
|
||||
vec_res.resize(input_rows_count);
|
||||
|
||||
const auto expand = [mask](const UInt64 value, const UInt8 column_id)
|
||||
{
|
||||
if (mask)
|
||||
return value << mask->getColumn(column_id).getUInt(0);
|
||||
return value;
|
||||
};
|
||||
|
||||
const ColumnPtr & col0 = non_const_arguments[0 + vector_start_index].column;
|
||||
if (num_dimensions == 1)
|
||||
{
|
||||
for (size_t i = 0; i < input_rows_count; ++i)
|
||||
{
|
||||
vec_res[i] = expand(col0->getUInt(i), 0);
|
||||
}
|
||||
return col_res;
|
||||
}
|
||||
|
||||
const ColumnPtr & col1 = non_const_arguments[1 + vector_start_index].column;
|
||||
if (num_dimensions == 2)
|
||||
{
|
||||
for (size_t i = 0; i < input_rows_count; ++i)
|
||||
{
|
||||
vec_res[i] = FunctionHilbertEncode2DWIthLookupTableImpl<3>::encode(
|
||||
expand(col0->getUInt(i), 0),
|
||||
expand(col1->getUInt(i), 1));
|
||||
}
|
||||
return col_res;
|
||||
}
|
||||
|
||||
throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
|
||||
"Illegal number of UInt arguments of function {}: should be not more than 2 dimensions",
|
||||
getName());
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
REGISTER_FUNCTION(HilbertEncode)
|
||||
{
|
||||
factory.registerFunction<FunctionHilbertEncode>(FunctionDocumentation{
|
||||
.description=R"(
|
||||
Calculates a Hilbert curve index for a list of unsigned integers to map multidimensional data to a one-dimensional integer space.
|
||||
Calculates code for Hilbert Curve for a list of unsigned integers
|
||||
|
||||
The function has two modes of operation:
|
||||
- Simple
|
||||
@ -17,20 +240,22 @@ The function has two modes of operation:
|
||||
|
||||
Simple: accepts up to 2 unsigned integers as arguments and produces a UInt64 code.
|
||||
[example:simple]
|
||||
Produces: `31`
|
||||
|
||||
Expanded: accepts a range mask (tuple) as a first argument and up to 2 unsigned integers as other arguments.
|
||||
Each number in mask configures the amount of bits that corresponding argument will be shifted left
|
||||
Each number in the mask configures the number of bits by which the corresponding argument will be shifted left, effectively scaling the argument within its range.
|
||||
[example:range_expanded]
|
||||
Produces: `4031541586602`
|
||||
Note: tuple size must be equal to the number of the other arguments
|
||||
|
||||
Range expansion can be beneficial when you need a similar distribution for arguments with wildly different ranges (or cardinality)
|
||||
For example: 'IP Address' (0...FFFFFFFF) and 'Country code' (0...FF)
|
||||
|
||||
Hilbert encoding for one argument is always the argument itself.
|
||||
For a single argument without a tuple, the function returns the argument itself as the Hilbert index, since no dimensional mapping is needed.
|
||||
[example:identity]
|
||||
Produces: `1`
|
||||
|
||||
You can expand one argument too:
|
||||
If a single argument is provided with a tuple specifying bit shifts, the function shifts the argument left by the specified number of bits.
|
||||
[example:identity_expanded]
|
||||
Produces: `512`
|
||||
|
||||
@ -40,13 +265,13 @@ The function also accepts columns as arguments:
|
||||
But the range tuple must still be a constant:
|
||||
[example:from_table_range]
|
||||
|
||||
Please note that you can fit only so much bits of information into Morton code as UInt64 has.
|
||||
Please note that you can fit only so much bits of information into Hilbert code as UInt64 has.
|
||||
Two arguments will have a range of maximum 2^32 (64/2) each
|
||||
All overflow will be clamped to zero
|
||||
)",
|
||||
.examples{
|
||||
{"simple", "SELECT hilbertEncode(1, 2, 3)", ""},
|
||||
{"range_expanded", "SELECT hilbertEncode((1,6), 1024, 16)", ""},
|
||||
{"simple", "SELECT hilbertEncode(3, 4)", ""},
|
||||
{"range_expanded", "SELECT hilbertEncode((10,6), 1024, 16)", ""},
|
||||
{"identity", "SELECT hilbertEncode(1)", ""},
|
||||
{"identity_expanded", "SELECT hilbertEncode(tuple(2), 128)", ""},
|
||||
{"from_table", "SELECT hilbertEncode(n1, n2) FROM table", ""},
|
||||
|
||||
@ -1,234 +0,0 @@
|
||||
#pragma once
|
||||
#include <Columns/ColumnConst.h>
|
||||
#include <Columns/ColumnTuple.h>
|
||||
#include <Columns/ColumnsNumber.h>
|
||||
#include <Common/BitHelpers.h>
|
||||
#include <Functions/FunctionSpaceFillingCurve.h>
|
||||
#include <Functions/IFunction.h>
|
||||
#include <Functions/PerformanceAdaptors.h>
|
||||
#include <limits>
|
||||
#include <optional>
|
||||
|
||||
|
||||
namespace DB
|
||||
{
|
||||
|
||||
namespace ErrorCodes
|
||||
{
|
||||
extern const int ILLEGAL_TYPE_OF_ARGUMENT;
|
||||
extern const int ARGUMENT_OUT_OF_BOUND;
|
||||
}
|
||||
|
||||
namespace HilbertDetails
|
||||
{
|
||||
|
||||
template <UInt8 bit_step>
|
||||
class HilbertEncodeLookupTable
|
||||
{
|
||||
public:
|
||||
constexpr static UInt8 LOOKUP_TABLE[0] = {};
|
||||
};
|
||||
|
||||
template <>
|
||||
class HilbertEncodeLookupTable<1>
|
||||
{
|
||||
public:
|
||||
constexpr static UInt8 LOOKUP_TABLE[16] = {
|
||||
4, 1, 11, 2,
|
||||
0, 15, 5, 6,
|
||||
10, 9, 3, 12,
|
||||
14, 7, 13, 8
|
||||
};
|
||||
};
|
||||
|
||||
template <>
|
||||
class HilbertEncodeLookupTable<2>
|
||||
{
|
||||
public:
|
||||
constexpr static UInt8 LOOKUP_TABLE[64] = {
|
||||
0, 51, 20, 5, 17, 18, 39, 6,
|
||||
46, 45, 24, 9, 15, 60, 43, 10,
|
||||
16, 1, 62, 31, 35, 2, 61, 44,
|
||||
4, 55, 8, 59, 21, 22, 25, 26,
|
||||
42, 41, 38, 37, 11, 56, 7, 52,
|
||||
28, 13, 50, 19, 47, 14, 49, 32,
|
||||
58, 27, 12, 63, 57, 40, 29, 30,
|
||||
54, 23, 34, 33, 53, 36, 3, 48
|
||||
};
|
||||
};
|
||||
|
||||
|
||||
template <>
|
||||
class HilbertEncodeLookupTable<3>
|
||||
{
|
||||
public:
|
||||
constexpr static UInt8 LOOKUP_TABLE[256] = {
|
||||
64, 1, 206, 79, 16, 211, 84, 21, 131, 2, 205, 140, 81, 82, 151, 22, 4,
|
||||
199, 8, 203, 158, 157, 88, 25, 69, 70, 73, 74, 31, 220, 155, 26, 186,
|
||||
185, 182, 181, 32, 227, 100, 37, 59, 248, 55, 244, 97, 98, 167, 38, 124,
|
||||
61, 242, 115, 174, 173, 104, 41, 191, 62, 241, 176, 47, 236, 171, 42, 0,
|
||||
195, 68, 5, 250, 123, 60, 255, 65, 66, 135, 6, 249, 184, 125, 126, 142,
|
||||
141, 72, 9, 246, 119, 178, 177, 15, 204, 139, 10, 245, 180, 51, 240, 80,
|
||||
17, 222, 95, 96, 33, 238, 111, 147, 18, 221, 156, 163, 34, 237, 172, 20,
|
||||
215, 24, 219, 36, 231, 40, 235, 85, 86, 89, 90, 101, 102, 105, 106, 170,
|
||||
169, 166, 165, 154, 153, 150, 149, 43, 232, 39, 228, 27, 216, 23, 212, 108,
|
||||
45, 226, 99, 92, 29, 210, 83, 175, 46, 225, 160, 159, 30, 209, 144, 48,
|
||||
243, 116, 53, 202, 75, 12, 207, 113, 114, 183, 54, 201, 136, 77, 78, 190,
|
||||
189, 120, 57, 198, 71, 130, 129, 63, 252, 187, 58, 197, 132, 3, 192, 234,
|
||||
107, 44, 239, 112, 49, 254, 127, 233, 168, 109, 110, 179, 50, 253, 188, 230,
|
||||
103, 162, 161, 52, 247, 56, 251, 229, 164, 35, 224, 117, 118, 121, 122, 218,
|
||||
91, 28, 223, 138, 137, 134, 133, 217, 152, 93, 94, 11, 200, 7, 196, 214,
|
||||
87, 146, 145, 76, 13, 194, 67, 213, 148, 19, 208, 143, 14, 193, 128,
|
||||
};
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
|
||||
template <UInt8 bit_step>
|
||||
class FunctionHilbertEncode2DWIthLookupTableImpl
|
||||
{
|
||||
static_assert(bit_step <= 3, "bit_step should not be more than 3 to fit in UInt8");
|
||||
public:
|
||||
static UInt64 encode(UInt64 x, UInt64 y)
|
||||
{
|
||||
UInt64 hilbert_code = 0;
|
||||
const auto leading_zeros_count = getLeadingZeroBits(x | y);
|
||||
const auto used_bits = std::numeric_limits<UInt64>::digits - leading_zeros_count;
|
||||
|
||||
auto [current_shift, state] = getInitialShiftAndState(used_bits);
|
||||
while (current_shift >= 0)
|
||||
{
|
||||
const UInt8 x_bits = (x >> current_shift) & STEP_MASK;
|
||||
const UInt8 y_bits = (y >> current_shift) & STEP_MASK;
|
||||
const auto hilbert_bits = getCodeAndUpdateState(x_bits, y_bits, state);
|
||||
hilbert_code |= (hilbert_bits << getHilbertShift(current_shift));
|
||||
current_shift -= bit_step;
|
||||
}
|
||||
|
||||
return hilbert_code;
|
||||
}
|
||||
|
||||
private:
|
||||
// for bit_step = 3
|
||||
// LOOKUP_TABLE[SSXXXYYY] = SSHHHHHH
|
||||
// where SS - 2 bits for state, XXX - 3 bits of x, YYY - 3 bits of y
|
||||
// State is rotation of curve on every step, left/up/right/down - therefore 2 bits
|
||||
static UInt64 getCodeAndUpdateState(UInt8 x_bits, UInt8 y_bits, UInt8& state)
|
||||
{
|
||||
const UInt8 table_index = state | (x_bits << bit_step) | y_bits;
|
||||
const auto table_code = HilbertDetails::HilbertEncodeLookupTable<bit_step>::LOOKUP_TABLE[table_index];
|
||||
state = table_code & STATE_MASK;
|
||||
return table_code & HILBERT_MASK;
|
||||
}
|
||||
|
||||
// hilbert code is double size of input values
|
||||
static constexpr UInt8 getHilbertShift(UInt8 shift)
|
||||
{
|
||||
return shift << 1;
|
||||
}
|
||||
|
||||
static std::pair<Int8, UInt8> getInitialShiftAndState(UInt8 used_bits)
|
||||
{
|
||||
UInt8 iterations = used_bits / bit_step;
|
||||
Int8 initial_shift = iterations * bit_step;
|
||||
if (initial_shift < used_bits)
|
||||
{
|
||||
++iterations;
|
||||
}
|
||||
else
|
||||
{
|
||||
initial_shift -= bit_step;
|
||||
}
|
||||
UInt8 state = iterations % 2 == 0 ? LEFT_STATE : DEFAULT_STATE;
|
||||
return {initial_shift, state};
|
||||
}
|
||||
|
||||
constexpr static UInt8 STEP_MASK = (1 << bit_step) - 1;
|
||||
constexpr static UInt8 HILBERT_SHIFT = getHilbertShift(bit_step);
|
||||
constexpr static UInt8 HILBERT_MASK = (1 << HILBERT_SHIFT) - 1;
|
||||
constexpr static UInt8 STATE_MASK = 0b11 << HILBERT_SHIFT;
|
||||
constexpr static UInt8 LEFT_STATE = 0b01 << HILBERT_SHIFT;
|
||||
constexpr static UInt8 DEFAULT_STATE = bit_step % 2 == 0 ? LEFT_STATE : 0;
|
||||
};
|
||||
|
||||
|
||||
class FunctionHilbertEncode : public FunctionSpaceFillingCurveEncode
|
||||
{
|
||||
public:
|
||||
static constexpr auto name = "hilbertEncode";
|
||||
static FunctionPtr create(ContextPtr)
|
||||
{
|
||||
return std::make_shared<FunctionHilbertEncode>();
|
||||
}
|
||||
|
||||
String getName() const override { return name; }
|
||||
|
||||
ColumnPtr executeImpl(const ColumnsWithTypeAndName & arguments, const DataTypePtr &, size_t input_rows_count) const override
|
||||
{
|
||||
size_t num_dimensions = arguments.size();
|
||||
size_t vector_start_index = 0;
|
||||
const auto * const_col = typeid_cast<const ColumnConst *>(arguments[0].column.get());
|
||||
const ColumnTuple * mask;
|
||||
if (const_col)
|
||||
mask = typeid_cast<const ColumnTuple *>(const_col->getDataColumnPtr().get());
|
||||
else
|
||||
mask = typeid_cast<const ColumnTuple *>(arguments[0].column.get());
|
||||
if (mask)
|
||||
{
|
||||
num_dimensions = mask->tupleSize();
|
||||
vector_start_index = 1;
|
||||
for (size_t i = 0; i < num_dimensions; i++)
|
||||
{
|
||||
auto ratio = mask->getColumn(i).getUInt(0);
|
||||
if (ratio > 32)
|
||||
throw Exception(ErrorCodes::ARGUMENT_OUT_OF_BOUND,
|
||||
"Illegal argument {} of function {}, should be a number in range 0-32",
|
||||
arguments[0].column->getName(), getName());
|
||||
}
|
||||
}
|
||||
|
||||
auto non_const_arguments = arguments;
|
||||
for (auto & argument : non_const_arguments)
|
||||
argument.column = argument.column->convertToFullColumnIfConst();
|
||||
|
||||
auto col_res = ColumnUInt64::create();
|
||||
ColumnUInt64::Container & vec_res = col_res->getData();
|
||||
vec_res.resize(input_rows_count);
|
||||
|
||||
const auto expand = [mask](const UInt64 value, const UInt8 column_id)
|
||||
{
|
||||
if (mask)
|
||||
return value << mask->getColumn(column_id).getUInt(0);
|
||||
return value;
|
||||
};
|
||||
|
||||
const ColumnPtr & col0 = non_const_arguments[0 + vector_start_index].column;
|
||||
if (num_dimensions == 1)
|
||||
{
|
||||
for (size_t i = 0; i < input_rows_count; ++i)
|
||||
{
|
||||
vec_res[i] = expand(col0->getUInt(i), 0);
|
||||
}
|
||||
return col_res;
|
||||
}
|
||||
|
||||
const ColumnPtr & col1 = non_const_arguments[1 + vector_start_index].column;
|
||||
if (num_dimensions == 2)
|
||||
{
|
||||
for (size_t i = 0; i < input_rows_count; ++i)
|
||||
{
|
||||
vec_res[i] = FunctionHilbertEncode2DWIthLookupTableImpl<3>::encode(
|
||||
expand(col0->getUInt(i), 0),
|
||||
expand(col1->getUInt(i), 1));
|
||||
}
|
||||
return col_res;
|
||||
}
|
||||
|
||||
throw Exception(ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
|
||||
"Illegal number of UInt arguments of function {}: should be not more than 2 dimensions",
|
||||
getName());
|
||||
}
|
||||
};
|
||||
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user