422 lines
9.5 KiB
Lua
422 lines
9.5 KiB
Lua
local Numeric = {}
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local NUM_ZERO = Vector3.zero
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local NUM_ONE, NUM_SIX_FOUR
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local NUM_BIT_26, NUM_BIT_52
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local bit_lshift = bit32.lshift
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local bit_rshift = bit32.rshift
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local bit_arshift = bit32.arshift
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local bit_and = bit32.band
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local bit_or = bit32.bor
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local bit_xor = bit32.bxor
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local bit_not = bit32.bnot
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local bit_extract = bit32.extract
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local bit_replace = bit32.replace
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local from_u32, from_u64, into_u64
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local num_subtract, num_divide_unsigned, num_negate
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local num_or, num_shift_left, num_shift_right_unsigned
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local num_is_less_unsigned
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-- X: a[0 ..21]
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-- Y: a[22..31]
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-- | b[0 ..11]
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-- Z: b[12..31]
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local constructor = Vector3.new
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function Numeric.from_u32(data_1, data_2)
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local x = bit_and(data_1, 0x3FFFFF)
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local y = bit_and(data_2, 0x3FFFFF)
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local z = bit_replace(bit_rshift(data_1, 22), bit_rshift(data_2, 22), 10, 10)
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return constructor(x, y, z)
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end
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local function num_is_zero(value)
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return value == NUM_ZERO
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end
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local function load_d1(value)
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return bit_replace(bit_and(value.X, 0x3FFFFF), value.Z, 22, 10)
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end
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local function load_d2(value)
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return bit_replace(bit_and(value.Y, 0x3FFFFF), bit_rshift(value.Z, 10), 22, 10)
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end
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local function into_u32(value)
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return load_d1(value), load_d2(value)
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end
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Numeric.into_u32 = into_u32
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function Numeric.from_u64(value)
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return from_u32(bit_and(value % 0x100000000), bit_and(value / 0x100000000))
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end
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function Numeric.into_u64(value)
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local value_1, value_2 = into_u32(value)
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return value_1 + value_2 * 0x100000000
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end
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function Numeric.add(lhs, rhs)
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local lhs_1, lhs_2 = into_u32(lhs)
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local rhs_1, rhs_2 = into_u32(rhs)
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local data_1 = lhs_1 + rhs_1
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local data_2 = lhs_2 + rhs_2
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if data_1 >= 0x100000000 then
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data_1 = data_1 - 0x100000000
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data_2 = data_2 + 1
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end
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if data_2 >= 0x100000000 then
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data_2 = data_2 - 0x100000000
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end
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return from_u32(data_1, data_2)
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end
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function Numeric.subtract(lhs, rhs)
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local lhs_1, lhs_2 = into_u32(lhs)
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local rhs_1, rhs_2 = into_u32(rhs)
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local data_1 = lhs_1 - rhs_1
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local data_2 = lhs_2 - rhs_2
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if data_1 < 0 then
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data_1 = data_1 + 0x100000000
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data_2 = data_2 - 1
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end
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if data_2 < 0 then
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data_2 = data_2 + 0x100000000
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end
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return from_u32(data_1, data_2)
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end
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function Numeric.multiply(lhs, rhs)
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if num_is_zero(lhs) or num_is_zero(rhs) then
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return NUM_ZERO
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elseif num_is_less_unsigned(lhs, NUM_BIT_26) and num_is_less_unsigned(rhs, NUM_BIT_26) then
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return from_u64(load_d1(lhs) * load_d1(rhs))
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end
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-- Divide each long into 4 chunks of 16 bits, and then add up 4x4 products.
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-- We can skip products that would overflow.
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local lhs_1, lhs_2 = into_u32(lhs)
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local rhs_1, rhs_2 = into_u32(rhs)
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local a48 = bit_rshift(lhs_2, 16)
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local a32 = bit_and(lhs_2, 0xFFFF)
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local a16 = bit_rshift(lhs_1, 16)
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local a00 = bit_and(lhs_1, 0xFFFF)
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local b48 = bit_rshift(rhs_2, 16)
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local b32 = bit_and(rhs_2, 0xFFFF)
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local b16 = bit_rshift(rhs_1, 16)
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local b00 = bit_and(rhs_1, 0xFFFF)
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local c00 = a00 * b00
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local c16 = bit_rshift(c00, 16)
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c00 = bit_and(c00, 0xFFFF)
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c16 = c16 + a16 * b00
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local c32 = bit_rshift(c16, 16)
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c16 = bit_and(c16, 0xFFFF)
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c16 = c16 + a00 * b16
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c32 = c32 + bit_rshift(c16, 16)
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c16 = bit_and(c16, 0xFFFF)
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c32 = c32 + a32 * b00
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local c48 = bit_rshift(c32, 16)
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c32 = bit_and(c32, 0xFFFF)
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c32 = c32 + a16 * b16
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c48 = c48 + bit_rshift(c32, 16)
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c32 = bit_and(c32, 0xFFFF)
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c32 = c32 + a00 * b32
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c48 = c48 + bit_rshift(c32, 16)
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c32 = bit_and(c32, 0xFFFF)
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c48 = c48 + a48 * b00 + a32 * b16 + a16 * b32 + a00 * b48
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c48 = bit_and(c48, 0xFFFF)
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local data_1 = bit_replace(c00, c16, 16, 16)
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local data_2 = bit_replace(c32, c48, 16, 16)
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return from_u32(data_1, data_2)
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end
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function Numeric.divide_unsigned(lhs, rhs)
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if num_is_zero(rhs) then
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error("division by zero")
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elseif num_is_zero(lhs) then
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return NUM_ZERO, NUM_ZERO
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elseif num_is_less_unsigned(lhs, NUM_BIT_52) and num_is_less_unsigned(rhs, NUM_BIT_52) then
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local lhs_u = into_u64(lhs)
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local rhs_u = into_u64(rhs)
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return from_u64(lhs_u / rhs_u), from_u64(lhs_u % rhs_u)
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end
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local quotient = NUM_ZERO
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local remainder = NUM_ZERO
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local num_1, num_2 = into_u32(lhs)
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for i = 63, 0, -1 do
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local rem_1, rem_2 = into_u32(num_shift_left(remainder, NUM_ONE))
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if i > 31 then
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rem_1 = bit_or(rem_1, bit_extract(num_2, i - 32, 1))
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else
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rem_1 = bit_or(rem_1, bit_extract(num_1, i, 1))
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end
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remainder = from_u32(rem_1, rem_2)
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if not num_is_less_unsigned(remainder, rhs) then
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remainder = num_subtract(remainder, rhs)
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quotient = num_or(quotient, num_shift_left(NUM_ONE, from_u32(i, 0)))
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end
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end
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return quotient, remainder
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end
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local function num_is_negative(value)
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return value.Z >= 0x80000
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end
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function Numeric.divide_signed(lhs, rhs)
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local left_negative = num_is_negative(lhs)
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local right_negative = num_is_negative(rhs)
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if left_negative then
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lhs = num_negate(lhs)
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end
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if right_negative then
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rhs = num_negate(rhs)
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end
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local quotient, remainder = num_divide_unsigned(lhs, rhs)
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if left_negative ~= right_negative then
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quotient = num_negate(quotient)
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end
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if left_negative then
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remainder = num_negate(remainder)
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end
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return quotient, remainder
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end
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function Numeric.negate(value)
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local value_1, value_2 = into_u32(value)
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local data_1 = bit_not(value_1) + 1
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local data_2 = bit_not(value_2)
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if data_1 >= 0x100000000 then
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data_1 = data_1 - 0x100000000
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data_2 = data_2 + 1
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end
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if data_2 >= 0x100000000 then
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data_2 = data_2 - 0x100000000
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end
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return from_u32(data_1, data_2)
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end
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function Numeric.bit_and(lhs, rhs)
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local x = bit_and(lhs.X, rhs.X)
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local y = bit_and(lhs.Y, rhs.Y)
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local z = bit_and(lhs.Z, rhs.Z)
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return constructor(x, y, z)
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end
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function Numeric.bit_not(value)
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local x = bit_and(bit_not(value.X), 0xFFFFFF)
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local y = bit_and(bit_not(value.Y), 0xFFFFFF)
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local z = bit_and(bit_not(value.Z), 0xFFFFFF)
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return constructor(x, y, z)
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end
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function Numeric.bit_or(lhs, rhs)
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local x = bit_or(lhs.X, rhs.X)
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local y = bit_or(lhs.Y, rhs.Y)
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local z = bit_or(lhs.Z, rhs.Z)
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return constructor(x, y, z)
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end
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function Numeric.bit_xor(lhs, rhs)
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local x = bit_xor(lhs.X, rhs.X)
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local y = bit_xor(lhs.Y, rhs.Y)
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local z = bit_xor(lhs.Z, rhs.Z)
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return constructor(x, y, z)
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end
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function Numeric.shift_left(lhs, rhs)
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local count = rhs.X % 64
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if count == 0 then
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return lhs
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elseif count < 32 then
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local pad = 32 - count
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local lhs_1, lhs_2 = into_u32(lhs)
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local data_1 = bit_lshift(lhs_1, count)
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local data_2 = bit_replace(bit_rshift(lhs_1, pad), lhs_2, count, pad)
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return from_u32(data_1, data_2)
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else
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local lhs_1 = load_d1(lhs)
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return from_u32(0, bit_lshift(lhs_1, count - 32))
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end
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end
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function Numeric.shift_right_unsigned(lhs, rhs)
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local count = rhs.X % 64
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if count == 0 then
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return lhs
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elseif count < 32 then
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local lhs_1, lhs_2 = into_u32(lhs)
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local data_1 = bit_replace(bit_rshift(lhs_1, count), lhs_2, 32 - count, count)
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local data_2 = bit_rshift(lhs_2, count)
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return from_u32(data_1, data_2)
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else
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local lhs_2 = load_d2(lhs)
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return from_u32(bit_rshift(lhs_2, count - 32), 0)
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end
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end
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function Numeric.shift_right_signed(lhs, rhs)
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local count = rhs.X % 64
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if count == 0 then
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return lhs
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elseif count < 32 then
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local lhs_1, lhs_2 = into_u32(lhs)
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local data_1 = bit_replace(bit_rshift(lhs_1, count), lhs_2, 32 - count, count)
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local data_2 = bit_arshift(lhs_2, count)
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return from_u32(data_1, data_2)
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else
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local lhs_2 = load_d2(lhs)
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local data_1 = bit_arshift(lhs_2, count - 32)
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local data_2 = lhs_2 >= 0x80000000 and 0xFFFFFFFF or 0
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return from_u32(data_1, data_2)
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end
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end
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function Numeric.rotate_left(lhs, rhs)
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if num_is_zero(rhs) then
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return lhs
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else
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local data_1 = num_shift_left(lhs, rhs)
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local data_2 = num_shift_right_unsigned(lhs, num_subtract(NUM_SIX_FOUR, rhs))
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return num_or(data_1, data_2)
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end
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end
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function Numeric.rotate_right(lhs, rhs)
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if num_is_zero(rhs) then
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return lhs
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else
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local data_1 = num_shift_right_unsigned(lhs, rhs)
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local data_2 = num_shift_left(lhs, num_subtract(NUM_SIX_FOUR, rhs))
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return num_or(data_1, data_2)
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end
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end
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function Numeric.is_equal(lhs, rhs)
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return lhs == rhs
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end
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function Numeric.is_less_unsigned(lhs, rhs)
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local data_l_2 = load_d2(lhs)
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local data_r_2 = load_d2(rhs)
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return data_l_2 < data_r_2 or (data_l_2 == data_r_2 and load_d1(lhs) < load_d1(rhs))
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end
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function Numeric.is_greater_unsigned(lhs, rhs)
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local data_l_2 = load_d2(lhs)
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local data_r_2 = load_d2(rhs)
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return data_l_2 > data_r_2 or (data_l_2 == data_r_2 and load_d1(lhs) > load_d1(rhs))
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end
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function Numeric.is_less_signed(lhs, rhs)
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local neg_a = num_is_negative(lhs)
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local neg_b = num_is_negative(rhs)
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if neg_a and not neg_b then
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return true
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elseif not neg_a and neg_b then
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return false
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else
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return num_is_negative(num_subtract(lhs, rhs))
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end
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end
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function Numeric.is_greater_signed(lhs, rhs)
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local neg_a = num_is_negative(lhs)
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local neg_b = num_is_negative(rhs)
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if neg_a and not neg_b then
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return false
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elseif not neg_a and neg_b then
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return true
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else
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return num_is_negative(num_subtract(rhs, lhs))
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end
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end
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from_u32 = Numeric.from_u32
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from_u64 = Numeric.from_u64
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into_u64 = Numeric.into_u64
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num_subtract = Numeric.subtract
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num_divide_unsigned = Numeric.divide_unsigned
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num_negate = Numeric.negate
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num_or = Numeric.bit_or
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num_shift_left = Numeric.shift_left
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num_shift_right_unsigned = Numeric.shift_right_unsigned
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Numeric.is_negative = num_is_negative
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Numeric.is_zero = num_is_zero
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num_is_less_unsigned = Numeric.is_less_unsigned
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NUM_ONE = from_u64(1)
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NUM_SIX_FOUR = from_u64(64)
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NUM_BIT_26 = from_u64(0x4000000)
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NUM_BIT_52 = from_u64(0x10000000000000)
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Numeric.ZERO = NUM_ZERO
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Numeric.ONE = NUM_ONE
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return table.freeze(Numeric)
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