411 lines
9.4 KiB
Lua
411 lines
9.4 KiB
Lua
local Numeric = {}
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local BIT_SET_31 = 0x80000000
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local BIT_SET_32 = 0x100000000
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local K_ZERO, K_ONE, K_BIT_SET_26
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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_replace = bit32.replace
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local math_ceil = math.ceil
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local math_floor = math.floor
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local math_log = math.log
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local math_max = math.max
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local math_pow = math.pow
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local table_freeze = table.freeze
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local from_u32, into_u32, from_u64, into_u64
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local num_add, num_subtract, num_multiply, num_divide_unsigned, num_negate
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local num_is_negative, num_is_zero, num_is_equal, num_is_less_unsigned, num_is_greater_unsigned
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-- TODO: Eventually support Vector3
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function Numeric.from_u32(data_1, data_2)
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return table_freeze({ data_1, data_2 })
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end
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function Numeric.into_u32(data)
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return data[1], data[2]
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end
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function Numeric.from_u64(value)
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return from_u32(bit_and(value), math_floor(value / BIT_SET_32))
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end
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function Numeric.into_u64(value)
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local data_1, data_2 = into_u32(value)
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return data_1 + data_2 * BIT_SET_32
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end
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function Numeric.add(lhs, rhs)
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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local data_1 = data_l_1 + data_r_1
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local data_2 = data_l_2 + data_r_2
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if data_1 >= BIT_SET_32 then
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data_1 = data_1 - BIT_SET_32
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data_2 = data_2 + 1
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end
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if data_2 >= BIT_SET_32 then
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data_2 = data_2 - BIT_SET_32
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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 data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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local data_1 = data_l_1 - data_r_1
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local data_2 = data_l_2 - data_r_2
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if data_1 < 0 then
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data_1 = data_1 + BIT_SET_32
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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 + BIT_SET_32
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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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local function set_absolute(lhs, rhs)
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local has_negative = false
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if num_is_negative(lhs) then
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lhs = num_negate(lhs)
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has_negative = not has_negative
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end
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if num_is_negative(rhs) then
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rhs = num_negate(rhs)
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has_negative = not has_negative
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end
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return has_negative, lhs, rhs
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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 K_ZERO
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end
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local has_negative
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has_negative, lhs, rhs = set_absolute(lhs, rhs)
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-- If both longs are small, use float multiplication
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if num_is_less_unsigned(lhs, K_BIT_SET_26) and num_is_less_unsigned(rhs, K_BIT_SET_26) then
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local data_l_1, _ = into_u32(lhs)
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local data_r_1, _ = into_u32(rhs)
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local result = from_u64(data_l_1 * data_r_1)
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if has_negative then
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result = num_negate(result)
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end
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return result
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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 data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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local a48 = bit_rshift(data_l_2, 16)
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local a32 = bit_and(data_l_2, 0xFFFF)
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local a16 = bit_rshift(data_l_1, 16)
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local a00 = bit_and(data_l_1, 0xFFFF)
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local b48 = bit_rshift(data_r_2, 16)
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local b32 = bit_and(data_r_2, 0xFFFF)
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local b16 = bit_rshift(data_r_1, 16)
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local b00 = bit_and(data_r_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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local result = from_u32(data_1, data_2)
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if has_negative then
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result = num_negate(result)
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end
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return result
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end
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local function get_approx_delta(rem, rhs)
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local approx = math_max(1, math_floor(rem / rhs))
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local log = math_ceil(math_log(approx, 2))
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local delta = log <= 48 and 1 or math_pow(2, log - 48)
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return approx, delta
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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 0
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end
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local rhs_number = into_u64(rhs)
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local rem = lhs
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local res = K_ZERO
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while num_is_greater_unsigned(rem, rhs) or num_is_equal(rem, rhs) do
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local res_approx, delta = get_approx_delta(into_u64(rem), rhs_number)
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local res_temp = from_u64(res_approx)
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local rem_temp = num_multiply(res_temp, rhs)
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while num_is_negative(rem_temp) or num_is_greater_unsigned(rem_temp, rem) do
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res_approx = res_approx - delta
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res_temp = from_u64(res_approx)
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rem_temp = num_multiply(res_temp, rhs)
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end
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if num_is_zero(res_temp) then
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res_temp = K_ONE
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end
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res = num_add(res, res_temp)
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rem = num_subtract(rem, rem_temp)
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end
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return res
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end
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function Numeric.divide_signed(lhs, rhs)
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local has_negative
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has_negative, lhs, rhs = set_absolute(lhs, rhs)
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local result = num_divide_unsigned(lhs, rhs)
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if has_negative then
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result = num_negate(result)
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end
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return result
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end
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function Numeric.negate(value)
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return num_add(bit_not(value), K_ONE)
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end
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function Numeric.bit_and(lhs, rhs)
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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return from_u32(bit_and(data_l_1, data_r_1), bit_and(data_l_2, data_r_2))
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end
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function Numeric.bit_not(value)
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local data_1, data_2 = into_u32(value)
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return from_u32(bit_not(data_1), bit_not(data_2))
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end
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function Numeric.bit_or(lhs, rhs)
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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return from_u32(bit_or(data_l_1, data_r_1), bit_or(data_l_2, data_r_2))
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end
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function Numeric.bit_xor(lhs, rhs)
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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return from_u32(bit_xor(data_l_1, data_r_1), bit_xor(data_l_2, data_r_2))
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end
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function Numeric.shift_left(lhs, rhs)
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local count = into_u64(rhs)
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if count < 32 then
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local pad = 32 - count
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_1 = bit_lshift(data_l_1, count)
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local data_2 = bit_replace(bit_rshift(data_l_1, pad), data_l_2, count, pad)
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return from_u32(data_1, data_2)
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elseif count == 32 then
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local data_l_1, _ = into_u32(lhs)
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return from_u32(0, data_l_1)
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else
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local data_l_1, _ = into_u32(lhs)
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return from_u32(0, bit_lshift(data_l_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 = into_u64(rhs)
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if count < 32 then
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_1 = bit_replace(bit_rshift(data_l_1, count), data_l_2, 32 - count, count)
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local data_2 = bit_rshift(data_l_2, count)
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return from_u32(data_1, data_2)
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elseif count == 32 then
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local _, data_l_2 = into_u32(lhs)
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return from_u32(data_l_2, 0)
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else
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local _, data_l_2 = into_u32(lhs)
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return from_u32(bit_rshift(data_l_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 = into_u64(rhs)
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if count < 32 then
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_1 = bit_replace(bit_rshift(data_l_1, count), data_l_2, 32 - count, count)
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local data_2 = bit_arshift(data_l_2, count)
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return from_u32(data_1, data_2)
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else
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local _, data_l_2 = into_u32(lhs)
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local data_1 = bit_arshift(data_l_2, count - 32)
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local data_2 = data_l_2 > BIT_SET_31 and BIT_SET_32 - 1 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.is_negative(value)
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local _, data_2 = into_u32(value)
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return data_2 > BIT_SET_31
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end
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function Numeric.is_zero(value)
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local data_1, data_2 = into_u32(value)
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return data_1 == 0 and data_2 == 0
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end
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function Numeric.is_equal(lhs, rhs)
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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return data_l_1 == data_r_1 and data_l_2 == data_r_2
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end
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function Numeric.is_less_unsigned(lhs, rhs)
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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return data_l_2 < data_r_2 or (data_l_2 == data_r_2 and data_l_1 < data_r_1)
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end
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function Numeric.is_greater_unsigned(lhs, rhs)
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local data_l_1, data_l_2 = into_u32(lhs)
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local data_r_1, data_r_2 = into_u32(rhs)
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return data_l_2 > data_r_2 or (data_l_2 == data_r_2 and data_l_1 > data_r_1)
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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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into_u32 = Numeric.into_u32
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from_u64 = Numeric.from_u64
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into_u64 = Numeric.into_u64
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num_add = Numeric.add
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num_subtract = Numeric.subtract
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num_multiply = Numeric.multiply
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num_divide_unsigned = Numeric.divide_unsigned
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num_negate = Numeric.negate
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num_is_negative = Numeric.is_negative
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num_is_zero = Numeric.is_zero
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num_is_equal = Numeric.is_equal
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num_is_less_unsigned = Numeric.is_less_unsigned
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num_is_greater_unsigned = Numeric.is_greater_unsigned
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K_ZERO = from_u64(0)
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K_ONE = from_u64(1)
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K_BIT_SET_26 = from_u64(0x4000000)
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Numeric.K_ZERO = K_ZERO
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Numeric.K_ONE = K_ONE
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return table_freeze(Numeric)
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