local Numeric = {} Numeric.__index = Numeric local bit_band = bit32.band local bit_bnot = bit32.bnot local bit_bor = bit32.bor local bit_xor = bit32.bxor local bit_lshift = bit32.lshift local bit_rshift = bit32.rshift local bit_arshift = bit32.arshift local math_floor = math.floor local N_2_TO_31 = 0x80000000 local N_2_TO_32 = 0x100000000 local VAL_ZERO local VAL_ONE local VAL_2_TO_24 local op_is_equal local op_is_greater_unsigned local op_is_less_unsigned local op_is_negative local op_is_zero local op_bnot local op_negate -- TODO: Eventually support Vector3 local function from_u32(low, high) return setmetatable({ low, high }, Numeric) end local function to_u32(value) return value[1], value[2] end local function from_f64(value) if value < 0 then return op_negate(from_f64(-value)) else return from_u32(value % N_2_TO_32, math_floor(value / N_2_TO_32)) end end local function to_f64(value) local low, high = to_u32(value) return low + high * N_2_TO_32 end local function op_add(lhs, rhs) local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) local low = low_a + low_b local high = high_a + high_b if low >= N_2_TO_32 then low = low - N_2_TO_32 high = high + 1 end if high >= N_2_TO_32 then high = high - N_2_TO_32 end return from_u32(low, high) end local function op_subtract(lhs, rhs) local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) local low = low_a - low_b local high = high_a - high_b if low < 0 then low = low + N_2_TO_32 high = high - 1 end if high < 0 then high = high + N_2_TO_32 end return from_u32(low, high) end local function set_absolute(lhs, rhs) local has_negative = false if op_is_negative(lhs) then lhs = op_negate(lhs) has_negative = not has_negative end if op_is_negative(rhs) then rhs = op_negate(rhs) has_negative = not has_negative end return has_negative, lhs, rhs end local function op_multiply(lhs, rhs) if op_is_zero(lhs) or op_is_zero(rhs) then return VAL_ZERO end local has_negative has_negative, lhs, rhs = set_absolute(lhs, rhs) -- If both longs are small, use float multiplication if op_is_less_unsigned(lhs, VAL_2_TO_24) and op_is_less_unsigned(rhs, VAL_2_TO_24) then local low_a = to_u32(lhs) local low_b = to_u32(rhs) local result = from_f64(low_a * low_b) if has_negative then result = op_negate(result) end return result end -- Divide each long into 4 chunks of 16 bits, and then add up 4x4 products. -- We can skip products that would overflow. local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) local a48 = bit_rshift(high_a, 16) local a32 = bit_band(high_a, 0xFFFF) local a16 = bit_rshift(low_a, 16) local a00 = bit_band(low_a, 0xFFFF) local b48 = bit_rshift(high_b, 16) local b32 = bit_band(high_b, 0xFFFF) local b16 = bit_rshift(low_b, 16) local b00 = bit_band(low_b, 0xFFFF) local c48, c32, c16, c00 = 0, 0, 0, 0 c00 = c00 + a00 * b00 c16 = c16 + bit_rshift(c00, 16) c00 = bit_band(c00, 0xFFFF) c16 = c16 + a16 * b00 c32 = c32 + bit_rshift(c16, 16) c16 = bit_band(c16, 0xFFFF) c16 = c16 + a00 * b16 c32 = c32 + bit_rshift(c16, 16) c16 = bit_band(c16, 0xFFFF) c32 = c32 + a32 * b00 c48 = c48 + bit_rshift(c32, 16) c32 = bit_band(c32, 0xFFFF) c32 = c32 + a16 * b16 c48 = c48 + bit_rshift(c32, 16) c32 = bit_band(c32, 0xFFFF) c32 = c32 + a00 * b32 c48 = c48 + bit_rshift(c32, 16) c32 = bit_band(c32, 0xFFFF) c48 = c48 + a48 * b00 + a32 * b16 + a16 * b32 + a00 * b48 c48 = bit_band(c48, 0xFFFF) local low_v = bit_bor(bit_lshift(c16, 16), c00) local high_v = bit_bor(bit_lshift(c48, 16), c32) local result = from_u32(low_v, high_v) if has_negative then result = op_negate(result) end return result end local math_ceil = math.ceil local math_log = math.log local math_max = math.max local math_pow = math.pow local function get_approx_delta(rem, rhs) local approx = math_max(1, math_floor(rem / rhs)) local log = math_ceil(math_log(approx, 2)) local delta = log <= 48 and 1 or math_pow(2, log - 48) return approx, delta end local function op_divide_unsigned(lhs, rhs) if op_is_zero(rhs) then error("division by zero") elseif op_is_zero(lhs) then return 0 end local rhs_number = to_f64(rhs) local rem = lhs local res = VAL_ZERO while op_is_greater_unsigned(rem, rhs) or op_is_equal(rem, rhs) do local res_approx, delta = get_approx_delta(to_f64(rem), rhs_number) local res_temp = from_f64(res_approx) local rem_temp = op_multiply(res_temp, rhs) while op_is_negative(rem_temp) or op_is_greater_unsigned(rem_temp, rem) do res_approx = res_approx - delta res_temp = from_f64(res_approx) rem_temp = op_multiply(res_temp, rhs) end if op_is_zero(res_temp) then res_temp = VAL_ONE end res = op_add(res, res_temp) rem = op_subtract(rem, rem_temp) end return res end local function op_divide_signed(lhs, rhs) local has_negative has_negative, lhs, rhs = set_absolute(lhs, rhs) local result = op_divide_unsigned(lhs, rhs) if has_negative then result = op_negate(result) end return result end function op_negate(value) return op_add(op_bnot(value), VAL_ONE) end local function op_band(lhs, rhs) local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) return from_u32(bit_band(low_a, low_b), bit_band(high_a, high_b)) end function op_bnot(value) local low, high = to_u32(value) return from_u32(bit_bnot(low), bit_bnot(high)) end local function op_bor(lhs, rhs) local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) return from_u32(bit_bor(low_a, low_b), bit_bor(high_a, high_b)) end local function op_bxor(lhs, rhs) local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) return from_u32(bit_xor(low_a, low_b), bit_xor(high_a, high_b)) end local function op_shift_left(lhs, rhs) local count = to_f64(rhs) if count < 32 then local low_a, high_a = to_u32(lhs) local low_v = bit_lshift(low_a, count) local high_v = bit_bor(bit_lshift(high_a, count), bit_rshift(low_a, 32 - count)) return from_u32(low_v, high_v) else local _, high_a = to_u32(lhs) local high_v = bit_lshift(high_a, count - 32) return from_u32(0, high_v) end end local function op_shift_right_unsigned(lhs, rhs) local count = to_f64(rhs) if count < 32 then local low_a, high_a = to_u32(lhs) local low_v = bit_bor(bit_rshift(low_a, count), bit_lshift(high_a, 32 - count)) local high_v = bit_rshift(high_a, count) return from_u32(low_v, high_v) elseif numBits == 32 then local _, high_a = to_u32(lhs) return from_u32(high_a, 0) else local _, high_a = to_u32(lhs) return from_u32(bit_rshift(high_a, count - 32), 0) end end local function op_shift_right_signed(lhs, rhs) local count = to_f64(rhs) if count < 32 then local low_a, high_a = to_u32(lhs) local low_v = bit_bor(bit_rshift(low_a, count), bit_lshift(high_a, 32 - count)) local high_v = bit_arshift(high_a, count) return from_u32(low_v, high_v) else local low_a, high_a = to_u32(lhs) local low_v = bit_arshift(high_a, count - 32) local high_v = high_a > N_2_TO_31 and N_2_TO_32 - 1 or 0 return from_u32(low_v, high_v) end end function op_is_negative(value) local _, high = to_u32(value) return high > N_2_TO_31 end function op_is_zero(value) local low, high = to_u32(value) return low == 0 and high == 0 end function op_is_equal(lhs, rhs) local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) return low_a == low_b and high_a == high_b end function op_is_less_unsigned(lhs, rhs) local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) return high_a < high_b or (high_a == high_b and low_a < low_b) end function op_is_greater_unsigned(lhs, rhs) local low_a, high_a = to_u32(lhs) local low_b, high_b = to_u32(rhs) return high_a > high_b or (high_a == high_b and low_a > low_b) end local function op_is_less_signed(lhs, rhs) local neg_a = op_is_negative(lhs) local neg_b = op_is_negative(rhs) if neg_a and not neg_b then return true elseif not neg_a and neg_b then return false else return op_is_negative(op_subtract(lhs, rhs)) end end local function op_is_greater_signed(lhs, rhs) local neg_a = op_is_negative(lhs) local neg_b = op_is_negative(rhs) if neg_a and not neg_b then return false elseif not neg_a and neg_b then return true else return op_is_negative(op_subtract(rhs, lhs)) end end local function to_bytes_le(value) local low, high = to_u32(value) return { bit_band(low, 0xFF), bit_band(bit_rshift(low, 8), 0xFF), bit_band(bit_rshift(low, 16), 0xFF), bit_band(bit_rshift(low, 24), 0xFF), bit_band(high, 0xFF), bit_band(bit_rshift(high, 8), 0xFF), bit_band(bit_rshift(high, 16), 0xFF), bit_band(bit_rshift(high, 24), 0xFF), } end VAL_ZERO = from_f64(0) VAL_ONE = from_f64(1) VAL_2_TO_24 = from_f64(0x1000000) Numeric.from_f64 = from_f64 Numeric.from_u32 = from_u32 Numeric.__add = op_add Numeric.__sub = op_subtract Numeric.__mul = op_multiply Numeric.__div = op_divide_unsigned Numeric.__unm = op_negate Numeric.__eq = op_is_equal Numeric.__lt = op_is_less_unsigned function Numeric.__le(lhs, rhs) return op_is_less_unsigned(lhs, rhs) or op_is_equal(lhs, rhs) end function Numeric.__tostring(value) return tostring(to_f64(value)) end return Numeric