Add experimental i64

wasm/runtime/numeric.lua

@@ -0,0 +1,430 @@
+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