modlib/binary.lua

-- Localize globals
local assert, math_huge, math_frexp, math_floor
	= assert, math.huge, math.frexp, math.floor

local positive_nan, negative_nan = modlib.math.positive_nan, modlib.math.negative_nan

-- Set environment
local _ENV = {}
setfenv(1, _ENV)

-- All little endian

--+ Reads an IEEE 754 single-precision floating point number (f32)
function read_single(read_byte)
	-- First read the mantissa
	local mantissa = read_byte() / 0x100
	mantissa = (mantissa + read_byte()) / 0x100

	-- Second and first byte in big endian: last bit of exponent + 7 bits of mantissa, sign bit + 7 bits of exponent
	local exponent_byte = read_byte()
	local sign_byte = read_byte()
	local sign = 1
	if sign_byte >= 0x80 then
		sign = -1
		sign_byte = sign_byte - 0x80
	end
	local exponent = sign_byte * 2
	if exponent_byte >= 0x80 then
		exponent = exponent + 1
		exponent_byte = exponent_byte - 0x80
	end
	mantissa = (mantissa + exponent_byte) / 0x80
	if exponent == 0xFF then
		if mantissa == 0 then
			return sign * math_huge
		end
		-- Differentiating quiet and signalling nan is not possible in Lua, hence we don't have to do it
		return sign == 1 and positive_nan or negative_nan
	end
	assert(mantissa < 1)
	if exponent == 0 then
		-- subnormal value
		return sign * 2^-126 * mantissa
	end
	return sign * 2 ^ (exponent - 127) * (1 + mantissa)
end

--+ Reads an IEEE 754 double-precision floating point number (f64)
function read_double(read_byte)
	-- First read the mantissa
	local mantissa = 0
	for _ = 1, 6 do
		mantissa = (mantissa + read_byte()) / 0x100
	end
	-- Second and first byte in big endian: last 4 bits of exponent + 4 bits of mantissa; sign bit + 7 bits of exponent
	local exponent_byte = read_byte()
	local sign_byte = read_byte()
	local sign = 1
	if sign_byte >= 0x80 then
		sign = -1
		sign_byte = sign_byte - 0x80
	end
	local exponent = sign_byte * 0x10
	local mantissa_bits = exponent_byte % 0x10
	exponent = exponent + (exponent_byte - mantissa_bits) / 0x10
	mantissa = (mantissa + mantissa_bits) / 0x10
	if exponent == 0x7FF then
		if mantissa == 0 then
			return sign * math_huge
		end
		-- Differentiating quiet and signalling nan is not possible in Lua, hence we don't have to do it
		return sign == 1 and positive_nan or negative_nan
	end
	assert(mantissa < 1)
	if exponent == 0 then
		-- subnormal value
		return sign * 2^-1022 * mantissa
	end
	return sign * 2 ^ (exponent - 1023) * (1 + mantissa)
end

--+ Reads doubles (f64) or floats (f32)
--: double reads an f64 if true, f32 otherwise
function read_float(read_byte, double)
	return (double and read_double or read_single)(read_byte)
end

function read_uint(read_byte, bytes)
	local factor = 1
	local uint = 0
	for _ = 1, bytes do
		uint = uint + read_byte() * factor
		factor = factor * 0x100
	end
	return uint
end

function read_int(read_byte, bytes)
	local uint = read_uint(read_byte, bytes)
	local max = 0x100 ^ bytes
	if uint >= max / 2 then
		return uint - max
	end
	return uint
end

function write_uint(write_byte, uint, bytes)
	for _ = 1, bytes do
		write_byte(uint % 0x100)
		uint = math_floor(uint / 0x100)
	end
	assert(uint == 0)
end

function write_int(write_byte, int, bytes)
	local max = 0x100 ^ bytes
	if int < 0 then
		assert(-int <= max / 2)
		int = max + int
	else
		assert(int < max / 2)
	end
	return write_uint(write_byte, int, bytes)
end

function write_single(write_byte, number)
	if number ~= number then -- nan: all ones
		for _ = 1, 4 do write_byte(0xFF) end
		return
	end

	local sign_byte, exponent_byte, mantissa_byte_1, mantissa_byte_2

	local sign_bit = 0
	if number < 0 then
		number = -number
		sign_bit = 0x80
	end

	if number == math_huge then -- inf: exponent = all 1, mantissa = all 0
		sign_byte, exponent_byte, mantissa_byte_1, mantissa_byte_2 = sign_bit + 0x7F, 0x80, 0, 0
	else -- real number
		local mantissa, exponent = math_frexp(number)
		if exponent <= -126 or number == 0 then -- must write a subnormal number
			mantissa = mantissa * 2 ^ (exponent + 126)
			exponent = 0
		else -- normal numbers are stored as 1.<mantissa>
			mantissa = mantissa * 2 - 1
			exponent = exponent - 1 + 127 -- mantissa << 1 <=> exponent--
			assert(exponent < 0xFF)
		end

		local exp_lowest_bit = exponent % 2

		sign_byte = sign_bit + (exponent - exp_lowest_bit) / 2

		mantissa = mantissa * 0x80
		exponent_byte = exp_lowest_bit * 0x80 + math_floor(mantissa)
		mantissa = mantissa % 1

		mantissa = mantissa * 0x100
		mantissa_byte_1 = math_floor(mantissa)
		mantissa = mantissa % 1

		mantissa = mantissa * 0x100
		mantissa_byte_2 = math_floor(mantissa)
		mantissa = mantissa % 1

		assert(mantissa == 0) -- no truncation allowed: round numbers properly using modlib.math.fround
	end

	write_byte(mantissa_byte_2)
	write_byte(mantissa_byte_1)
	write_byte(exponent_byte)
	write_byte(sign_byte)
end

function write_double(write_byte, number)
	if number ~= number then -- nan: all ones
		for _ = 1, 8 do write_byte(0xFF) end
		return
	end

	local sign_byte, exponent_byte, mantissa_bytes

	local sign_bit = 0
	if number < 0 then
		number = -number
		sign_bit = 0x80
	end

	if number == math_huge then -- inf: exponent = all 1, mantissa = all 0
		sign_byte, exponent_byte, mantissa_bytes = sign_bit + 0x7F, 0xF0, {0, 0, 0, 0, 0, 0}
	else -- real number
		local mantissa, exponent = math_frexp(number)
		if exponent <= -1022 or number == 0 then -- must write a subnormal number
			mantissa = mantissa * 2 ^ (exponent + 1022)
			exponent = 0
		else -- normal numbers are stored as 1.<mantissa>
			mantissa = mantissa * 2 - 1
			exponent = exponent - 1 + 1023 -- mantissa << 1 <=> exponent--
			assert(exponent < 0x7FF)
		end

		local exp_low_nibble = exponent % 0x10

		sign_byte = sign_bit + (exponent - exp_low_nibble) / 0x10

		mantissa = mantissa * 0x10
		exponent_byte = exp_low_nibble * 0x10 + math_floor(mantissa)
		mantissa = mantissa % 1

		mantissa_bytes = {}
		for i = 1, 6 do
			mantissa = mantissa * 0x100
			mantissa_bytes[i] = math_floor(mantissa)
			mantissa = mantissa % 1
		end
		assert(mantissa == 0)
	end

	for i = 6, 1, -1 do
		write_byte(mantissa_bytes[i])
	end
	write_byte(exponent_byte)
	write_byte(sign_byte)
end

--: on_write function(double)
--: double true - f64, false - f32
function write_float(write_byte, number, double)
	(double and write_double or write_single)(write_byte, number)
end

-- Export environment
return _ENV