Fix binary.(read|write)_(float|single|double)

binary.lua

@@ -10,27 +10,26 @@ setfenv(1, _ENV)
 
 -- All little endian
 
---+ Reads doubles (f64) or floats (f32)
---: double reads an f64 if true, f32 otherwise
-function read_float(read_byte, double)
+--+ Reads an IEEE 754 single-precision floating point number (f32)
+function read_single(read_byte)
 	-- First read the mantissa
-	local mantissa = 0
-	for _ = 1, double and 6 or 2 do
+	local mantissa = read_byte() / 0x100
 	mantissa = (mantissa + read_byte()) / 0x100
-	end
+
 	-- Second and first byte in big endian: last bit of exponent + 7 bits of mantissa, sign bit + 7 bits of exponent
-	local byte_2, byte_1 = read_byte(), read_byte()
+	local exponent_byte = read_byte()
+	local sign_byte = read_byte()
 	local sign = 1
-	if byte_1 >= 0x80 then
+	if sign_byte >= 0x80 then
 		sign = -1
-		byte_1 = byte_1 - 0x80
+		sign_byte = sign_byte - 0x80
 	end
-	local exponent = byte_1 * 2
-	if byte_2 >= 0x80 then
+	local exponent = sign_byte * 2
+	if exponent_byte >= 0x80 then
 		exponent = exponent + 1
-		byte_2 = byte_2 - 0x80
+		exponent_byte = exponent_byte - 0x80
 	end
-	mantissa = (mantissa + byte_2) / 0x80
+	mantissa = (mantissa + exponent_byte) / 0x80
 	if exponent == 0xFF then
 		if mantissa == 0 then
 			return sign * math_huge
@@ -46,14 +45,44 @@ function read_float(read_byte, double)
 	return sign * 2 ^ (exponent - 127) * (1 + mantissa)
 end
 
---+ Reads a single floating point number (f32)
-function read_single(read_byte)
-	return read_float(read_byte)
+--+ 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 == 0x800 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 a double (f64)
-function read_double(read_byte)
-	return read_float(read_byte, true)
+--+ 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)
@@ -94,56 +123,113 @@ function write_int(write_byte, int, bytes)
 	return write_uint(write_byte, int, bytes)
 end
 
---: on_write function(double)
---: double set to true to force f64, false for f32, nil for auto
-function write_float(write_byte, number, on_write, double)
-	local sign = 0
+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 = 0x80
+		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)
-	exponent = exponent + 127
-	if number == 0 then exponent = 0 end -- zero must be written as a subnormal number
-	if exponent > 1 then
-		-- TODO ensure this deals properly with subnormal numbers
-		mantissa = mantissa * 2 - 1
-		exponent = exponent - 1
-	elseif exponent < 0 then -- number is currently sub-subnormal, subnormalize
-		mantissa = mantissa * 2^(exponent-1)
+		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 sign_byte = sign + math_floor(exponent / 2)
-	if double == nil then
-		double = mantissa % 2^-23 ~= 0
-	end
-	if on_write then
-		on_write(double)
-	end
+
+		local exp_lowest_bit = exponent % 2
+
+		sign_byte = sign_bit + (exponent - exp_lowest_bit) / 2
+
 		mantissa = mantissa * 0x80
-	local exponent_byte = (exponent % 2) * 0x80 + math_floor(mantissa)
+		exponent_byte = exp_lowest_bit * 0x80 + math_floor(mantissa)
 		mantissa = mantissa % 1
-	local mantissa_bytes = {}
-	local len = double and 6 or 2
-	for index = 1, len do
+
 		mantissa = mantissa * 0x100
-		mantissa_bytes[index] = math_floor(mantissa)
+		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 < 2^12) -- 11 exponent bits
+		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) -- no truncation allowed; round your numbers properly or use auto
-	for index = len, 1, -1 do
-		write_byte(mantissa_bytes[index])
+		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
 
-function write_single(write_byte, number)
-	return write_float(write_byte, number, nil, false)
-end
-
-function write_double(write_byte, number)
-	return write_float(write_byte, number, nil, true)
+--: 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