modlib/binary.lua

237 lines
6.2 KiB
Lua
Raw Permalink Normal View History

-- Localize globals
2021-07-07 12:52:37 +02:00
local assert, math_huge, math_frexp, math_floor
= assert, math.huge, math.frexp, math.floor
2021-08-09 13:58:10 +02:00
local positive_nan, negative_nan = modlib.math.positive_nan, modlib.math.negative_nan
2021-06-17 19:45:08 +02:00
-- 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)
2021-03-27 20:10:49 +01:00
-- First read the mantissa
local mantissa = read_byte() / 0x100
mantissa = (mantissa + read_byte()) / 0x100
2021-03-27 20:10:49 +01:00
-- 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()
2021-03-27 20:10:49 +01:00
local sign = 1
if sign_byte >= 0x80 then
2021-03-27 20:10:49 +01:00
sign = -1
sign_byte = sign_byte - 0x80
2021-03-27 20:10:49 +01:00
end
local exponent = sign_byte * 2
if exponent_byte >= 0x80 then
2021-03-27 20:10:49 +01:00
exponent = exponent + 1
exponent_byte = exponent_byte - 0x80
2021-03-27 20:10:49 +01:00
end
mantissa = (mantissa + exponent_byte) / 0x80
2021-03-27 20:10:49 +01:00
if exponent == 0xFF then
if mantissa == 0 then
2021-07-07 12:52:37 +02:00
return sign * math_huge
2021-03-27 20:10:49 +01:00
end
-- Differentiating quiet and signalling nan is not possible in Lua, hence we don't have to do it
2021-08-09 13:58:10 +02:00
return sign == 1 and positive_nan or negative_nan
2021-03-27 20:10:49 +01:00
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
2022-07-03 13:28:34 +02:00
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)
2021-03-27 20:10:49 +01:00
local factor = 1
local uint = 0
for _ = 1, bytes do
uint = uint + read_byte() * factor
factor = factor * 0x100
end
return uint
end
2021-10-10 18:14:35 +02:00
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)
2021-03-27 20:10:49 +01:00
for _ = 1, bytes do
write_byte(uint % 0x100)
2021-07-07 12:52:37 +02:00
uint = math_floor(uint / 0x100)
2021-03-27 20:10:49 +01:00
end
assert(uint == 0)
end
2021-10-10 18:14:35 +02:00
function write_int(write_byte, int, bytes)
2022-06-08 09:48:10 +02:00
local max = 0x100 ^ bytes
2021-10-10 18:14:35 +02:00
if int < 0 then
2022-06-08 09:48:10 +02:00
assert(-int <= max / 2)
int = max + int
2021-10-10 18:14:35 +02:00
else
2022-06-08 09:48:10 +02:00
assert(int < max / 2)
2021-10-10 18:14:35 +02:00
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
2021-03-27 20:10:49 +01:00
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
2021-03-27 20:10:49 +01:00
mantissa = mantissa * 0x100
mantissa_byte_1 = math_floor(mantissa)
2021-03-27 20:10:49 +01:00
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
2021-03-27 20:10:49 +01:00
end
write_byte(mantissa_byte_2)
write_byte(mantissa_byte_1)
2021-03-27 20:10:49 +01:00
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)
2021-06-17 19:45:08 +02:00
end
-- Export environment
return _ENV