How to represent decimals in binary?

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#1

For my SimpleBit module, I have made an adder and multiplier that work 30x faster than arithmetic * and +. however, I have run into an issue, How do I represent digital numbers, and most importantly, how do I run that through the tonumber(_,2) to get my result?

What I was thinking was a 64 bit system,

00000000 00000000 00000000 00000000  00000000 00000000 00000000 00000000

I assume that I could run tonumber() on the last 4 bytes (that represent decimal) and then do:

local result = tonumber(''..tonumber(PosBits,2)..'.'..tonumber(NegBits,2),2)

But I am not sure if that would even work.
But what are your ideas? I am interested.

#2

You could use a double, they’re 64 bits: Double-precision floating-point format - Wikipedia

That’s actually what a lua number is stored as anyways. I’m assuming you’re doing this for fun though :slight_smile:

This would require a lot more work than just tonumber though!

#3

Decimal can be represented by the inverse of 2 to the power of whatever place you’re after.

1.5 would be 1.1b (1 * 2^0 + 1 * 2^-1 = 1 + 0.5)
5.25 would be 101.01b (1 * 2^2 + 1 * 2^0 + 1 * 2^-2 = 4 + 1 + 0.25)

You may allocate the last 4 bytes as you’ve mentioned to store strictly decimal values. However, keep in mind that IEEE 754 Floating Point is the standard format for storing decimal values now.

In terms of tonumber() and decimal places, it seems like there’s really no way to combine the two. Isolating the decimal portion then passing it through tonumber() won’t give you the right numbers. You’ll have to make your own converter or use another function/approach.

#4

I’d also suggest taking a look at the string.pack functions. They’re undocumented by roblox but they’re there: Lua 5.3 Reference Manual

They let you use the characters of a string as bytes:

local num = 123.45

-- convert it to a string
local asAString = string.pack("d", num) -- "d" means "as double"
print(string.len(asAString)) -- 8 (like 8 bytes)

-- convert back to a number
local asANumber = string.unpack("d", asAString)
print(asANumber) -- 123.45
#5

Well, it’s all useless if it’s in Unicode! This is how you’d do it if you wanted to convert it to a binary string

local floor,insert = math.floor, table.insert
function basen(n,b)
    n = floor(n)
    if not b or b == 10 then return tostring(n) end
    local digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
    local t = {}
    local sign = ""
    if n < 0 then
        sign = "-"
    n = -n
    end
    repeat
        local d = (n % b) + 1
        n = floor(n / b)
        insert(t, 1, digits:sub(d,d))
    until n == 0
    return sign .. table.concat(t,"")
end


local binaryStr = string.pack("d", 124.4)
local stringStream = ""
for i=1,#binaryStr do
  local c = string.byte(binaryStr:sub(i,i))
  local byte = basen(c,2)
  while (#byte ~= 8) do
    byte = "0"..byte
  end
  stringStream = byte..stringStream 
end
print(stringStream)
#6

image
This is how my Bit32 adder works. I am not sure if it is compatible with that.

#7

The list of bit32 operations for the adder is just this circuit broken down,
Which makes the adder extremely fast

image
image1324×522 47.4 KB

Incase you want to see that video for yourself, click here

#8

I think you are missing the purpose of using bitwise functions. They are meant to transform data into a number so that it can be used as an address for an instant lookup, unlike a dictionary creating this number is instant with bitwise functions unlike the costly string interning lookup operation for the key generation. Sure, it is faster to do integer math like this but if you want to get floats im pretty sure the fastest is already there