How to get value, which will follow formula y = (x-1) % 16 + 1, but also for negative numbers?

Hello, guys. Iā€™m making mining game. For it I wanted to use chunk system, with chunk size = 16.
Chunk have blocks, starting from 1 and ending with 16th.
To get block chunk position, I used formula:

math.floor((Position - 1) / 16) + 1
--------------correct--------------
math.floor((24 - 1) / 16) + 1 = 2
math.floor((0 - 1) / 16) + 1 = 0
math.floor((-16 - 1) / 16) + 1 = -2

To get block position in chunk I used formula:

(Position - 1) % 16 + 1
--------------correct--------------
(15 - 1) % 16 + 1 = 15
(24 - 1) % 16 + 1 = 8
-------------incorrect-------------
(-20 - 1) % 16 + 1 = -4 -- need result 12

Can someone help me with making furmula, which will also work with negative numbers, because IDK what I need to do to work it with negative numbers with hard-coded if-else statements?

Block position but from what? Like, a position of a rayhit from some other module?

No. My system uses integer values, to determine XYZ position of block, like 92, 14, -12
Also, blocks are placed inside chunks, which are 16x16x16 blocks. First chunk have block from 1-16. Second one - 17-32. third - 33-48. Zero chunk have -15 to 0, Minus first chunk have -31 to -16 blocks.

That block positions are only code accessible, so I need to get specific block data:

Blockgrid[ChunkX][ChunkY][ChunkZ][BlockX][BlockY][BlockZ] = Block data

local function getBlockPosition(x)
	local bp
	if x >= 0 then
		bp = (x-1) % 16 + 1
	else
		bp = (math.fmod(x-1, 16) + 16) % 16 + 1
	end
	return bp
end

print(getBlockPosition(15)) -- 15
print(getBlockPosition(24)) -- 8
print(getBlockPosition(-20)) -- 12

The original formula is already correct and will result in 12.
Roblox_PositiveRemainder

To explain, what you need to do is get the positive remainder when the Position value is divided by 16.

One thing about negative remainders inferred from the Lua 5.1 Reference Manual and the Roblox documentation:

  • For ā€œa % bā€, the remainder will be negative when b is negative.
  • For ā€œmath.fmod(x, y)ā€, the remainder will be negative when x is negative.

In your example, you are using ā€œa % bā€ where b is 16, so it will always return a positive remainder.

-- a % b is negative only when b is negative
(Position - 1) % 16 + 1

In the case where you are using ā€œmath.fmod(x, y)ā€, it is better to define a function that adds absolute value of y to the remainder when it is negative.

function positiveMod(x, y)
	local remainder = math.fmod(x, y)
	if remainder < 0 then
		remainder += math.abs(y)
	end
	return remainder
end
-- the formula will then be
positiveMod(Position - 1, 16) + 1
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