[Question] floor(mod(x,y))

[Sythalin]

Been searching around how to to covert copper to g/s/c readout. GetCoinText() is too bulky and I apparently still fail at using gsub correctly. I found this solution, but the silver calculation has me confused:

copper = 123456
gold = floor(copper/10000) -- makes sense
copper = floor(mod(copper, 100) -- makes sense
 
silver = floor(mod(copper/100, 100)) -- um, wut?

My working (and apparently incorrect) understanding:
s = floor(mod(x,y))
1) x = 123456/100 = 1234.56
2) x/y = 1234.56/ 100 = 12.3456
3) mod(12.3456) = 3456
4) floor(3456) = 3456

I'm not seeing how the answer "34" is obtained by this method, yet somehow works. Can anyone shine some light on this?

[Xubera]

Originally Posted by ChaosInc copper = 123456 gold = floor(copper/10000) -- makes sense copper = floor(mod(copper, 100) -- makes sense   silver = floor(mod(copper/100, 100)) -- um, wut? I'm not seeing how the answer "34" is obtained by this method, yet somehow works. Can anyone shine some light on this?

copper is 123456 so we know is 12g 34s 56c

mod(123456, 100) is 56, because if you divide 123456, you get 1234.56 the remainder is 56

now silver is 123456/100/100 so its 12.3456, and since the mod is 100 the remainder is 34.56, but its been floored to 34.

[Sythalin]

Originally Posted by Xubera copper is 123456 so we know is 12g 34s 56c mod(123456, 100) is 56, because if you divide 123456, you get 1234.56 the remainder is 56 now silver is 123456/100/100 so its 12.3456, and since the mod is 100 the remainder is 34.56, but its been floored to 34.

I'm even more confused than before. Obviously I know that 34 is supposed to be the silver amount. It's how it gets there that I'm confused by. The equation shows division by 100 twice (arg1 = 123456/100 and y = 100) yet your explanation throws in a third non-existent 100 (to my understanding at this point).

123456/100 => 1234.56
1234.56/100 => 12.3456
mod(12.3456) => 3456
??? => 34.56
floor(34.56) => 34

I'm not seeing how the decimal point seems to "magically" move over two spaces in order to floor it to 34.

[Vrul]

I think your issue is trying to separate mod(x, y) into two steps when it doesn't quite work that way. The function mod(x, y) is basically solving the equation x = floor(x / y) + (r / y) and returning the value r.

-- silver = floor(mod(copper/100, 100))
silver = copper / 100 -- 1234.56
silver = mod(silver, 100) -- 34.56
silver = floor(silver) -- 34

Or maybe this is easier to look at:
silver = floor(copper / 100 % 100)

And here is some code I've used for something similar:

local cuInd = [[|TInterface\MoneyFrame\UI-CopperIcon:0:1:2:0|t]]
local agInd = [[|TInterface\MoneyFrame\UI-SilverIcon:0:1:2:0|t ]]
local auInd = [[|TInterface\MoneyFrame\UI-GoldIcon:0:1:2:0|t ]]

local function MoneyToString(ammount)
	local cu = ammount % 100
	ammount = floor(ammount / 100)
	local ag, au = ammount % 100, floor(ammount / 100)
	if au > 0 then
		return au .. auInd .. ag .. agInd .. cu .. cuInd
	elseif ag > 0 then
		return ag .. agInd .. cu .. cuInd
	end
	return cu .. cuInd
end

[Xubera]

the function mod(x,y) will first divide x by y and then produce the remainder

so if

x = 123456
y = 100
print(mod(x,y)) --outputs 56 because x/y is 1234.56 and the remainder is 0.56.

or
x1 = 15
x2 = 16
y = 5
print(mod(x1,y)) --outputs 0 because x1/y is exactly 3, so the remainder is 0
print(mod(x2,y)) --outputs 1 because x2/y is 3 and 1/5th, so the remainder is 1

in the above floor(mod(copper/100, 100))

its really saying

floor(mod(123456/100, 100))
floor(mod(1234.56,100))
floor(34.56) --because the remainder of 12.3456 is 34.56
34

[nightcracker]

local money = 1234562
local copper = money % 100 -- take the last two digits
local silver = floor(money / 100) % 100 -- first shift two digits to the right and then take the last two digits
local gold = floor(money / 10000) -- shift four digits to the right and take the remaining digits

[Sythalin]

mod(1234.56, 100)

This is where my confusion lies. Unless I'm suddenly failing at math, isn't 1234.56/100=12.3456? Then would be mod(12.3456)=3456?

[Ailae]

Originally Posted by ChaosInc This is where my confusion lies. Unless I'm suddenly failing at math, isn't 1234.56/100=12.3456? Then would be mod(12.3456)=3456?

When using modulus you're asking what the remainder is after you've completed the division. Think of it as "how many times can I fit my second value into my first? What is left if I remove that value that many times?".

You can subtract twelve 100s from 1234.56, and thus 34.56 is the remainder.

Example:
4 mod 4 = 0, because there's nothing left when you've removed as many 4s as you can (1).
5 mod 4 = 1, now there's 1 left.

Ergo, 15 mod 3 = 0 (cause 5 times 3 is 15), 16 mod 3 = 1 (5 times 3 is 15, can't get another 3 out of the remaining 1), and so on.

Wikipedia entry: http://en.wikipedia.org/wiki/Modulo_operation (but it's pretty daunting..)

[Sythalin]

Originally Posted by Ailae When using modulus you're asking what the remainder is after you've completed the division. Think of it as "how many times can I fit my second value into my first? What is left if I remove that value that many times?". You can subtract twelve 100s from 1234.56, and thus 34.56 is the remainder. Example: 4 mod 4 = 0, because there's nothing left when you've removed as many 4s as you can (1). 5 mod 4 = 1, now there's 1 left. Ergo, 15 mod 3 = 0 (cause 5 times 3 is 15), 16 mod 3 = 1 (5 times 3 is 15, can't get another 3 out of the remaining 1), and so on. Wikipedia entry: http://en.wikipedia.org/wiki/Modulo_operation (but it's pretty daunting..)

Ah, so there is a "hidden" step in there (work with me here, this how my brain understands things lol). Actually, the Wikipedia page made much more sense to me than Lua's "finds the remainder of x/y" which presents that it's just straight division when it's technically not.

I get it now. Thanks to all for your patience in my noob questions. Haven't gotten to modulus yet in my courses so I haven't had anything prior to work with to help understand.

Edit: Actually, it is like straight division now that I reflect upon it. It's just been a long time since I've worked with non-decimal division. It's like learning 5th grade math all over lol.

[Vrul]

Well, you say you understand now but here is another way of looking at it:

mod(x, y) = x % y = x - floor(x / y) * y

[Xubera]

Originally Posted by ChaosInc This is where my confusion lies. Unless I'm suddenly failing at math, isn't 1234.56/100=12.3456? Then would be mod(12.3456)=3456?

yeah, hopefully this wont aid in the confusion, but

mod(1234.56, 100) is 12.3456 (like you said above) but that is really

12     34.56
   and  -----  (this is a fraction :)  sorry for bad artwork)
        100

and yeah like you said, its like the division you learned in primary school, before they taught about decimals. the mod function goes ahead and rounds that down. so its 34.

and like the other examples mod(15,5) and mod(16,5) are 0 and 1 because its

3  0          3   1
   --   and      --
   5              5

respectively. the remainder is 0, and the remainder is 1 giving our answers of what mod(15,5) and (16,5) are

edit:above in code for formatting