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Here's a preview from my zine, How Integers and Floats Work! If you want to see more comics like this, sign up for my saturday comics newsletter or browse more comics!

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floating point is weird

floating point 10.0 is not the same as the integer 10

10 (64-bit integer): 0x000000000000000a

10.0 (64-bit float): 0x4024000000000000

(what’s this 4024 doing???)

computer integers work almost exactly the way you’d expect

1 + 2 - 3 = 0

but floating point numbers don’t:

(0.1 + 0.2) - 0.3 = 0.0000000000000000555

checking for float equality is dangerous

if x == 0.3: bad!

(0.1 + 0.2) is not equal to 0.3!

Instead, check if x is very close to 0.3, something like this:

if abs(x 0.3) 0.0000001:

in floating point, very large integers get rounded

For example: 10000000000000001.0 == 10000000000000000.0

(16 zeros)

(try comparing those 2 numbers in your favourite language! they’re the same!)

(x + y) + z is not the same as x + (y + z)

For example: (9007199254740992.0+ 1.0) 1.0 = 9007199254740991.0

(the math term for this problem is “floating point addition isn’t associative”)

some intuition for precision

32-bit floats have about 8 digits of precision

64-bit floats have about 16 digits of precision

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