I want to code a function makeFraction :: Float -> Float -> (Int, Int) which returns (x,y) whenever I say makeFraction a b such that x/y is a proper fraction equivalent to a / b. For eg, makeFraction 17.69 5.51 should return (61,19).
I have a subroutine to calculate gcd of two numbers but my first task is to convert a and b to Int e.g. 17.69 and 5.51 should be converted into 1769 and 551.
Now I want to do it for numbers with arbitrary decimal places. Prelude function does not help me much. For instance, when I say toFraction(0.2); it returns 3602879701896397 % 18014398509481984 which would severely strain the correctness of my later computations.
Later I tried getting fractional values by using another library function properFraction(17.69) which suppose to give me only 0.69 but it produces 0.69000…013 which is not I would accept in a proper state of mind.
It does look like a problem arising from Floating point arithmatic. Till now I am not doing any data manipulation but only asking for the part of stored bits which I should be able to fetch from processor registers/memory location. Is there any special function library in Haskell to do such tasks?
PS: Seems like some useful tips are here How to parse a decimal fraction into Rational in Haskell? . But since I have typed so much, I would like to post it. At least the context is different here.
Yes, it is the limited precision of floating-point arithmetic you’re encountering. The floating-point format cannot represent 0.2 exactly, so
toFractionis actually giving you the exact rational value of the Float number you get when you ask for 0.2.Similarly, 17.69 cannot be represented exactly, and because the point floats, its best representation has a larger absolute error than the error in the representation of 0.69. Thus, when you take away the integer part, the resulting bits are not the same as if you had asked to represent 0.69 as good as possible from the beginning, and this difference can be seen when the implementation prints out the result in decimal form.