Question

I have a float value that must be constrained to an multiple of 0.25.

Examples of valid values:
1.0, 1.25, 2.0, 2.5, 20.25, 20.5, 21.0, 21.25, …

Examples of invalid values:
0.93, 3.31, 4.249, 5.02, …

Is there an mathematic function or something convenient to achieve this? When the value is invalid, I would round it up to the nearest valid value.

Answer 1

What functions are available to you depends on the language you’re using. Is this C? C++? Java? In any case, the “best” solution depends on how you’re getting the value to check. Are you mathematically computing the value and you then want to make sure it’s a multiple of 0.25? Or is a user inputting a value and you then want to make sure it’s a multiple of 0.25?

If you’re mathematically calculating it, just multiply all of your calculations by 4, use integer math, then divide the result by 4.0. This guarantees a result that is a multiple of 0.25

If a user is entering a value then you can’t just convert it to an integer without risking losing the decimal. The “best” solution in this case would be to look for an existing ceiling function. Multiply their number by 4, take the ceiling, then divide by 4. This will round up to the nearest 0.25. Calculating a “ceiling” directly is an infinite series and would thus leave your program running forever (until you ran out of significant digits of accuracy and you were infinitely adding 0). If there is no “ceiling” function in the language you’re using, most languages posses a modulus function. This modulus actually contains the exact same infinite series used in calculating a ceiling, so through substitution we can use it.

ceiling(x) = floor(x – 2*(x%1) + 1)

Remembering that floor(x) = (int)(x), we can just cast “x-2*(x%1)+1” as an int and we have the ceiling.

If your language doesn’t have a modulus OR a ceiling function then for many practical purposes with sufficient significant digits you can add 1 and cast it as an int, but this will not work in cases of exact integers. Alternatively you could add something like 0.99 then cast it as an int, as this will only fail for numbers greater than n and less than n+0.01 (for any integer n). The more 9’s you append the greater accuracy of the approximation (until you have more 9’s than the computer can store, then it will round to 1 and you’ll have the original problem)