[Haskell-cafe] Fractional Part
Chris Smith
cdsmith at gmail.com
Wed Aug 3 01:21:14 CEST 2011
On Wed, 2011-08-03 at 02:06 +0300, Ata Jafari wrote:
> In the first step I want to write a little code that can give me only
> the decimal part of a float. For instance:
properFraction from the RealFrac type class will divide into the real
and fractional parts. Once you've got the fractional part, converting
that into an integer is a bit trickier.
First, you should realize that it's only possible if the number has a
terminating decimal representation, which happens precisely when it is
rational, and in reduced fraction form, the denominator has only 2 and 5
as prime factors. Conveniently, an IEEE floating point number will
always be of that form, so if you assume that the implementation uses an
IEEE floating point format, you're golden!
You'll then want to multiply both the numerator and denominator by a
common multiplier to get the number of 2s and 5s in the factorization of
the denominator to be the same. Then the denominator is a power of 10,
so the numerator is your answer.
Some simple code might look like:
toDecimalPart x = n * (5^k)
where (_, fracPart) = properFraction x
r = toRational fracPart
d = denominator r
n = numerator r
k = log2 d
log2 1 = 0
log2 n | even n && n > 1 = 1 + log2 (n `quot` 2)
| otherwise = error "log2 not an integer"
--
Chris Smith
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