Agreed, but in terms of efficiency wouldn’t it make more sense to put the sign bit right before the mantissa in order to keep the memory layout more consistent with powers of two?
Having the sign bit in front, makes them compare like sign-bit-integers and if they are compared/sorted like 2s-complement integers, the negatives are reversed but still come after the positives.
It’s not “mimicking” a fraction. It is a fraction.
It’s also the most compact fraction representation around.
Show how 1/3 can be precisely represented in floating point.
fl_numerator = 1
fl_denominator = 3
And division is a “stretch goal” once we get funding.
How many decimal places can it be stretched?
As usual, the best jokes are in the comments. (Though goddamn I chuckled at the meme.)
Do you have a computer type that can represent the entire rational set?
Yes. Have a structure with 2 BigInts. Treat one as the numerator. The other as denominators.
It might not be efficient or fast. But it is possible.
You are proposing that can represent the entire rational set?
Yes that is correct. A BigInt represents the entire integer set.
Rational numbers are defined by just 2 integers. Therefore, 2 BigInts represent the entire rational set.
No. They all need to mimic certain numbers.
So, you have a notation that can represent the entire rational set?
What exactly is being mimicked?
Agreed, but in terms of efficiency wouldn’t it make more sense to put the sign bit right before the mantissa in order to keep the memory layout more consistent with powers of two?
Having the sign bit in front, makes them compare like sign-bit-integers and if they are compared/sorted like 2s-complement integers, the negatives are reversed but still come after the positives.
I doubt the layout is relevant there as the FPU should be just physically wired to handle it.