Question

Computer Science Disscucion bored

Most modern languages adapt the IEEE 754 standard for representing floating point values. Discuss the advantages of this approach.

Answer 1

Simply stated, floating points achieve a high domain (from very small numbers close to zero to very high numbers, sometimes even higher than the number of atoms in the universe). Floating points achieve this by keeping the relative error constant. I.e. the number will start to be rounded after an fixed number of decimals (this is a simplification, but helps to understand the principle). This is very similar to the concept of "significant figures" from most natural sciences. However this means that floating point numbers are always somehow rounded. If you add a very small number to a very big number, the small number will just be truncated and the big number will stay. This happens when the small number is below the the threshold. If you add many numbers it might sometimes be necessary to sort them first and adding the small ones before the big ones. There is also the concept of numeric stability to consider, i.e. how an algorithm will drift of from the correct result due to the rounding.