To begin with, allow me to confess that I'm an experienced programmer, who has over 10 years of programming experience. However, the question I'm asking here is the one, which has bugged me ever since, I first picked up a book on C about a decade back.
Below is an excerpt from a book on Python, explaining about Python Floating type.
Floating-point numbers are represented using the native
double-precision (64-bit) representation of floating-point numbers on
the machine. Normally this is IEEE 754, which provides approximately
17 digits of precision and an exponent in the range of –308 to
308.This is the same as the double type in C.
What I never understood is the meaning of the phrase
" ... which provides approximately 17 digits of precision and an
exponent in the range of –308 to 308 ... "
My intuition here goes astray, since i can understand the meaning of precision, but how can range be different from that. I mean, if a floating point number can represent a value up to 17 digits, (i.e. max of 1,000,000,000,000,000,00 - 1), then how can exponent be +308. wouldn't that make a 308 digit number if exponent is 10 or a rough 100 digit number if exponent is 2.
I hope, I'm able to express my confusion.
Regards
Vaid, Abhishek
Suppose that we write 1500 with two digits of precision. That means we are being precise enough to distinguish 1500 from 1600 and 1400, but not precise enough to distinguish 1500 from 1510 or 1490. Telling those numbers apart would require three digits of precision.
Even though I wrote four digits, floating-point representation doesn't necessarily contain all these digits. 1500 is 1.5 * 10^3. In decimal floating-point representation, with two digits of precision, only the first two digits of the number and the exponent would be stored, which I will write (1.5, 3).
Why is there a distinction between the "real" digits and the placeholder zeros? Because it tells us how precisely we can represent numbers, that is, what fraction of their value is lost due to approximation. We can distinguish 1500 = (1.5, 3) from 1500+100 = (1.6, 3). But if we increase the exponent, we can't distinguish 15000 = (1.5, 4) from 15000+100 = (1.51, 4). At best, we can approximate numbers within +/- 10% with two decimal digits of precision. This is true no matter how small or large the exponent is allowed to be.
From Wiki, Double Precision Floating Point numbers are expected to have a precision to 17 digits, or 17 SF. The exponent can be in the range -1022 to 1023.
Their -308 to 308 would appear to be an error, or else an idea not fully explained.
