I don't really know much about MPFR

It's good for reference - if you want to be assured of correctness in assignment, rounding and calculation. I've just now used it to demonstrate to myself that one cannot guarantee that either the "left-to-right" or "right-to-left" exponentiation calculations are going to be as (or more) accurate than performing the requisite number of multiplications.

The example I'll give is the calculation of 5.35 ** 107 - correct figure for which (to 15 decimal digits) is 8.58726126272004e77. Using double precision, the right-to-left method yields 8.58726126271995e77, left-to-right yields 8.58726126271996e77 and cumulatively multiplying 5.35 by itself 106 times yields 8.58726126271998e77 which is closest to the actual value.
(Both perl and mpfr are returning the same results.)

I.e. decimals are normally human made!

But it's those human made numbers that we're normally interested in. When I multiply (on a computer) A by B I'm generally not really interested in finding the product of the base 2 approximations of A and B.
I usually just want to know what A times B is.
And it would surely seem strange to aliens that our human made machines that we use to process our human made decimal numbers in fact don't process *those* numbers.
Doesn't seem strange to us of course - we're all well and truly accustomed to that just being a fact of life ;-)

Cheers,
Rob

In reply to Re^9: Decimal Floating Point (DFP) and does Perl needs DFP? by syphilis
in thread Decimal Floating Point (DFP) and does Perl needs DFP? by flexvault

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