b+ String Math Update

[Pete]

Wow! It's all that's and a pound-and-a-half of bananas. I'll even through in a grapefruit... because my wife really hates those.

Long enough ago it's hard for me to remember, but I thought I maxed out in multiplication at 8-digits at a time.

Pete

[SMcNeill]

You have 20 digits for unsigned integer 64.

9 digits x 9 digits should always be less than 18 digits.  Right?

[Pete]

Well if we take 999999999 * 999999999 = 999999998000000001 (18-digits) so the 9 x 9 appears to be withing the type limit.

Ah, I think I see why I went with eight. I used _Integer64, which tops out at 8 x 8. While 9 x 9 works with the unsigned type. Now if folks read this and say, but the unsigned type can handle 20 digits, don't forget that the max number is: 18,446,744,073,709,551,615 so no, 10 x 10 as in 9999999999 * 9999999999 is not going to be less than that 18... max.

Pete

[SMcNeill]

Even an integer 64 handles up to 19 digits without problem:   9,223,372,036,854,775,807

Since 9 digits * 9 digits = max 18 digits, you'd still be able to hold the answer without overflow.

As for tracking any sort of sign.... *WHY* for goodness's sake?!

Do this:

positive * positive = positive
negative * negative = positive
positive * negative = negative
negative * positive = negative

Simple rule, settled from the beginning with your numbers and now you're only dealing with the positive values with the sign safely already stored off to the side.

3 * 3 .... positive numbers only
-3 * -3 .... negative * negative = positive so it's just the same as 3 * 3
-3 * 3 .... negative * positive = negated (3 * 3)

Either way, you're always just doing multiplication with positive values... The sign of the answer is sorted out easily elsewhere in the code.

[Pete]

Right usable with _integer64 and one more, 19, with _unsigned _integer64.

I think we both approached this by stripping out signs, decimal, etc. 

Well, I'm stumped why I topped out my approach at 8, since signs were not an issue for me either, I could have used 9.

I would probably look into Jack's method if I ever go back to expanding on the project. Things like higher order roots really started to slow down my string calc routine. It would do them, but not as fast as online versions for those types of calculation.

Pete