Kids can do math better than x86 cpu's.

Ant not one of them understand the implications of R's representations and R's-1 representations.

How about you research the 40 year old Booth's algorithm, or the 50 year old Wallace tree method. You just might learn something about how modern hardware actually works. I happen to know that most modern general purpose processors use a combination of the two, specifically later x86, SPARC, and PPC families.

I have very fond memories of BIX, I used to be snipped-for-privacy@bix.com, frow well before BIX became box.com and got an internet SMTP gateway. :-)

OK.

I've written long division routines that work the same way.

For table-driven multiplication I'm partial to x^2 tables, they make it trivial to fit at least an 8-bit wide table into fast memory.

Terje

I think you've just demonstrated why no kid is likely to solve that several hundred digit problem you posted earlier, which another kind poster solved in a few seconds using fixed sized arithmetic hardware.

Now, how much money were you offering?

Shades of "Cheaper by the Dozen" where Pa Gilbreth had his kids memorize the squares of 1 through 50 for multiplication. What scares me is that I read the book 40 years ago and still remember that detail...

- Erik

Multiplication as thought to kids in school is based on the "math table" , "lookup table", "and table" concept.

If one understand the full algorithm one can do arbitrary/infinite precision math.

Let's discuss a little bit how a modern cpu could achieve this.

Since a modern cpu does need to do some multi tasking.

Maybe the cpu could do it in little pieces and safe it's memory state during context switches, or maybe a special coprocessors is preferred... ?

I also wonder how much faster or slower the hardware implementation would be compared to the same optimal software implementation.

Bye, Skybuck.

For square, there's a short-cut that makes memorizing them not-so-useful. And for numbers ending in 5, it's even easier.

Jan

I had a pair of Nova computers about 15 years ago.

In article , Terje Mathisen wrote: [...]

The LSB of (A-B) is the same as the LSB of (A+B)

(A+B)^2 - (A-B)^2

= A^2 + 2AB + B^2 - A^2 + 2AB -B^2

= 4AB

You can improve the speed by a little creative table generation.

The LGP-30 [my first computer!] was bit serial, with discrete vacuum tubes! And in fact, only 15 bits of state were stored in the vacuum tube flip-flops -- all of the rest of it was stored on the drum, including the PC, the instruction register, and the accumulator. Despite that, it had hardware multiply (two kinds: save upper 31 bits of result or save lower 31 bits) and hardware divide. See:

-Rob

----- Rob Warnock

Sounds vaguely like the G-15: (CAUTION! 2.8 MB .pdf file)

Which was the first computer I learned to program, in about 1966. :-)

Cheers! Rich