Interesting. I have a vague feeling that shift and add is easier for binary, and log/anti log easier in BCD. Might that be true?

_________________
x86?  We ain't got no x86.  We don't NEED no stinking x86!

Thanks for those cycle counts.

Hmm, it strikes me that a 10-times-table wouldn't be very large and might help collapse some of those repeated additions.


Ah, I think you didn't read the patent! By computing the log/antilog you can operate at full precision. I can't quite see a table being a good tradeoff.


Careful! It's inexact as soon as you have general division (or even multiplication if you were working on say 2 decimal places) - I recently found an article in an HP newsletter which put it well:

(from http://www.ebbsoft.com/hp/hp-cpu.htm which is garish, so try http://www.readability.com/articles/f2p9aaxc)

The advantages of BCD lie mostly in the ease of display and the ease of addition: ideal for point of sale or calculator. Don't make the mistake of thinking that decimal is in any way more true to the nature of numbers than binary is.

Cheers
Ed

What we do in non-calculator (embedded systems) scaled-integer hex though is to represent a cent or a mill by 1, then a dollar is 100 (64H) or 1000 (3E8H), and they are absolutely exact.

_________________
http://WilsonMinesCo.com/ lots of 6502 resources
The "second front page" is http://wilsonminesco.com/links.html .
What's an additional VIA among friends, anyhow?

Exact until you have to multiply by some fraction, such a tax?

You can do the same thing, scaling it as necessary. Tax multiplications require rounding to the nearest cent anyway. For example, if we have 8.25% sales tax on a $14.99 purchase, 1499*825=1236675 ( or 12DEC3 in a hex integer), so the tax is $1.236675 (converted to non-integer decimal at output time), rounded to $1.24, for a total of $16.23. For the rounding, we add half a cent's value, 5000 in decimal or 1388 in hex, before forming the output and truncating at two digits past the decimal point.

_________________
http://WilsonMinesCo.com/ lots of 6502 resources
The "second front page" is http://wilsonminesco.com/links.html .
What's an additional VIA among friends, anyhow?

I suppose what I'm thinking is that you can happily make cent-accurate calculations on individual items, but totals won't match with a cent-accurate calculation on a total. Fixed-point is certainly a useful tactic, but (again) it's a mistake to think of it as being a flawless representation of number. You end up calculating extra digits, rounding, and still you will be left with a few anomalies. The most common example might be a column of percentages not adding up to 100.

On the subject of BCD multiplication and logarithms: it looks like the calculation of logs by Wang's method is approximately as expensive as multiplying by repeated addition for each digit. If so, the total cost of a multiply by logs would be a little more than the cost of multiply by repeated addition by digit, but the total cost of division or square root might well come out lower. If we had a 10x10 multiplication table to hand, then operating by digits might well come out faster.

Cheers
Ed

_________________
x86?  We ain't got no x86.  We don't NEED no stinking x86!