>6.64 halving and n-digit doubling operations per digit of the multiplier
Where do you get this from? Intuitively I'd reckon you'd need no more than log2 operations. Whatever this result is it certainly doesn't hold for small n.
>mediation and duplation of 69 · 21
21 69 *
10 138
5 276 *
2 552
1 1104 *
Am I mistaken in reading this as RPN? You put the operator to the side of the operands rather than the middle. Slightly unorthodox to put the op on the right, but still obvious in meaning.
Your English is obviously perfect, but you have a very idiosyncratic way of writing math that I've never seen before. For example you wrote "from the 01950s". I've never seen anyone use a 5 digit year format, and rarely if ever have I seen anyone include a leading zero in a number at all. Its not bad or wrong, I just don't know what this style is except possibly a type foreign accent?
> Where do you get this from? Intuitively I'd reckon you'd need no more than log2 operations. Whatever this result is it certainly doesn't hold for small n.
2 log₂ 10. a multiplier m with 5 digits has a log₂ between 13.29 and 16.61, 3.32 per digit; you need log₂ m halving operations and log₂ m doubling operations. so 6.64 is an upper bound but it's usually pretty close. in the example there, it would have led you to expect 13.28 halving and n-digit doubling operations, when the reality was 8 halving and doubling operations, of which three were n+1-digit doublings
n is the number of digits of the multiplicand, so it holds just as well for small or large n, except in the sense that n can be a bad estimate for how many digits you need in the doublings when it's small
> Am I mistaken in reading this as RPN?
yes; those asterisks mark the rows where the mediation column was odd, as i explained below in 'now we add the starred duplation column items where the mediated multiplicand was odd'. they do not denote multiplication or any other operation on the two numbers to their left. you are surely not the only person who misinterpreted this, and i apologize for the lack of clarity
Where do you get this from? Intuitively I'd reckon you'd need no more than log2 operations. Whatever this result is it certainly doesn't hold for small n.
>mediation and duplation of 69 · 21
Am I mistaken in reading this as RPN? You put the operator to the side of the operands rather than the middle. Slightly unorthodox to put the op on the right, but still obvious in meaning.Your English is obviously perfect, but you have a very idiosyncratic way of writing math that I've never seen before. For example you wrote "from the 01950s". I've never seen anyone use a 5 digit year format, and rarely if ever have I seen anyone include a leading zero in a number at all. Its not bad or wrong, I just don't know what this style is except possibly a type foreign accent?