Help for a student project on calculator algorithms

[Albert Chan]

(08-14-2018 01:39 PM)Bill (Smithville NJ) Wrote:  Indeed there is a pdf of the series:

Algorithms Series

Thanks for the link. I were peeking the first article on doing square root.
I thought Newton's method is great for doing square root.

Seems, the old calculator is too under-powered to do that.
Even squaring a number is too costly, replace by sum of odd numbers.

The algorithm turns out to be like doing it by hand, grade-school style.
Guess the hundreds, guess the tens, ..., like this:

SQRT(x = 1936) = 40 + b

b error = x - (40+b)^2 = (x - 1600) - 80b - b^2
0 1936 - 1600 = 336
1 336 - 80 - 1 = 255
2 255 - 80 - 3 = 172
3 172 - 80 - 5 = 87
4 87 - 80 - 7 = 0 --> SQRT(1936) = 44

Edit: HP engineer were amazing. Subtractions cut in half:

b 5*error = 5x - 5(40+b)^2 = (9680 - 8000) - (400b + 5b^2)
0 9680 - 8000 = 1680
1 1680 - 405 = 1275
2 1275 - 415 = 860
3 860 - 425 = 435
4 435 - 435 = 0 --> SQRT(1936) = 44