Square Root Process Similar to Long Division
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09-17-2021, 11:58 PM
Post: #2
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RE: Square Root Process Similar to Long Division
(09-17-2021 11:00 PM)jeejohn Wrote: I saw the thread "Third Order Convergence for Square Roots..." Nice. By the way, you can cut/paste table inside code block (like mine) I just deleted a post about old-school square root from Third Order Convergence thread. It really should belong here. Here goes. For sqrt of value very close to 1, it is is even closer to 1. √(1+2ε) ≈ 1+ε We can even *assume* result is 1, then adjust for it. Example, √(0.9996) Here is old school method for square root. With nice divisor = 1, we do 3-digits at a time. Numbers are scaled so that we work mostly with integer. 0.9996E6 = 1E3^2 - 400 // X = 1E3 Newtons correction (S-X*X)/2/X, for 2nd 3-digits. -400E3/2 = -200E3 = -200X + 0 Negative digits OK, we will fix later. It just meant √(0.9996) ≈ 0.999800 Other digits followed below patterns: 1st column = quotient 2nd column = remainder, then corrected (shell-like cross multiply, except center) Code: 1000 Normalize base-1000 digits: √(.9996) = 0.999 799 979 995 998 999 719 915 973 591 ... Ref: book "Dead Reckoning: Calculating without instruments", chapter on roots |
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Messages In This Thread |
Square Root Process Similar to Long Division - jeejohn - 09-17-2021, 11:00 PM
RE: Square Root Process Similar to Long Division - Albert Chan - 09-17-2021 11:58 PM
RE: Square Root Process Similar to Long Division - Albert Chan - 09-18-2021, 01:51 AM
RE: Square Root Process Similar to Long Division - Albert Chan - 09-18-2021, 12:46 PM
RE: Square Root Process Similar to Long Division - Albert Chan - 09-18-2021, 01:07 PM
RE: Square Root Process Similar to Long Division - jeejohn - 09-18-2021, 08:55 PM
RE: Square Root Process Similar to Long Division - Thomas Klemm - 11-06-2022, 04:33 PM
RE: Square Root Process Similar to Long Division - Thomas Okken - 11-06-2022, 07:25 PM
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