Square Root Process Similar to Long Division

09172021, 11:58 PM
Post: #2




RE: Square Root Process Similar to Long Division
(09172021 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 oldschool 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 3digits at a time. Numbers are scaled so that we work mostly with integer. 0.9996E6 = 1E3^2  400 // X = 1E3 Newtons correction (SX*X)/2/X, for 2nd 3digits. 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 (shelllike cross multiply, except center) Code: 1000 Normalize base1000 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  09172021, 11:00 PM
RE: Square Root Process Similar to Long Division  Albert Chan  09172021 11:58 PM
RE: Square Root Process Similar to Long Division  Albert Chan  09182021, 01:51 AM
RE: Square Root Process Similar to Long Division  Albert Chan  09182021, 12:46 PM
RE: Square Root Process Similar to Long Division  Albert Chan  09182021, 01:07 PM
RE: Square Root Process Similar to Long Division  jeejohn  09182021, 08:55 PM

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