Re: [Jprogramming] Square roots

sqr=: 3 : '0j50": (<. @ %: y * 10x^100) % 10x^50' sqr 1023810239x 31997.03484699793241139948300855562366372711733217036789 On Sun, Sep 24, 2023 at 10:19 AM 'Skip Cave' via Programming < programm...@jsoftware.com> wrote: > How to get more accurate square roots? > > %:1023810239x > > 31997 > > 1

[Jprogramming] Square roots

How to get more accurate square roots? %:1023810239x 31997 1023810239x ^ 1r2 31997 31997x^2 1023808009 Skip Cave Cave Consulting LLC -- For information about J forums see http://www.jsoftware.com/forums.htm

Re: [Jprogramming] Square Roots and Extended Arithmetic

8 12:25 AM To: programm...@jsoftware.com Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic Linda, NB. Generate the integers from 2 to 21, store them in a, and display a: ]a=.2+i.20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 NB. Take the square root of the integers in a, store t

Re: [Jprogramming] Square Roots and Extended Arithmetic

│ ┌─ 2 │ ├─ | └─┤ ┌─ _ └─┼─ q: └─ ] Linda -Original Message- From: Programming On Behalf Of Linda Alvord Sent: Saturday, November 3, 2018 10:03 PM To: programm...@jsoftware.com Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic

Re: [Jprogramming] Square Roots and Extended Arithmetic

8 10:43 AM To: programm...@jsoftware.com Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic Also, there's a completely different way to attack the problem of finding perfect squares using the dyadic form of q: (Prime Exponents). I discovered this while reading NuVoc about q: fps1 =

Re: [Jprogramming] Square Roots and Extended Arithmetic

t: Re: [Jprogramming] Square Roots and Extended Arithmetic Also, there's a completely different way to attack the problem of finding perfect squares using the dyadic form of q: (Prime Exponents). I discovered this while reading NuVoc about q: fps1 =: 13 :'y#~0=+/"1]2|_ q:y' fps1 2

Re: [Jprogramming] Square Roots and Extended Arithmetic

Also, there's a completely different way to attack the problem of finding perfect squares using the dyadic form of q: (Prime Exponents). I discovered this while reading NuVoc about q: fps1 =: 13 :'y#~0=+/"1]2|_ q:y' fps1 2+i.100 4 9 16 25 36 49 64 81 100 fps1 8200+i.1000 8281 8464 8649 8836

Re: [Jprogramming] Square Roots and Extended Arithmetic

8281 %:8281 91 fps ] #~ [: (= >.) %: ;:' ] #~ [: (= >.) %:' ┌─┬─┬─┬──┬─┬─┬──┬─┬──┐ │]│#│~│[:│(│=│>.│)│%:│ └─┴─┴─┴──┴─┴─┴──┴─┴──┘ You can spot a hook by the parentheses. Linda Sent from my Verizon, Samsung Galaxy smartphone Original message From: Skip Cave Date: 11/3/18 12:25 AM (GMT-05:00) To: "programm...@jsoftware.com" Subject: Re: [Jprogramming

Re: [Jprogramming] Square Roots and Extended Arithmetic

kip Cave > Date: 11/2/18 12:06 PM (GMT-05:00) > To: "programm...@jsoftware.com" > Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic > > Thanks for all the comments and help in understanding why trying to get an > extended integer result from a square root

Re: [Jprogramming] Square Roots and Extended Arithmetic

What does (=>.) do in this example? Linda Sent from my Verizon, Samsung Galaxy smartphone Original message From: Skip Cave Date: 11/2/18 12:06 PM (GMT-05:00) To: "programm...@jsoftware.com" Subject: Re: [Jprogramming] Square Roots and Extended Arithmetic T

Re: [Jprogramming] Square Roots and Extended Arithmetic

Thanks for all the comments and help in understanding why trying to get an extended integer result from a square root is a bad idea. I think the functional symmetry of square *: and square root %: led me to subconsciously forget that the results of squared integers (all integers) are not symmetric

Re: [Jprogramming] Square Roots and Extended Arithmetic

Heron was ahead of his time- this is actually   now called Newton Rhapson   iteration . The basic process can be used to solve  some very large order (in variables) simultaneous non-linear equations   as in power system  load flow  problems that can have hundreds or more variables (first applie

Re: [Jprogramming] Square Roots and Extended Arithmetic

See https://code.jsoftware.com/wiki/Essays/Extended_Precision_Functions, in particular the Square Root section. On Thu, Nov 1, 2018 at 12:13 PM Skip Cave wrote: > a=:1234567890101020405060708090x > > > a=2^~a^1r2 > > 1 > > a=2^~%:a > > 1 > > a-:2^~a^1r2 > > 1 > > a-:2^~%:a > > 1 > > > NB. All l

Re: [Jprogramming] Square Roots and Extended Arithmetic

If the number is not a perfect square, square root always converts the result to float. b is not an integer. It is float. And there are digits after the decimal. 0j6":b 35136418287882.219000 But when b is squared only the first 16 (approx) digits are kept. 0j3":b^2 1234567890101024100

Re: [Jprogramming] Square Roots and Extended Arithmetic

Hi, A good read on the subject of square roots : A Perfect Square Root Routine E.E. McDonnell http://www.jsoftware.com/papers/eem/sqrt.htm On Thu, Nov 1, 2018 at 3:32 PM Raul Miller wrote: > Square roots cannot (in the typical case) be represented using > extended precision numbers (which are

Re: [Jprogramming] Square Roots and Extended Arithmetic

Square roots cannot (in the typical case) be represented using extended precision numbers (which are integers). a=:1234567890101020405060708090x a^1r2 3.51364e13 datatype a^1r2 floating This floating representation represents numbers using a representation of sign * 1+fraction * 2^exp

[Jprogramming] Square Roots and Extended Arithmetic

a=:1234567890101020405060708090x a=2^~a^1r2 1 a=2^~%:a 1 a-:2^~a^1r2 1 a-:2^~%:a 1 NB. All looking good. However: x:2^~a^1r2 1234567890101024064259751936 a 1234567890101020405060708090 NB. Clearly not equal. x:2^~%:a 1234567890101020490846961664 a 1234567890101020405060708090