There is also an algorithm that uses only right-shifts and subtractions, I think it is much faster because the maximum number of rounds grows linearly with the number of bits in the value. Interestingly, if I remember it right, it always shifts two bits at a time (divides by four). Isaac Em 5/12/2011 13:17, Tamas Rudnai escreveu: > I think there was a table optimization for this as well, so that you had = a > table with a number of roots and its squares, you pick up the highest one > so you start the subtraction from there. So for example you want to know > the square of 70000, which would be 264, therefore 264 loops in the > original algorithm. But then you pick the number 65536 which has the root > of 256, so you start with your calculus from there saving 256 steps. The > finest resolution your table is the more steps you can save in average, > however, there is a lag for the table lookup too. > > Tamas > > > > > On 5 December 2011 14:56, dipten wrote: > >> This is because >> *1+3+5+7+... +n th odd integer =3D n square.* >> This can be proved by simple arithmetic series sum formula. >> Deep. >> >> >> On Mon, Dec 5, 2011 at 7:48 PM, Electron wrote= : >> >>> Hello, >>> >>> analogously to [division] computing the quotient by counting how many >>> times you >>> can subtract the divisor, you can compute the square root of a number >>> counting >>> how many times you can subtract sequential odd numbers (1,3,5,7,9,=85). >>> >>> [ try it -- it works!]. e.g. 25 -1-3-5-7-9 =3D 0 >>> >>> OK, but can someone explain me *why* it works? :-) >>> >>> Thanks, >>> Mario >>> >>> -- >>> http://www.piclist.com PIC/SX FAQ & list archive >>> View/change your membership options at >>> http://mailman.mit.edu/mailman/listinfo/piclist >>> >> >> >> -- >> >> "The purpose of life is not to be happy. It is to be useful, to be >> honourable, to be compassionate, to have it make some difference that yo= u >> have lived and lived well." --- *Ralph Waldo Emerson* >> -- >> http://www.piclist.com PIC/SX FAQ & list archive >> View/change your membership options at >> http://mailman.mit.edu/mailman/listinfo/piclist >> > > --=20 http://www.piclist.com PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .