[erlang-questions] Integer square root
Angel Alvarez
clist@REDACTED
Tue Jan 26 09:56:46 CET 2010
El Martes, 26 de Enero de 2010 02:26:47 Kenji Rikitake escribió:
> Very long time ago I was trying to solve the square root
> problem, but I didn't because handling in the float numbers
> gave the sufficient precision for me.
>
> In general, a quick method of
> solving X when Y = X * X and Y is given (X, Y are bignums) as:
>
> 1) Obtain approximation of X by float sqrt of Y
> separately to significand and exponent
> (note: IEEE754 format has its own limits in
> the digits of exponent too)
>
> 2) applying Newton-Raphson method so that
> Xnew = (X + (Y / X)) / 2
>
> 3) Repeat finding Xnew on 2) until Xnew =:= X
>
> Things you need to invent:
>
> * bignum integer dividing program
> (bignum / bignum -> bignum (+ remainder, maybe))
> (This is NOT provided by Erlang)
>
> FYI
> Kenji Rikitake
In fact after Richard's call of atention, (How could I made this!!??)
I approached a naive Newton version , but after all Now Its clear
for me that isqrt() is probably of use in cripto (!) so lloking erlang
sources (as i use to do for lerarnign porpouses...)
that's it...
The app SSH uses:
isqrt(0) -> 0;
isqrt(1) -> 1;
isqrt(X) when X >= 0 ->
R = X div 2,
isqrt(X div R, R, X).
isqrt(Q,R,X) when Q < R ->
R1 = (R+Q) div 2,
isqrt(X div R1, R1, X);
isqrt(_, R, _) -> R.
that its entirely on integer domain and supposely handled well by erlang bignums
routines. I tested this with some nig numbers and seems correct.
it doesnt deserve more attention where the fundamental subject its to avoid
making NOVICE MISTAKES (This is me!!!) like forgetting what is not integer arithmetic.
Again Thaks to all!!, for you advice and sugestions
>
> In the message <73BF5BD8-2DBB-44E3-BD45-C658B4059206@REDACTED>
> dated Mon, Jan 25, 2010 at 07:33:03PM +1300,
> Richard O'Keefe <ok@REDACTED> writes:
> > Didn't we have exactly this conversation several months ago?
> > At the time I said that it is straightforward to write an
> > integer square root function, and by that I meant >> in Erlang <<,
> > no port programs needed.
>
> ________________________________________________________________
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> erlang-questions (at) erlang.org
>
>
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