How to make the code efficient?

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Ammy
Ammy on 8 Jun 2021
Answered: Steven Lord on 8 Jun 2021
I have made the following code .
x=[0:n-1];
y=[0:n-1];
k = 0;
for i=1:n
for j=1:n
if rem(((y(j))^2)-((x(i))^3)-2*(x(i))-3,n)==0
k = k+1;
xy_mtx(k,:) = [x(i) y(j)];
end
end
end
I want to make it efficient, as efficient as it can be. Is this possible

Answers (3)

David Hill
David Hill on 8 Jun 2021
n=10;
[x,y]=meshgrid(0:n-1);
idx=mod(y.^2-x.^3-2*x-3,n)==0;
xy_mtx=[x(idx),y(idx)];
  4 Comments
David Hill
David Hill on 8 Jun 2021
Edited: David Hill on 8 Jun 2021
You could try the help memory suggestions to try to increase memory, or you could add nested for-loop and do the meshgrids in batches of 2e4 (will be slower). Also keep in mind floating point limitations.
n=1e6;
xy_mtx=[];
for k=1:50
for j=1:50
[x,y]=meshgrid(0+(k-1)*2e4:min(2e4-1+(k-1)*2e4,n-1),0+(j-1)*2e4:min(2e4-1+(j-1)*2e4,n-1));
idx=mod(y.^2-x.^3-2*x-3,n)==0;
xy_mtx=[xy_mtx;x(idx),y(idx)];
end
end

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Joseph Cheng
Joseph Cheng on 8 Jun 2021
You can do things all at once cine you're not dependent on previous values.
n=4
n = 4
x=[0:n-1];
y=[0:n-1];
k = 0;
%%Orig_code
tic
for i=1:n
for j=1:n
if rem(((y(j))^2)-((x(i))^3)-2*(x(i))-3,n)==0
k = k+1;
xy_mtx(k,:) = [x(i) y(j)];
end
end
end
time1=toc;
tic
%%do everything at once
[X Y] = meshgrid(x,y); %generate combinations of x and y
REMmat = rem((Y.^2)-(X.^3)-2*(X)-3,n); %perform all rem calculations at once
[indexies]=find(REMmat==0); %find which index has a rem of 0
xy_mtxM = [X(indexies) Y(indexies)]; %put only the X and Y comb. where rem above is -
time2=toc;
disp([xy_mtx xy_mtxM])
3 0 3 0 3 2 3 2
disp(['time original:' num2str(time1) 's'])
time original:0.008312s
disp(['time new:' num2str(time2) 's'])
time new:0.016845s
disp(['time delta:' num2str(time1-time2) 's'])
time delta:-0.008533s
  2 Comments

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Steven Lord
Steven Lord on 8 Jun 2021
Are you trying to find the points on an elliptic curve over F_n?
You could probably try a variant of the naive approach given on this Wikipedia page.

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