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Derek O'Connor

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University College, Dublin
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Comments and Ratings by Derek View all
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22 Nov 2009 Variable Precision Integer Arithmetic Arithmetic with integers of fully arbitrary size. Arrays and vectors of vpi numbers are supported. Author: John D'Errico

John,

The demo_vpi.m needs your consolidator function:

http://www.mathworks.com/matlabcentral/fileexchange/8354-consolidator

Great package.

Derek O'Connor
15 Sep 2009 INT64 arithmetic in MATLAB Enables int64 Addition, subtraction, multiplication, division and modulus. Author: Petter

John -- Thanks for pointing out that Int64 matrix multiplication is element-wise. I should have been more careful, given that the description clearly states that "multiplication and division are element-wise only". This of course explains the O(n^2) behavior.

On a more general point, I wish there was a consistent standard for matrix multiplicaton. For example, in O-Matrix, C= A*B is the same as Matlab, but C=A^2 gives cij = (aij)^2. This is really confusing. In Fortran 90, C=A*B gives cij = aij*bij.
15 Sep 2009 INT64 arithmetic in MATLAB Enables int64 Addition, subtraction, multiplication, division and modulus. Author: Petter

This seems to be an excellent package. I used it to test matrix multiplication
and obtained very surprising results : multiplying two 10^4x10^4 int64 matrices took about 2 secs while two doubles took about 35 secs. The double mat-mult used the Math Kernel and all 8 cores while the int64 did not use the Math Kernel.

Also, a 2-degree polyfit of the int64 mat-mult times was very good, i.e., t(n) is O(n^2)!

Can anyone enlighten me? Here is the test function:

function times = TimesInt64(v,degree);
% Test matrix multiplication using int64arithmetic
% int64arithmetic compiled with Microsoft Visual C++ 2008
% Dell Precision 690, 2xQuadcore Xeon 5345, 2.3GHz, 16GB
% Windows Vista 64
% Example : >> times = TimesInt64(1:15,2);

% Derek O'Connor Sept 2009

nvals = v'*10^3;
times = zeros(length(nvals),1);
c = intmax('int64');
for k = 1:length(nvals)
    n = nvals(k);
    A64=int64(floor(c*rand(n,n)));
    B64=int64(floor(c*rand(n,n)));

    tic; A64*B64; times(k) = toc;
end;

p=polyfit(nvals,times,degree);
ptimes = polyval(p,nvals);
plot(nvals,times,'.',nvals,ptimes,'-')

% End Function TimesInt64(v,degree)

% n times (secs)
% 1000 0.0176
% 2000 0.06972
% 3000 0.15354
% 4000 0.34136
% 5000 0.50145
% 6000 0.63655
% 7000 0.9838
% 8000 1.2829
% 9000 1.5717
% 10000 2.0059
% 11000 2.4728
% 12000 3.0439
% 13000 3.4914
% 14000 4.2588
% 15000 4.9525

% p(x) = 0.098649 - 5.6075e-005*x + 2.5027e-008*x^2

01 Aug 2009 Fractions Toolbox create and manipulate fractions (K+N/D) using exact arithmetic Author: Ben Petschel

This is a very useful toolbox, especially when used with
John D'Errico's Variable Precision Integer Toolbox.

Here are two tests I ran :

   function z = RumpFrac(x,y)

   % Testing John D'Errico's Variable Precision Integer Toolbox
   % and Ben Petschel's Fractions Toolbox using
   % Rump's polynomial. Derek O'Connor Aug 01 2009

     x = fr(vpi(x));
     y = fr(vpi(y));

    R1 = (33375/100)*y^6+ x^2*(11*x^2*y^2-y^6- 121*y^4- 2)
    R2 = (55/10)*y^8
    R3 = x/(2*y)
    z1 = R1+R2
    z = z1 + R3;

%
% R1 =
% -7917111340668961361101134701524942850
% R2 =
% 7917111340668961361101134701524942848
% R3 =
% 1 + 11425 / 66192
% z1 =
% -2
% z =
% -1 + 11425 / 66192 = -54767/66192 --- Correct.

% z = -1.180591620717411e+021 without first two statements

and

function z = JuddFrac(x,y)
   % Testing John D'Errico's Variable Precision Integer Toolbox
   % and Ben Petschel's Fractions Toolbox using
   % Judd's polynomial. Derek O'Connor Aug 01 2009

     x = fr(vpi(x));
     y = fr(vpi(y));

 J1 = 1682*x*y^4
 J2 = 3*x^3
 J3 = 29*x*y^2
 J4 = - 2*x^5
 z1 = J1+J2
 z2 = z1+J3
 z3 = z2+J4
 z4 = z3+832
 z = z4/107751

% z = JuddFrac(192119201,35675640);
% J1 =
% 523460426438903533308340192814390277120000
% J2 =
% 21273236588999014470832803
% J3 =
% 7091078862999671298158400
% J4 =
% -523460426438903561672655644813075853992002
% z1 =
% 523460426438903554581576781813404747952803
% z2 =
% 523460426438903561672655644813076046111203
% z3 =
% 192119201
% z4 =
% 192120033
% z =
% 1783 --- Correct.

% z = 7.721506064908910e-003 without first two statements
10 Jul 2009 Binary Search for numeric vector Search given value in a sorted vector, returns the index of location where the value is found. Author: Dr. Murtaza Khan

Dear Dr Khan,
The comma should not have been included at the end of the link

http://www.derekroconnor.net/NA/Notes/NA-4-Latex.pdf

Please note that your Binary Search of rows of m by n matrix
also suffers from this error.

http://www.mathworks.com/matlabcentral/fileexchange/9095

Derek O'Connor
 

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