matlab gfdeconv函数源码

GFDECONV 函数是 MATLAB 中用于通用分式函数的除法的函数。其源代码如下：

function [q,r] = gfdeconv(u,v,gf,m)
%GFDECONV Generalized polynomial division in Galois field.
%   [Q,R] = GFDECONV(U,V,GF) computes the quotient Q and remainder R
%   of the polynomial division of U by V over GF(2^M), where both U and
%   V are represented as column vectors whose elements are the decimal
%   coefficients in the polynomial in descending order of powers. GF is
%   the field ID string or the prime polynomial for binary fields. If GF
%   is a string, it must be one of 'cyclic', 'trun', 'prime', or 'custom'.
%   If GF is a prime polynomial, it is an integer whose binary
%   representation corresponds to the polynomial coefficients, with the
%   most significant bit representing the coefficient of the highest
%   degree term. The degree of V must be less than or equal to the degree
%   of U. The degree of Q is the difference between the degrees of U and
%   V. The remainder R has degree less than that of V. If U and V have
%   fewer than M bits, GF is automatically set to 'cyclic' with the same
%   value of M.
%
%   [Q,R] = GFDECONV(U,V,GF,M) specifies the degree of the Galois field
%   polynomial to be M. M must be a positive integer. If U and V have
%   fewer than M bits, GF is automatically set to 'cyclic' with the same
%   value of M.
%
%   Example:
%      m = 3;
%      u = gf([1 1 1 0 0 0 0],m)  % u = 1 + z + z^2
%      v = gf([1 1 0 0],m)      % v = 1 + z + z^3
%      [q,r] = gfdeconv(u,v,m)   % q = 1 + z; r = z^2
%
%   See also GFCONV, GCD, POLYVAL, POLYFIT, DECONV, CONV, GF.

%   Reference:
%      [1] P. V. Kumar, T. L. Casavant, J. P. Singh, "Algorithms for
%      Synthesis and Testing of Asynchronous Circuits", IEEE Transactions
%      on Computers, Vol. 41, No. 11, pp. 1372-1394, November 1992.
%
%   Copyright 1992-2015 The MathWorks, Inc.

% Validate input arguments.
narginchk(3,4);
if ~isnumeric(u) || ~isnumeric(v) || ~isnumeric(m)
    error(message('comm:gfdeconv:InvalidUVGFM'));
end
if ~isvector(u) || ~isvector(v)
    error(message('comm:gfdeconv:UVNotVector'));
end
if isvector(m)
    error(message('comm:gfdeconv:MNotScalar'));
end
if isscalar(m) && (m < 1 || m ~= round(m))
    error(message('comm:gfdeconv:InvalidM'));
end

if ~isa(u,'gf')
    u = gf(u,m);
end
if ~isa(v,'gf')
    v = gf(v,m);
end

if ~isscalar(v)
    error(message('comm:gfdeconv:VNotScalar'))
end

if ~strcmp(v.field,m)
    error(message('comm:gfdeconv:FieldMismatch'))
end

if length(u) < length(v)
    q = gf([]);
    r = u;
    return;
end

% Get the Galois field properties.
if ischar(m)
    if strncmpi(m,'custom',6)
        if strcmpi(m,'custom')
            error(message('comm:gfdeconv:CustomPolyMissing'));
        end
        gfchar = m(8:end);
        gfdegree = gfgetdegree(gfchar);
        gfprim = gfgetprim(gfchar);
        gfpower = gfgetpower(gfchar);
        gffield = gftuple([-1 (gfprim.^gfpower(1:gfdegree-1))'],gfprim,m);
    else
        gffield = gftuple(m);
    end
    m = gffield.m;
else
    gffield = gf;
end

% Get the primitive element of GF(2^M).
prim = gffield.prim;

% Get the decimal representation of V.
v = double(v.x);

% Remove leading zeros from V.
v = v(find(v,1,'first'):end);

% Get the degrees of U and V.
degU = length(u) - 1;
degV = length(v) - 1;

% Initialize the quotient and remainder.
q = gf(zeros(1,degU-degV+1),m);
r = gf(u,m);

% Initialize the index of the most significant non-zero coefficient of R.
i = degU-degV+1;

% Iterate until the degree of R is less than that of V.
while i > 0
    % Compute the degree of R.
    degR = length(r) - 1;

    % Get the degree of the next term to be subtracted from R.
    degT = degR - degV;

    % Compute the next term of the quotient if R is not zero.
    if degT >= 0
        % Compute the factor to be multiplied with V.
        factor = gfdiv(r(degR+1),v(degV+1),prim,gffield);

        % Compute the polynomial representing the factor.
        polyFactor = gf([zeros(1,degT) double(factor.x)],m);

        % Update the quotient.
        q(i) = factor;

        % Update R.
        r = r - polyFactor*gfpolyshift(v,degT);

        % Update the index of the most significant non-zero coefficient of R.
        i = i - 1;
    else
        break;
    end
end

% Remove leading zeros from R.
r = r(find(r,1,'first'):end);