Incorrect fimath in expression 'x'

Hello,

I am trying to generate Cooley-Tukey FFTs that take in fixed-point and output fixed-point numbers. For various reasons, I don't have access to the dsp.FFT toolbox, so I need to create custom functions. I want to .mex compile them as well to make them run faster. The functions are listed below.

function X = cooley_tukey_fixed_fft(x)

    % Define global fimath settings
    F = fimath('OverflowMode', 'Saturate', ...
               'RoundingMethod', 'Nearest', ...
               'ProductMode', 'KeepMSB', ...
               'SumMode', 'KeepLSB');

    % x = fi(x, 1, 16, 15, 'fimath', F);

    % Predefine DFT matrices for small lengths
    W_tables.W2  = fi(dftmtx(2)/2,  1, 16, 15, 'fimath', F);
    W_tables.W3  = fi(dftmtx(3)/3,  1, 16, 15, 'fimath', F);
    W_tables.W4  = fi(dftmtx(4)/4,  1, 16, 15, 'fimath', F);
    W_tables.W5  = fi(dftmtx(5)/5,  1, 16, 15, 'fimath', F);
    W_tables.W7  = fi(dftmtx(7)/7,  1, 16, 15, 'fimath', F);
    W_tables.W11 = fi(dftmtx(11)/11,1, 16, 15, 'fimath', F);
    W_tables.W13 = fi(dftmtx(13)/13,1, 16, 15, 'fimath', F);

    N = length(x);
    factors = factor(N);
    X = recursive_mixed_radix_fft(x, factors, F, W_tables);
    X = fi(X, 1, 16, 15, 'fimath', F);
end

function X = recursive_mixed_radix_fft(x, factors, F, W_tables)

    if isscalar(factors)
        X = naive_dft(x, length(x), F, W_tables);
        return;
    end

    m = factors(1);
    N = length(x);
    M = N / m;

    x = reshape(x, m, M);

    % FFT along columns
    for i = 1:m
        x(i, :) = recursive_mixed_radix_fft(x(i, :), factors(2:end), F, W_tables);
    end

    % Twiddle factors
    [k, n] = ndgrid(0:m-1, 0:M-1);
    W = fi(exp(-2j * pi .* k .* n / N), 1, 16, 15, 'fimath', F);
    x = x .* W;

    % FFT along rows
    for j = 1:M
        x(:, j) = naive_dft(x(:, j).', m, F, W_tables).';
    end

    X = reshape(x.', N, 1);
end

function X = naive_dft(x, N, F, W_tables)
    switch N
        case 2
            W = W_tables.W2;
        case 3
            W = W_tables.W3;
        case 4
            W = W_tables.W4;
        case 5
            W = W_tables.W5;
        case 7
            W = W_tables.W7;
        case 11
            W = W_tables.W11;
        case 13
            W = W_tables.W13;
        otherwise
            W = fi(dftmtx(N)/N, 1, 16, 15, 'fimath', F); % fallback for other lengths
    end
    % x = fi(x(:), 1, 16, 15, 'fimath', F); % Attach fimath explicitly
    X = W * x(:);                            % Arithmetic inherits attached fimath
end

function X = cooley_tukey_fixed_ifft(x)

    % Define global fimath settings
    F = fimath('OverflowMode', 'Saturate', ...
               'RoundingMethod', 'Nearest', ...
               'ProductMode', 'KeepMSB', ...
               'SumMode', 'KeepLSB');

    % x = fi(x, 1, 16, 15, 'fimath', F);

    % Predefine DFT matrices for small lengths
    W_tables.W2  = fi(conj(dftmtx(2)),  1, 16, 15, 'fimath', F);
    W_tables.W3  = fi(conj(dftmtx(3)),  1, 16, 15, 'fimath', F);
    W_tables.W4  = fi(conj(dftmtx(4)),  1, 16, 15, 'fimath', F);
    W_tables.W5  = fi(conj(dftmtx(5)),  1, 16, 15, 'fimath', F);
    W_tables.W7  = fi(conj(dftmtx(7)),  1, 16, 15, 'fimath', F);
    W_tables.W11 = fi(conj(dftmtx(11)), 1, 16, 15, 'fimath', F);
    W_tables.W13 = fi(conj(dftmtx(13)), 1, 16, 15, 'fimath', F);

    N = length(x);
    factors = factor(N);
    X = recursive_mixed_radix_fft(x, factors, F, W_tables);
    X = fi(X, 1, 16, 15, 'fimath', F);
end

function X = recursive_mixed_radix_fft(x, factors, F, W_tables)

    if isscalar(factors)
        X = naive_dft(x, length(x), F, W_tables);
        return;
    end

    m = factors(1);
    N = length(x);
    M = N / m;

    x = reshape(x, m, M);

    % FFT along columns
    for i = 1:m
        x(i, :) = recursive_mixed_radix_fft(x(i, :), factors(2:end), F, W_tables);
    end

    % Twiddle factors
    [k, n] = ndgrid(0:m-1, 0:M-1);
    W = fi(exp(2j * pi .* k .* n / N), 1, 16, 15, 'fimath', F);
    x = x .* W;

    % FFT along rows
    for j = 1:M
        x(:, j) = naive_dft(x(:, j).', m, F, W_tables).';
    end

    X = reshape(x.', N, 1);
end

function X = naive_dft(x, N, F, W_tables)
    switch N
        case 2
            W = W_tables.W2;
        case 3
            W = W_tables.W3;
        case 4
            W = W_tables.W4;
        case 5
            W = W_tables.W5;
        case 7
            W = W_tables.W7;
        case 11
            W = W_tables.W11;
        case 13
            W = W_tables.W13;
        otherwise
            W = fi(conj(dftmtx(N)), 1, 16, 15, 'fimath', F); % fallback for other lengths
    end
    % x = fi(x(:),1,16,15,'fimath',F);
    X = W * x(:);                            % Arithmetic inherits attached fimath
end

I compile the codes with the following lines:

fiaccel cooley_tukey_fixed_fft -args {coder.typeof(fi(complex(0,0),1,16,15),[16384 1],1)} -report
fiaccel cooley_tukey_fixed_ifft -args {coder.typeof(fi(complex(0,0),1,16,15),[16384 1],1)} -report

However, when I run this code:

clear; clc; close all;

N = 8192;

sig = 0.5*exp(1i*2*pi*3/N*(0:N-1));
sig = (sig + 0.1*(randn(1,N)+1i*randn(1,N)));
x = fi(complex(real(sig),imag(sig)), 1, 16, 15);

tic;
y_CT = cooley_tukey_fixed_fft(x(:));
toc;
tic
y_CTM = cooley_tukey_fixed_fft_mex(x(:));
toc;
tic;
y_float = fft(sig)/N;
toc;
tic;
y_fix5 = cooley_tukey_fixed_1500_mex(x(1:1500));
toc;
tic;
y_fix6 = cooley_tukey_fixed_1600_mex(x(1:1600));
toc;

figure;
plot(abs(y_CT))
figure; 
plot(abs(y_float))
figure;
plot(abs(double(y_CTM(:)) - y_float(:)))
figure;
plot(abs(y_fix5))
figure;
plot(abs(y_fix6))

tic;
temp = cooley_tukey_fixed_ifft(y_CTM);
toc;

tic;
temp2 = cooley_tukey_fixed_ifft_mex(y_CTM(:));
toc;

isequal(temp,temp2)

figure; plot(real(temp(:))-real(x(:)))

It runs up until line 41, but breaks with the error:

Incorrect fimath in expression 'x'.

Error in cooley_tukey_fixed_ifft_mex

Error in Test_CooleyTukey (line 41)

temp2 = cooley_tukey_fixed_ifft_mex(y_CTM(:));

I also tried running it with the coder, but this also breaks with the error:

Error using cooley_tukey_fixed_ifft_mex (line 0)

Incorrect fimath in expression 'x'.

Error in Test_CooleyTukey (line 45)

temp = cooley_tukey_fixed_ifft(y_CTM);

I am not sure what could be going wrong as the functions are nearly identical, and the output of each function is re-cast to the same type as the input. Any help would be greatly appreciated.

Answer 1

[Alex Batts]

I see the error that I made. .mex files cannot take in embedded fi inputs with fimath properties. Therefore, editing the following line in both functions solved the problem:

X = fi(removefimath(X),1,16,15);

It seems weird that even if the fimath properties of the input were identical to the fimath properties internal to the mex function that it would still break, however I guess this is the solution for now.