function X = xing
% Perfect simulation of the time taken for a BM to hit +/- 1 starting at 0
% Zaeem Burq 23.3.06, Owen Jones 24.3.06
accepted = 0;
while ~accepted 
    X = gamrnd(1.088870, 0.810570);
    Y = rand*1.243707*gampdf(X, 1.088870, 0.810570);
    sqrt2piX3 = sqrt(2*pi*X^3);
    N = max([ceil(0.275*X), 3]);
    K = (1+2*[-N:N]);
    fN0 = sum((-1).^[-N:N].*K.*exp(-K.^2./(2*X)))/sqrt2piX3;
    N = N + 1;
    fN1 = fN0 + (-1)^N*((1-2*N)*exp(-(1-2*N)^2/(2*X)) ...
        + (1+2*N)*exp(-(1+2*N)^2/(2*X)))/sqrt2piX3;
    while sign((Y - fN0)*(Y - fN1)) == -1
        fN0 = fN1;
        N = N + 1;
        fN1 = fN0 + (-1)^N*((1-2*N)*exp(-(1-2*N)^2/(2*X)) ...
            + (1+2*N)*exp(-(1+2*N)^2/(2*X)))/sqrt2piX3;
    end
    if Y <= fN1, accepted = 1; end
end