function v = longhex(u, digits)
%LONGHEX Long hexadecimal format.
%   V=LONGHEX(U,N) takes a positive decimal fraction less than 1 and converts
%   it to a binary fraction of length digits. It then converts it to a IEEE
%   double precision number but possibly with a longer mantissa. U is a vector
%   of decimal digits in the range [0-9] with the decimal point to the 'left'
%   of U(1). N is the length in binary digits to save. V is a string of hexidecimal
%   digits of the IEEE double number, but with possibly longer mantiassa
%
%   Algorithm: Knuth, Vol. 2, p. 319, Method 2a

%   By: Martin Knapp-Cordes
%   The MathWorks, Inc.
%
%   Date: Apr 2001 - 09

u2 = zeros(size(u,1)+1,1);
u2(2:end) = u;
b = zeros(digits,1);
for i=1:digits
u2 = mult2(u2);
b(i) = u2(1);
u2(1) = 0;
end

% Always produce an least an IEEE double.
o = find(b == 1);
base = o(1);
s = size(b,1);
v = dec2hex(1023-base,3);
n = max(ceil((s - base) / 4), 13);
v2 = zeros(n * 4,1);
v2(1:(s - base)) = b((base+1):end);
for i=1:4:n*4
v = [ v dec2hex(bin2dec(sprintf('%d',v2(i:i+3))))];
end
v = lower(v);

%----------------------------------------------------------------
function u2 = mult2(u)
% Multiply by 2 with carry.
u2 = 2 .* u;
c = (u2>=10);
u2(1:end-1) = u2(1:end-1) + c(2:end) - c(1:end-1) .* 10;
u2(end) = u2(end) - c(end) .* 10