Does MATLAB provide a lossless coversion function from double to string?

Question

tl;dr

I'm just looking for two functions, f from double to string and g from string to double, such that g(f(d)) == d for any double d (scalar and real double).

Original question

How do I convert a double to a string or char array in a reversible way? I mean, in such a way that afterward I can convert that string/char array back to double retrieving the original result.

I've found formattedDisplayText, and in some situations it works:

>> x = eps

x =

     2.220446049250313e-16

>> double(formattedDisplayText(x, 'NumericFormat', 'long')) - x

ans =

     0

But in others it doesn't

x = rand(1)

x =

   0.546881519204984

>> double(formattedDisplayText(x, 'NumericFormat', 'long')) - x

ans =

     1.110223024625157e-16

As regards this and other tools like num2str, mat2str, at the end they all require me to decide a precision, whereas I would like to express the idea of "use whatever precision is needed for you (MATLAB) to be able to read back your own number".

Answer 1

Here are two simpler solutions to convert a single double value to a string and back without loss.

I want the string to be a human-readable representation of the number

Use num2str to obtain 17 decimal digits in string form, and str2double to convert back:

>> s = mat2str(x,17) 
s =
    '2.2204460492503131e-16'
>> y = str2double(s);
>> y==x
ans =
  logical
   1

Note that 17 digits are always enough to represent any IEEE double-precision floating-point number.

I want a more compact string representation of the number

Use matlab.net.base64encode to encode the 8 bytes of the number. Unfortunately you can only encode strings and integer arrays, so we type cast to some integer array (we use uint8 here, but uint64 would work too). We reverse the process to get the same double value back:

>> s = matlab.net.base64encode(typecast(x,'uint8'))
s =
    'AAAAAAAAsDw='
>> y = typecast(matlab.net.base64decode(s),'double');
>> x==y
ans =
  logical
   1

Base64 encodes every 3 bytes in 4 characters, this is the most compact representation you can easily create. A more complex algorithm could likely convert into a smaller UTF-8-encoded string (which uses more than 6 bytes per displayable character).

Answer 2

Function f: from double real-valued scalar x to char vector str

str = num2str(typecast(x, 'uint8'));

str is built as a string containing 8 numbers, which correspond to the bytes in the internal representation of x. The function typecast extracts the bytes as a numerical vector, and num2str converts to a char vector with numbers separated by spaces.

Function g: from char vector str to double real-valued scalar y

y = typecast(uint8(str2double(strsplit(str))), 'double');

The char vector is split at spaces using strsplit. The result is a cell array of char vectors, each of which is then interpreted as a number by str2double, which produces a numerical vector. The numbers are cast to uint8 and then typecast interprets them as the internal representation of a double real-valued scalar.

Note that str2double(strsplit(str)) is preferred over the simpler str2num(str), because str2num internally calls eval, which is considered evil bad practice.

Example

>> format long
>> x = sqrt(pi)
x =
   1.772453850905516
>> str = num2str(typecast(x, 'uint8'))
str =
    '106  239  180  145  248   91  252   63'
>> y = typecast(uint8(str2double(strsplit(str))), 'double')
y =
   1.772453850905516
>> x==y
ans =
  logical
   1