At the moment, I am stuck with using single-precision float, and double-precision float. So, the maximum represent-able value for single is 1<<24 while for double, it is 1<<53.

Because of this, I made the following script here - https://gist.github.com/Reptorian1125/71e3eec41e44e2e3d896a10f2a51448e .

Allow me to clarify on the script above. On the first part, rep_bin2dec does is to return the converted values into the status. So, when I do ${} or variable=${rep_bin2dec\ ???}, I get the status string.

On the second part, rep_bin2dec_base is the basis for getting rep_bin2dec to work. _rep_bin2dec_base prints the base_10M array into a string.

So, how does rep_bin2dec_base converts a big binary into big decimal?

1. If the binary image is less than dimension of 54, then the script will use 0b{} which allows me to directly convert binary to decimal, and 0b is a binary literal much in the same way that Python and C++ does it. From this point, it's pretty obvious on what to do there. So, if it less than dimension 54, this step 1 is pretty much done. If not, move on to step 2.

2. Convert the binary image as a image of base (1<<24) representing the value of that image. Note that there are two channels "[ output_value , y ]". y in this case represents the digit position in base (1<<24).

3. Make the converted image as a dynamic array image. This allows us to remove unused digits. You can look at step 2, and step 3 as converting a binary string into an array of base (1<<24) into a dynamic array. Also, note that start_value is stored. That's the very first digit.

4. Note that the number_of_decimals is the predicted number of characters after conversion of binary to decimal. And the, there's multi-threading that gets activated depending on the size of dynamic array image. decimal_conversion_array_size,result_conversion_array_size is used to define array size as they're temporary arrays to convert from base (1<<24) into base 10M. Finally, there's a new image which is going to be using base 10 million for easy printing, and set is used to add the first digit of base (1<<24) which will then be converted to base 10M.

5. On eval[-2], we are now processing the base (1<<24) image, and then convert it into base 10M. There's a implicit loop, so you can add a "for y" after begin(), and begin() can be seen as the setup code.

Some notes, copy() basically allows me to alter an array. In this case, opacity is negative, so it will add the multiplication of the positive opacity. If opacity was between 0-1, then it will get treated similar to how opacity of one layer alters a image. And the multiplication algorithm being used to convert between bases is Schönhage-Strassen multiplication, but without the FFT part.

So, here how that works.

   9   9
x  1   9
_________
  81  81
9  9
_________
1  8  8 1

Basically, it's long multiplication, and you can see that there's carrying of the remainder. 81 -> 1 (Remainder 8). 81 + 9 + R8 = 89 + 9 = 8 R ( 1+ 8 ) = 8 R 9. Then 9 + 9 is 18. So, you can see how this results in 1881.

6. After the conversion to base 10M, depending on your inputs, it'll set the status value to the decimal representation or preserves it as a base 10M for easy printing with _rep_bin2dec_base after alteration.

There's some more details, but I find it really hard to explain this.

So, my question is what are some good algorithm to print out huge binaries as decimal? I know Python is insanely good at that, but I can't seem to understand how it does that so well. I know that they do involve conversion to base 2^30 or 1<<30.

At the moment, I can convert a 90000 digits binary in .35 s, and that's bad to what I seen in Python. It's really bad with 1M binary digits.