Large numbers multiplication in MATLAB

Question

I have a question out of sheer curiosity. How is multiplication of large numbers implemented in MATLAB ? Is it Karatsuba,Toom-3, Fürer or something entirely different ?

Answer 1

If you are interested in the algorithm for computing for example 139676498390139139676498390676498390*8745566554641239676498390676498390, then this is what happens:

• both numbers are converted to double in IEEE® Standard 754
• as such, the representation is not accurate, because doubles can only accurately represent integers of up to 2^53-1 (check documentation of bitmax function) (~10^15, while your numbers are on the order of 10^35).
• multiplication is performed using double precision floating point numbers, and is thus also approximate

Have a look at this example code:

>> a=139676498390139139676498390676498390;
>> num2str(a)

ans =

139676498390139141600015724509659136

which is clearly not exactly the value you assigned to a - only the first 16 digits match.