CODEWITHSUNDEEP
matlab
slezadav
slezadav

Reputation: 6141

Large numbers multiplication in MATLAB

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 ?

Upvotes: 10

Views: 2656

Answers (4)

Argyll
Argyll

Reputation: 9875

If your numbers are only big, but you don't require a large number of significant digits. You can multiple a small number with each multiplication, such as $10^-1$. Keep track of the number of multiplications $N$ and obtain a value in terms of $10^{-N}$. This can be a temporary work around.

Upvotes: 0

angainor
angainor

Reputation: 11810

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.

Upvotes: 5

bla
bla

Reputation: 26069

Adding to the answer, if you need more digits of accuracy, you can try to use this fex file

Upvotes: 3

Andrey Rubshtein
Andrey Rubshtein

Reputation: 20915

There is no built-in BigInteger class, if that is what you mean. You can either use the fixed point toolbox, or import relevant java/.NET classes.

By default, numbers are represented in IEEE double precision floating point format.

Upvotes: 3

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