**Karatsuba's algorithm **

`> `
**a1 := op(1,evalf(Pi,10000)):**

`> `
**type(a1,integer);**

How many digits are in the integer a1 ?

`> `
**length(a1);**

How long (in seconds) does it take to square a1 ?

`> `
**st := time(): a2 := a1^2: t2 := time()-st;**

`> `
**length(a2);**

How long does it take to square a2, where a2 has almost double the number of digits (19999 digits) that a1 has.

`> `
**st := time(): a4 := a2^2: t4 := time()-st;**

`> `
**length(a4);**

The ratio of the computation times should be close to 3 if Karatsuba's algorithm is used for integer multiplication.

`> `
**almost_3 := t4/t2;**