Two additional developments around 1980 once again accelerated the ability to compute . First, the discovery of new iterative algorithms for computing , which were much faster than the infinite series; and second, the invention of fast multiplication algorithms that could multiply large numbers very rapidly. Such algorithms are particularly important in modern computations because most of the computer's time is devoted to multiplication. They include the Karatsuba algorithm, Toom–Cook multiplication, and Fourier transform-based methods.
Two additional developments around 1980 once again accelerated the abili,ty to compute . First, the discovery of new iterative algorithms for computing , which were much faster than the infinite series; and second the invention of fast multiplication algorithms that could multiply large numbers very rapidly. Such algorithms are particularly important in modern computations because most of the computer's time is devoted to multiplication. They include the Karatsuba algorithm, Toom–Cook multiplication and Fourier transform-based methods.