www.delorie.com/gnu/docs/gmp/gmp_85.html

search

	Buy GNU books!

GNU MP 4.1.2

16.1.1 Basecase Multiplication

Basecase NxM multiplication is a straightforward rectangular set of cross-products, the same as long multiplication done by hand and for that reason sometimes known as the schoolbook or grammar school method. This is an O(N*M) algorithm. See Knuth section 4.3.1 algorithm M (see section B. References), and the `mpn/generic/mul_basecase.c' code.

Assembler implementations of mpn_mul_basecase are essentially the same as the generic C code, but have all the usual assembler tricks and obscurities introduced for speed.

A square can be done in roughly half the time of a multiply, by using the fact that the cross products above and below the diagonal are the same. A triangle of products below the diagonal is formed, doubled (left shift by one bit), and then the products on the diagonal added. This can be seen in `mpn/generic/sqr_basecase.c'. Again the assembler implementations take essentially the same approach.

u0 u1 u2 u3 u4 +---+---+---+---+---+ u0 | d | | | | | +---+---+---+---+---+ u1 | | d | | | | +---+---+---+---+---+ u2 | | | d | | | +---+---+---+---+---+ u3 | | | | d | | +---+---+---+---+---+ u4 | | | | | d | +---+---+---+---+---+

In practice squaring isn't a full 2x faster than multiplying, it's usually around 1.5x. Less than 1.5x probably indicates mpn_sqr_basecase wants improving on that CPU.

On some CPUs mpn_mul_basecase can be faster than the generic C mpn_sqr_basecase. SQR_BASECASE_THRESHOLD is the size at which to use mpn_sqr_basecase, this will be zero if that routine should be used always.