  We present algorithms to perform modular polynomial multiplication or modular
dot product efficiently in a single machine word. We pack polynomials into
integers and perform several modular operations with machine integer or
floating point arithmetic. The modular polynomials are converted into integers
using Kronecker substitution (evaluation at a sufficiently large integer). With
some control on the sizes and degrees, arithmetic operations on the polynomials
can be performed directly with machine integers or floating point numbers and
the number of conversions can be reduced. We also present efficient ways to
recover the modular values of the coefficients. This leads to practical gains
of quite large constant factors for polynomial multiplication, prime field
linear algebra and small extension field arithmetic.
