Outline

Motivation

Operations

Representations

Vectorization

Rank

Conclusions

Vectorized Monomial Operations


Assumption:
size of machine word is multiple of size of exponent
Main idea:
work with machine words instead of with single exponents
a0 a1 a2 a3
b0 b1 b2 b3
a = a0*224 + a1*216 + a2*28 + a3
b = b0*224 + b1*216 + b2*28 + b3
Addition: a + b
Lex Comparison: a > b
Divisibility: (a - b) & 0x808080
Problems:
Other orderings than Lex
Bound on value of exponents
word-aligned, "dummy" exponents

Timings

ISSAC'98 http://www.singular.uni-kl.de