Description of The Algorithm
Given an arbitrary polynomial Pn(x)= C0 + C1x + C2x2 + C3x3 + ... + Cnxn one can isolate sub-expressions of the form (A + Bx) and of the form x2n.
Rewritten using Estrin's scheme we get Pn(x) = (C0 + C1x) + (C2 + C3x) x2 + ((C4 + C5x) + (C6 + C7x) x2))x4 + ...
x2n can be evaluated once and kept until no longer required. As is evident from looking at this expression there are many sub-expression that may be evaluated in parallel.
The sub-expressions of form (A+ Bx) can be evaluated using a native multiply–accumulate instruction on some architectures, an advantage that is shared with the Horner scheme.
Read more about this topic: Estrin's Scheme
Famous quotes containing the words description of the, description of and/or description:
“As they are not seen on their way down the streams, it is thought by fishermen that they never return, but waste away and die, clinging to rocks and stumps of trees for an indefinite period; a tragic feature in the scenery of the river bottoms worthy to be remembered with Shakespeare’s description of the sea-floor.”
—Henry David Thoreau (1817–1862)
“The Sage of Toronto ... spent several decades marveling at the numerous freedoms created by a “global village” instantly and effortlessly accessible to all. Villages, unlike towns, have always been ruled by conformism, isolation, petty surveillance, boredom and repetitive malicious gossip about the same families. Which is a precise enough description of the global spectacle’s present vulgarity.”
—Guy Debord (b. 1931)
“Why does philosophy use concepts and why does faith use symbols if both try to express the same ultimate? The answer, of course, is that the relation to the ultimate is not the same in each case. The philosophical relation is in principle a detached description of the basic structure in which the ultimate manifests itself. The relation of faith is in principle an involved expression of concern about the meaning of the ultimate for the faithful.”
—Paul Tillich (1886–1965)