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
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—Horace Walpole (1717–1797)
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