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Topic: Fast exponent and logarithm, given initial estimate
Replies: 29   Last Post: Nov 8, 2004 2:31 AM

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Christer Ericson

Posts: 34
Registered: 12/6/04
Re: Fast exponent and logarithm, given initial estimate
Posted: Oct 21, 2004 3:31 AM
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In article <9215d7ac.0410201951.2d5f07f6@posting.google.com>,
glenlow@pixelglow.com says...
> [...]
> On second thought, it would probably be slower on an Altivec (or other
> modern pipelined) machine. Here's why:
>
> A 6-degree polynomial using the standard Horner's rule takes exactly 5
> fused multiply-adds to run. On a G5, that would take 5 x 8 cyles = 40
> cyles, since each fma depends on the last.

Yes. Horner's method is, somewhat contrary to popular opinion,
not the best way of evaluating polynomials (on a computer).
Horner's method creates an expression tree that is deep, rather
than wide, so you fall victim to instruction latencies in
evaluating the expression.

On modern architectures you want a wide expression tree so
that subtrees can be evaluated in parallel (without stalling
due to latency dependencies).

A method that improves on Horner's method in this aspect
is Estrin's method. It rewrites the polynomial as a (mostly
balanced) binary tree using x^2 and A*x+B terms (where A
and B are different subexpressions).

Christer Ericson
Sony Computer Entertainment, Santa Monica



Date Subject Author
10/18/04
Read Fast exponent and logarithm, given initial estimate
Glen Low
10/18/04
Read Re: Fast exponent and logarithm, given initial estimate
Jeremy Watts
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
Peter Spellucci
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/18/04
Read Re: Fast exponent and logarithm, given initial estimate
bv
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
George Russell
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/20/04
Read Re: Fast exponent and logarithm, given initial estimate
George Russell
10/20/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/21/04
Read Re: Fast exponent and logarithm, given initial estimate
Christer Ericson
10/21/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/22/04
Read Re: Fast exponent and logarithm, given initial estimate
Christer Ericson
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
Martin Brown
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
Richard Mathar
10/19/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/20/04
Read Re: Fast exponent and logarithm, given initial estimate
Gert Van den Eynde
10/20/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/20/04
Read Re: Fast exponent and logarithm, given initial estimate
Richard Mathar
10/21/04
Read Re: Fast exponent and logarithm, given initial estimate
Gert Van den Eynde
10/21/04
Read Re: Fast exponent and logarithm, given initial estimate
bv
10/22/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/22/04
Read Re: Fast exponent and logarithm, given initial estimate
Peter Spellucci
10/22/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low
10/23/04
Read Re: Fast exponent and logarithm, given initial estimate
bv
10/24/04
Read Re: Fast exponent and logarithm, given initial estimate
Gert Van den Eynde
10/25/04
Read Re: Fast exponent and logarithm, given initial estimate
Peter Spellucci
10/20/04
Read Re: Fast exponent and logarithm, given initial estimate
Gert Van den Eynde
11/8/04
Read Re: Fast exponent and logarithm, given initial estimate
Glen Low

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