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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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Richard Mathar

Posts: 96
Registered: 12/13/04
Re: Fast exponent and logarithm, given initial estimate
Posted: Oct 19, 2004 9:48 AM
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In article <9215d7ac.0410180730.16880959@posting.google.com>,
glenlow@pixelglow.com (Glen Low) writes:
>Hi all
>
>I'm new to the group, so excuse this post if it's too elementary.
I also excuse the post if it is not elementary -:)
>
>I need a fast exponent and logarithm routine for floats. It should
>preferably use only adds, subtracts and multiplies; divides and square
>roots are permissible if necessary. It should not use large lookup
>tables. An additional wrinkle (or help) is that there's a exponent and
>a logarithm estimate available. (In case you're wondering, this is the
>situation with the Altivec SIMD instruction set.)
> <snap>
..
In case the exponentials are of some limited range (say -0.5 to 0.5 or
-10 to 10 for example), and if some lookup tables are allowed, one
could use static lookup tables of the exponent function that cover the
individual decimals of the exponentials. Example: to calculate exp(7.345)
one needs exp(7), exp(0.3), exp(0.04) and exp(0.005) (all of these
are obviously to be multiplied to get the result), and these could be
provided in lookup tables that store
[exp(0)],exp(1),exp(2),..exp(10)
exp(0.1),exp(0.2),..exp(0.9)
exp(0.01),exp(0.02),..exp(0.09)
..
as deep as the final accuracy requires. Note that the density of these
lookup tables does not the be of that kind; the only request to it is that
any exponential can be decomposed into a sum of entries in the table. So
a lookup table with exp(8),exp(4),exp(2),exp(1), exp(1/2), exp(1/4),
exp(1/8),...exp(1/2^n)
would serve an equivalent purpose, for instance.



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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