The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Glen Low

Posts: 41
Registered: 12/13/04
Fast exponent and logarithm, given initial estimate
Posted: Oct 18, 2004 11:30 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


Hi all

I'm new to the group, so excuse this post if it's too 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.)

Newton-Raphson seems of no use since I can't use the inverse function.

This thread looked promising:

<a href="http://groups.google.com/groups?hl=en&amp;lr=&amp;threadm=c1lmjl%24jqu%242%40news.btv.ibm.com&amp;rnum=2&amp;prev=/groups%3Fhl%3Den%26lr%3D%26q%3Dfast%2Blogarithm%26btnG%3DSearch%26meta%3Dgroup%253Dsci.math.num-analysis">http://groups.google.com/groups?hl=en&amp;lr=&amp;threadm=c1lmjl%24jqu%242%40news.btv.ibm.com&amp;rnum=2&amp;prev=/groups%3Fhl%3Den%26lr%3D%26q%3Dfast%2Blogarithm%26btnG%3DSearch%26meta%3Dgroup%253Dsci.math.num-analysis</a>

Brian Webb stated a method (Brent-Salamin) using

Lnx = pi*x*(1+4/(x^2))*(1-1/Lnx))/(2*AGM(x,4))

However on checking the referenced "rpb028" I see

Lnx = pi / (2* AGM (1, 4/x))

instead and don't see how to get from the latter equation to the
former? Any chance of somehow plugging in the log estimate or exponent
estimate in there and getting an iterative method?

Cheers,
Glen Low, Pixelglow Software
www.pixelglow.com



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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.