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Fast exponent and logarithm, given initial estimate
Posted:
Oct 18, 2004 11:30 AM
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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&lr=&threadm=c1lmjl%24jqu%242%40news.btv.ibm.com&rnum=2&prev=/groups%3Fhl%3Den%26lr%3D%26q%3Dfast%2Blogarithm%26btnG%3DSearch%26meta%3Dgroup%253Dsci.math.num-analysis">http://groups.google.com/groups?hl=en&lr=&threadm=c1lmjl%24jqu%242%40news.btv.ibm.com&rnum=2&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
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