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Re: What is the command to do a power of a value

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From	"glen herrmannsfeldt" <glen.herrmannsfeldt@1:261/38.remove-dpk-this>
Subject	Re: What is the command to do a power of a value
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  To: Patricia Shanahan
From: glen herrmannsfeldt <gah@ugcs.caltech.edu>

Patricia Shanahan <patricia.shanahan@1:261/38.remove-rf4-this> wrote:

(snip, someone wrote)
>>   x ^ n  =  exp ( log(x) * n )    |  x = (1 + i/100)
>>          = exp ( log( 1 + i/100 ) * n)
>>          = exp ( log1p ( i/100 ) * n)

(snip)

> I am curious about why you expect this to be more precise than:
> "The computed result must be within 1 ulp of the exact result.
> Results must be semi-monotonic." (From the pow description).
> Or do you know of cases where Math.pow gets an over-large
> rounding error?

I didn't know about the log1p function. (Does Java have one?)

As x gets small log(1+x) loses precision. Consider:

      log(1+1e-60)

The x87 instruction set has an instruction for evaluating log(1+x) and one for 
evaluating exp(x-1). Most HLLs don't.

-- glen

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Thread

What is the command to do a power of a value "xvictoryeohx" <xvictoryeohx@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
  Re: What is the command to do a power of a value "bugbear" <bugbear@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
  Re: What is the command to do a power of a value "glen herrmannsfeldt" <glen.herrmannsfeldt@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
    Re: What is the command to do a power of a value "xvictoryeohx" <xvictoryeohx@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
  Re: What is the command to do a power of a value "Roedy Green" <roedy.green@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
    Re: What is the command to do a power of a value "Andreas Leitgeb" <andreas.leitgeb@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
      Re: What is the command to do a power of a value "Patricia Shanahan" <patricia.shanahan@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
        Re: What is the command to do a power of a value "Patricia Shanahan" <patricia.shanahan@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
        Re: What is the command to do a power of a value "glen herrmannsfeldt" <glen.herrmannsfeldt@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
          Re: What is the command to do a power of a value "Patricia Shanahan" <patricia.shanahan@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
          Re: What is the command to do a power of a value "Andreas Leitgeb" <andreas.leitgeb@1:261/38.remove-dpk-this> - 2012-07-31 18:02 +0000
        Re: What is the command to do a power of a value "Andreas Leitgeb" <andreas.leitgeb@1:261/38.remove-x1c-this> - 2012-07-31 20:07 +0000

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