Path: csiph.com!usenet.pasdenom.info!aioe.org!.POSTED!not-for-mail
From: glen herrmannsfeldt <gah@ugcs.caltech.edu>
Newsgroups: comp.lang.java.programmer
Subject: Re: What is the command to do a power of a value
Date: Mon, 30 Jul 2012 22:26:15 +0000 (UTC)
Organization: Aioe.org NNTP Server
Lines: 25
Message-ID: <jv71m7$o8m$1@speranza.aioe.org>
References: <5016CF47.55648.calajapr@time.synchro.net> <5016CF47.55649.calajapr@time.synchro.net>
NNTP-Posting-Host: H0vc4U5LIRkRHNPyGCs2dA.user.speranza.aioe.org
X-Complaints-To: abuse@aioe.org
User-Agent: tin/1.9.6-20100522 ("Lochruan") (UNIX) (Linux/2.6.32-5-amd64 (x86_64))
X-Notice: Filtered by postfilter v. 0.8.2
Xref: csiph.com comp.lang.java.programmer:16685

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