Pathologically Eclectic Rubbish Lister PerlMonks

### Comment on

 ( #3333=superdoc: print w/ replies, xml ) Need Help??
If you have log available, you can use Newton method to easyly find the solution to the equation f(z) = log(z) - y * log x = 0 :
```#!/usr/bin/perl

use strict;
use warnings;

my (\$X, \$Y, \$n) = @ARGV;
\$n ||= 20;

my \$Z = \$X ** \$Y;

# f(z) = log z - y * log x = 0;
# f'(z) = f1(z) = 1/z

my \$ylogx = \$Y * log \$X;

my \$z = 1;
for my \$i (1..\$n) {
my \$fz = log(\$z) - \$ylogx;
my \$f1z = 1 / \$z;
\$z = \$z - \$fz / \$f1z;
my \$e = abs(\$z - \$Z);
printf "%3d: z=%8f, e=%8f\n", \$i, \$z, \$e;
}
This method does not handle correctly values of y < 0 but this is not a problem because z(y) = 1 / z(-y).

Also, note that even if the algorithm converges in very few iterations, it uses log that is usually an expensive operation and so, other methods requiring more iterations may be actually faster.

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":

• Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
• Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
• Read Where should I post X? if you're not absolutely sure you're posting in the right place.
• Posts may use any of the Perl Monks Approved HTML tags:
a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
• You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
 For: Use: & & < < > > [ [ ] ]
• Link using PerlMonks shortcuts! What shortcuts can I use for linking?

Create A New User
Chatterbox?
and the web crawler heard nothing...

How do I use this? | Other CB clients
Other Users?
Others meditating upon the Monastery: (8)
As of 2016-05-05 20:44 GMT
Sections?
Information?
Find Nodes?
Leftovers?
Voting Booth?
What font do you use for programming?

Results (103 votes). Check out past polls.