I’m doing these Project Euler mathematical puzzles as a simple practical exercise for teaching myself PHP, and I’d appreciate any feedback on my code.

Comparing two numbers written in index form like 2^{11}and 3^{7}is not difficult, as any calculator would confirm that 2^{11}= 2048 < 3^{7}= 2187.

However, confirming that 632382^{518061}> 519432^{525806}would be much more difficult, as both numbers contain over three million digits.

Using base_exp.txt, a 22K text file containing one thousand lines with a base/exponent pair on each line, determine which line number has the greatest numerical value.

NOTE: The first two lines in the file represent the numbers in the example given above.

Interesting, sounds quite difficult. At first I thought I could use the BC Math functions which have proven so useful in many of the previous puzzles and “*support numbers of any size and precision”*. However they didn’t seem to work; according to this StackExchange question they “*can handle numbers greater than 2^1000000 (which is 301,030+ digits)*“. We’re dealing with numbers here that are ten-fold of that! So I used the GMP functions instead, which “*allow you to work with arbitrary-length integers”*.

<?php $pairs = file('p099_base_exp.txt'); $max = 0; foreach($pairs as $key=>$pair) { $numbers = explode(",", $pair); $base = $numbers[0]; $exponent = $numbers[1]; $power = gmp_pow($base, intval($exponent)); if (gmp_cmp($power, $max) > 0) { $max = $power; $lineNumber = $key; } } echo $lineNumber+1;

I read the file in using file(), turning each line into an array element. I then loop over those 1000 array elements, using explode() to split each line into its base and exponent parts.

Then I use the gmp_pow() function; however when I tried it initially simply using *gmp_pow($base, $exponent)* it threw up this error: “*A non well formed numeric value encountered*“. It expects $exponent to be an integer, which to all intents and purposes, it seems to be. However I had to explicitly cast it to an integer, using either *intval($exponent)* or *(int)$exponent* – both seemed to work.

Initially I thought I had to use a GMP number for the base, so was using gmp_init() to create one from $base. However in the end that didn’t seem to be necessary. So the gmp_pow() function is fussy about what kind of value it gets for the exponenent, but less-so for the base… curious.

After working out the power, I then compare it the maximum power so far, using gmp_cmp(). Each time I get a new maximum value I keep track of which line number that belongs to. At the end when I output that I increment it by 1, due to PHP arrays being zero-indexed.

This is very slow code, taking close to 5 minutes!

PS: to get the GMP functions to work on my Windows environment I had to uncomment this line in php.ini:

extension=php_gmp.dll