Log is non-monotonic in PHP and Lua

If a > b > 1 and x > 1, you can prove that log a ⁡ x < log b ⁡ x. (As a reminder, log a ⁡ x denotes the value t such that x = a t.) This is very intuitive if you think about it: for “normal” numbers, the greater a, the smaller t you will need to get the same x.

Yet if you ask PHP what it thinks, it will tell you you’re wrong in a couple rare cases:

?php
$x = 2.93;
$a = 10 + 2 ** - 49;
$b = 10;
assert ( $a > $b );
var_dump ( log ( $x, $a ) < log ( $x, $b ));
var_dump ( log ( $x, $a ) == log ( $x, $b ));

To be clear, this is not the usual floating-point inaccuracy. Everyone already knows floating-point operations are imprecise and it wouldn’t be fun to blog about. This example was deliberately engineered to trigger something different.