Why is range() not inclusive when given with float range and interval?

Question

The documentation states that the $end of the range is inclusive. And this is the case most of the time, but when both $end and $step are floats, the last value is missing. Why is that?

print_r(range(1, 13, 1));
print_r(range(1, 13, 0.1));
print_r(range(0.1, 1.3, 0.1));

Output:

Array
(
    [0] => 1
    [1] => 2
    // ...
    [11] => 12
    [12] => 13
)
Array
(
    [0] => 0.1
    [1] => 0.2
    // ...
    [119] => 12.9
    [120] => 13
)
Array
(
    [0] => 0.1
    [1] => 0.2
    // ...
    [10] => 1.1
    [11] => 1.2
    // 12 => 1.3 is missing
)

Answer 1

The range is inclusive; however, your assumptions about the numbers adding up are incorrect.

0.1 cannot be represented in binary with exact precision. When you use it in a calculation in php, you'll actually get a number that's a little higher or lower. Take a look at the following codepad:

http://codepad.org/MkoWgAA1

<?php

$sum = 1.0 + 0.1 + 0.1;

if ($sum > 1.2) {
  print("1.2 > 1.2");
} else if ($sum < 1.2) {
  print("1.2 < 1.2");
} else {
  print("1.2 == 1.2");
}

Output:

1.2 > 1.2