PHP: Cumulative/Prefix Summing. Use these functions to sum up a numeric array for subsequent processing.

cumulative_slice.php

<?php

// count inclusive from x to y keys (x and y keys are the keys for the prefix sum, not the keys of the original array)
function cumulative_slice($prefix, $x, $y){
    return $prefix[$y] - $prefix[$x];
}

// here's a more flexible function:
// run with X, Y when using original array indexes
// run with X, null, Z  when using cumulative array indexes
function cumulative_range_sum($cumulative, $X, $Y, $Z = null){
    // range summing is between the X index inclusive, to the Y index inclusive, which requires Z to be Y+1
    if(is_null($Z)){
        $Z = $Y + 1;
    }
    return $cumulative[$Z] - $cumulative[$X];
}

cumulative_sum.php

<?php

function cumulative_sum($A){
    $length = count($A);
    $summed = array_fill(0, $length + 1, 0);
    for($i = 1; $i <= $length; $i++){
        $summed[$i] = $summed[$i - 1] + $A[$i - 1];
    }
    return $summed;
}