Fastest Way to Serve a File Using PHP

I'm trying to put together a function that receives a file path, identifies what it is, sets the appropriate headers, and serves it just like Apache would.

The reason I am doing this is because I need to use PHP to process some information about the request before serving the file.

Speed is critical

virtual() isn't an option

Must work in a shared hosting environment where the user has no control of the web server (Apache/nginx, etc)

Here's what I've got so far:

File::output($path);

<?php
class File {
static function output($path) {
    // Check if the file exists
    if(!File::exists($path)) {
        header('HTTP/1.0 404 Not Found');
        exit();
    }

    // Set the content-type header
    header('Content-Type: '.File::mimeType($path));

    // Handle caching
    $fileModificationTime = gmdate('D, d M Y H:i:s', File::modificationTime($path)).' GMT';
    $headers = getallheaders();
    if(isset($headers['If-Modified-Since']) && $headers['If-Modified-Since'] == $fileModificationTime) {
        header('HTTP/1.1 304 Not Modified');
        exit();
    }
    header('Last-Modified: '.$fileModificationTime);

    // Read the file
    readfile($path);

    exit();
}

static function mimeType($path) {
    preg_match("|\.([a-z0-9]{2,4})$|i", $path, $fileSuffix);

    switch(strtolower($fileSuffix[1])) {
        case 'js' :
            return 'application/x-javascript';
        case 'json' :
            return 'application/json';
        case 'jpg' :
        case 'jpeg' :
        case 'jpe' :
            return 'image/jpg';
        case 'png' :
        case 'gif' :
        case 'bmp' :
        case 'tiff' :
            return 'image/'.strtolower($fileSuffix[1]);
        case 'css' :
            return 'text/css';
        case 'xml' :
            return 'application/xml';
        case 'doc' :
        case 'docx' :
            return 'application/msword