Counts number of attachments for the mime type(s).

If you set the optional mime_type parameter, then an array will still be
returned, but will only have the item you are looking for. It does not give
you the number of attachments that are children of a post. You can get that
by counting the number of children that post has.

function wp_count_attachments( $mime_type = '' ) {
	global $wpdb;

	$cache_key = sprintf(
		'attachments%s',
		! empty( $mime_type ) ? ':' . str_replace( '/', '_', implode( '-', (array) $mime_type ) ) : ''
	);

	$counts = wp_cache_get( $cache_key, 'counts' );
	if ( false == $counts ) {
		$and   = wp_post_mime_type_where( $mime_type );
		$count = $wpdb->get_results( "SELECT post_mime_type, COUNT( * ) AS num_posts FROM $wpdb->posts WHERE post_type = 'attachment' AND post_status != 'trash' $and GROUP BY post_mime_type", ARRAY_A );

		$counts = array();
		foreach ( (array) $count as $row ) {
			$counts[ $row['post_mime_type'] ] = $row['num_posts'];
		}
		$counts['trash'] = $wpdb->get_var( "SELECT COUNT( * ) FROM $wpdb->posts WHERE post_type = 'attachment' AND post_status = 'trash' $and" );

		wp_cache_set( $cache_key, (object) $counts, 'counts' );
	}

	/**
	 * Modifies returned attachment counts by mime type.
	 *
	 * @since 3.7.0
	 *
	 * @param stdClass        $counts    An object containing the attachment counts by
	 *                                   mime type.
	 * @param string|string[] $mime_type Array or comma-separated list of MIME patterns.
	 */
	return apply_filters( 'wp_count_attachments', (object) $counts, $mime_type );
}