[PHP] Total values rounding adjustment algorythm.

rounding.php

<?php

/*
 * Rounds the given values and add them up in order to fix in the total value.
 * It prevents differences of total values caused by the default rounding method.
 * Do not use more than 2 decimals for accuracy purposes.
 *
 * Inspired of : http://stackoverflow.com/a/13483710/4022804
 * This function adjusts the rounded values by adding up the ones that have the highest decimals.
 */
public function round($values, $maxValue, $decimals) {
    // Round the max value :
    // e.g.: 5.801 with 2 decimals => 5.80
    $roundedMaxValue = round($maxValue, $decimals);

    // Round each value down :
    // e.g.:
    // 1.234 with 2 decimals => 1.23
    // 4.567 with 2 decimals => 4.56
    $flooredTotals = [];
    foreach ($values as $key => $value) {
        $flooredTotals[$key] = floor($value * pow(10, $decimals)) / pow(10, $decimals);
    }

    // Use the floored values as a basis for the values add up
    $roundedTotals = $flooredTotals;

    // Calculate the difference caused by the rounding :
    // 1.234 + 4.564 = 5.801
    // Rounded : 1.23 + 4.56 = 5.80 ===> difference of 1 !
    $roundingDifference = floor(round($roundedMaxValue * pow(10, $decimals)));
    foreach ($roundedTotals as $key => $value) {
        $roundingDifference -= floor(round($value * pow(10, $decimals)));
    }

    // Find which way the rounding must be done :
    // (if the value must be added or substracted 1)
    // $roundingSign === 1 if $roundingDifference is positive
    // $roundingSign === -1 if $roundingDifference is negative
    $roundingSign = ($roundingDifference > 0) - ($roundingDifference < 0);

    // Find the N one(s) with the highest decimal values (on the right of the rounding) :
    // 1.234 with 2 decimals => 1.23|4
    // 4.567 with 2 decimals => 4.56|7 => has the highest value on the right of the rounding
    $valuesToAdjust = [];
    $valuesToTake = $values;
    for ($i = 0; $i < $roundingDifference; $i++) {
        if (!isset($valuesToAdjust[$i])) {
            reset($valuesToTake);
            $valuesToAdjust[$i] = key($valuesToTake);
        }
        foreach ($valuesToTake as $key => $value) {
            // Compare the values on the right the decimals to round
            // and save the value that must have a rounding adjustment
            $loopValueDecimals = $valuesToTake[$valuesToAdjust[$i]] - floor($valuesToTake[$valuesToAdjust[$i]]);
            $loopValueDecimalsAfterRounding = ($loopValueDecimals * pow(10, $decimals)) - floor($loopValueDecimals * pow(10, $decimals));
            $valueDecimals = $value - floor($value);
            $valueDecimalsAfterRounding = ($valueDecimals * pow(10, $decimals)) - floor($valueDecimals * pow(10, $decimals));
            if ($valuesToTake[$key] !== 0) {
                $valuesToAdjust[$i] = $key;
                $valuesToTake[$key] = 0;
            }
        }
    }

    // Recalculate the rounding of the values to adjust
    // (there is as much $valuesToAdjust as $roundingDifference(s))
    foreach ($valuesToAdjust as $key => $value) {
        $newDecimal = ((int)(($values[$value] - floor($values[$value])) * pow(10, $decimals)) + $roundingSign) / pow(10, $decimals);
        $newValue = floor($values[$value]) + $newDecimal;
        $roundedTotals[$value] = $newValue;
    }

    return $roundedTotals;
}