4. Application Exercise - IMPOTS
4.1. The Problem
We aim to write a program to calculate a taxpayer’s tax. We consider the simplified case of a taxpayer who has only their salary to report:
- we calculate the number of shares for the employee nbParts = nbEnfants/2 + 1 if they are unmarried, nbEnfants/2+2 if they are married, where nbEnfants is the number of children.
- We calculate his taxable income R = 0.72 * S, where S is his annual salary
- we calculate his family coefficient Q = R/N
we calculate his tax I based on the following data
12620.0 | 0 | 0 |
13,190 | 0.05 | 631 |
15,640 | 0.1 | 1,290.5 |
24,740 | 0.15 | 2,072.5 |
31,810 | 0.2 | 3,309.5 |
39,970 | 0.25 | 4,900 |
48,360 | 0.3 | 6898.5 |
55,790 | 0.35 | 9,316.5 |
92,970 | 0.4 | 12,106 |
127,860 | 0.45 | 16,754.5 |
151,250 | 0.50 | 23,147.5 |
172,040 | 0.55 | 30,710 |
195,000 | 0.60 | 39,312 |
0 | 0.65 | 49,062 |
Each row has 3 fields. To calculate tax I, we look for the first row where QF <= field1. For example, if QF = 30000, we will find the row
Tax I is then equal to 0.15*R - 2072.5*nbParts. If QF is such that the relation QF <= field1 is never satisfied, then the coefficients from the last row are used. Here:
which gives the tax I=0.65*R – 49062*nbParts.
4.2. Version with tables (impots_01)
We present an initial program where:
- the data needed to calculate the tax are in three tables (limits, coeffR, coeffN)
- the taxpayer data (married, children, salary) is in a first text file
- the results of the tax calculation (married, children, salary, tax) are stored in a second text file
<?php
// definition of constants
$DATA = "data.txt";
$RESULTATS = "resultats.txt";
$limites = array(12620, 13190, 15640, 24740, 31810, 39970, 48360, 55790, 92970, 127860, 151250, 172040, 195000);
$coeffR = array(0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65);
$coeffN = array(0, 631, 1290.5, 2072.5, 3309.5, 4900, 6898.5, 9316.5, 12106, 16754.5, 23147.5, 30710, 39312, 49062);
// reading data
$data = fopen($DATA, "r");
if (!$data) {
print "Impossible d'ouvrir en lecture le fichier des données [$DATA]\n";
exit;
}
// open results file
$résultats = fopen($RESULTATS, "w");
if (!$résultats) {
print "Impossible de créer le fichier des résultats [$RESULTATS]\n";
exit;
}
// use the current line of the data file
while ($ligne = fgets($data, 100)) {
// remove any end-of-line marker
$ligne = cutNewLineChar($ligne);
// we retrieve the 3 fields married,children,salary which form $ligne
list($marié, $enfants, $salaire) = explode(",", $ligne);
// tax calculation
$impôt = calculImpots($marié, $enfants, $salaire, $limites, $coeffR, $coeffN);
// enter the result in the results file
fputs($résultats, "$marié:$enfants:$salaire:$impôt\n");
// next taxpayer
}
// close files
fclose($data);
fclose($résultats);
// end
exit;
// --------------------------------------------------------------------------
function cutNewLinechar($ligne) {
// delete the end-of-line mark from $ligne if it exists
$L = strlen($ligne); // line length
while (substr($ligne, $L - 1, 1) == "\n" or substr($ligne, $L - 1, 1) == "\r") {
$ligne = substr($ligne, 0, $L - 1);
$L--;
}
// end
return($ligne);
}
// --------------------------------------------------------------------------
function calculImpots($marié, $enfants, $salaire, $limites, $coeffR, $coeffN) {
// $marié : yes, no
// $enfants : number of children
// $salaire: annual salary
// $limites, $coeffR, $coeffN: tax calculation data tables
// number of shares
$marié = strtolower($marié);
if ($marié == "oui")
$nbParts = $enfants / 2 + 2;
else
$nbParts=$enfants / 2 + 1;
// an additional 1/2 share if at least 3 children
if ($enfants >= 3)
$nbParts+=0.5;
// taxable income
$revenuImposable = 0.72 * $salaire;
// family quotient
$quotient = $revenuImposable / $nbParts;
// is set at the end of the limit table to stop the following loop
array_push($limites, $quotient);
// tAX CALCULATION
$i = 0;
while ($quotient > $limites[$i])
$i++;
// because $quotient has been placed at the end of the $limites array, the previous loop
// cannot exceed the table $limites
// now we can calculate the tax
return floor($revenuImposable * $coeffR[$i] - $nbParts * $coeffN[$i]);
}
?>
The data.txt data file (married, children, salary):
The résultats.txt file (married, children, salary, tax) of the results obtained:
oui:2:200000:22504
non:2:200000:33388
oui:3:200000:16400
non:3:200000:22504
oui:5:50000:0
non:0:3000000:1354938
Comments
- line 4: the name of the text file containing taxpayer data (married, children, salary)
- line 5: the name of the text file containing the results (married, children, salary, tax) of the tax calculation
- lines 6–8: the three data tables used to calculate the tax
- lines 11-15: open the taxpayer data file for reading
- lines 18–22: open the results file for writing
- line 25: loop to read the lines (married, children, salary) from the taxpayer file
- line 27: the end-of-line marker is removed
- line 29: the components (married, children, salary) of the line are retrieved
- line 31: tax is calculated
- line 33: the tax is stored in the results file
- lines 37-38: once the taxpayer file has been fully processed, the files are closed
- line 44: the function that removes the end-of-line character from a line $ligne. The end-of-line character is the string "\r\n" on Windows systems, "\n" on Unix systems. The result is the input string without its end-of-line character.
- lines 47–48: substr($chaîne,$début,$taille) is the substring of $chaîne starting at the character $début and having at most $taille characters.
- line 63: strtolower($chaîne) converts $chaîne to lowercase
- line 76: array_push($tableau,$élément) adds $élément to the end of the array $tableau. Note that the array $limites is passed by value to the function calculerImpot (line 56). This addition of an element is therefore performed on the copy of the actual parameter, which remains unchanged.
- Line 84: The function floor($x) returns the integer value immediately less than $x.
4.3. Version with text files (impots_02)
This new version differs from the previous one only in that the data ($limites, $coeffR, $coeffN) required for tax calculation are now in a text file in the following format:
File impots.txt:
12620:13190:15640:24740:31810:39970:48360:55790:92970:127860:151250:172040:195000:0
0:0.05:0.1:0.15:0.2:0.25:0.3:0.35:0.4:0.45:0.5:0.55:0.6:0.65
0:631:1290.5:2072.5:3309.5:4900:6898.5:9316.5:12106:16754.5:23147.5:30710:39312:49062
The new version simply reads the data from the [impots.txt] file in order to place it into three tables ($limites, $coeffR, $coeffN). This brings us back to the previous case. We will only present the changes:
<?php
// definition of constants
$DATA = "data.txt";
$RESULTATS = "resultats.txt";
$IMPOTS = "impots.txt";
// the data required to calculate the tax has been placed in the $IMPOTS file
// one line per table in the form
// val1:val2:val3,...
list($erreur, $limites, $coeffR, $coeffN) = getTables($IMPOTS);
// was there a mistake?
if ($erreur) {
print "$erreur\n";
exit;
}//if
// reading user data
...
// end
exit;
// --------------------------------------------------------------------------
function cutNewLinechar($ligne) {
// delete the end-of-line mark from $ligne if it exists
...
}
// --------------------------------------------------------------------------
function calculImpots($marié, $enfants, $salaire, $limites, $coeffR, $coeffN) {
// $marié : yes, no
// $enfants : number of children
// $salaire: annual salary
// $limites, $coeffR, $coeffN: tax calculation data tables
...
}
// --------------------------------------------------------------------------
function getTables($IMPOTS) {
// $IMPOTS: name of the file containing data from tables $limites, $coeffR, $coeffN
// does the $IMPOTS file exist?
if (!file_exists($IMPOTS))
return array("Le fichier $IMPOTS n'existe pas","","","");
// file block playback
$tables = file($IMPOTS);
if (!$tables)
return array("Erreur lors de l'exploitation du fichier $IMPOTS","","","");
// create the 3 tables - assume the rows are syntactically correct
$limites = explode(":", cutNewLineChar($tables[0]));
$coeffR = explode(":", cutNewLineChar($tables[1]));
$coeffN = explode(":", cutNewLineChar($tables[2]));
// end
return array("", $limites, $coeffR, $coeffN);
}
?>
Comments
- line 11: the function getTables($IMPOTS) processes the text file $IMPOTS to extract the three arrays ($limites, $coeffR, $coeffN). The result returned is ($erreur, $limites, $coeffR, $coeffN), where $erreur is an error message, empty if no error occurred.
- line 40: the function getTables($IMPOTS).
- line 43: the function files_exists(nom_fichier) returns true if the file nom_fichier exists, false otherwise.
- Line 46: The function file(nom_fichier) reads the entire text file nom_fichier. It returns an array where each element is a line of the text file. Since, in this case, the file impots.txt has three lines of text, the function will return an array with three elements.
- Lines 50–52: Use the three retrieved lines to create the three arrays ($limites, $coeffR, $coeffN)
The results obtained are the same as those obtained in the previous version.