calculate factorials as floats (#283)

Author: PhilippImhof

classes/local/functions.php

@@ -833,11 +833,16 @@ public static function rshuffle(array $ar): array {
      * Note: technically, the function accepts a float, because in some
      * PHP versions, if one passes a float to a function that expectes an int,
      * the float will be converted. We'd rather detect that and print an error.
+     * Although the returned value is an integer, we use the float type, because
+     * PHP_FLOAT_MAX is much larger than PHP_INT_MAX.
+     * Beware: Due to the limited precision of floats (~ 16 digits), factorials
+     * larger than 27! are not guaranteed to be accurate, or rather, they are
+     * guaranteed not to be accurate...
      *
      * @param float $n the number
-     * @return int
+     * @return float
      */
-    public static function fact(float $n): int {
+    public static function fact(float $n): float {
         $n = self::assure_numeric(
             $n,
             get_string('error_func_nnegint', 'qtype_formulas', 'fact()'),
@@ -848,7 +853,7 @@ public static function fact(float $n): int {
         }
         $result = 1;
         for ($i = 1; $i <= $n; $i++) {
-            if ($result > PHP_INT_MAX / $i) {
+            if ($result > PHP_FLOAT_MAX / $i) {
                 self::die('error_fact_toolarge', $n);
             }
             $result *= $i;

classes/local/random_variable.php

@@ -89,7 +89,7 @@ public function how_many(): int {
                 // TODO: non-capturing catch.
                 return PHP_INT_MAX;
             }
-            return $result;
+            return $result >= PHP_INT_MAX ? PHP_INT_MAX : (int) $result;
         }
         return count($this->reservoir);
     }

tests/functions_test.php

@@ -268,6 +268,9 @@ public static function provide_fact(): array {
             [2, 'fact(2)'],
             [6, 'fact(3)'],
             [720, 'fact(6)'],
+            [15511210043330985984000000, 'fact(25)'],
+            [403291461126605635584000000, 'fact(26)'],
+            [10888869450418352160768000000, 'fact(27)'],
             ['fact() expects its argument to be a non-negative integer.', 'fact(-2)'],
             ['fact() expects its argument to be a non-negative integer.', 'fact(2.5)'],
             ['Cannot compute 250! on this platform, the result is bigger than PHP_MAX_INT.', 'fact(250)'],