Jul
03
Вычисления с произвольной точностью BCMath
Вычисления с произвольной точностью BCMath
- Введение
- Установка и настройка
- Предопределенные константы
- BC Math Функции
- bcadd — Сложить 2 числа произвольной точности
- bccomp — Сравнение двух чисел произвольной точности
- bcdiv — Операция деления для чисел произвольной точности
- bcmod — Получает остаток от деления чисел с произвольной точностью
- bcmul — Умножение двух чисел с произвольной точностью
- bcpow — Возведение в степень чисел с произвольной точностью
- bcpowmod — Возводит одно число в степень другого и возвращает остаток от деления
результата на третье число
- bcscale — Задает количество чисел после десятичной точки по умолчанию для всех
bc math функций.
- bcsqrt — Извлекает квадратный корень из числа с произвольной точностью
- bcsub — Вычитает одно число с произвольной точностью из другого
Коментарии
Needed to compute some permutations and found the BC extension great but poor on functions, so untill this gets implemented here's the factorial function:
<?php
/* BC FACTORIAL
* n! = n * (n-1) * (n-2) .. 1 [eg. 5! = 5 * 4 * 3 * 2 * 1 = 120]
*/
function bcfact($n){
$factorial=$n;
while (--$n>1) $factorial=bcmul($factorial,$n);
return $factorial;
}
print bcfact(50);
//30414093201713378043612608166064768844377641568960512000000000000
?>
It's worth noting that this library is named very wrongly.
It may be called 'Binary Calculator', but what you're getting is a decimal calculator that can represent base-10 fractions accurately.
Note that when you use implementation of factorial that ClaudiuS made, you get results even if you try to calculate factorial of number that you normally can't, e.g. 2.5, -2, etc. Here is safer implementation:
<?php
/**
* Calculates a factorial of given number.
* @param string|int $num
* @throws InvalidArgumentException
* @return string
*/
function bcfact($num)
{
if (!filter_var($num, FILTER_VALIDATE_INT) || $num <= 0) {
throw new InvalidArgumentException(sprintf('Argument must be natural number, "%s" given.', $num));
}
for ($result = '1'; $num > 0; $num--) {
$result = bcmul($result, $num);
}
return $result;
}
?>
This extension is an interface to the GNU implementation as a library of the Basic Calculator utility by Philip Nelson; hence the name.
Useful function for bcround
function getBcRound($number, $precision = 0)
{
$precision = ($precision < 0)
? 0
: (int) $precision;
if (strcmp(bcadd($number, '0', $precision), bcadd($number, '0', $precision+1)) == 0) {
return bcadd($number, '0', $precision);
}
if (getBcPresion($number) - $precision > 1) {
$number = getBcRound($number, $precision + 1);
}
$t = '0.' . str_repeat('0', $precision) . '5';
return $number < 0
? bcsub($number, $t, $precision)
: bcadd($number, $t, $precision);
}
function getBcPresion($number) {
$dotPosition = strpos($number, '.');
if ($dotPosition === false) {
return 0;
}
return strlen($number) - strpos($number, '.') - 1;
}
var_dump(getBcRound('3', 0) == number_format('3', 0));
var_dump(getBcRound('3.4', 0) == number_format('3.4', 0));
var_dump(getBcRound('3.56', 0) == number_format('3.6', 0));
var_dump(getBcRound('1.95583', 2) == number_format('1.95583', 2));
var_dump(getBcRound('5.045', 2) == number_format('5.045', 2));
var_dump(getBcRound('5.055', 2) == number_format('5.055', 2));
var_dump(getBcRound('9.999', 2) == number_format('9.999', 2));
var_dump(getBcRound('5.0445', 5) == number_format('5.044500', 5));
var_dump(getBcRound('5.0445', 4) == number_format('5.04450', 4));
var_dump(getBcRound('5.0445', 3) == number_format('5.0445', 3));
var_dump(getBcRound('5.0445', 2) == number_format('5.045', 2));
var_dump(getBcRound('5.0445', 1) == number_format('5.05', 1));
var_dump(getBcRound('5.0445', 0) == number_format('5.0', 0));//
var_dump(getBcRound('5.04455', 2) == number_format('5.045', 2));
var_dump(getBcRound('99.999', 2) == number_format('100.000', 2));
var_dump(getBcRound('99.999') == number_format('99.999', 0));
var_dump(getBcRound('99.999', 'a') == number_format('99.999', 0));
var_dump(getBcRound('99.999', -1.5) == number_format('99.999', 0));
var_dump(getBcRound('-0.00001', 2) == number_format('-0.000', 2));
var_dump(getBcRound('-0.0000', 2) == number_format('0', 2));
var_dump(getBcRound('-4.44455', 2) == number_format('-4.445', 2));
var_dump(getBcRound('-4.44555', 0) == number_format('-4.5', 0));
var_dump(getBcRound('-4.444444444444444444444444444444444444444444445', 0) == number_format('-4.5', 0));
Useful function for bcround
function getBcRound($number, $precision = 0)
{
$precision = ($precision < 0)
? 0
: (int) $precision;
if (strcmp(bcadd($number, '0', $precision), bcadd($number, '0', $precision+1)) == 0) {
return bcadd($number, '0', $precision);
}
if (getBcPresion($number) - $precision > 1) {
$number = getBcRound($number, $precision + 1);
}
$t = '0.' . str_repeat('0', $precision) . '5';
return $number < 0
? bcsub($number, $t, $precision)
: bcadd($number, $t, $precision);
}
function getBcPresion($number) {
$dotPosition = strpos($number, '.');
if ($dotPosition === false) {
return 0;
}
return strlen($number) - strpos($number, '.') - 1;
}
var_dump(getBcRound('3', 0) == number_format('3', 0));
var_dump(getBcRound('3.4', 0) == number_format('3.4', 0));
var_dump(getBcRound('3.56', 0) == number_format('3.6', 0));
var_dump(getBcRound('1.95583', 2) == number_format('1.95583', 2));
var_dump(getBcRound('5.045', 2) == number_format('5.045', 2));
var_dump(getBcRound('5.055', 2) == number_format('5.055', 2));
var_dump(getBcRound('9.999', 2) == number_format('9.999', 2));
var_dump(getBcRound('5.0445', 5) == number_format('5.044500', 5));
var_dump(getBcRound('5.0445', 4) == number_format('5.04450', 4));
var_dump(getBcRound('5.0445', 3) == number_format('5.0445', 3));
var_dump(getBcRound('5.0445', 2) == number_format('5.045', 2));
var_dump(getBcRound('5.0445', 1) == number_format('5.05', 1));
var_dump(getBcRound('5.0445', 0) == number_format('5.0', 0));//
var_dump(getBcRound('5.04455', 2) == number_format('5.045', 2));
var_dump(getBcRound('99.999', 2) == number_format('100.000', 2));
var_dump(getBcRound('99.999') == number_format('99.999', 0));
var_dump(getBcRound('99.999', 'a') == number_format('99.999', 0));
var_dump(getBcRound('99.999', -1.5) == number_format('99.999', 0));
var_dump(getBcRound('-0.00001', 2) == number_format('-0.000', 2));
var_dump(getBcRound('-0.0000', 2) == number_format('0', 2));
var_dump(getBcRound('-4.44455', 2) == number_format('-4.445', 2));
var_dump(getBcRound('-4.44555', 0) == number_format('-4.5', 0));
var_dump(getBcRound('-4.444444444444444444444444444444444444444444445', 0) == number_format('-4.5', 0));