Arbitrary Precision Maths Functions in PHP (BC Math)

Author — Nitish Kumar

Arbitrary Precision Maths Functions in PHP
Function NameFunction Description
bcadd()Add two arbitrary precision numbers
bccomp()Compare two arbitrary precision numbers
bcdiv()Divide two arbitrary precision numbers
bcmod()Get modulus of an arbitrary precision number
bcmul()Multiply two arbitrary precision numbers
bcpow()Raise an arbitrary precision number to another
bcpowmod()Raise an arbitrary precision number to another, reduced by a specified modulus
bcscale()Set or get default scale parameter for all bc math functions
bcsqrt()Get the square root of an arbitrary precision number
bcsub()Subtract one arbitrary precision number from another
On This Page
  1. PHP bcadd() Function
    1. PHP bcadd() Usage
    2. PHP bcadd() Syntax
    3. PHP bcadd() Parameters
    4. PHP bcadd() Return Value
    5. PHP bcadd() Working Examples
      1. 1. bcadd() example
    6. Additional Tips from Fellow Developers
  2. PHP bccomp() Function
    1. PHP bccomp() Usage
    2. PHP bccomp() Syntax
    3. PHP bccomp() Parameters
    4. PHP bccomp() Return Value
    5. PHP bccomp() Working Examples
      1. 1. bccomp() example
    6. Additional Tips from Fellow Developers
  3. PHP bcdiv() Function
    1. PHP bcdiv() Usage
    2. PHP bcdiv() Syntax
    3. PHP bcdiv() Parameters
    4. PHP bcdiv() Return Value
    5. PHP bcdiv() Working Examples
      1. 1. bcdiv() example
  4. PHP bcmod() Function
    1. PHP bcmod() Usage
    2. PHP bcmod() Syntax
    3. PHP bcmod() Parameters
    4. PHP bcmod() Return Value
    5. PHP bcmod() Working Examples
      1. 1. bcmod() example
      2. 2. bcmod() with decimals
    6. Changelog for PHP bcmod() Function
  5. PHP bcmul() Function
    1. PHP bcmul() Usage
    2. PHP bcmul() Syntax
    3. PHP bcmul() Parameters
    4. PHP bcmul() Return Value
    5. PHP bcmul() Working Examples
      1. 1. bcmul() example
      2. 2. bcmul() scale example
    6. Changelog for PHP bcmul() Function
    7. Important Points about PHP bcmul() Function
  6. PHP bcpow() Function
    1. PHP bcpow() Usage
    2. PHP bcpow() Syntax
    3. PHP bcpow() Parameters
    4. PHP bcpow() Return Value
    5. PHP bcpow() Working Examples
      1. 1. bcpow() example
      2. 2. bcpow() scale example
    6. Changelog for PHP bcpow() Function
    7. Important Points about PHP bcpow() Function
  7. PHP bcpowmod() Function
    1. PHP bcpowmod() Usage
    2. PHP bcpowmod() Syntax
    3. PHP bcpowmod() Parameters
    4. PHP bcpowmod() Return Value
    5. Important Points about PHP bcpowmod() Function
  8. PHP bcscale() Function
    1. PHP bcscale() Usage
    2. PHP bcscale() Syntax
    3. PHP bcscale() Parameters
    4. PHP bcscale() Return Value
    5. PHP bcscale() Working Examples
      1. 1. bcscale() example
    6. Changelog for PHP bcscale() Function
    7. Additional Tips from Fellow Developers
  9. PHP bcsqrt() Function
    1. PHP bcsqrt() Usage
    2. PHP bcsqrt() Syntax
    3. PHP bcsqrt() Parameters
    4. PHP bcsqrt() Return Value
    5. PHP bcsqrt() Working Examples
      1. 1. bcsqrt() example
  10. PHP bcsub() Function
    1. PHP bcsub() Usage
    2. PHP bcsub() Syntax
    3. PHP bcsub() Parameters
    4. PHP bcsub() Return Value
    5. PHP bcsub() Working Examples
      1. 1. bcsub() example

PHP bcadd() Function

PHP bcadd() Usage

The PHP bcadd() function will sums left_operand and right_operand.

PHP bcadd() Syntax

 bcadd ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string

PHP bcadd() Parameters

  1. left_operand — The left operand, as a string.

  2. right_operand — The right operand, as a string.

  3. scale — This optional parameter is used to set the number of digits after the decimal place in the result. If omitted, it will default to the scale set globally with the bcscale() function, or fallback to 0 if this has not been set.

PHP bcadd() Return Value

The PHP bcadd() function returns the sum of the two operands, as a string.

PHP bcadd() Working Examples

1. bcadd() example

<?php
$a = '1.234';
$b = '5';
echo bcadd($a, $b);     // 6
echo bcadd($a, $b, 4);  // 6.2340
?>

Additional Tips from Fellow Developers

Contributed By: Nitrogen

I made this to add an unlimited size of numbers together.. 
 
This could be useful for those without the BCMath extension. 
 
It allows decimals, and optional $Scale parameter.  If $Scale isn't specified, then it'll automatically adjust to show the correct number of decimals. 
 

<?php 
 
function Add($Num1,$Num2,$Scale=null) { 
  // check if they're valid positive numbers, extract the whole numbers and decimals 
  if(!preg_match("/^\+?(\d+)(\.\d+)?$/",$Num1,$Tmp1)|| 
     !preg_match("/^\+?(\d+)(\.\d+)?$/",$Num2,$Tmp2)) return('0'); 
 
  // this is where the result is stored 
  $Output=array(); 
 
  // remove ending zeroes from decimals and remove point 
  $Dec1=isset($Tmp1[2])?rtrim(substr($Tmp1[2],1),'0'):''; 
  $Dec2=isset($Tmp2[2])?rtrim(substr($Tmp2[2],1),'0'):''; 
 
  // calculate the longest length of decimals 
  $DLen=max(strlen($Dec1),strlen($Dec2)); 
 
  // if $Scale is null, automatically set it to the amount of decimal places for accuracy 
  if($Scale==null) $Scale=$DLen; 
 
  // remove leading zeroes and reverse the whole numbers, then append padded decimals on the end 
  $Num1=strrev(ltrim($Tmp1[1],'0').str_pad($Dec1,$DLen,'0')); 
  $Num2=strrev(ltrim($Tmp2[1],'0').str_pad($Dec2,$DLen,'0')); 
 
  // calculate the longest length we need to process 
  $MLen=max(strlen($Num1),strlen($Num2)); 
 
  // pad the two numbers so they are of equal length (both equal to $MLen) 
  $Num1=str_pad($Num1,$MLen,'0'); 
  $Num2=str_pad($Num2,$MLen,'0'); 
 
  // process each digit, keep the ones, carry the tens (remainders) 
  for($i=0;$i<$MLen;$i++) { 
    $Sum=((int)$Num1{$i}+(int)$Num2{$i}); 
    if(isset($Output[$i])) $Sum+=$Output[$i]; 
    $Output[$i]=$Sum%10; 
    if($Sum>9) $Output[$i+1]=1; 
  } 
 
  // convert the array to string and reverse it 
  $Output=strrev(implode($Output)); 
 
  // substring the decimal digits from the result, pad if necessary (if $Scale > amount of actual decimals) 
  // next, since actual zero values can cause a problem with the substring values, if so, just simply give '0' 
  // next, append the decimal value, if $Scale is defined, and return result 
  $Decimal=str_pad(substr($Output,-$DLen,$Scale),$Scale,'0'); 
  $Output=(($MLen-$DLen<1)?'0':substr($Output,0,-$DLen)); 
  $Output.=(($Scale>0)?".{$Decimal}":''); 
  return($Output); 
} 
 
$A="5650175242.508133742"; 
$B="308437806.831153821478770"; 
 
printf("  Add(%s,%s);\r\n// %s\r\n\r\n",$A,$B,  Add($A,$B)); 
printf("BCAdd(%s,%s);\r\n// %s\r\n\r\n",$A,$B,BCAdd($A,$B)); 
 
/* 
  This will produce the following.. 
    Add(5650175242.508133742,308437806.831153821478770); 
  // 5958613049.33928756347877 
 
  BCAdd(5650175242.508133742,308437806.831153821478770); 
  // 5958613049 
*/ 
 
?>
 
 
It was a fun experience making, and thought I'd share it. 
Enjoy, 
Nitrogen.

PHP bccomp() Function

PHP bccomp() Usage

The PHP bccomp() function will give you the result as an integer.

PHP bccomp() Syntax

 bccomp ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : int

PHP bccomp() Parameters

  1. left_operand — The left operand, as a string.

  2. right_operand — The right operand, as a string.

  3. scale — The optional scale parameter is used to set the number of digits after the decimal place which will be used in the comparison.

PHP bccomp() Return Value

The PHP bccomp() function returns 0 if the two operands are equal, 1 if the left_operand is larger than the right_operand, -1 otherwise.

PHP bccomp() Working Examples

1. bccomp() example

<?php
echo bccomp('1', '2') . "\n";   // -1
echo bccomp('1.00001', '1', 3); // 0
echo bccomp('1.00001', '1', 5); // 1
?>

Additional Tips from Fellow Developers

Contributed By: Robert Lozyniak

Beware that negative zero does not compare equal to positive zero.

PHP bcdiv() Function

PHP bcdiv() Usage

The PHP bcdiv() function will divides the dividend by the divisor.

PHP bcdiv() Syntax

 bcdiv ( string $dividend , string $divisor [, int $scale = 0 ] ) : string

PHP bcdiv() Parameters

  1. dividend — The dividend, as a string.

  2. divisor — The divisor, as a string.

  3. scale — This optional parameter is used to set the number of digits after the decimal place in the result. If omitted, it will default to the scale set globally with the bcscale() function, or fallback to 0 if this has not been set.

PHP bcdiv() Return Value

The PHP bcdiv() function returns the result of the division as a string, or NULL if divisor is 0.

PHP bcdiv() Working Examples

1. bcdiv() example

<?php
echo bcdiv('105', '6.55957', 3);  // 16.007
?>

PHP bcmod() Function

PHP bcmod() Usage

The PHP bcmod() function will get modulus of an arbitrary precision number.

PHP bcmod() Syntax

 bcmod ( string $dividend , string $divisor [, int $scale = 0 ] ) : string

PHP bcmod() Parameters

  1. dividend — The dividend, as a string.

  2. divisor — The divisor, as a string.

PHP bcmod() Return Value

The PHP bcmod() function returns the modulus as a string, or NULL if divisor is 0.

PHP bcmod() Working Examples

1. bcmod() example

<?php
bcscale(0);
echo bcmod( '5',  '3'); //  2
echo bcmod( '5', '-3'); //  2
echo bcmod('-5',  '3'); // -2
echo bcmod('-5', '-3'); // -2
?>

2. bcmod() with decimals

<?php
bcscale(1);
echo bcmod('5.7', '1.3'); // 0.5 as of PHP 7.2.0; 0 previously
?>

Changelog for PHP bcmod() Function

7.2.0 — dividend and divisor are no longer truncated to integer, so now the behavior of bcmod() follows fmod() rather than the % operator.

7.2.0 — The scale parameter was added.

PHP bcmul() Function

PHP bcmul() Usage

The PHP bcmul() function will multiply two arbitrary precision numbers.

PHP bcmul() Syntax

 bcmul ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string

PHP bcmul() Parameters

  1. left_operand — The left operand, as a string.

  2. right_operand — The right operand, as a string.

  3. scale — This optional parameter is used to set the number of digits after the decimal place in the result. If omitted, it will default to the scale set globally with the bcscale() function, or fallback to 0 if this has not been set.

PHP bcmul() Return Value

The PHP bcmul() function returns the result as a string.

PHP bcmul() Working Examples

1. bcmul() example

<?php
echo bcmul('1.34747474747', '35', 3); // 47.161
echo bcmul('2', '4'); // 8
?>

2. bcmul() scale example

<?php
echo bcmul('5', '2', 2);     // prints "10", not "10.00"
?>

Changelog for PHP bcmul() Function

7.3.0 — bcmul() now returns numbers with the requested scale. Formerly, the returned numbers may have omitted trailing decimal zeroes.

Important Points about PHP bcmul() Function

  1. Before PHP 7.3.0 bcmul() may return a result with fewer digits after the decimal point than the scale parameter would indicate. This only occurs when the result doesn't require all of the precision allowed by the scale. For example:

    2. <?php
echo bcmul('5', '2', 2);     // prints "10", not "10.00"
?>

PHP bcpow() Function

PHP bcpow() Usage

The PHP bcpow() function will raise an arbitrary precision number to another.

PHP bcpow() Syntax

 bcpow ( string $base , string $exponent [, int $scale = 0 ] ) : string

PHP bcpow() Parameters

  1. base — The base, as a string.

  2. exponent — The exponent, as a string. If the exponent is non-integral, it is truncated. The valid range of the exponent is platform specific, but is at least -2147483648 to 2147483647.

  3. scale — This optional parameter is used to set the number of digits after the decimal place in the result. If omitted, it will default to the scale set globally with the bcscale() function, or fallback to 0 if this has not been set.

PHP bcpow() Return Value

The PHP bcpow() function returns the result as a string.

PHP bcpow() Working Examples

1. bcpow() example

<?php
echo bcpow('4.2', '3', 2); // 74.08
?>

2. bcpow() scale example

<?php
echo bcpow('5', '2', 2);     // prints "25", not "25.00"
?>

Changelog for PHP bcpow() Function

7.3.0 — bcpow() now returns numbers with the requested scale. Formerly, the returned numbers may have omitted trailing decimal zeroes.

Important Points about PHP bcpow() Function

  1. Before PHP 7.3.0 bcpow() may return a result with fewer digits after the decimal point than the scale parameter would indicate. This only occurs when the result doesn't require all of the precision allowed by the scale. For example:

    2. <?php
echo bcpow('5', '2', 2);     // prints "25", not "25.00"
?>

PHP bcpowmod() Function

PHP bcpowmod() Usage

The PHP bcpowmod() function will raise an arbitrary precision number to another, reduced by a specified modulus.

PHP bcpowmod() Syntax

 bcpowmod ( string $base , string $exponent , string $modulus [, int $scale = 0 ] ) : string

PHP bcpowmod() Parameters

  1. base — The base, as an integral string (i.e. the scale has to be zero).

  2. exponent — The exponent, as an non-negative, integral string (i.e. the scale has to be zero).

  3. modulus — The modulus, as an integral string (i.e. the scale has to be zero).

  4. scale — This optional parameter is used to set the number of digits after the decimal place in the result. If omitted, it will default to the scale set globally with the bcscale() function, or fallback to 0 if this has not been set.

PHP bcpowmod() Return Value

The PHP bcpowmod() function returns the result as a string, or FALSE if modulus is 0 or exponent is negative.

Important Points about PHP bcpowmod() Function

  1. Because this method uses the modulus operation, numbers which are not positive integers may give unexpected results.

PHP bcscale() Function

PHP bcscale() Usage

The PHP bcscale() function will set or get default scale parameter for all bc math functions.

PHP bcscale() Syntax

 bcscale ( int $scale ) : int
 bcscale ( void ) : int

PHP bcscale() Parameters

  1. scale — The scale factor.

PHP bcscale() Return Value

The PHP bcscale() function returns the old scale when used as setter. Otherwise the current scale is returned.

PHP bcscale() Working Examples

1. bcscale() example

<?php
// default scale : 3
bcscale(3);
echo bcdiv('105', '6.55957'); // 16.007
// this is the same without bcscale()
echo bcdiv('105', '6.55957', 3); // 16.007
?>

Changelog for PHP bcscale() Function

7.3.0 — bcscale() can now be used to get the current scale factor; when used as setter, it now returns the old scale value. Formerly, scale was mandatory, and bcscale() always returned TRUE.

Additional Tips from Fellow Developers

Contributed By: sicerwork

Executing bcsacle() will change the scale value of fpm.conf, not only the current process.

Contributed By: mwgamera

These functions DO NOT round off your values. No arbitrary precision libraries do it this way. It stops calculating after reaching scale of decimal places, which mean that your value is cut off after scale number of digits, not rounded. To do the rounding use something like this:

<?php
        function bcround($number, $scale=0) {
                $fix = "5";
                for ($i=0;$i<$scale;$i++) $fix="0$fix";
                $number = bcadd($number, "0.$fix", $scale+1);
                return    bcdiv($number, "1.0",    $scale);
        }
?>

PHP bcsqrt() Function

PHP bcsqrt() Usage

The PHP bcsqrt() function will get the square root of an arbitrary precision number.

PHP bcsqrt() Syntax

 bcsqrt ( string $operand [, int $scale = 0 ] ) : string

PHP bcsqrt() Parameters

  1. operand — The operand, as a string.

  2. scale — This optional parameter is used to set the number of digits after the decimal place in the result. If omitted, it will default to the scale set globally with the bcscale() function, or fallback to 0 if this has not been set.

PHP bcsqrt() Return Value

The PHP bcsqrt() function returns the square root as a string, or NULL if operand is negative.

PHP bcsqrt() Working Examples

1. bcsqrt() example

<?php
echo bcsqrt('2', 3); // 1.414
?>

PHP bcsub() Function

PHP bcsub() Usage

The PHP bcsub() function will subtract one arbitrary precision number from another.

PHP bcsub() Syntax

 bcsub ( string $left_operand , string $right_operand [, int $scale = 0 ] ) : string

PHP bcsub() Parameters

  1. left_operand — The left operand, as a string.

  2. right_operand — The right operand, as a string.

  3. scale — This optional parameter is used to set the number of digits after the decimal place in the result. If omitted, it will default to the scale set globally with the bcscale() function, or fallback to 0 if this has not been set.

PHP bcsub() Return Value

The PHP bcsub() function returns the result of the subtraction, as a string.

PHP bcsub() Working Examples

1. bcsub() example

<?php
$a = '1.234';
$b = '5';
echo bcsub($a, $b);     // -3
echo bcsub($a, $b, 4);  // -3.7660
?>

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