V. BCMath Arbitrary Precision Mathematics Functions

Introduction

For arbitrary precision mathematics PHP offers the Binary Calculator which supports numbers of any size and precision, represented as strings.

Requirements

Since PHP 4.0.4, libbcmath is bundled with PHP. You don't need any external libraries for this extension.

Installation

These functions are only available if PHP was configured with --enable-bcmath. In PHP 3, these functions are only available if PHP was not configured with --disable-bcmath.

The windows version of PHP has built in support for this extension. You do not need to load any additional extension in order to use these functions.

Runtime Configuration

The behaviour of these functions is affected by settings in php.ini.

Table 1. BC math configuration options

Name	Default	Changeable	Changelog
bcmath.scale	"0"	PHP_INI_ALL	Available since PHP 5.0.0.

For further details and definitions of the PHP_INI_* constants, see the Appendix H.

Here's a short explanation of the configuration directives.

bcmath.scale integer: Number of decimal digits for all bcmath functions. See also bcscale().

Resource Types

This extension has no resource types defined.

Predefined Constants

This extension has no constants defined.

Table of Contents
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 number
bcpow -- Raise an arbitrary precision number to another
bcpowmod -- Raise an arbitrary precision number to another, reduced by a specified modulus
bcscale -- Set 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

User Contributed Notes
BCMath Arbitrary Precision Mathematics Functions

stonehew ut gm a il det com
24-Nov-2004 11:31


Like any other bc function, you can't trust the last couple of digits, but everything else seems to check out.  If you want to use this for anything important, you may want to verify this against other sources of pi before use.  This function calculates 100 decimal places of pi in 329 iterations -- not exactly fast (each iteration calls the factorial function, from below, twice), so I try to avoid calling it more than once.



<?

//arbitrary precision pi approximator

//author tom boothby

//free for any use



function bcpi() {

    $r=2;

    $i=0;

    $or=0;



    while(bccomp($or,$r)) {

        $i++;

        $or=$r;

        $r = bcadd($r,bcdiv(bcmul(bcpow(bcfact($i),2),

                        bcpow(2,$i+1)),bcfact(2*$i+1)));

    }



    return $r;

}



?>

stonehew et g m a i l dut com
24-Nov-2004 01:20


I hacked these taylor expansions up to make diagrams for some physics homework.  I don't think you'll be wanting to do any real science with PHP... but what the hell, why not?  I plan to implement either a spigot algorithm or something similar to generate pi in the near future.



<?

// arbitrary precision sin and cosine functions

// author tom boothby

// free for any use



function bcfact($n) {

    $r = $n--;

    while($n>1) $r=bcmul($r,$n--);

    return $r;

}



function bcsin($a) {

    $or= $a;

    $r = bcsub($a,bcdiv(bcpow($a,3),6));

    $i = 2;

    while(bccomp($or,$r)) {

        $or=$r;

        switch($i%2) {

          case 0:  $r = bcadd($r,bcdiv(bcpow($a,$i*2+1),bcfact($i*2+1))); break;

          default: $r = bcsub($r,bcdiv(bcpow($a,$i*2+1),bcfact($i*2+1))); break;

        }

        $i++;

    }

    return $r;

}



function bccos($a) {

    $or= $a;

    $r = bcsub(1,bcdiv(bcpow($a,2),2));

    $i = 2;

    while(bccomp($or,$r)) {

        $or=$r;

        switch($i%2) {

          case 0:  $r = bcadd($r,bcdiv(bcpow($a,$i*2),bcfact($i*2))); break;

          default: $r = bcsub($r,bcdiv(bcpow($a,$i*2),bcfact($i*2))); break;

        }

        $i++;

    }

    return $r;

}



?>

Diabolos at GMail dot com
28-Oct-2004 01:42


Here's a function to compute the natural exponential function in arbitrary precision using the basic bcMath arithmetic operations.



EXAMPLE:

To compute the exponential function of 1.7 to 36 decimals:



$y = bcExp("1.7", 36);



The result:

4.331733759839529271053448625299468628



would be returned in variable $y



NOTE:

In practice, the last couple of digits may be inaccurate due to small rounding errors.  If you require a specific degree of precision, always compute 3-4 decimals beyond the required precision.



The program code for the natural exponential function is:

******************************************



  Function bcExp($xArg, $NumDecimals)



{

   $x = Trim($xArg);



   $PrevSum  = $x - 1;

   $CurrTerm = 1;

   $CurrSum  = bcAdd("1", $x, $NumDecimals);

   $n        = 1;



   While (bcComp($CurrSum, $PrevSum, $NumDecimals))



  {

   $PrevSum  = $CurrSum;

   $CurrTerm = bcDiv(bcMul($CurrTerm, $x, $NumDecimals), $n + 1, $NumDecimals);

   $CurrSum  = bcAdd($CurrSum, $CurrTerm, $NumDecimals);



   $n++;

  }



   Return $CurrSum;

}

robert at scabserver dot com
03-Jun-2004 11:58


I spent some time looking for how to generate a large random number, in the end I've settled for reading directly from /dev/urandom



I know this is a *nix only solution, but I figured that it might come in handy to someone else.



The value $size is the size in bits, it could be simplified greatly if you want the size in bytes, but bits was more helpful to what I needed.



<?php

function bcrand($size)

{

    $filename = "/dev/urandom";

    $handle = fopen($filename, "r");

    $bin_urand = fread($handle, ceil($size/8.0));

    fclose($handle);

    $mask = (($size % 8 < 5) ? '0' : '') . dechex(bindec(str_repeat('1', $size % 8))) . str_repeat('FF', floor($size/8));

    $binmask = pack("H*", $mask);

    $binrand = $binmask & $bin_urand;

    $hexnumber = unpack("H*", $binrand);

    $hexnumber = $hexnumber[''];

    $numlength = strlen($hexnumber);

    $decnumber = 0;

    for($x = 1; $x <= $numlength; $x++)

    {

        $place = $numlength - $x;

        $operand = hexdec(substr($hexnumber,$place,1));

        $exponent = bcpow(16,$x-1);

        $decValue = bcmul($operand, $exponent);

        $decnumber = bcadd($decValue, $decnumber);

    }

    return $decnumber;

}

?>

pulstar at mail dot com
15-Apr-2003 07:12


A little comment for the simplified example above: you can do base converting without BCMath functions using only math operators, but you will not able to manage very large values or work with strings to compress or scramble data. If you have BCMath installed in your system it worth use it for this.

oliver at summertime dot net
01-Mar-2003 12:12


A simplier Version of the Script above:



function dec2base($dec, $digits) {

 $value = "";

 $base  = strlen($digits);

 while($dec>$base-1) {

  $rest = $dec % $base;

  $dec  = $dec / $base;

  $value = $digits[$rest].$value;

 }

 $value = $digits[intval($dec)].$value;

 return (string) $value;

}



function base2dec($value, $digits) {

 $value = strtoupper($value);

 $base  = strlen($digits);

 $size  = strlen($value);

 $dec   = '0';

 for ($loop = 0; $loop<$size; $loop++) {

  $element = strpos($digits,$value[$loop]);

  $power   = pow($base,$size-$loop-1);

  $dec    += $element * $power;

 }

 return (string) $dec;

}



$digits = "ABCDEFGHJKLMNPQRSTUVWXYZ23456789";

echo dec2base('1000', $digits);

pulstar at mail dot com
20-Sep-2002 09:23


A found a little fix to do in my base2dec() function:

The line "if($base<37) $value=strtolower($value);" should be removed if you want to specify another digits for your base conversions. Change it this way:



if(!$digits) {

$digits=digits($base);

if($base<37) {

$value=strtolower($value);

}

}



Another example using these functions is to generate a key for a session, to name temporary files or something else:



srand((double) microtime()*1000000);

$id=uniqid(rand(10,999));

$mykey=dec2base(base2dec($id,16),64);



$mykey is a base64 value, which is a good key for passing thru an URL and also is shorter than a MD5 string (it will be allways 11 chars long). If you need something more secure, just scramble the 64 digits in the digits() function.



Well, I hope you enjoy it.



Regards,

Edemilson Lima

pulstar at mail dot com
19-Sep-2002 10:27


A good use for BCMath functions:

The functions below can convert a number in any base (from 2 to 256) to its decimal value and vice-versa.



// convert a decimal value to any other base value

function dec2base($dec,$base,$digits=FALSE) {

    if($base<2 or $base>256) die("Invalid Base: ".$base);

    bcscale(0);

    $value="";

    if(!$digits) $digits=digits($base);

    while($dec>$base-1) {

        $rest=bcmod($dec,$base);

        $dec=bcdiv($dec,$base);

        $value=$digits[$rest].$value;

    }

    $value=$digits[intval($dec)].$value;

    return (string) $value;

}



// convert another base value to its decimal value

function base2dec($value,$base,$digits=FALSE) {

    if($base<2 or $base>256) die("Invalid Base: ".$base);

    bcscale(0);

    if($base<37) $value=strtolower($value);

    if(!$digits) $digits=digits($base);

    $size=strlen($value);

    $dec="0";

    for($loop=0;$loop<$size;$loop++) {

        $element=strpos($digits,$value[$loop]);

        $power=bcpow($base,$size-$loop-1);

        $dec=bcadd($dec,bcmul($element,$power));

    }

    return (string) $dec;

}



function digits($base) {

    if($base>64) {

        $digits="";

        for($loop=0;$loop<256;$loop++) {

            $digits.=chr($loop);

        }

    } else {

        $digits ="0123456789abcdefghijklmnopqrstuvwxyz";

        $digits.="ABCDEFGHIJKLMNOPQRSTUVWXYZ-_";

    }

    $digits=substr($digits,0,$base);

    return (string) $digits;

}



The purpose of digits() function above is to supply the characters that will be used as digits for the base you want. NOTE: You can use any characters for that when you convert to another base, but when you convert again to the decimal base, you need to use the same characters or you will get another unexpected result.

benjcarson at digitaljunkies dot ca
07-Jul-2002 07:00


In addition to my last note, here are  a quick pair of functions to convert exponential notation values into bcmath-style number strings:



// exp2int converts numbers in the

// form "1.5e4" into strings

function exp2int($exp) {

  list($mantissa, $exponent) = spliti("e", $exp);

  list($int, $dec) = split("\.", $mantissa);

  bcscale ($dec);

  return bcmul($mantissa, bcpow("10", $exponent));

}



// float2exp converts floats into exponential notation

function float2exp($num) {



  if (0 == $num) { return "0E1";}

  list($int, $dec) = split("\.", $num);



  // Extract sign

  if ($int[0] == "+" || $int[0] == "-") {

    $sign = substr($int, 0,1);

    $int = substr($int, 1);

  }



  if (strlen($int) <= 1) {   // abs($num) is less than 1

    $i=0;

    for ($i=0; $dec[$i]=='0' && $i < strlen($dec); $i++);

      $exp = -$i-1;       

      $mantissa = substr($dec,$i,1).".".substr($dec,$i+1);                              

    } else { // abs($num) is greater than 1

    $i=0;

    for ($i=0; $int[$i]=='0' && $i < strlen($int); $i++);

      $exp = strlen($int)-1 - $i;

      $mantissa = substr($int,$i,1).".".substr($int,$i+1).$dec;

    }



  return ($sign . $mantissa . "E" . $exp);

}

benjcarson at digitaljunkies ca
07-Jul-2002 06:17


Note that bcmath doesn't seem to handle numbers in exponential notation (i.e. "1e4"), although PHP considers such a value a number.



example:



$exp1 = "1E5";

$exp2 = "2E4";

$ans1 = bcadd($exp1, $exp2, 3);

$ans2 = $exp1 + exp2;

echo("bcadd: $exp1 + $exp2 = $ans1");

echo("php: $exp1 + $exp2 = $ans2");



// Output:

bcadd: 1E5 + 2E4 = 0.000

php: 1E5 + 2E4 = 120000



Just a gotcha if you're using passing PHP numbers into bcmath functions...