PHP: BCMath Arbitrary Precision Mathematics Functions - Manual

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Last updated: Fri, 26 Jan 2007

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# VII. BCMath Arbitrary Precision Mathematics Functions

# Введение

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

# Требования

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

# Установка

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`.

Версия `PHP` для Windows имеет встроенную поддержку данного расширения. Это означает, что для использования данных функций не требуется загрузка никаких дополнительных расширений.

# Настройка во время выполнения

Поведение этих функций зависит от установок в `php.ini`.

Таблица 1. BC math configuration options

Name | Default | Changeable | Changelog
--- | --- | --- | ---
bcmath.scale | "0" | PHP_INI_ALL |

Для подробного описания констант PHP_INI_*, обратитесь к документации функции ini_set().

Краткое разъяснение конфигурационных директив.

`bcmath.scale` integer

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

# Типы ресурсов

Данное расширение не определяет никакие типы ресурсов.

# Предопределенные константы

Данное расширение не определяет никакие константы.

add a note User Contributed Notes
BCMath Arbitrary Precision Mathematics Functions
udochen at gmail dot com
27-Feb-2007 11:48
`Code below implements standard rounding on 5 or higer round up, else don't round. There wasn't a round function for the BC functions, so here is a simple one that works. Same args as round, except takes strings and returns a string for more BC operations.
----------------
function roundbc($x, $p) {
$x = trim($x);
$data = explode(".",$x);
if(substr($data[1],$p,1) >= "5") {
//generate the add string.
$i=0;
$addString = "5";
while($i < $p) {
$addString = "0" . $addString;
$i++;
}//end while.
$addString = "." . $addString;
//now add the addString to the original fraction.
$sum = bcadd($data[0] . "." . $data [1],$addString,$p+1);
//explode the result.
$sumData = explode(".",$sum);
//now, return the correct precision on the rounded number.
return $sumData[0] . "." . substr($sumData[1],0,$p);
} else {
//don't round the value and return the orignal to the desired
//precision or less.
return $data[0] . "." . substr($data[1],0,$p);
}//end if/else.
}//end roundbc.`
mgcclx at gmail dot com
29-Jan-2007 06:52
`I wrote this function with many BCMath functions. It should be the fastest function in PHP to find the number pi into any precision, my test is it generate 2000 digits after the dot in 8 seconds. I don't think you need anything more than that.
<?php
//bcpi function with Gauss-Legendre algorithm
//by Chao Xu (Mgccl)
function bcpi($precision){
$limit = ceil(log($precision)/log(2))-1;
bcscale($precision+6);
$a = 1;
$b = bcdiv(1,bcsqrt(2));
$t = 1/4;
$p = 1;
while($n < $limit){
$x = bcdiv(bcadd($a,$b),2);
$y = bcsqrt(bcmul($a, $b));
$t = bcsub($t, bcmul($p,bcpow(bcsub($a,$x),2)));
$a = $x;
$b = $y;
$p = bcmul(2,$p);
++$n;
}
return bcdiv(bcpow(bcadd($a, $b),2),bcmul(4,$t),$precision);
}
?>`
marcus at synchromedia dot co dot uk
09-Aug-2006 09:17
`Oops, first posting contained wrong code... sorry.
An amendment to the entry by pulstar at mail dot com - the digits() function can be made much faster (remove the line breaks from the big string, and make sure you don't miss any characters!):
function digits2($base) {
if($base < 64) {
return substr('0123456789abcdefghijklmnopqrstuvwxyz
ABCDEFGHIJKLMNOPQRSTUVWXYZ-_', 0, $base);
} else {
return substr("\x0\x1\x2\x3\x4\x5\x6\x7\x8\x9\xa\xb\xc\xd
\xe\xf\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d
\x1e\x1f\x20!\x22#\x24%&'()*+,-./0123456789:;<=>
\x3f@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]
^_`abcdefghijklmnopqrstuvwxyz{|}~\x7f\x80\x81\x82\x83\x84\x85
\x86\x87\x88\x89\x8a\x8b\x8c\x8d\x8e\x8f\x90\x91\x92\x93\x94\x95
\x96\x97\x98\x99\x9a\x9b\x9c\x9d\x9e\x9f\xa0\xa1\xa2\xa3\xa4\xa5
\xa6\xa7\xa8\xa9\xaa\xab\xac\xad\xae\xaf\xb0\xb1\xb2\xb3\xb4\xb5
\xb6\xb7\xb8\xb9\xba\xbb\xbc\xbd\xbe\xbf\xc0\xc1\xc2\xc3\xc4\xc5
\xc6\xc7\xc8\xc9\xca\xcb\xcc\xcd\xce\xcf\xd0\xd1\xd2\xd3\xd4\xd5
\xd6\xd7\xd8\xd9\xda\xdb\xdc\xdd\xde\xdf\xe0\xe1\xe2\xe3\xe4\xe5
\xe6\xe7\xe8\xe9\xea\xeb\xec\xed\xee\xef\xf0\xf1\xf2\xf3\xf4\xf5\xf6
\xf7\xf8\xf9\xfa\xfb\xfc\xfd\xfe\xff", 0, $base);
}
}
in my benchmarks, this is around 150x faster for 256 digits`
stonehew ut gm a il det com
24-Nov-2004 09:31
`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 $r;
}
?>`
stonehew et g m a i l dut com
23-Nov-2004 11:20
`I hacked these taylor expansions up to make diagrams for some physics homework. I don't think you'll be wanting to do any real science with PHP... but what the hell, why not? I plan to implement either a spigot algorithm or something similar to generate pi in the near future.
<?
// arbitrary precision sin and cosine functions
// author tom boothby
// free for any use
function bcfact($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 11:42
`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 09:58
`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 $decnumber;
}
?>`
pulstar at mail dot com
15-Apr-2003 05:12
`A little comment for the simplified example above: you can do base converting without BCMath functions using only math operators, but you will not able to manage very large values or work with strings to compress or scramble data. If you have BCMath installed in your system it worth use it for this.`
oliver at summertime dot net
01-Mar-2003 10:12
`A simplier Version of the Script above:
function dec2base($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', $digits);`
pulstar at mail dot com
20-Sep-2002 07:23
`A found a little fix to do in my base2dec() function:
The line "if($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);
$mykey is a base64 value, which is a good key for passing thru an URL and also is shorter than a MD5 string (it will be allways 11 chars long). If you need something more secure, just scramble the 64 digits in the digits() function.
Well, I hope you enjoy it.
Regards,
Edemilson Lima`
pulstar at mail dot com
19-Sep-2002 08:27
`A good use for BCMath functions:
The functions below can convert a number in any base (from 2 to 256) to its decimal value and vice-versa.
// convert a decimal value to any other base value
function dec2base($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) $digits;
}
The purpose of digits() function above is to supply the characters that will be used as digits for the base you want. NOTE: You can use any characters for that when you convert to another base, but when you convert again to the decimal base, you need to use the same characters or you will get another unexpected result.`
benjcarson at digitaljunkies dot ca
07-Jul-2002 05:00
`In addition to my last note, here are a quick pair of functions to convert exponential notation values into bcmath-style number strings:
// exp2int converts numbers in the
// form "1.5e4" into strings
function exp2int($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 04:17
`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...`
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Last updated: Fri, 26 Jan 2007
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