aspell_suggest
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,$p);
}//end if/else.
}//end roundbc.
IV. BCMath 임의 정확도 수치연산 함수
소개
임의의 정확도를 갖는 수치연산을 위해 PHP는 이진 계산기를 제공한다. 이 이진 계산기(Binary Calculator)는 가능한 모든 크기와 정확도를 갖는 수들을 지원하고, 문자열로 표현된다.
요구 사항
PHP 4.0.4 이후부터 libbcmath가 PHP에서 같이 제공된다. 이 확장에 대해 외부적인 라이브러리가 필요치 않다.
설치
PHP 4에서, 이 함수를 사용하려면 PHP가 --enable-bcmath 옵션으로 설정되어야 한다. PHP 3에서, 이 함수를 사용하려면 PHP가 --disable-bcmath 옵션으로 설정되면 안된다.
PHP 윈도우 버전에서는 이 확장 모듈에 대한 지원이 포함되어 있습니다. 이 함수들을 이용하기 위해서 추가로 확장 모듈을 읽어들일 필요가 없습니다.
런타임 설정
이 함수의 작동은 php.ini 설정에 영향을 받습니다.
For further details and definition of the PHP_INI_* constants see ini_set().
위 설정 지시어에 대한 간단한 설명입니다.
리소스 종류
이 확장 모듈은 리소스형을 정의하지 않습니다.
상수 정의
이 확장 모듈은 상수를 정의하지 않습니다.
- 차례
- bcadd -- 두개의 임의 정확도 수를 더한다
- bccomp -- 두개의 임의 정확도 수를 비교한다
- bcdiv -- 두개의 임의 정확도 수를 나눈다
- bcmod -- 임의 정확도 수의 나머지를 구한다
- bcmul -- 두개의 임의 정확도 수를 곱한다
- bcpow -- 임의 정밀도 수를 제곱한다
- bcpowmod -- Raise an arbitrary precision number to another, reduced by a specified modulus. 임의 정밀도 수를 계수에 의해 감소하는 다른 수로 제곱한다.
- bcscale -- 모든 bc 수치계산 함수의 scale 매개변수의 기본값을 설정한다
- bcsqrt -- 임의 정확도 수의 제곱근을 구한다
- bcsub -- 임의 정확도 수를 다른 임의 정확도 수에서 뺀다
add a note
User Contributed NotesBCMath 임의 정확도 수치연산 함수
udochen at gmail dot com
27-Feb-2007 11:48
27-Feb-2007 11:48
mgcclx at gmail dot com
29-Jan-2007 06:52
29-Jan-2007 06:52
I wrote this function with many BCMath functions. It should be the fastest function in PHP to find the number pi into any precision, my test is it generate 2000 digits after the dot in 8 seconds. I don't think you need anything more than that.
<?php
//bcpi function with Gauss-Legendre algorithm
//by Chao Xu (Mgccl)
function bcpi($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),$precision);
}
?>
marcus at synchromedia dot co dot uk
09-Aug-2006 09:17
09-Aug-2006 09:17
Oops, first posting contained wrong code... sorry.
An amendment to the entry by pulstar at mail dot com - the digits() function can be made much faster (remove the line breaks from the big string, and make sure you don't miss any characters!):
function digits2($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
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 $r;
}
?>
stonehew et g m a i l dut com
23-Nov-2004 11:20
23-Nov-2004 11:20
I hacked these taylor expansions up to make diagrams for some physics homework. I don't think you'll be wanting to do any real science with PHP... but what the hell, why not? I plan to implement either a spigot algorithm or something similar to generate pi in the near future.
<?
// arbitrary precision sin and cosine functions
// author tom boothby
// free for any use
function bcfact($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
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
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 $decnumber;
}
?>
pulstar at mail dot com
15-Apr-2003 05:12
15-Apr-2003 05:12
A little comment for the simplified example above: you can do base converting without BCMath functions using only math operators, but you will not able to manage very large values or work with strings to compress or scramble data. If you have BCMath installed in your system it worth use it for this.
oliver at summertime dot net
01-Mar-2003 10:12
01-Mar-2003 10:12
A simplier Version of the Script above:
function dec2base($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', $digits);
pulstar at mail dot com
20-Sep-2002 07:23
20-Sep-2002 07:23
A found a little fix to do in my base2dec() function:
The line "if($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);
$mykey is a base64 value, which is a good key for passing thru an URL and also is shorter than a MD5 string (it will be allways 11 chars long). If you need something more secure, just scramble the 64 digits in the digits() function.
Well, I hope you enjoy it.
Regards,
Edemilson Lima
pulstar at mail dot com
19-Sep-2002 08:27
19-Sep-2002 08:27
A good use for BCMath functions:
The functions below can convert a number in any base (from 2 to 256) to its decimal value and vice-versa.
// convert a decimal value to any other base value
function dec2base($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) $digits;
}
The purpose of digits() function above is to supply the characters that will be used as digits for the base you want. NOTE: You can use any characters for that when you convert to another base, but when you convert again to the decimal base, you need to use the same characters or you will get another unexpected result.
benjcarson at digitaljunkies dot ca
07-Jul-2002 05:00
07-Jul-2002 05:00
In addition to my last note, here are a quick pair of functions to convert exponential notation values into bcmath-style number strings:
// exp2int converts numbers in the
// form "1.5e4" into strings
function exp2int($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
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...