Números de ponto flutuante
Números de ponto flutuante (também conhecidos como "floats", "doubles" ou "números reais") podem ser especificados utilizando qualquer uma das seguintes sintaxes:
<?php
$a = 1.234;
$b = 1.2e3;
$c = 7E-10;
?>LNUM [0-9]+
DNUM ([0-9]*[\.]{LNUM}) | ({LNUM}[\.][0-9]*)
EXPONENT_DNUM ( ({LNUM} | {DNUM}) [eE][+-]? {LNUM})Aviso
Precisão de números de ponto flutuante
É típico que frações simples como 0.1 ou 0.7 não podem ser convertidos em sua representação binária interna sem uma pequena perda de precisão. Isto pode causar erros confusos: por exemplo, floor((0.1+0.7)*10) irá retornar 7 em vez do esperado 8, como resultado da representação interna realmente ser algo como 7.9999999999....
Isto está relacionado ao fato de que é impossível expressar, exatamente, algumas frações em notação decimal com um número finito de dígitos. Por exemplo, 1/3 na forma decimal se torna 0.3333333. . ..
Então, nunca confie em resultados com números de ponto flutuante até a última casa e nunca compare números de ponto flutuante em igualdades. Se você realmente precisar de alta precisão, você pode utilizar as funções matemáticas de precisão arbitrária ou as funções relacionadas ao gmp.
Convertendo para float
Para informações sobre a conversão de strings para floats, veja a seção entitulada Conversão de Strings para números. Para valores de outros tipos, o valor é primeiro convertido para inteiro e então para float. Veja a seção Convertendo para inteiros para mais informações. No PHP 5, um aviso é emitido se você tentar converter um objeto para float.
User Contributed Notes
maxiumswarp at gmail dot com 27-Apr-2011 10:12
I found that to compare floats correctly I had to use this, it works very good for doing price comparison, such as order validation to make sure final prices are correct before they send. This is make your statements return true are false correctly.
<?php
$number1=number_format($float1,2,'.','');
$number2=number_format($float2,2,'.''');
if($number1!=$number2){
echo 'do correction here!';
}
?>zelko at mojeime dot com 31-Mar-2011 09:02
<?php
$binarydata32 = pack('H*','00000000');
$float32 = unpack("f", $binarydata32); // 0.0
$binarydata64 = pack('H*','0000000000000000');
$float64 = unpack("d", $binarydata64); // 0.0
?>
I get 0 both for 32-bit and 64-bit numbers.
But, please don't use your own "functions" to "convert" from float to binary and vice versa. Looping performance in PHP is horrible. Using pack/unpack you use processor's encoding, which is always correct. In C++ you can access the same 32/64 data as either float/double or 32/64 bit integer. No "conversions".
To get binary encoding:
<?php
$float32 = pack("f", 5300231);
$binarydata32 =unpack('H*',$float32); //"0EC0A14A"
$float64 = pack("d", 5300231);
$binarydata64 =unpack('H*',$float64); //"000000C001385441"
?>
And my example from half a year ago:
<?php
$binarydata32 = pack('H*','0EC0A14A');
$float32 = unpack("f", $binarydata32); // 5300231
$binarydata64 = pack('H*','000000C001385441');
$float64 = unpack("d", $binarydata64); // 5300231
?>
And please mind the Big and Little endian boys...manasseh at smartcomputerinc.com 07-Mar-2011 03:35
I found that 00000000 hex was converting to 1.0 decimal. From the Wikipedia article on IEEE-754 floating point:
The true significand includes 23 fraction bits to the right of the binary point and an implicit leading bit (to the left of the binary point) with value 1 unless the exponent is stored with all zeros.
In hex2float32n, replace:
$intnumber=bindec("1".$binint);
with
if ($exp <> -127)
{ $intnumber=bindec("1".$binint); };
and then 00000000 works correctly without affecting "normal" numbers.Nstiac (info at nstiac dot com) 28-Jan-2011 10:56
There are many scripts/functions to convert a Hex string to a Floating point number, but i could'nt find any usable function to convert a float2hex (float number to hexadecimal) .. so i went on an made one! .. to my surprise.. it didn't matched the other existing functions results exactly due to different methods used on each .. so i went on an created a complementary function to have both results match float2hex32n<->hex2float32n.
<?php
/** Complementary functions to CONVERT PHP FLOATING POINT NUMBERS or DECIMALS
* (IEEE 754 single-precision 32 bit) TO HEXADECIMAL AND BACK.
*
* @author NSTIAC (Jorge D. Baigorri Salas) <http://www.nstiac.com> <http://www.n2works.com>
* @created on 28/Jan/2010 / time spent: 2hours approx.
* @special thanks to Thomas Finley's article "Floating Point"
* <http://tfinley.net/notes/cps104/floating.html>
*
* These functions allow to convert any php floating point numbers with the
* notation 1.234 (or fixed point numbers) into their corresponding 8 digits
* hexadecimal notation. (i.e.- 1557897.40 -> 49BE2C4B <- 1557897.40) by
* disregarding their implicit format and treating them at will as either
* integer, decimals, binary numbers, hexadecimal values, or plain text.
*
**/
/** FLOAT2HEX32n
* (Convert php float numbers or decimals (single-precision 32bits) to 8 digit Hexadecimal)
* Accepts only fixed point notation decimal numbers or fractions on a string (i.e.- "1.23456")
* @usage:
* float2hex32n("-1557897.13"); returns "c9be2c49"
**/
function float2hex32n($number) {
//Convert non-decimal to decimal.
$number=number_format($number,23,'.','');
//Get the integer portion of $number
if ($number>0) {
$intnumber=substr($number,0,strpos($number,"."));
} else {
//Check whether is a negative number to remove - sign.
$intnumber=substr($number,1,strpos($number,"."));
}
//Convert integer to binary
$binint=decbin($intnumber);
//Get the decimal fraction of the number
$pointnumber=substr($number,strpos($number,"."));
//Add a 0 to treat as single decimal fraction
$pointnumber="0".$pointnumber;
//Convert decimal values to base 2
$tmppoint=number_format($pointnumber*2,23,'.','');
for ($i=0; $i<23; $i++) {
$binpoint.=substr((string)$tmppoint,0,1);
$tmppoint=substr((string)$tmppoint,1);
$tmppoint=number_format($tmppoint*2,23,'.','');
}
//Gather both values to get base 2 binary fraction
$scibin=$binint.".".$binpoint;
//Find fraction separator "." position
$exp=strpos($scibin,".");
//Transform to scientific notation (1.x^exp)
$scibin=substr($binint,0,1).".".substr($binint,1).$binpoint;
//Create mantissa
if ($scibin>1) {
$mantissa=substr($scibin,2);
} else {
$mantissa=substr($scibin,1);
}
//Fill mantissa to 23 bit value
$fill23=23-strlen($mantissa);
for ($i=0; $i<$fill23; $i++) {
$mantissa.="0";
}
//Convert fraction separator position to exponent value
if ($exp>0) { $exp--; }
//Adjust to binary notation exponent value
$exp+=127;
//Convert to 8 bit binary
$exp=decbin($exp);
//Find 1 bit sign value
if ($number>0) { $sign=0; } else { $sign=1; }
//Compose final binary value
$binfinal=$sign.$exp.$mantissa;
//Reorganizae number into 4digit/bits packets and
//finally convert to decimal value and to hex.
$hexfinal.=dechex(bindec(substr($binfinal,0,4)));
$hexfinal.=dechex(bindec(substr($binfinal,4,4)));
$hexfinal.=dechex(bindec(substr($binfinal,8,4)));
$hexfinal.=dechex(bindec(substr($binfinal,12,4)));
$hexfinal.=dechex(bindec(substr($binfinal,16,4)));
$hexfinal.=dechex(bindec(substr($binfinal,20,4)));
$hexfinal.=dechex(bindec(substr($binfinal,24,4)));
$hexfinal.=dechex(bindec(substr($binfinal,28,4)));
return $hexfinal;
}
/** Using either function will return a value which can be used on the other function
* to return the original input. (Hope it helps =)
**/
?>
Second function (HEX2FLOAT32n) converts Hexadecimal 8 digit strings to fixed decimals float numbers.
(complementary to FLOAT2HEX32n above)
<?php
/** Complementary functions to CONVERT PHP FLOATING POINT NUMBERS or DECIMALS
* (IEEE 754 single-precision 32 bit) TO HEXADECIMAL AND BACK.
*
* @author NSTIAC (Jorge D. Baigorri Salas) <http://www.nstiac.com> <http://www.n2works.com>
* @created on 28/Jan/2010 / time spent: 2hours approx.
* @special thanks to Thomas Finley's article "Floating Point"
* <http://tfinley.net/notes/cps104/floating.html>
*
* These functions allow to convert any php floating point numbers with the
* notation 1.234 (or fixed point numbers) into their corresponding 8 digits
* hexadecimal notation. (i.e.- 1557897.40 -> 49BE2C4B <- 1557897.40) by
* disregarding their implicit format and treating them at will as either
* integer, decimals, binary numbers, hexadecimal values, or plain text.
*
**/
/** HEX2FLOAT32n
* (Convert 8 digit hexadecimal values to fixed decimals float numbers (single-precision 32bits)
* Accepts 8 digit hexadecimal values on a string (i.e.- F1A9B02C) and single integer to fix number of decimals
* @usage:
* hex2float32n("c9be2c49",2); returns -> "-1557897.13"
**/
function hex2float32n($number,$nd) {
//Separate each hexadecimal digit
for ($i=0; $i<strlen($number); $i++) {
$hex[]=substr($number,$i,1);
}
//Convert each hexadecimal digit to integer
for ($i=0; $i<count($hex); $i++) {
$dec[]=hexdec($hex[$i]);
}
//Convert each decimal value to 4bit binary and join on a string
for ($i=0; $i<count($dec); $i++) {
$binfinal.=sprintf("%04d",decbin($dec[$i]));
}
//Get sign 1bit value
$sign=substr($binfinal,0,1);
//Get exponent 8bit value
$exp=substr($binfinal,1,8);
//Get mantissa 23bit value
$mantissa=substr($binfinal,9);
//Convert & adjunt binary exponent to integer
$exp=bindec($exp);
$exp-=127;
//Assign mantissa to pre-scientific binary notation
$scibin=$mantissa;
//Split $scibin into integral & fraction parts through exponent
$binint=substr($scibin,0,$exp);
$binpoint=substr($scibin,$exp);
//Convert integral binary part to decimal integer
$intnumber=bindec("1".$binint);
//Split each binary fractional digit
for ($i=0; $i<strlen($binpoint); $i++) {
$tmppoint[]=substr($binpoint,$i,1);
}
//Reverse order to work backwards
$tmppoint=array_reverse($tmppoint);
//Convert base 2 digits to decimal
$tpointnumber=number_format($tmppoint[0]/2,strlen($binpoint),'.','');
for ($i=1; $i<strlen($binpoint); $i++) {
$pointnumber=number_format($tpointnumber/2,strlen($binpoint),'.','');
$tpointnumber=$tmppoint[$i+1].substr($pointnumber,1);
}
//Join both decimal section to get final number
$floatfinal=$intnumber+$pointnumber;
//Convert to positive or negative based on binary sign bit
if ($sign==1) { $floatfinal=-$floatfinal; }
//Format float number to fixed decimals required
return number_format($floatfinal,$nd,'.','');
}
/** Using either function will return a value which can be used on the other function
* to return the original input. (Hope it helps =)
**/
?>Julian L 09-Dec-2010 03:51
Convert a hex string into a 32-bit IEEE 754 float number. This function is 2 times faster then the below hex to 32bit function. This function only changes datatypes (string to int) once. Also, this function is a port from the hex to 64bit function from below.
<?php
function hexTo32Float($strHex) {
$v = hexdec($strHex);
$x = ($v & ((1 << 23) - 1)) + (1 << 23) * ($v >> 31 | 1);
$exp = ($v >> 23 & 0xFF) - 127;
return $x * pow(2, $exp - 23);
}
?>
<?php
//example
echo hexTo32Float("C4028000"); // outputs: -522
echo hexTo32Float("457F9000"); // outputs: 4089
echo hexTo32Float("2D7F5"); // outputs: 6.00804264307E-39
echo hexTo32Float("0002D7F5"); // outputs: 6.00804264307E-39
echo hexTo32Float("47D9F95E"); // outputs: 111602.734375
?>Marc 06-Oct-2010 02:29
Small float compare function
<?php
function floatcmp($a,$b,$decimals=6) {
return sprintf('%01.'.$decimals.'f',$a)==sprintf('%01.'.$decimals.'f',$b);
}
?>v_gournay at hotmail dot com 06-Oct-2010 12:10
A simple way to check for equality of two floating point numbers. Change the default precision according to your needs:
<?php
function IsFloatEqual($x,$y,$precision=0.0000001)
{
return ($x+$precision >= $y) && ($x-$precision <= $y);
}
?>sbditto85 11-Aug-2010 08:38
for float comparison i cast them as strings:
<?php (string) $floatOne == (string) $floatTwo ?>
and that seems to work...although that seems sooooo wrong to do that.zelko at mojeime dot com 05-Jun-2010 08:43
The was talk about "converting" 32 and 64 bit IEEE754 binary numbers to PHP float. The issue isn't as much converting, since they are already in binary form, as it is casting. PHP doesn't allow direct accessing of memory, but you can still get around a bit.
The right was to read floats (32 and 64 bit) is this:
<?php
$binarydata32 = pack('H*','0EC0A14A');
$float32 = unpack("f", $binarydata32);
$binarydata64 = pack('H*','000000C001385441');
$float64 = unpack("d", $binarydata64);
var_dump($float32,$float64,$float32==$float64);
?>
The result of dump():
<?php
array(1) {
[1]=>
float(5300231)
}
array(1) {
[1]=>
float(5300231)
}
bool(true)
?>
Note: mind the Big and Little endian boysmagicaltux at php dot net 02-Jun-2010 02:02
In some cases you may want to get the maximum value for a float without getting "INF".
var_dump(1.8e308); will usually show: float(INF)
I wrote a tiny function that will iterate in order to find the biggest non-infinite float value. It comes with a configurable multiplicator and affine values so you can share more CPU to get a more accurate estimate.
I haven't seen better values with more affine, but well, the possibility is here so if you really thing it's worth the cpu time, just try to affine more.
Best results seems to be with mul=2/affine=1. You can play with the values and see what you get. The good thing is this method will work on any system.
<?php
function float_max($mul = 2, $affine = 1) {
$max = 1; $omax = 0;
while((string)$max != 'INF') { $omax = $max; $max *= $mul; }
for($i = 0; $i < $affine; $i++) {
$pmax = 1; $max = $omax;
while((string)$max != 'INF') {
$omax = $max;
$max += $pmax;
$pmax *= $mul;
}
}
return $omax;
}
?>inforsci at gmail dot com 28-Apr-2010 06:48
convert 32bit HEX values into IEEE 754 floating point
<?php
$strHex = "C45F82ED";
$bin = str_pad(base_convert($strHex, 16, 2), 32, "0", STR_PAD_LEFT);
$sign = $bin[0];
$exp = bindec(substr($bin, 1, 8)) - 127;
$man = (2 << 22) + bindec(substr($bin, 9, 23));
$dec = $man * pow(2, $exp - 23) * ($sign ? -1 : 1);
echo "Answer = " . $dec . "<BR>\n";
?>Anonymous 26-Apr-2010 06:48
Calculations involving float types become inaccurate when it deals with numbers with more than approximately 8 digits long where ever the decimal point is. This is because of how 32bit floats are commonly stored in memory. This means if you rely on float types while working with tiny fractions or large numbers, your calculations can end up between tiny fractions to several trillion off.
This usually won't matter when converting to binary memory storage form and editing many applications' float memory addresses directly, or dealing with smaller length numbers. But if you're working with larger scale numbers and decimals, it's best to switch to working with other types: https://www.php.net/manual/pt_BR/refs.math.phppyrosphere 02-Apr-2010 10:47
While testing equality between two floats is usually a bad idea, if you learn how floats work on computers, you should be able to figure out when testing for equality will work and when it won't, and use this knowledge to know where you can avoid unnecessary checks that could be the straw that breaks the camel's back. Remember, rules were made to be broken, and in the real world sometimes they have to be.pgarvin76+phpmanual at gmail dot com 13-Jan-2010 03:36
When converting from float to string trailing zeros will be dropped. Consider the following example. Tested on PHP 5.3.1.
<?php
$a = 5.00500;
$b = 30.00;
echo "a = $a\n";
echo "b = $b\n";
/* outputs:
a = 5.005
b = 30
*/
?>francois dot barbier at gmail dot com 13-Aug-2009 03:49
As "m dot lebkowski+php at gmail dot com" (http://www.php.net/language.types.float#81416) noted 9 comments below :
When PHP converts a float to a string, the decimal separator used depends on the current locale conventions.
However, to declare a floating point number, one must always use a full stop otherwhise the code would be locale dependent (imagine the nightmare):
<?php
$float = 1.5; // float(1.5)
$float = 1,5; // Parse error: syntax error, unexpected ','
$float = (float) '1.5'; // float(1.5)
$float = (float) '1,5'; // float(1)
?>
Now, if you have a string containing a localized number, you can convert it back to a floating point number using the following function:
<?php
/**
* Convert a localized number string into a floating point number
*
* @param string $sNumber The localized number string to convert.
* @return float The converted number.
*/
function str2num($sNumber)
{
$aConventions = localeConv();
$sNumber = trim((string) $sNumber);
$bIsNegative = (0 === $aConventions['n_sign_posn'] && '(' === $sNumber{0} && ')' === $sNumber{strlen($sNumber) - 1});
$sCharacters = $aConventions['decimal_point'].
$aConventions['mon_decimal_point'].
$aConventions['negative_sign'];
$sNumber = preg_replace('/[^'.preg_quote($sCharacters).'\d]+/', '', trim((string) $sNumber));
$iLength = strlen($sNumber);
if (strlen($aConventions['decimal_point']))
{
$sNumber = str_replace($aConventions['decimal_point'], '.', $sNumber);
}
if (strlen($aConventions['mon_decimal_point']))
{
$sNumber = str_replace($aConventions['mon_decimal_point'], '.', $sNumber);
}
$sNegativeSign = $aConventions['negative_sign'];
if (strlen($sNegativeSign) && 0 !== $aConventions['n_sign_posn'])
{
$bIsNegative = ($sNegativeSign === $sNumber{0} || $sNegativeSign === $sNumber{$iLength - 1});
if ($bIsNegative)
{
$sNumber = str_replace($aConventions['negative_sign'], '', $sNumber);
}
}
$fNumber = (float) $sNumber;
if ($bIsNegative)
{
$fNumber = -$fNumber;
}
return $fNumber;
}
?>
Example:
<?php
setLocale(LC_ALL, 'fr_BE.UTF-8'); // decimal separator is now a comma
$float = -123456.789;
$string = (string) $float;
var_dump($float); // float(-123456,789)
var_dump($string); // string(11) "-123456,789"
var_dump((float) $string); // float(-123456)
var_dump(str2num($string)); // float(-123456,789)
?>
It also works with strings returned by the number_format() function:
<?php
setLocale(LC_ALL, 'fr_BE.UTF-8'); // decimal separator is now a comma
$conv = localeconv();
$float = -123456.789;
$string = $conv['int_curr_symbol'].number_format($float, $conv['frac_digits'], $conv['decimal_point'], $conv['thousands_sep']);
var_dump($float); // float(-123456,789)
var_dump($string); // string(15) "EUR -123.456,79"
var_dump((float) $string); // float(0)
var_dump(str2num($string)); // float(-123456,79)
?>rob at willo dot org 03-Jun-2009 04:18
PHP will parse ".123" with no leading digit; just a decimal point. For a command-line example:
php -r "echo 1 + .123;"
The regular expression provided above does not parse it.
My correction is:
EXPONENT_DNUM = "[+-]?({DNUM} | ({LNUM} | {DNUM}) [eE][+-]? {LNUM})"
NOTE: {LNUM} by itself is an integer, not a floating point.Bob 08-May-2009 05:04
Here is a function to convert an exponential-format float to a decimal-format float; e.g. 1.6e+12 to 1600000000000.
It will help addressing the problem specified by kjohnson above.
I have tested it, but not in any real world situation so any feedback/improvements/bug-reports would be appreciated.
<?php
function exp_to_dec($float_str)
// formats a floating point number string in decimal notation, supports signed floats, also supports non-standard formatting e.g. 0.2e+2 for 20
// e.g. '1.6E+6' to '1600000', '-4.566e-12' to '-0.000000000004566', '+34e+10' to '340000000000'
// Author: Bob
{
// make sure its a standard php float string (i.e. change 0.2e+2 to 20)
// php will automatically format floats decimally if they are within a certain range
$float_str = (string)((float)($float_str));
// if there is an E in the float string
if(($pos = strpos(strtolower($float_str), 'e')) !== false)
{
// get either side of the E, e.g. 1.6E+6 => exp E+6, num 1.6
$exp = substr($float_str, $pos+1);
$num = substr($float_str, 0, $pos);
// strip off num sign, if there is one, and leave it off if its + (not required)
if((($num_sign = $num[0]) === '+') || ($num_sign === '-')) $num = substr($num, 1);
else $num_sign = '';
if($num_sign === '+') $num_sign = '';
// strip off exponential sign ('+' or '-' as in 'E+6') if there is one, otherwise throw error, e.g. E+6 => '+'
if((($exp_sign = $exp[0]) === '+') || ($exp_sign === '-')) $exp = substr($exp, 1);
else trigger_error("Could not convert exponential notation to decimal notation: invalid float string '$float_str'", E_USER_ERROR);
// get the number of decimal places to the right of the decimal point (or 0 if there is no dec point), e.g., 1.6 => 1
$right_dec_places = (($dec_pos = strpos($num, '.')) === false) ? 0 : strlen(substr($num, $dec_pos+1));
// get the number of decimal places to the left of the decimal point (or the length of the entire num if there is no dec point), e.g. 1.6 => 1
$left_dec_places = ($dec_pos === false) ? strlen($num) : strlen(substr($num, 0, $dec_pos));
// work out number of zeros from exp, exp sign and dec places, e.g. exp 6, exp sign +, dec places 1 => num zeros 5
if($exp_sign === '+') $num_zeros = $exp - $right_dec_places;
else $num_zeros = $exp - $left_dec_places;
// build a string with $num_zeros zeros, e.g. '0' 5 times => '00000'
$zeros = str_pad('', $num_zeros, '0');
// strip decimal from num, e.g. 1.6 => 16
if($dec_pos !== false) $num = str_replace('.', '', $num);
// if positive exponent, return like 1600000
if($exp_sign === '+') return $num_sign.$num.$zeros;
// if negative exponent, return like 0.0000016
else return $num_sign.'0.'.$zeros.$num;
}
// otherwise, assume already in decimal notation and return
else return $float_str;
}
?>Bob 08-May-2009 03:34
In MySQL, many floating point number types can have a range specified using 2 values, the "precision" and the "scale" E.g. 'float(precision,scale)' for the datatype. This syntax means a number may be <precision> bits long, but may only have <scale> bits after the decimal point. E.g. a 'float(5,2)' field may have the values -999.99 to 999.99.
Here is a function to validate a PHP float using this syntax:
<?php
function validate_float($float, $precision, $scale)
{
$max = (float)str_pad("", $precision-$scale, '9').'.'.str_pad("", $scale, '9');
$min = (float)"-$max";
if(($float < $min) || ($float > $max)) return false;
else return true;
}
?>mriviera at videostrip dot com 26-Mar-2009 09:21
Converting IEEE754 64 bit binary to PHP float:
<?php
$v = hexdec('402E1CAC083126E9');
$x = (($v & ((1 << 52) - 1)) + ( 1 << 52)) * ($v >> 63 | 1);
$exp = ($v >> 52 & 0x7FF) - 1075;
$float = $x * pow(2, $exp);
?>Boylett 25-Mar-2009 06:06
I had trouble with comparing floats. Basicly, I was reading floats from a database, and comparing with other floats from a database, and ended up with (5.0 != 5.0) being true.
Anyway, i made some simple functions which fix the problem:
<?php
function floatcmp($f1,$f2,$precision = 10) // are 2 floats equal
{
$e = pow(10,$precision);
$i1 = intval($f1 * $e);
$i2 = intval($f2 * $e);
return ($i1 == $i2);
}
function floatgtr($big,$small,$precision = 10) // is one float bigger than another
{
$e = pow(10,$precision);
$ibig = intval($big * $e);
$ismall = intval($small * $e);
return ($ibig > $ismall);
}
function floatgtre($big,$small,$precision = 10) // is on float bigger or equal to another
{
$e = pow(10,$precision);
$ibig = intval($big * $e);
$ismall = intval($small * $e);
return ($ibig >= $ismall);
}
?>info at forrest79 dot net 10-Feb-2009 08:55
My BIN to FLOAT (IEEE754), the first one doesn't work for me:
<?php
function binToFloat($bin) {
if(strlen($bin) > 32) {
return false;
} else if(strlen($bin) < 32) {
$bin = str_repeat('0', (32 - strlen($bin))) . $bin;
}
$sign = 1;
if(intval($bin[0]) == 1) {
$sign = -1;
}
$binExponent = substr($bin, 1, 8);
$exponent = -127;
for($i = 0; $i < 8; $i++) {
$exponent += (intval($binExponent[7 - $i]) * pow(2, $i));
}
$binBase = substr($bin, 9);
$base = 1.0;
for($x = 0; $x < 23; $x++) {
$base += (intval($binBase[$x]) * pow(0.5, ($x + 1)));
}
$float = (float) $sign * pow(2, $exponent) * $base;
return $float;
}
?>an dot kovacs at gmail dot com 09-Jun-2008 04:59
Converting IEEE754 binary representation to php float:
function bin2float ($bin) {
if((ord($bin[0])>>7)==0) $sign=1;
else $sign=-1;
if((ord($bin[0])>>6)%2==1) $exponent=1;
else $exponent=-127;
$exponent+=(ord($bin[0])%64)*2;
$exponent+=ord($bin[1])>>7;
$base=1.0;
for($k=1;$k<8;$k++) {
$base+=((ord($bin[1])>>(7-$k))%2)*pow(0.5,$k);
}
for($k=0;$k<8;$k++) {
$base+=((ord($bin[2])>>(7-$k))%2)*pow(0.5,$k+8);
}
for($k=0;$k<8;$k++) {
$base+=((ord($bin[3])>>(7-$k))%2)*pow(0.5,$k+16);
}
$float=(float)$sign*pow(2,$exponent)*$base;
return $float;
}kjohnson at zootweb dot com 02-Jun-2008 07:23
PHP switches from the standard decimal notation to exponential notation for certain "special" floats. You can see a partial list of such "special" values with this:
<?php
for( $tmp = 0, $i = 0; $i < 100; $i++ ) {
$tmp += 100000;
echo round($tmp),"\n";
}
?>
So, if you add two floats, end up with a "special" value, e.g. 1.2E+6, then put that value unmodified into an update query to store the value in a decimal column, say, you will likely get a failed transaction, since the database will see "1.2E+6" as varchar data, not decimal. Likewise, you will likely get an XSD validation error if you put the value into xml.
I have to be honest: this is one of the strangest things I have seen in any language in over 20 years of coding, and it is a colossal pain to work around.m dot lebkowski+php at gmail dot com 27-Feb-2008 09:18
Just another note about the locales. Consider the following code:
<?php
// in polish locale decimal separator is ","
setlocale(LC_ALL, "pl_PL");
$a = 5/2;
echo (float)(string)$a;
/// prints "2", so the decimal part is dropped
?>
This causes very serious problems in my opinion. In some locale combination the typecasting can be destructive.
Maybe when locale decimal separator is ",", then (float)"2,5" should be recognized as "two and a half"?
Anyway - bare that in mind and be very careful when casting floats to strings and back.helly at php dot net 22-Oct-2007 07:10
Floating point values have a limited precision. Hence a value might not have the same string representation after any processing. That also includes writing a floating point value in your script and directly printing it without any mathematical operations.
If you would like to know more about "floats" and what IEEE 754 is read this: http://docs.sun.com/source/806-3568/ncg_goldberg.htmlsinuhet 14-Nov-2006 04:04
<?php
define('EPSILON', 1.0e-8);
function real_cmp($r1, $r2)
{
$diff = $r1 - $r2;
if( abs($diff) < EPSILON )
return 0;
else
return $diff < 0 ? -1 : 1;
}
function real_lt($r1, $r2)
{
return real_cmp($r1, $r2) < 0;
}
echo "raw compare\n";
$n = 0;
for($i = 0.1; $i < 1.0; $i += 0.1) {
$n++;
echo "$i\t$n\n";
}
echo "\nepsilon compare\n";
$n = 0;
for($i = 0.1; real_lt($i, 1.0); $i += 0.1) {
$n++;
echo "$i\t$n\n";
}
/*
Outputs:
raw compare
0.1 1
0.2 2
0.3 3
0.4 4
0.5 5
0.6 6
0.7 7
0.8 8
0.9 9
1 10
epsilon compare
0.1 1
0.2 2
0.3 3
0.4 4
0.5 5
0.6 6
0.7 7
0.8 8
0.9 9
*/
?>
So moral of this program? "Never compare floating point numbers for equality" solves only half of the problem. As seen above, even raw comparing of floats for less than (or grater than) is dangerous and epsilon (round, etc.) must be used.TAS 27-Jul-2006 11:02
An update regarding the james dot cridland at virginradio dot co dot uk note below, I recently tried his formula using PHP 5 and it is necessary to specify the integer precision when using the round function, otherwise the output will be 0.
<? echo round((69.1-floor(69.1))); ?> // prints 0
<? echo round((69.1-floor(69.1)), 1); ?> // prints 0.1
Also, it appears that "small numbers" include everything up to 64.0. So that
<? echo (63.1-floor(63.1)); ?>
will print 0.1 and
<? echo (64.0-floor(64.0)); ?>
will print 0, but
<? echo round(64.1-floor(64.1)); ?>
will print 0.099999999999994.david at davidmosesNO dot SPAM dot ca 25-Mar-2006 09:48
Re: rick at ninjafoo dot com
There is no need to "always" use the BCMath functions. We just need to heed the documentation and "never compare floating point numbers for equality".
The reason (19.6*100) !== (double)1960, is because inside a computer they are not equal.
Try this:
<?php
printf("%.15f", (19.6*100));
?>
Outputs: 1960.000000000000227 (not 1960 as somewhat expected)
If comparison is required a few options come to mind (other than BCMath):
1) Round numbers before comparison:
<?php
$sig_figs = 5;
echo (round((19.6*100), $sig_figs) !== round((double)1960, $sig_figs)) ? 'not equal' : 'equal';
?>
Outputs: equal
2) Another method is to use a tolerance value, and consider numbers equal if their difference is less than the tolerance.Luzian 17-Nov-2005 08:03
Be careful when using float values in strings that are used as code later, for example when generating JavaScript code or SQL statements. The float is actually formatted according to the browser's locale setting, which means that "0.23" will result in "0,23". Imagine something like this:
$x = 0.23;
$js = "var foo = doBar($x);";
print $js;
This would result in a different result for users with some locales. On most systems, this would print:
var foo = doBar(0.23);
but when for example a user from Germany arrives, it would be different:
var foo = doBar(0,23);
which is obviously a different call to the function. JavaScript won't state an error, additional arguments are discarded without notice, but the function doBar(a) would get 0 as parameter. Similar problems could arise anywhere else (SQL, any string used as code somewhere else). The problem persists, if you use the "." operator instead of evaluating the variable in the string.
So if you REALLY need to be sure to have the string correctly formatted, use number_format() to do it!TRI0N 24-Sep-2005 02:01
Here is a simple formula to break down a number and get rid of the decimal values. I built this to take a number in seconds and convert it to a readable value for Server Uptimes.
<?php
$day = floor(($uptime / 86400)*1.0) ;
$calc1 = $day * 86400 ;
$calc2 = $uptime - $calc1 ;
$hour = floor(($calc2 / 3600)*1.0) ;
if ($hour < 10) {
$hour = "0".$hour ;
}
$calc3 = $hour * 3600 ;
$calc4 = $calc2 - $calc3 ;
$min = floor(($calc4 / 60)*1.0) ;
if ($min < 10) {
$min = "0".$min ;
}
$calc5 = $min * 60 ;
$sec = floor(($calc4 - $calc5)*1.0) ;
if ($min < 10) {
$sec = "0".$sec ;
}
$uptime2 = $day." Days, ".$hour.":".$min.":".$sec ;
?>
Place this where you want the results to be seen:
<?php echo $uptime2 ; ?>
For a Value of 1455587 seconds the results will show as followed:
16 Days, 20:19:47
Enjoyrick at ninjafoo dot com 06-Jul-2005 08:04
Concider the following:
(19.6*100) != 1960
echo gettype(19.6*100) returns 'double', However even .....
(19.6*100) !== (double)1960
19.6*100 cannot be compaired to anything without manually
casting it as something else first.
(string)(19.6*100) == 1960
Rule of thumb, if it has a decimal point, use the BCMath functions.feline at NOSPAM dot penguin dot servehttp dot com 13-Aug-2004 01:36
General computing hint: If you're keeping track of money, do yourself and your users the favor of handling everything internally in cents and do as much math as you can in integers. Store values in cents if at all possible. Add and subtract in cents. At every operation that wii involve floats, ask yourself "what will happen in the real world if I get a fraction of a cent here" and if the answer is that this operation will generate a transaction in integer cents, do not try to carry fictional fractional accuracy that will only screw things up later.gallico_ at hotmail dot com 07-Sep-2003 03:34
To complete the thread about testing two floating point numbers for equality, here's the way it works for *every* programming language:
<?php
// two fp numbers should be considered equal if their absolute
// difference does not exceed a certain value epsilon:
$epsilon = 0.0001; // this defines the precision of your comparision
// check their absolute difference
if (abs($one_float - $another_float) < $epsilon)
// what to be done in case the numbers are equal goes here
?>james dot cridland at virginradio dot co dot uk 28-Apr-2003 02:44
The 'floating point precision' box in practice means:
<? echo (69.1-floor(69.1)); ?>
Think this'll return 0.1?
It doesn't - it returns 0.099999999999994
<? echo round((69.1-floor(69.1))); ?>
This returns 0.1 and is the workaround we use.
Note that
<? echo (4.1-floor(4.1)); ?>
*does* return 0.1 - so if you, like us, test this with low numbers, you won't, like us, understand why all of a sudden your script stops working, until you spend a lot of time, like us, debugging it.
So, that's all lovely then.dev at maintainfit dot com 15-Apr-2003 06:27
I was programming an accounting application in MySql that required me to sum a collection of floats and ensure that they equal zero before commiting a transaction, but as seen above a sum of floats cannot always be trusted (as was my case). I kept getting a very small remainder (like 1.4512431231e-14). Since I had used number_format(num,2) to set the precision of the numbers in the database to only two (2) decimal places, when the time comes to calculate the sum I simply multiply every number by ten (10), therby eliminating and decimal places and leaving me with integers to preform my sum. This worked great.01-Apr-2003 10:20
In response to "...the author probably knows what they are talking about..." above:
Of course the author knows what they're talking about. The previous poster missunderstood the semantics of the author's example of the decimal representation of 1/3. The author is not suggesting that some property of decimal numbers causes the behaviour, but that the property of finite binary representations of real numbers which does cause the problem is shared by finite decimal representations. To paraphrase, the author is saying "10*(0.1+0.7) gives 7.99999... because of the binary equivalent of the fact that 1/3+2/3 gives 0.99999... when using finite decimal representations (where 1/3 == 0.33333... and 2/3 == 0.66666..., so 1/3+2/3 == (0.33333...)+(0.66666...) == 0.99999... instead of 1)."
The problem occurs with finite representations of real numbers, regardless of base of the number system used.Theo Diem 26-Mar-2003 06:35
Just to mention ....
$something = "12.20";
$value = (float) $something;
Depending you locale settings (see setlocale) this will return a float number 12.2 or 12 (without decimal part, if you locale uses another symbol than dot for decimal part)
Be aware if u are working with PHP using one locale setting (by setlocale) and a SQL database with other locale ....Julian Suggate 10-Mar-2003 02:22
Never never never compare floats for equality! Even a >= is asking too much of any binary computer (that's pretty much all of them ;-). It will sometimes work, but the best you can hope for is a subtle bug that will occasionally cause non-deterministic behaviour.
Floats must only ever be used for proper inequalities.backov at spotbrokers-nospamplz dot com 05-Mar-2003 09:16
I'd like to point out a "feature" of PHP's floating point support that isn't made clear anywhere here, and was driving me insane.
This test (where var_dump says that $a=0.1 and $b=0.1)
if ($a>=$b) echo "blah!";
Will fail in some cases due to hidden precision (standard C problem, that PHP docs make no mention of, so I assumed they had gotten rid of it). I should point out that I originally thought this was an issue with the floats being stored as strings, so I forced them to be floats and they still didn't get evaluated properly (probably 2 different problems there).
To fix, I had to do this horrible kludge (the equivelant of anyway):
if (round($a,3)>=round($b,3)) echo "blah!";
THIS works. Obviously even though var_dump says the variables are identical, and they SHOULD BE identical (started at 0.01 and added 0.001 repeatedly), they're not. There's some hidden precision there that was making me tear my hair out. Perhaps this should be added to the documentation?www.sarioz.com 05-Feb-2003 06:49
just a comment on something the "Floating point precision" inset, which goes: "This is related to .... 0.3333333."
While the author probably knows what they are talking about, this loss of precision has nothing to do with decimal notation, it has to do with representation as a floating-point binary in a finite register, such as while 0.8 terminates in decimal, it is the repeating 0.110011001100... in binary, which is truncated. 0.1 and 0.7 are also non-terminating in binary, so they are also truncated, and the sum of these truncated numbers does not add up to the truncated binary representation of 0.8 (which is why (floor)(0.8*10) yields a different, more intuitive, result). However, since 2 is a factor of 10, any number that terminates in binary also terminates in decimal.27-Sep-2002 06:45
much easier:
e.g. round(3.1415927,2) => 3.14
round(1092,-2) => 1100jeroen at php dot net 24-May-2001 02:13
If you want to round a floating point number to the nearest multiple of some number n, use the following trick:
$rounded = round($number / n) * n
For example, to round 12874.49 to the nearest 100-multiple (i.e. 12900), use
$rounded = round($number / 100) * 100
Use ceil() or floor() if you want to round down/up.