Floating point numbers

Floating point numbers (AKA "floats", "doubles" or "real numbers") can be specified using any of the following syntaxes:


<?php

$a = 1.234; 

$b = 1.2e3; 

$c = 7E-10;

?>

Formally:


LNUM          [0-9]+

DNUM          ([0-9]*[\.]{LNUM}) | ({LNUM}[\.][0-9]*)

EXPONENT_DNUM ( ({LNUM} | {DNUM}) [eE][+-]? {LNUM})

The size of a float is platform-dependent, although a maximum of ~1.8e308 with a precision of roughly 14 decimal digits is a common value (that's 64 bit IEEE format).

Floating point precision

It is quite usual that simple decimal fractions like 0.1 or 0.7 cannot be converted into their internal binary counterparts without a little loss of precision. This can lead to confusing results: for example, floor((0.1+0.7)*10) will usually return 7 instead of the expected 8 as the result of the internal representation really being something like 7.9999999999....

This is related to the fact that it is impossible to exactly express some fractions in decimal notation with a finite number of digits. For instance, 1/3 in decimal form becomes 0.3333333. . ..

So never trust floating number results to the last digit and never compare floating point numbers for equality. If you really need higher precision, you should use the arbitrary precision math functions or gmp functions instead.

Converting to float

For information on when and how strings are converted to floats, see the section titled String conversion to numbers. For values of other types, the conversion is the same as if the value would have been converted to integer and then to float. See the Converting to integer section for more information. As of PHP 5, notice is thrown if you try to convert object to float.

User Contributed Notes
Floating point numbers

vic at liveforspeed dot net
25-Mar-2005 02:48


I couldn't find any function to read a float from a file written by C++ (PC?) for example. This format has reversed byte order compared to PHP and in addition, there is just no bin2float function afaik, so I wrote my own binary float 2 usable php float import function.

It does not support SNaN and QNaN values though (didn't need to check for them for my purpose).

Hope it'll be to some use for some:



<?

// $bin must be 4 bytes, MSB first (Most Significant Byte)

function bin2float ($bin) {

    $float = (float) 0;



    // Read Exponent and Sign (+/-)

    $exponent = ord ($bin{3});

    if ($sign = $exponent & 128) $exponent -= 128;

    $exponent <<= 1;



    // Read the remaining bit for Exponent and loop through Mantissa, calculating the Fraction

    $fraction = (float) 1;

    $div = 1;

    for ($x=2; $x>=0; $x--) {

        $byte = ord ($bin{$x});

        for ($y=7; $y>=0; $y--) {

          if ($x==2 && $y==7) {

            if ($byte & (1 << $y)) $exponent += 1;

          } else {

            $div *= 0.5;

            if ($byte & (1 << $y)) $fraction += $div;

          }

        }

    }



    // 0 value check

    if (!$exponent && $fraction == 1) return 0;



    // Final calc, returning the converted float

    $exponent -= 127;



    $float = pow (2, $exponent) * $fraction;

    if ($sign) $float = -($float);



    return $float;

}



echo bin2float (chr (0xb1).chr (0x5c).chr (0xbc).chr (0x41))."\n";

echo bin2float (chr (0x00).chr (0x18).chr (0x5c).chr (0x3f))."\n";

echo bin2float (chr (0).chr (0).chr (160).chr (193))."\n";

echo bin2float (chr (0).chr (0).chr (0).chr (0));

?>



returns:

23.5452594757

0.859741210938

-20

0



(to understand the workings of floats better, I found http://www.randelshofer.ch/fhw/gri/float.html to be a good reference)

edsko at edsko dot net
17-Feb-2005 06:31


The formal specification of the floating point numbers as specified above is not complete. For one thing, it is not immediately obvious which of the three rules describes "floating point numbers" (in general). The disjunction of all three perhaps? My interpretation is that a floating point number is either a DNUM or an EXPONENT_DNUM. 



Moreover, the specification as stated does not allow for signs (+ or -). Yet, PHP does actually allow for signs in the specification of floating point numbers (as one would expect):



<?php

$f = (float) "-0.5";

var_dump($f); // outputs "float(-0.5)"

?>



Thus, the following specification is more complete:



FLOAT           [+-]?({DNUM}|{EXPONENT_DNUM})

LNUM            [0-9]+

DNUM            ([0-9]*[\.]{LNUM}) | ({LNUM}[\.][0-9]*)

EXPONENT_DNUM  ( ({LNUM} | {DNUM}) [eE][+-]? {LNUM})

feline at NOSPAM dot penguin dot servehttp dot com
12-Aug-2004 08:36


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 10:34


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 09:44


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 01:27


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 04:20


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 12:35


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 08:22


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 03:16


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) then 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)) then 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?

04-Mar-2003 05:31


Having had problems with floatval() and doubleval() (on some servers the former doesn't work, on some the latter doesn't), I finally decided to convert variables to floats with this:



$string = '-12.5';

$float = $string + 0.0;

www.sarioz.com
05-Feb-2003 12:49


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 01:45


much easier:

   

  e.g. round(3.1415927,2) => 3.14

        round(1092,-2) => 1100

jeroen at php dot net
23-May-2001 09:13


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.