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PHP : Language Reference : Types : Floating point numbers

# 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.

## Code Examples / Notes » language.types.float

gallico_

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
?>

edsko

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})

james dot cridland

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.

david

Re: rick at ninjafoo dot com
There is no need to â€œalwaysâ€ use the BCMath functions. We just need to heed the documentation and â€œnever compare floating point numbers for equalityâ€.
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.

julian suggate

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.

27-sep-2002 07:45

much easier:

e.g. round(3.1415927,2) => 3.14
round(1092,-2) => 1100

theo diem

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 ....

www.sarioz.com

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.

01-apr-2003 11:20

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.

jeroen

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.

backov

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?

dev

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.

justin

I was playing around with a benchmark script:
<?php
\$st = array_sum (explode (' ', microtime ()));
ob_start ();
for (\$i = 1; \$i < 10000; \$i++) {
echo "<!-- Hello, World! " .  (\$i % round(sqrt(\$i*2))) ^ \$i .  " -->\n";
}
ob_end_flush ();
echo round ((array_sum (explode (' ',microtime ())) - \$st), 5) . "\n";
?>
Be careful with numbers, they can print out inpredictable things.  (For example, this printed out [uncommented])...
&#6410; ¯ƒ&#2671;&#3352;&#3328;¦&#4363; ¯ƒ&#2927;&#3344;&#3328;¦&#4875; ¯ƒ&#2927;&#3346;&#3328;¦&#5387; ¯ƒ&#2927;&#3348;&#3328;¦&#5899; ¯ƒ&#2927;&#3350;&#3328;¦&#6411; ¯ƒ&#2927;&#3352;&#3328;¦&#4356; ¯ƒ&#1135;&#3344;&#3328;¦&#4868; ¯ƒ&#1135;&#3346;&#3328;¦&#5380; ¯ƒ&#1135;&#3348;&#3328;¦&#5892; ¯ƒ&#1135;&#3350;&#3328;¦&#6404; ¯ƒ&#1135;&#3352;&#3328;¦&#4357; ¯ƒ&#1391;&#3344;&#3328;¦&#4869; ¯ƒ&#1391;&#3346;&#3328;¦&#5381; ¯ƒ&#1391;&#3348;&#3328;¦&#5893; ¯ƒ&#1391;&#3350;&#3328;¦&#6405; ¯...

tri0n

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
Enjoy

feline

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.

helly

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.html

rick

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.

luzian

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!

tas

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.

sinuhet

<?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.

### Change Language

Introduction
Booleans
Integers
Floating point numbers
Strings
Arrays
Objects
Resource
NULL
Pseudo-types and variables used in this documentation
Type Juggling