Floating point numbers

Floating point numbers (also known as "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 (the 64 bit IEEE format).

Warning

Floating point precision

Floating point numbers have limited precision. Although it depends on the system, PHP typically uses the IEEE 754 double precision format, which will give a maximum relative error due to rounding in the order of 1.11e-16. Non elementary arithmetic operations may give larger errors, and, of course, error propagation must be considered when several operations are compounded.

Additionally, rational numbers that are exactly representable as floating point numbers in base 10, like 0.1 or 0.7, do not have an exact representation as floating point numbers in base 2, which is used internally, no matter the size of the mantissa. Hence, they cannot be converted into their internal binary counterparts without a small 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, since the internal representation will be something like 7.9999999999999991118....

So never trust floating number results to the last digit, and do not compare floating point numbers directly for equality. If higher precision is necessary, the arbitrary precision math functions and gmp functions are available.

For a "simple" explanation, see the » floating point guide that's also titled "Why don’t my numbers add up?"

Converting to float

For information on converting strings to float, see String conversion to numbers. For values of other types, the conversion is performed by converting the value to integer first and then to float. See Converting to integer for more information. As of PHP 5, a notice is thrown if an object is converted to float.

Comparing floats

As noted in the warning above, testing floating point values for equality is problematic, due to the way that they are represented internally. However, there are ways to make comparisons of floating point values that work around these limitations.

To test floating point values for equality, an upper bound on the relative error due to rounding is used. This value is known as the machine epsilon, or unit roundoff, and is the smallest acceptable difference in calculations.

$a and $b are equal to 5 digits of precision.


<?php
$a = 1.23456789;
$b = 1.23456780;
$epsilon = 0.00001;

if(abs($a-$b) < $epsilon) {
    echo "true";
}
?>

NaN

Some numeric operations can result in a value represented by the constant NAN. This result represents an undefined or unrepresentable value in floating-point calculations. Any loose or strict comparisons of this value against any other value, including itself, but except TRUE, will have a result of FALSE.

Because NAN represents any number of different values, NAN should not be compared to other values, including itself, and instead should be checked for using is_nan.