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Números de punto flotante

Los números de punto flotante (también conocidos como "de coma flotante" en español, y "floats" en inglés) pueden ser especificados usando cualquiera de las siguientes sintaxis:

<?php
$a
= 1.234;
$b = 1.2e3;
$c = 7E-10;
$d = 1_234.567; // a partir de PHP 7.4.0
?>

Formalmente a partir de PHP 7.4.0 (anteriormente, no se permitían los guiones bajos):

LNUM          [0-9]+(_[0-9]+)*
DNUM          ([0-9]*(_[0-9]+)*[\.]{LNUM}) | ({LNUM}[\.][0-9]*(_[0-9]+)*)
EXPONENT_DNUM (({LNUM} | {DNUM}) [eE][+-]? {LNUM})

El tamaño de un 'float' depende de la plataforma, aunque un valor común consiste en un máximo de aproximadamente 1.8e308 con una precisión cercana a los 14 dígitos decimales (el formato de 64 bit del IEEE).

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Precisión del punto flotante

Los números de punto flotante tienen una precisión limitada. Aunque depende del sistema, PHP típicamente utiliza el formato de doble precisión IEEE 754, el cual dará un error relativo máximo por aproximación del orden de 1.11e-16. Las operaciones aritméticas elementales no podrán generar grandes errores y, por supuesto, se han de considrar los errores por propagación al componer varias operaciones.

Adicionalmente, los numeros racionales que son representables exactamente como números de punto flotante en base 10, como 0.1 o 0.7, no tienen una representación exacta como números de punto flotante en base 2, que es la base empleada internamente, sin importar el tamaño de la mantisa. Por lo tanto, no se pueden convertir en sus equivalentes binarios internos sin una pequeña pérdida de precisión. Esto puede conducir a resultados confusos: Por ejemplo, floor((0.1+0.7)*10) usualmente devolverá 7 en lugar del 8 previsto, ya que la representación interna será algo así como 7.9999999999999991118....

Por tanto, nunca se ha de confiar en resultados de números flotantes hasta el último dígito, y no comparar la igualdad de números de punto flotante directamente. Si fuera necesaria una mayor precisión, están disponibles las funciones matemáticas de precisión arbitraria y las funciones de gmp.

Para una explicación "simple", véase la » guía del punto flotante que también se titula "¿Por qué no sale la cuenta?"

Conversión al tipo float

Para más información sobre las conversiones de string a float, véase la Conversión de cadenas a números. Para valores de otros tipos, la conversión es la misma que si el valor hubiese sido convertido primero a integer y luego a float. Véase la Conversión a al tipo integer para más información. A partir de PHP 5, se genera un aviso si se intenta convertir un object a float.

Comparación del tipo float

Como se indica en la advertencia anterior, comprobar la igualdad de valores de punto flotante es problemático debido a la forma en que se representan internamente. Sin embargo, hay maneras de hacer comparaciones de los valores de punto flotante que evitan estas limitaciones.

Para comprobar la igualdad de valores de punto flotante, se utiliza un límite superior en el error relativo debido al redondeo. Este valor se conoce como el épsilon de la máquina o unidad de redondeo, y es la menor diferencia aceptable en los cálculos.

$a y $b son iguales en 5 dígitos de precisión.

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

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

NaN

Algunas operaciones numéricas pueden resultar en un valor representado por la constante NAN. Este resultado representa un valor no definido o no representable mediante cálculos de punto flotante. Cualquier comparación, ya sea estricta o no, de este valor con cualquier otro valor, incluido él mismo, pero excepto true, tendrá un resultado de false.

Ya que NAN representa cualquier número de diferentes valores, NAN no debería compararse con otros valores, incluido él mismo; en su lugar debería comprobarse usando la función is_nan().

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User Contributed Notes 11 notes

up
251
catalin dot luntraru at gmail dot com
10 years ago
$x = 8 - 6.4; // which is equal to 1.6
$y = 1.6;
var_dump($x == $y); // is not true

PHP thinks that 1.6 (coming from a difference) is not equal to 1.6. To make it work, use round()

var_dump(round($x, 2) == round($y, 2)); // this is true

This happens probably because $x is not really 1.6, but 1.599999.. and var_dump shows it to you as being 1.6.
up
112
feline at NOSPAM dot penguin dot servehttp dot com
19 years ago
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.
up
61
www.sarioz.com
21 years ago
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.
up
1
251701981 at qq dot com
6 months ago
<?php

//Please consider the following code
printf("%.53f\n",0.7+0.1); // 0.79999999999999993338661852249060757458209991455078125

var_dump(0.7+0.1); // float(0.8)

var_dump(0.799999999999999); //float(0.8)

var_dump(0.7999999); // float(0.7999999)

//Conclusion: PHP can support up to 53 decimal places, but in some output functions such as var_ Dump, when outputting decimals exceeding 14 places, will round off the 15th place, which causes significant misleading
//experimental environment:linux x64,php7.2.x
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19
backov at spotbrokers-nospamplz dot com
20 years ago
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?
up
5
lwiwala at gmail dot com
6 years ago
To compare two numbers use:

$epsilon = 1e-6;

if(abs($firstNumber-$secondNumber) < $epsilon){
// equals
}
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7
Luzian
18 years ago
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!
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5
james dot cridland at virginradio dot co dot uk
20 years ago
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.
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5
magicaltux at php dot net
13 years ago
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;
}
?>
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4
zelko at mojeime dot com
12 years ago
<?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...
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3
rick at ninjafoo dot com
18 years ago
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.
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