CascadiaPHP 2024

Numeri floating point

I valori floating point (anche conosciuti come "float", "double", o "numeri reali") possono essere specificati utilizzando una delle seguenti sintassi:

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

Formalmente a partire da PHP 7.4.0 (in precedenza, i trattini bassi non erano consentiti):

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

La dimensione di una variabile float dipende dalla piattaforma in uso, sebbene un massimo di circa 1.8e308 con una precisione di circa 14 cifre decimali sia il valore comune (il formato a 64 bit IEEE).

Avviso

Precisione di un valore floating point

I numeri floating point hanno una precisione limitata. Nonostante questa dipenda dal sistema in uso. PHP tipicamente utilizza il formato IEEE 754 double-precision, il quale pone un errore relativo massimo causato dall'arrotondamento nell'ordine di 1.11e-16. Operazioni aritmetiche non elementari possono restituire un errore maggiore e, di conseguenza, la propagazione dell'errore deve essere considerata quando più operazioni vengono eseguite in successione.

In più, alcuni numeri razionali che sono esattamente rappresentabili come numeri floating point in base 10, ad esempio 0.1 o 0.7), non hanno, al contrario, una rappresentazione come numeri floating point in base 2, la quale viene utilizzata internamente dal sistema, indipendentemente dalla dimensione della mantissa. Dunque, questi non possono essere convertiti nella loro controparte binaria interna senza una piccola perdita di precisione. Ciò può portare a risultati confusionari: per esempio, floor((0.1+0.7)*10) solitamente ritornerà come risultato 7 invece di 8, in quanto la sua rappresentazione interna sarà qualcosa di simile a 7.9999999999999991118....

Perciò non fate mai affidamento sui risultati numerici decimali sino all'ultima cifra e non comparate numeri floating point direttamente per uguaglianza. Se è necessaria una maggior precisione, sono disponibili le funzioni matematiche con precisione arbitraria e le funzioni gmp.

Per una "semplice" spiegazione, vedere la » guida per floating point, la quale è anche intitolata "Why don’t my numbers add up?"

Conversione a float

Da stringhe

Se la stringa è numerica o inizia con un numero, verrà risolta nel valore float corrispondente, altrimenti verrà convertita in zero (0).

Da altri tipi

Per i valori di altri tipi, la conversione viene eseguita convertendo il valore prima in int e poi in float. Vedere Conversione in numero intero per ulteriori informazioni.

Nota:

Poiché alcuni tipi hanno un comportamento indefinito durante la conversione in int, lo stesso vale durante la conversione in float.

Comparare float

Come fatto notare nell'esempio sopra, comparare valori floating point per uguaglianza potrebbe risultare problematico a causa della loro rappresentazione interna. Tuttavia esistono dei metodi per comparare dei valori floating point che aggirano queste limitazioni.

Per confrontare valori floating point per uguaglianza viene scelto un limite superiore all'errore relativo creato dall'arrotondamento. Questo valore è conosciuto come la macchina epsilon, o unità roundoff, ed è la più piccola differenza accettabile nel calcolo.

$a e $b sono uguali per 5 cifre di precisione.

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

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

NaN

Alcune operazioni possono ritornare un valore rappresentato dalla costante NAN. Questo risultato rappresenta un valore indefinito o non presentabile nei calcoli di numeri floating point. Qualsiasi comparazione per uguaglianza o per identicità di questo valore con qualsiasi altro, incluso sé stesso, risulterà false.

Poiché NAN rappresenta un qualsiasi numero di differenti valori, NAN non dovrebbe essere comparato ad altri valori, incluso se stesso, e dovrebbe invece essere verificato tramite la funzione is_nan().

add a note

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
10 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
21 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
7 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
21 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
14 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
13 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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