Los números de punto flotante (también conocidos como "floats",
"doubles", o "números reales")
pueden ser especificados utilizando 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, los guiones bajos no estaban permitidos):
LNUM [0-9]+(_[0-9]+)*
DNUM ({LNUM}?"."{LNUM}) | ({LNUM}"."{LNUM}?)
EXPONENT_DNUM (({LNUM} | {DNUM}) [eE][+-]? {LNUM})
El tamaño de un float depende de la plataforma, sin embargo, un número máximo de aproximadamente 1.8e308 con una precisión de 14 dígitos es un valor común (formato de 64 bits IEEE).
Los números de punto flotante tienen una precisión limitada. Aunque dependen del sistema, PHP utiliza el formato de precisión decimal IEEE 754, que dará un error relativo máximo del orden de 1.11e-16 (debido a los redondeos). Las operaciones aritméticas no elementales pueden dar errores más grandes y, por supuesto, los errores deben ser tenidos en cuenta cuando se realizan múltiples operaciones.
Asimismo, los números racionales exactamente representables 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, utilizada internamente, y esto independientemente del tamaño de la mantisa. Por lo tanto, no pueden
ser convertidos sin una pequeña pérdida de precisión. Esto puede llevar a resultados confusos: por ejemplo, floor((0.1+0.7)*10) normalmente devolverá
7 en lugar del 8 esperado, ya que la representación interna será algo como 7.9999999999999991118....
Por lo tanto, nunca se debe confiar en los últimos dígitos de un número de punto flotante, y tampoco se debe comparar la igualdad de 2 números de punto flotante directamente. Si se necesita una mayor precisión, las funciones matemáticas de precisión arbitraria y las funciones gmp están disponibles.
Para una explicación "simple", ver el » guía relativa a los números de punto flotante.
Si una cadena es
numérica
o numérica de cabeza entonces será transformada en su valor de punto flotante
correspondiente, de lo contrario será convertida a cero(0).
Para los valores de otros tipos, la conversión se realiza convirtiendo el valor primero en int y luego en float. Ver conversión a entero para más información.
Nota:
Como algunos tipos tienen un comportamiento indefinido al convertirse en int, esto también es el caso al convertirse en float.
Como se mencionó anteriormente, la prueba de igualdad de valores de números de punto flotante es problemática, debido a la forma en que se representan internamente. Sin embargo, existen formas de realizar esta comparación.
Para probar la igualdad de valores de números de punto flotante, se utiliza un límite superior del error relativo al redondeo. Este valor es conocido
como el epsilon de la máquina, o el unit roundoff,
y es la diferencia más pequeña aceptable en los cálculos.
$a y $b son iguales en 5 números después de la coma.
Ejemplo #1 Comparación de números de punto flotante
<?php
$a = 1.23456789;
$b = 1.23456780;
$epsilon = 0.00001;
if( abs($a - $b) < $epsilon) {
echo "true";
}
?>
Algunas operaciones numéricas pueden dar como resultado un valor
representado por la constante NAN. Este resultado representa
un valor indefinido o no representable en cálculos con números de punto flotante. Cualquier comparación, incluso estricta de este valor con
otro valor, incluyendo esta constante misma, excepto si es igual a true, dará un valor de false.
Debido a que NAN representa cualquier número de valores
diferentes, NAN no debe ser comparado con otros valores,
incluyendo esta constante misma, y en su lugar, debe ser verificado
utilizando la función is_nan().
$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.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.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.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?To compare two numbers use:
$epsilon = 1e-6;
if(abs($firstNumber-$secondNumber) < $epsilon){
// equals
}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 $js;
This would result in a different result for users with some locales. On most systems, this would print:
var foo = doBar(0.23);
but when for example a user from Germany arrives, it would be different:
var foo = doBar(0,23);
which is obviously a different call to the function. JavaScript won't state an error, additional arguments are discarded without notice, but the function doBar(a) would get 0 as parameter. Similar problems could arise anywhere else (SQL, any string used as code somewhere else). The problem persists, if you use the "." operator instead of evaluating the variable in the string.
So if you REALLY need to be sure to have the string correctly formatted, use number_format() to do it!The 'floating point precision' box in practice means:
<? echo (69.1-floor(69.1)); ?>
Think this'll return 0.1?
It doesn't - it returns 0.099999999999994
<? echo round((69.1-floor(69.1))); ?>
This returns 0.1 and is the workaround we use.
Note that
<? echo (4.1-floor(4.1)); ?>
*does* return 0.1 - so if you, like us, test this with low numbers, you won't, like us, understand why all of a sudden your script stops working, until you spend a lot of time, like us, debugging it.
So, that's all lovely then.In some cases you may want to get the maximum value for a float without getting "INF".
var_dump(1.8e308); will usually show: float(INF)
I wrote a tiny function that will iterate in order to find the biggest non-infinite float value. It comes with a configurable multiplicator and affine values so you can share more CPU to get a more accurate estimate.
I haven't seen better values with more affine, but well, the possibility is here so if you really thing it's worth the cpu time, just try to affine more.
Best results seems to be with mul=2/affine=1. You can play with the values and see what you get. The good thing is this method will work on any system.
<?php
function float_max($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;
}
?><?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...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.<?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