浮動小数点数 (あるいは "float", "double", "実数") は、次の構文により指定できます。
<?php
$a = 1.234;
$b = 1.2e3;
$c = 7E-10;
$d = 1_234.567; // PHP 7.4.0 以降
?>PHP 7.4.0 以降の規約(これより前のバージョンでは、アンダースコアは許されませんでした):
LNUM [0-9]+(_[0-9]+)*
DNUM ({LNUM}?"."{LNUM}) | ({LNUM}"."{LNUM}?)
EXPONENT_DNUM (({LNUM} | {DNUM}) [eE][+-]? {LNUM})
float の大きさはプラットフォーム依存です。ただし、通常はおよそ 10 進数で 14 桁の精度があり、最大値は およそ 1.8e308 (これは 64ビット IEEE フォーマットです) となります。
浮動小数点数の精度は有限です。 システムに依存しますが、PHP は通常 IEEE 754 倍精度フォーマットを使います。 この形式は、1.11e-16 のオーダーでの丸め処理で誤差が発生します。 複雑な算術演算をすると、誤差はさらに大きくなるでしょう。そしてもちろん、 いくつかの演算を組み合わせる場合にも誤差を考慮しなければなりません。
さらに、十進数では正確な小数で表せる有理数、たとえば
0.1 や 0.7 は、
二進数の浮動小数点数としては正確に表現できません。
これは、仮数部をいくら大きくしても同じです。
したがって、それを内部的な二進数表現に変換する際には、どうしても多少精度が落ちてしまいます。
その結果、不思議な結果を引き起こすことがあります。たとえば、
floor((0.1+0.7)*10) の結果はたいてい
7 となるでしょう。おそらくは
8 を想定していらっしゃるでしょうが、そのようにはなりません。
これは、(この計算結果の) 内部的な値が
7.9999999999999991118... のようになっているからです。
よって、小数の最後の桁を信用してはいけませんし、 小数を直接比較して等しいかどうかを調べてはいけません。より高い精度が必要な場合には、 任意精度数学関数または gmp 関数を代わりに使用してください。
もっと「シンプルな」説明が欲しければ、» floating point guide を見るといいでしょう。"Why don’t my numbers add up? (なんで数字が足されないの?)" というタイトルが付いています。
文字列が
数値形式の文字列
の場合、対応する float の値に解決されます。
そうでない場合、ゼロ(0)に変換されます。
先ほど警告したように、浮動小数点数値が等しいかどうかを比較するのには問題があります。 これは、浮動小数点数値の内部表現形式に起因するものです。 しかし、この制限を回避して浮動小数点数値の値を比較する方法もあります。
浮動小数点数値が等しいかどうかを調べるには、比較時の丸め誤差の上界を用います。 この値は計算機イプシロンあるいは丸め単位と呼ばれ、 計算時に扱える最小の差分を表します。
$a と $b は、精度 5 桁では等しくなります。
<?php
$a = 1.23456789;
$b = 1.23456780;
$epsilon = 0.00001;
if(abs($a-$b) < $epsilon) {
echo "true";
}
?>$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.<?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.xI'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.