Summary of PHP floating point precision issues, PHP floating point precision_PHP tutorial

Summary of PHP floating point number accuracy issues, PHP floating point number accuracy

1. PHP floating point number accuracy loss problem

Look at the following code first:
Copy code The code is as follows:
$f = 0.57;
echo intval($f * 100); //56

The result may be a bit surprising to you, PHP follows IEEE 754 double precision:

Floating point number, with 64-bit double precision, is represented by 1 sign bit (E), 11 exponent bits (Q), and 52-bit mantissa (M) (64 bits in total).
Sign bit: The highest bit indicates the sign of the data, 0 indicates a positive number, and 1 indicates a negative number.
Exponent bit: represents the data raised to the power of base 2, and the exponent is represented by an offset code
Mantissa: Indicates the significant digits after the decimal point of the data.

Let’s take a look at how decimals are expressed in binary:

Multiply by 2 and round up, arrange in order, that is, multiply the decimal part by 2, then take the integer part, continue to multiply the remaining decimal part by 2, then take the integer part, multiply the remaining decimal part by 2, and keep taking To the decimal part, but if you multiply a decimal like 0.57 like this, the decimal part cannot be 0. The decimal representation of the significant digits is infinite in binary.

The binary representation of 0.57 is basically (52 bits): 0010001111010111000010100011110101110000101000111101

If there are only 52 bits, 0.57 => 0.56999999999999995

It is not difficult to see the unexpected results above.

2. Precision problem of PHP floating point numbers

Let’s look at the question first:

Copy code The code is as follows:
$f = 0.58;
var_dump(intval($f * 100)); //Why does it output 57

I believe many students have had such questions.

For the specific principle, you can read an article by "Brother Bird", where there is a detailed explanation: Answers to a common question about PHP floating point numbers

So how to avoid this problem?
There are many ways, here are two:
1. sprintf
Copy code The code is as follows:
substr(sprintf("%.10f", ($a/ $b)), 0, -7);

2. round (note that it will be rounded)
Copy code The code is as follows:
round($a/$b, 3);

Or if you have a better way, please leave a message and tell me.

3. Answer to a common question about PHP floating point numbers

Regarding floating point numbers in PHP, I have written an article before: All ‘bogus’ about the float in PHP (All ‘bogus’ about the float in PHP)

However, I missed one thing, which is the answer to this common question:
Copy code The code is as follows:
$f = 0.58;
var_dump(intval($f * 100)); //Why is it output 57
?>

Why is the output 57? Is it a PHP bug?

I believe that many students have had such questions, because there are many people asking me similar questions, not to mention that people often ask questions on bugs.php.net...

To understand this reason, we first need to know the representation of floating point numbers (IEEE 754):

Floating point numbers, taking 64-bit length (double precision) as an example, will be represented by 1 sign bit (E), 11 exponent bits (Q), and 52-bit mantissa (M) (a total of 64 bits).

Sign bit: The highest bit represents the sign of the data, 0 represents a positive number, and 1 represents a negative number.

Exponent bit: indicates the data raised to the power of base 2, and the exponent is represented by an offset code

Mantissa: Indicates the significant digits after the decimal point of the data.

The key point here is the representation of decimals in binary. As for how decimals are represented in binary, you can search on Baidu. I won’t go into details here. The key thing we need to understand is that for binary representation, 0.58 is infinite. Long values ​​(numbers below omit the implicit 1)..

The binary representation of 0.58 is basically (52 bits): 0010100011110101110000101000111101011100001010001111
The binary representation of 0.57 is basically (52 bits): 0010001111010111000010100011110101110000101000111101
The binary numbers of the two, if calculated only through these 52 bits, are:
Copy code The code is as follows:
0.58 -> 0.57999999999999996
0.57 -> 0.56999999999999995

As for the specific floating-point number multiplication of 0.58 * 100, we will not consider it in detail. Those who are interested can look at the floating point. We will look at it vaguely through mental arithmetic... 0.58 * 100 = 57.999999999

Then if you intval it, it will naturally be 57…

It can be seen that the key point of this problem is: "Your seemingly finite decimal is actually infinite in the binary representation of the computer"

so, stop thinking this is a PHP bug, this is what it is...

http://www.bkjia.com/PHPjc/998816.htmlwww.bkjia.comtruehttp: //www.bkjia.com/PHPjc/998816.htmlTechArticleA summary of PHP floating point number accuracy issues, PHP floating point number accuracy 1. PHP floating point number accuracy loss problem first look at the following paragraph Code: Copy the code as follows: $f = 0.57; echo intval($f * 100); //...