In-depth understanding of the phenomenon of unequal floating point decimals in PHP

PHP is a programming language widely used in Web development, in which floating-point number processing has always been an issue that developers need to pay attention to. In actual development, we often encounter the phenomenon that floating point numbers are not equal, which is often due to the loss of precision caused by the binary form of floating point numbers in the computer. In this article, we’ll take a deep dive into floating point inequality in PHP and illustrate it with concrete code examples.

First, let's start with a simple example. Suppose we have two floating point numbers $a = 0.1 0.2$ and $b = 0.3$. We expect that these two numbers should be equal, but in actual programming, they may not be equal. Let us verify it with the following code:

$a = 0.1 + 0.2;
$b = 0.3;

if ($a == $b) {
    echo "相等";
} else {
    echo "不相等";
}

Run the above code, we will find that the output result is "not equal". This is because in computers, the numbers 0.1, 0.2, and 0.3 are infinitely recurring decimals when represented in binary, so they cannot be represented completely accurately. A slight error occurred when calculating $a = 0.1 0.2$, resulting in the value of $a$ actually being a number very close to 0.3 but not exactly equal to 0.3.

To understand this issue more deeply, let’s look at another example. Consider the following code:

$x = 0.7;
$y = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1;
if ($x == $y) {
    echo "相等";
} else {
    echo "不相等";
}

Running the above code, we will find that the output result is "not equal". This is because for the same reason, 0.1 cannot be represented exactly in a computer, and $y$ is actually a number slightly larger than 0.7. So, although we expect that the values ​​of $x$ and $y$ should be equal, they are not actually equal due to limitations in floating point precision.

To solve this problem, we usually use an error range to compare floating point numbers instead of using the equality operator directly. For example, we can modify the above code as follows:

$x = 0.7;
$y = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1;
$epsilon = 0.00001; // 定义一个误差范围

if (abs($x - $y) < $epsilon) {
    echo "相等";
} else {
    echo "不相等";
}

By introducing an allowed error range, we can compare floating point numbers more flexibly, thereby avoiding inequalities caused by precision issues.

In short, the phenomenon of unequal floating point numbers is a common problem in PHP. Due to the loss of precision due to the binary representation of floating point numbers, developers need to pay attention to handling this situation. By reasonably setting the error range or adopting other processing methods, the problem of unequal comparison of floating point numbers can be effectively solved to ensure the correctness and stability of the program.

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