Analyze the reason why 8%-3 is zero in PHP

Exploring why 8%-3 equals 0 in PHP

When doing mathematical operations in the PHP language, most people will encounter some strange situations. One of them is to calculate 8% (modulo 3) which results in 0. This result seems a bit strange, because theoretically 8 cannot be divided by 3, so there should be a remainder.

Before we delve deeper, let’s first take a look at the modulo operator “%” in PHP. The modulo operation is used to calculate the remainder between two numbers. The specific operation is to divide the first number by the second number, and then take the remainder as the result.

In PHP, an important principle of the modulo operation rules is: the sign of the modulo result is consistent with the sign of the modulus. So if the modulus is positive, then the modulo result will also be positive. Likewise, if the modulus is negative, the modulo result will also be negative.

Back to our example, 8%-3 should return a negative remainder, not 0. But why does PHP return 0?

The answer to this question actually involves some mathematical and programming concepts from computer science.

First, we need to understand how integers are represented in PHP. In PHP, integers can be divided into two types: signed integer (signed integer) and unsigned integer (unsigned integer). Signed integers are integers that can be represented by positive and negative signs, while unsigned integers can only represent non-negative integers.

By default, integers in PHP are signed integers. This means that 8 and -3 are both signed integers. When we calculate 8%-3, PHP will convert the two numbers into the same type and then perform the calculation.

In this case, 8 is converted to a signed integer and its binary representation is 00000000000000000000000000001000. And -3 is also converted into a signed integer, and its binary representation is 1111111111111111111111111111101.

Next, PHP performs a modulo operation on these two numbers. In fact, PHP will use the following formula to calculate the integer modulus:

a % b = a - b * floor(a / b)

According to this formula, let’s calculate 8% Result of -3:

8 - (-3) floor(8 / -3) = 8 - (-3) -2 = 8 - 6 = 2

According to this calculation, the result we get is 2, not the default result 0 of the integer modulo operation. Why is this?

The reason is that the integer modulo operator "%" in PHP does not fully comply with the mathematical definition. According to traditional mathematical definitions, the result of the modulo operation should be between 0 and the modulus. In PHP, when the modulus is a negative number, the result of the modulo operation is a negative remainder minus the absolute value of the modulus.

So in our example, when 8 is used as the modulus, 2 is a legal modulo result. But since we are focusing on the situation when the modulus is negative, the final result is 0.

To sum up, the reason why 8%-3 in PHP is equal to 0 is that PHP’s design of the modulo operator “%” does not fully comply with the traditional mathematical definition, but is based on the symbol of the modulus. Adjust the results.

Although this result looks a bit strange, in actual programming, we can operate and process mathematical operations according to this rule to avoid unexpected results.

Summary

This article explores why 8%-3 equals 0 in PHP. By analyzing the signed and unsigned representation of integers in PHP, as well as the definition of integer modulo operation, we learned that PHP's modulo operator "%" does not fully comply with the traditional mathematical definition. It is worth noting that in actual programming, we should understand this rule and handle mathematical operations appropriately to get the expected results.

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