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The mysterious world of integer overflow: How to avoid unexpected errors in computing?
In computer programming, integer overflow is a condition in which an integer arithmetic produces a value that exceeds the range of available representation. When the result of an operation exceeds the maximum or minimum representable value, the most common result is that the least significant digit of the result is stored so that the result wraps around to the maximum value. For some processors, such as graphics processing units (GPUs) and digital signal processors (DSPs), which support saturated operations, overflow results will be clamped to the representable range instead of simply wrapping around the overflow. Failure to foresee the possibility of integer overflow may cause the program to behave as expected, and may even affect the reliability and security of the program.
Integer overflow may cause unexpected behavior, which is a hidden trap in programming.
The root cause of integer overflow is that the width of the processor's register determines the range of values it can represent. While most computers can perform multiple-precision arithmetic in memory, allowing numbers to be arbitrarily long, the width of the registers limits the size of the numbers that can be added in a single operation (e.g., addition or subtraction). Generally speaking, the register width of unsigned integers includes 4 bits, 8 bits, 16 bits, 32 bits, and 64 bits. When the result of an unsigned integer operation exceeds the maximum value listed above, the result caused by overflow will retain the least significant digit of the number in modulo N to the power of 2, resulting in wrapping. For example, 254 + 2 will result in 0.
Integer overflow not only causes problems in programming, but can also lead to security risks. When an overflowed value is used as the number of characters to allocate a buffer, the buffer may be accidentally allocated too small, causing a buffer overflow and allowing malicious code to execute. If the variable is a signed integer, the program may think that the variable contains only positive values, but integer overflow will cause the value to wrap around to negative, resulting in a logical error.
Therefore, correctly using unsigned integer types to store values that are not expected to be negative is an effective way to avoid overflow.
For detecting integer overflow, many computers provide two dedicated processor flags to check for overflow conditions. When the result of an addition or subtraction exceeds the given number of bits without a sign, the carry flag is set to indicate that an overflow has occurred. Conversely, the overflow flag is set when the result of a signed operation does not match the expected sign of the operand, indicating that the actual result did not fit within the allocated bit range.
The definition and meaning of integer overflow may vary in different contexts. For example, in the C11 standard, there are many cases where overflow is not considered. Traditional programming languages such as C often have undefined behavior for overflow, while some newer languages such as Rust provide built-in detection options, allowing users to choose how to handle possible overflows according to their needs. As a result, the support and handling of integer overflow in different languages becomes an important factor in improving program security and reliability.
To effectively avoid integer overflow, some methods can be used, such as:
Detection: Use a runtime overflow detection tool such as UBSan, or use exact arithmetic in Java to catch overflow errors.Avoid: Allocate variables of a type that is large enough for all possible values that may be calculated and stored, or avoid overflow by using the order of operations.Handling: If overflow is expected to occur, insert detection code into the program.
Ensuring that integer operations do not unexpectedly overflow is critical to program stability.
The effects of integer overflow are not always obvious. In the case of the Therac-25 radiation therapy machine built between 1985 and 1987, errors due to integer overflows ultimately resulted in the deaths of at least six people. Such cases make us realize the importance of how to handle integer overflow in program design. It also reminds developers to think about what methods can be used to effectively prevent and handle integer overflow problems during the design process?
