11/13/2023 0 Comments Integer overflow errorA floating-point format may be able to represent 0, then various finite non-zero numbers, then infinity. They may be defined relative to the magnitude of the result, neglecting the sign, and they are defined relative to the finite non-zero range of the format. For floating-point arithmetic, these terms have somewhat different meanings. (Note: For integer arithmetic, “underflow” or “overflow” is defined relative to the absolute bounds L and U. The fact that it needs fewer bits to represent is irrelevant. When 10000111 2 is subtracted from 11110111 2, the result, 01110000 2 = 1110000 2, is within bounds, so there is no overflow or underflow. It does not mean that fewer bits are needed to represent the result. “Overflow” may also be used to refer to any exceeding of the bounds of the type, including in the low direction. “Underflow” and “overflow” mean the operation has gone out of the bounds of the type. If the ideal mathematical result of an operation is greater than U, the operation overflows. If the ideal mathematical result of an operation is less than L, the operation underflows. In other words, for whatever type you are using for arithmetic there is some lower limit L and some upper limit U that the type can represent. People may nonetheless use the terms “underflow” or “overflow” when discussing these operations, intended to refer to the mathematical issues rather than the defined C behavior. For example, with 32-bit unsigned arithmetic, subtracting 7 from 5 would produce 4,294,967,294 (in hexadecimal, FFFFFFFE 16), because it has wrapped modulo 2 32 = 4,294,967,296. In C, unsigned arithmetic is said not to underflow or overflow because the C standard defines the operations to be performed using modulo arithmetic instead of real-number arithmetic. Or, in an eight-bit signed type that can represent numbers from −128 to +127, subtracting 100 from −100 would ideally produce −200, but this cannot be represented in the type, so the operation underflows. If 7 is subtracted from 5 in unsigned arithmetic, the ideal mathematical result would be −2, but an unsigned type cannot represent −2, so the operation underflows. Generally, “underflow” means the ideal mathematical result of a calculation is below what the type can represent. The 1 1 0 row of the table has a 0 in the V column: no overflow. Applying the rules above, A = 1, B = 0 and C = 0. Subtracting 247 - 135 = 112 is clearly not overflow, since 247 is larger than 135. or the msb of b is 1 and that of c is also 1.or the msb of a is 0 and that of c is 1.In other words, overflow in the unsigned subtraction c = a - b happens whenever: From these, the overflow V is calculated like this: A B C | V What we need is the most significant bits from a, b and c. So, given that we have the wraparound arithmetic, we can detect whether wraparound (or overflow, depending on point of view) has taken place in a subtraction. Note also that in C we don't speak about "overflow", because there is no error condition: C unsigned integers provide that wraparound arithmetic that is commonly found in hardware. However, that's somewhat of a circular definition, because how many kinds of machines perform the a < b comparison is by subtracting the operands using wraparound arithmetic, and then detecting the overflow based on the two operands and the result. Underflow in unsigned subtraction c = a - b occurs whenever b is larger than a.
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