Think of this function: int f(int i) { return i+1 > i; } Mathematically speaking, i+1 should always be greater than i for any integer i. However, for a 32-bit int, there is one value of i that makes that statement false, which is 2147483647 (i.e. 0x7FFFFFFF, i.e. INT_MAX). Adding one to that number will … Read more
Math.addExact throws exception on overflow Since Java 8 there is a set of methods in the Math class: toIntExact(long) addExact(int,int) subtractExact(int,int) multiplyExact(int,int) …and versions for long as well. Each of these methods throws ArithmeticException if overflow happens. Otherwise they return the proper result if it fits within the range. Example of addition: int x = … Read more
If you need larger than 32-bits you could consider using 64-bit integers (long long), or use or write an arbitrary precision math library, e.g. GNU MP.
Exponentiation by squaring still “works” for modulo exponentiation. Your problem isn’t that 2 ^ 168277 is an exceptionally large number, it’s that one of your intermediate results is a fairly large number (bigger than 2^32), because 673109 is bigger than 2^16. So I think the following will do. It’s possible I’ve missed a detail, but … Read more
In MATLAB, one option you have is to overload the methods that handle arithmetic operations for integer data types, creating your own custom overflow behavior that will result in a “wrap-around” of the integer value. As stated in the documentation: You can define or overload your own methods for int* (as you can for any … Read more
This image shows what you’re looking for. In your case it’s obviously larger numbers, but the principle stays the same. Examples of limits in java are: int: −2,147,483,648 to 2,147,483,647. long: -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 In the image 0000, 0001 etc, shows the binary representation of the numbers. EDIT: In project euler you often have to … Read more
Signed overflow is undefined in C, and that’s for real. One solution follows: signed_result = (unsigned int)one_argument + (unsigned int)other_argument; The above solution involves implementation-defined behavior in the final conversion from unsigned to int but do not invoke undefined behavior. With most compilation platforms’ implementation-defined choices, the result is exactly the two’s complement result that … Read more
Integer overflow is the canonical example of “undefined behaviour” in C (noting that operations on unsigned integers never overflow, they are defined to wrap-around instead). This means that once you’ve executed x + y, if it overflowed, you’re already hosed. It’s too late to do any checking – your program could have crashed already. Think … Read more
Signed integer overflow is undefined behaviour, while unsigned integer overflow is well-defined; the value wraps around. In other words, the value is modulo divided by 2bits, where bits is the number of bits in the data type. Since you’ve a 32-bit int 4294967295 + 1 = 4294967296 % 232 = 0 it results in 0 … Read more
Signed integer variables do not have wrap-around behavior in C language. Signed integer overflow during arithmetic computations produces undefined behavior. Note BTW that GCC compiler you mentioned is known for implementing strict overflow semantics in optimizations, meaning that it takes advantage of the freedom provided by such undefined behavior situations: GCC compiler assumes that signed … Read more