My point is that there are traps out there if you are unwary and that it isn’t something specific to Julia. I don’t find it particularly interesting what type you get from literals, you could as easily have received it as a function argument, read it from a file, or obtained it from a large array which someone behind your back had optimized the storage of. Normalizing a vector to sum to one does not work?ĭid you forget copying the first assignment here? ![]() If you’re writing code where accuracy is important, then you need to use the right tools, understand those tools and what they guarantee and what they don’t, and most of all, you need to test, test, test. But that’s true of floating-point as well-if someone is using floats in any of these languages naively, there are many examples of how they can get completely wrong answers. You do have to understand these things and use the appropriate types for what you’re doing and understand their failure modes. Note that whether this is more correct depends on whether you care about the high bits or low bits of the computation. Octave, Matlab and R only give you the last option. Floating-point operations, which lose precision and are fast and don’t wrap around.Big integer operations, which never lose precision and never overflow but are very slow.Native integer operations, which never lose precision and are very fast but can wrap around.What you’ve found here is not that Julia is less accurate than Octave (or Matlab or R), but that Octave forces floating-point operations, whereas Julia gives you these choices: Julia, on the other hand, supports actual integer ^ which has no roundoff but does wrap around for native integer types.There is no way to do exact integer exponentiation in Octave without having floating-point round-off.Your exponentiation example doesn’t contradict that, rather it shows that Octave implements x^y as floating-point exponentiation, even if the arguments are integers.example shows that integers in Octave do overflow (by wrapping around)-operations with native integer types do this just as they do in Julia.This also applies where it is evident from the domain that no very large values will be involved. You will usually find in code bases that there is often no check where an uint or a ulong is used as an identifier because it is considered more trouble than it's worth. A classic case is that of hash codes that use the width of the integer as a kind of modulo. Naturally there are occasions on which it is legitimate to allow an integer to wrap around particularly in the case of unsigned values. If large integers are essential to your code then using the BigInteger type is an option. Problems with overflows for int and float can be mitigated by assigning the result to a variable of type long, decimal or double. Overflows that occur without an exception being thrown can be problematic because it's generally true that the earlier an error condition can be reported the better. There is a corresponding unchecked keyword for circumstances where you want to reverse the effect of unchecked inside a checked block or when the compiler setting has been used.Numbers of type decimal will cause an instance of OverflowException to be thrown.float and double types will adopt a state of infinity that can be tested wtih float.IsInfinity() etc.Overflow states in called functions are not caught. the checked state applies only to expressions directly in the block.If a literal expression would cause the variable to which it is assigned to overflow then a compile-time error occurs.Int expr2 = checked(int.MaxValue + one) // overflow exception is thrown Int expr = int.MaxValue + one // overflow exception is thrown int and long will behave similarly except that they wrap around to int.MinValue and long.minValue respectively. unsigned integers ( byte, ushort, uint, ulong) will wrap around to zero (the type's maximum value + 1 acts as a modulus) unless broadly speaking they appear within a checked block in which case an instance of OverflowException is thrown. ![]() when their capacity is insufficient to contain the value resulting from a computation such as an arithmetic operation or cast. ![]() The exercise shows the behavior of various numeric types when they overflow, i.e.
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