I'm writing C++ code in an environment in which I don't have access to the C++ standard library, specifically not to std::numeric_limits. Suppose I want to implement
template <typename T> constexpr T all_ones( /* ... */ )
Focusing on unsigned integral types, what do I put there? Specifically, is static_cast<T>(-1) good enough? (Other types I could treat as an array of unsigned chars based on their size I guess.)
Use the bitwise NOT operator ~ on 0.
T allOnes = ~(T)0;
A static_cast<T>(-1) assumes two's complement, which is not portable. If you are only concerned about unsigned types, hvd's answer is the way to go.
Working example: https://ideone.com/iV28u0
Focusing on unsigned integral types, what do I put there? Specifically, is static_cast(-1) good enough
If you're only concerned about unsigned types, yes, converting -1 is correct for all standard C++ implementations. Operations on unsigned types, including conversions of signed types to unsigned types, are guaranteed to work modulo (max+1).
This disarmingly direct way.
T allOnes;
memset(&allOnes, ~0, sizeof(T));
Focusing on unsigned integral types, what do I put there?
Specifically, is static_cast(-1) good enough
Yes, it is good enough.
But I prefer a hex value because my background is embedded systems, and I have always had to know the sizeof(T).
Even in desktop systems, we know the sizes of the following T:
uint8_t allones8 = 0xff;
uint16_t allones16 = 0xffff;
uint32_t allones32 = 0xffffffff;
uint64_t allones64 = 0xffffffffffffffff;
Another way is
static_cast<T>(-1ull)
which would be more correct and works in any signed integer format, regardless of 1's complement, 2's complement or sign-magnitude. You can also use static_cast<T>(-UINTMAX_C(1))
Because unary minus of an unsigned value is defined as
The negative of an unsigned quantity is computed by subtracting its value from 2^n, where n is the number of bits in the promoted operand."
Therefore -1u will always return an all-one-bits data in unsigned int. ll suffix is to make it work for any types narrower than unsigned long long. There's no extended integer types (yet) in C++ so this should be fine
However a solution that expresses the intention clearer would be
static_cast<T>(~0ull)
Suppose I have declared following variables :
some_dataType a,b,c; //a,b,c are positive
int res;
res=a+b-c;
And I have been provided with the information that the variable res cannot cross integer limit. Just to avoid overflow from the expression a+b in a+b-c I have following options-
declare a,b,c as long int
(a-c)+b
(long int)(a+b-c) //or some other type casting
My question is which of the above is good practice. Also, just to escape from all this, I prefer doing option 1. But it may increase the memory size of the program (not for this program though, but for large applications).
Assumption : long int is greater than int Thanks #Retired Ninja
There's no simple, general, portable way to avoid integer overflow.
Using a wider integer type is not a general solution, because there's no guarantee that there is a wider integer type. It's very common for the types int and long to be the same size on some systems. 32-bit systems typically make both int and long 32 bits; even some 64-bit systems do the same thing. And some 64-bit systems make both int and long 64 bits.
You wrote:
And I have been provided with the information that the variable res cannot cross integer limit.
It's best to be careful with terminology. Although the type name int is obviously an abbreviation of the word "integer", the words are not synonymous. In C and C++, int is just one of several integer types; others include unsigned char and long long.
Presumably what you mean is that the value of res must not be outside the range of type int, which is INT_MIN to INT_MAX.
If you use long long for the result, it's likely that you can avoid overflow; you can then compare the result to the values INT_MIN and INT_MAX, and take whatever corrective action is appropriate if it's out of range. But it's still possible for both int and long long to be 64 bits. What you do with that depends on how portable your code needs to be.
You cannot safely check whether a signed integer addition or subtraction overflowed after the fact. An overflow in signed arithmetic causes undefined behavior. Typically the result wraps around, but in principle your program could crash before you have a chance to examine the result.
Some compilers might provide functions that perform safe signed arithmetic and tell you whether there was an overflow. Consult your compiler's documentation.
There are ways to test the operands before performing the operation. They're complicated, and I'm too lazy to work out the details, but briefly:
If the operands of + are of opposite signs, or if one operand is 0, the addition is safe.
If both operands are positive, the addition is safe if x does not exceed INT_MAX - y.
If both operands are negative, the addition is safe if y is no less than INT_MIN - y.
I do not guarantee that the above is completely correct *I just wrote it off the top of my head), but in most cases it's probably more effort than it's worth.
Trust, but verify:
assert(a > 0);
assert(b > 0);
assert(c > 0);
assert((long)a - (long)c + (long)b <= INT_MAX);
int res = a - c + b;
I encountered a strange thing when I was programming under c++. It's about a simple multiplication.
Code:
unsigned __int64 a1 = 255*256*256*256;
unsigned __int64 a2= 255 << 24; // same as the above
cerr()<<"a1 is:"<<a1;
cerr()<<"a2 is:"<<a2;
interestingly the result is:
a1 is: 18446744073692774400
a2 is: 18446744073692774400
whereas it should be:(using calculator confirms)
4278190080
Can anybody tell me how could it be possible?
255*256*256*256
all operands are int you are overflowing int. The overflow of a signed integer is undefined behavior in C and C++.
EDIT:
note that the expression 255 << 24 in your second declaration also invokes undefined behavior if your int type is 32-bit. 255 x (2^24) is 4278190080 which cannot be represented in a 32-bit int (the maximum value is usually 2147483647 on a 32-bit int in two's complement representation).
C and C++ both say for E1 << E2 that if E1 is of a signed type and positive and that E1 x (2^E2) cannot be represented in the type of E1, the program invokes undefined behavior. Here ^ is the mathematical power operator.
Your literals are int. This means that all the operations are actually performed on int, and promptly overflow. This overflowed value, when converted to an unsigned 64bit int, is the value you observe.
It is perhaps worth explaining what happened to produce the number 18446744073692774400. Technically speaking, the expressions you wrote trigger "undefined behavior" and so the compiler could have produced anything as the result; however, assuming int is a 32-bit type, which it almost always is nowadays, you'll get the same "wrong" answer if you write
uint64_t x = (int) (255u*256u*256u*256u);
and that expression does not trigger undefined behavior. (The conversion from unsigned int to int involves implementation-defined behavior, but as nobody has produced a ones-complement or sign-and-magnitude CPU in many years, all implementations you are likely to encounter define it exactly the same way.) I have written the cast in C style because everything I'm saying here applies equally to C and C++.
First off, let's look at the multiplication. I'm writing the right hand side in hex because it's easier to see what's going on that way.
255u * 256u = 0x0000FF00u
255u * 256u * 256u = 0x00FF0000u
255u * 256u * 256u * 256u = 0xFF000000u (= 4278190080)
That last result, 0xFF000000u, has the highest bit of a 32-bit number set. Casting that value to a signed 32-bit type therefore causes it to become negative as-if 232 had been subtracted from it (that's the implementation-defined operation I mentioned above).
(int) (255u*256u*256u*256u) = 0xFF000000 = -16777216
I write the hexadecimal number there, sans u suffix, to emphasize that the bit pattern of the value does not change when you convert it to a signed type; it is only reinterpreted.
Now, when you assign -16777216 to a uint64_t variable, it is back-converted to unsigned as-if by adding 264. (Unlike the unsigned-to-signed conversion, this semantic is prescribed by the standard.) This does change the bit pattern, setting all of the high 32 bits of the number to 1 instead of 0 as you had expected:
(uint64_t) (int) (255u*256u*256u*256u) = 0xFFFFFFFFFF000000u
And if you write 0xFFFFFFFFFF000000 in decimal, you get 18446744073692774400.
As a closing piece of advice, whenever you get an "impossible" integer from C or C++, try printing it out in hexadecimal; it's much easier to see oddities of twos-complement fixed-width arithmetic that way.
The answer is simple -- overflowed.
Here Overflow occurred on int and when you are assigning it to unsigned int64 its converted in to 18446744073692774400 instead of 4278190080
What will the unsigned int contain when I overflow it? To be specific, I want to do a multiplication with two unsigned ints: what will be in the unsigned int after the multiplication is finished?
unsigned int someint = 253473829*13482018273;
unsigned numbers can't overflow, but instead wrap around using the properties of modulo.
For instance, when unsigned int is 32 bits, the result would be: (a * b) mod 2^32.
As CharlesBailey pointed out, 253473829*13482018273 may use signed multiplication before being converted, and so you should be explicit about unsigned before the multiplication:
unsigned int someint = 253473829U * 13482018273U;
Unsigned integer overflow, unlike its signed counterpart, exhibits well-defined behaviour.
Values basically "wrap" around. It's safe and commonly used for counting down, or hashing/mod functions.
It probably depends a bit on your compiler. I had errors like this years ago, and sometimes you would get runtime error, other times it would basically "wrap" back to a really small number that would result from chopping off the highest level bits and leaving the remainder, i.e if it's a 32 bit unsigned int, and the result of your multiplication would be a 34 bit number, it would chop off the high order 2 bits and give you the remainder. You would probably have to try it on your compiler to see exactly what you get, which may not be the same thing you would get with a different compiler, especially if the overflow happens in the middle of an expression where the end result is within the range of an unsigned int.
I've seen this pattern used a lot in C & C++.
unsigned int flags = -1; // all bits are true
Is this a good portable way to accomplish this? Or is using 0xffffffff or ~0 better?
I recommend you to do it exactly as you have shown, since it is the most straight forward one. Initialize to -1 which will work always, independent of the actual sign representation, while ~ will sometimes have surprising behavior because you will have to have the right operand type. Only then you will get the most high value of an unsigned type.
For an example of a possible surprise, consider this one:
unsigned long a = ~0u;
It won't necessarily store a pattern with all bits 1 into a. But it will first create a pattern with all bits 1 in an unsigned int, and then assign it to a. What happens when unsigned long has more bits is that not all of those are 1.
And consider this one, which will fail on a non-two's complement representation:
unsigned int a = ~0; // Should have done ~0u !
The reason for that is that ~0 has to invert all bits. Inverting that will yield -1 on a two's complement machine (which is the value we need!), but will not yield -1 on another representation. On a one's complement machine, it yields zero. Thus, on a one's complement machine, the above will initialize a to zero.
The thing you should understand is that it's all about values - not bits. The variable is initialized with a value. If in the initializer you modify the bits of the variable used for initialization, the value will be generated according to those bits. The value you need, to initialize a to the highest possible value, is -1 or UINT_MAX. The second will depend on the type of a - you will need to use ULONG_MAX for an unsigned long. However, the first will not depend on its type, and it's a nice way of getting the highest value.
We are not talking about whether -1 has all bits one (it doesn't always have). And we're not talking about whether ~0 has all bits one (it has, of course).
But what we are talking about is what the result of the initialized flags variable is. And for it, only -1 will work with every type and machine.
unsigned int flags = -1; is portable.
unsigned int flags = ~0; isn't portable because it
relies on a two's-complement representation.
unsigned int flags = 0xffffffff; isn't portable because
it assumes 32-bit ints.
If you want to set all bits in a way guaranteed by the C standard, use the first one.
Frankly I think all fff's is more readable. As to the comment that its an antipattern, if you really care that all the bits are set/cleared, I would argue that you are probably in a situation where you care about the size of the variable anyway, which would call for something like boost::uint16_t, etc.
A way which avoids the problems mentioned is to simply do:
unsigned int flags = 0;
flags = ~flags;
Portable and to the point.
I am not sure using an unsigned int for flags is a good idea in the first place in C++. What about bitset and the like?
std::numeric_limit<unsigned int>::max() is better because 0xffffffff assumes that unsigned int is a 32-bit integer.
unsigned int flags = -1; // all bits are true
"Is this a good[,] portable way to accomplish this?"
Portable? Yes.
Good? Debatable, as evidenced by all the confusion shown on this thread. Being clear enough that your fellow programmers can understand the code without confusion should be one of the dimensions we measure for good code.
Also, this method is prone to compiler warnings. To elide the warning without crippling your compiler, you'd need an explicit cast. For example,
unsigned int flags = static_cast<unsigned int>(-1);
The explicit cast requires that you pay attention to the target type. If you're paying attention to the target type, then you'll naturally avoid the pitfalls of the other approaches.
My advice would be to pay attention to the target type and make sure there are no implicit conversions. For example:
unsigned int flags1 = UINT_MAX;
unsigned int flags2 = ~static_cast<unsigned int>(0);
unsigned long flags3 = ULONG_MAX;
unsigned long flags4 = ~static_cast<unsigned long>(0);
All of which are correct and more obvious to your fellow programmers.
And with C++11: We can use auto to make any of these even simpler:
auto flags1 = UINT_MAX;
auto flags2 = ~static_cast<unsigned int>(0);
auto flags3 = ULONG_MAX;
auto flags4 = ~static_cast<unsigned long>(0);
I consider correct and obvious better than simply correct.
Converting -1 into any unsigned type is guaranteed by the standard to result in all-ones. Use of ~0U is generally bad since 0 has type unsigned int and will not fill all the bits of a larger unsigned type, unless you explicitly write something like ~0ULL. On sane systems, ~0 should be identical to -1, but since the standard allows ones-complement and sign/magnitude representations, strictly speaking it's not portable.
Of course it's always okay to write out 0xffffffff if you know you need exactly 32 bits, but -1 has the advantage that it will work in any context even when you do not know the size of the type, such as macros that work on multiple types, or if the size of the type varies by implementation. If you do know the type, another safe way to get all-ones is the limit macros UINT_MAX, ULONG_MAX, ULLONG_MAX, etc.
Personally I always use -1. It always works and you don't have to think about it.
As long as you have #include <limits.h> as one of your includes, you should just use
unsigned int flags = UINT_MAX;
If you want a long's worth of bits, you could use
unsigned long flags = ULONG_MAX;
These values are guaranteed to have all the value bits of the result set to 1, regardless of how signed integers are implemented.
Yes. As mentioned in other answers, -1 is the most portable; however, it is not very semantic and triggers compiler warnings.
To solve these issues, try this simple helper:
static const struct All1s
{
template<typename UnsignedType>
inline operator UnsignedType(void) const
{
static_assert(std::is_unsigned<UnsignedType>::value, "This is designed only for unsigned types");
return static_cast<UnsignedType>(-1);
}
} ALL_BITS_TRUE;
Usage:
unsigned a = ALL_BITS_TRUE;
uint8_t b = ALL_BITS_TRUE;
uint16_t c = ALL_BITS_TRUE;
uint32_t d = ALL_BITS_TRUE;
uint64_t e = ALL_BITS_TRUE;
On Intel's IA-32 processors it is OK to write 0xFFFFFFFF to a 64-bit register and get the expected results. This is because IA32e (the 64-bit extension to IA32) only supports 32-bit immediates. In 64-bit instructions 32-bit immediates are sign-extended to 64-bits.
The following is illegal:
mov rax, 0ffffffffffffffffh
The following puts 64 1s in RAX:
mov rax, 0ffffffffh
Just for completeness, the following puts 32 1s in the lower part of RAX (aka EAX):
mov eax, 0ffffffffh
And in fact I've had programs fail when I wanted to write 0xffffffff to a 64-bit variable and I got a 0xffffffffffffffff instead. In C this would be:
uint64_t x;
x = UINT64_C(0xffffffff)
printf("x is %"PRIx64"\n", x);
the result is:
x is 0xffffffffffffffff
I thought to post this as a comment to all the answers that said that 0xFFFFFFFF assumes 32 bits, but so many people answered it I figured I'd add it as a separate answer.
See litb's answer for a very clear explanation of the issues.
My disagreement is that, very strictly speaking, there are no guarantees for either case. I don't know of any architecture that does not represent an unsigned value of 'one less than two to the power of the number of bits' as all bits set, but here is what the Standard actually says (3.9.1/7 plus note 44):
The representations of integral types shall define values by use of a pure binary numeration system. [Note 44:]A positional representation for integers that uses the binary digits 0 and 1, in which the values represented by successive bits are additive, begin with 1, and are multiplied by successive integral power of 2, except perhaps for the bit with the highest position.
That leaves the possibility for one of the bits to be anything at all.
I would not do the -1 thing. It's rather non-intuitive (to me at least). Assigning signed data to an unsigned variable just seems to be a violation of the natural order of things.
In your situation, I always use 0xFFFF. (Use the right number of Fs for the variable size of course.)
[BTW, I very rarely see the -1 trick done in real-world code.]
Additionally, if you really care about the individual bits in a vairable, it would be good idea to start using the fixed-width uint8_t, uint16_t, uint32_t types.
Although the 0xFFFF (or 0xFFFFFFFF, etc.) may be easier to read, it can break portability in code which would otherwise be portable. Consider, for example, a library routine to count how many items in a data structure have certain bits set (the exact bits being specified by the caller). The routine may be totally agnostic as to what the bits represent, but still need to have an "all bits set" constant. In such a case, -1 will be vastly better than a hex constant since it will work with any bit size.
The other possibility, if a typedef value is used for the bitmask, would be to use ~(bitMaskType)0; if bitmask happens to only be a 16-bit type, that expression will only have 16 bits set (even if 'int' would otherwise be 32 bits) but since 16 bits will be all that are required, things should be fine provided that one actually uses the appropriate type in the typecast.
Incidentally, expressions of the form longvar &= ~[hex_constant] have a nasty gotcha if the hex constant is too large to fit in an int, but will fit in an unsigned int. If an int is 16 bits, then longvar &= ~0x4000; or longvar &= ~0x10000; will clear one bit of longvar, but longvar &= ~0x8000; will clear out bit 15 and all bits above that. Values which fit in int will have the complement operator applied to a type int, but the result will be sign extended to long, setting the upper bits. Values which are too big for unsigned int will have the complement operator applied to type long. Values which are between those sizes, however, will apply the complement operator to type unsigned int, which will then be converted to type long without sign extension.
As others have mentioned, -1 is the correct way to create an integer that will convert to an unsigned type with all bits set to 1. However, the most important thing in C++ is using correct types. Therefore, the correct answer to your problem (which includes the answer to the question you asked) is this:
std::bitset<32> const flags(-1);
This will always contain the exact amount of bits you need. It constructs a std::bitset with all bits set to 1 for the same reasons mentioned in other answers.
It is certainly safe, as -1 will always have all available bits set, but I like ~0 better. -1 just doesn't make much sense for an unsigned int. 0xFF... is not good because it depends on the width of the type.
Practically: Yes
Theoretically: No.
-1 = 0xFFFFFFFF (or whatever size an int is on your platform) is only true with two's complement arithmetic. In practice, it will work, but there are legacy machines out there (IBM mainframes, etc.) where you've got an actual sign bit rather than a two's complement representation. Your proposed ~0 solution should work everywhere.
I say:
int x;
memset(&x, 0xFF, sizeof(int));
This will always give you the desired result.
Leveraging on the fact that assigning all bits to one for an unsigned type is equivalent to taking the maximum possible value for the given type,
and extending the scope of the question to all unsigned integer types:
Assigning -1 works for any unsigned integer type (unsigned int, uint8_t, uint16_t, etc.) for both C and C++.
As an alternative, for C++, you can either:
Include <limits> and use std::numeric_limits< your_type >::max()
Write a custom templated function (This would also allow some sanity check, i.e. if the destination type is really an unsigned type)
The purpose could be add more clarity, as assigning -1 would always need some explanatory comment.
A way to make the meaning bit more obvious and yet to avoid repeating the type:
const auto flags = static_cast<unsigned int>(-1);
An additional effort to emphasize, why Adrian McCarthy's approach here might be the best solution at latest since C++11 in terms of a compromise between standard conformity, type safety/explicit clearness and reduction of possible ambiguities:
unsigned int flagsPreCpp11 = ~static_cast<unsigned int>(0);
auto flags = ~static_cast<unsigned int>(0); // C++11 initialization
predeclaredflags = ~static_cast<decltype(predeclaredflags)>(0); // C++11 assignment to already declared variable
I'm going to explain my preference in detail below. As Johannes mentioned totally correctly, the fundamental origin of irritations here is the question about value vs. according bit representation semantics and about what types we're talking about exactly (the assigned value type vs. the possible compile time integral constant's type). Since there's no standard built-in mechanism to explicitly ensure the set of all bits to 1 for the concrete use case of the OP about unsigned integer values, it's obvious, that it's impossible to be fully independent of value semantics here (std::bitset is a common pure bit-layer refering container but the question was about unsigned integers in general). But we might be able to reduce ambiguity here.
Comparison of the 'better' standard compliant approaches:
The OP's way:
unsigned int flags = -1;
PROs:
is "established" and short
is quite intuitive in terms of modulo perspective of value to "natural" bit value representation
changing the target unsigned type to unsigned long for instance is possible without any further adaptions
CONs:
At least beginners might not be sure about the standard conformity ("Do I have to concern about padding bits?").
Violates type ranges (in the heavier way: signed vs. unsigned).
Solely from the code, you do not directly see any bit semantics association.
Refering to maximum values via defines:
unsigned int flags = UINT_MAX;
This circumvents the signed unsigned transition issue of the -1 approach but introduces several new problems: In doubt, one has to look twice here again, at the latest if you want to change the target type to unsigned long for instance. And here, one has to be sure about the fact, that the maximum value leads to all bits set to 1 by the standard (and padding bit concerns again). Bit semantics are also not obvious here directly from the code solely again.
Refering to maximum values more explicitly:
auto flags = std::numeric_limits<unsigned int>::max();
On my opinion, that's the better maximum value approach since it's macro/define free and one is explicit about the involved type. But all other concerns about the approach type itself remain.
Adrian's approach (and why I think, it's the preferred one before C++11 and since):
unsigned int flagsPreCpp11 = ~static_cast<unsigned int>(0);
auto flagsCpp11 = ~static_cast<unsigned int>(0);
PROs:
Only the simplest integral compile time constant is used: 0. So no worries about further bit representation or (implicit) casts are justified. From an intuitive point of view, I think we all can agree on the fact, that the bit representation for zero is commonly clearer than for maximum values, not only for unsigned integrals.
No type ambiguities are involved, no further look-ups required in doubt.
Explicit bit semantics are involved here via the complement ~. So it's quite clear from the code, what the intention was. And it's also very explicit, on which type and type range, the complement is applied.
CONs:
If assigned to a member for instance, there's a small chance that you mismatch types with pre C++11:
Declaration in class:
unsigned long m_flags;
Initialization in constructor:
m_flags(~static_cast<unsigned int>(0))
But since C++11, the usage of decltype + auto is powerful to prevent most of these possible issues. And some of these type mismatch scenarios (on interface boundaries for instance) are also possible for the -1 approach.
Robust final C++11 approach for pre-declared variables:
m_flags(~static_cast<decltype(m_flags)>(0)) // member initialization case
So with a full view on the weighting of the PROs and CONs of all approaches here, I recommend this one as the preferred approach, at latest since C++11.
Update: Thanks to a hint by Andrew Henle, I removed the statement about its readability since that might be a too subjective statement. But I still think, its readability is at least not that worse than most of the maximum value approaches or the ones with explicit maximum value provision via compile time integrals/literals since static_cast-usage is "established" too and built-in in contrast to defines/macros and even the std-lib.
yes the representation shown is very much correct as if we do it the other way round u will require an operator to reverse all the bits but in this case the logic is quite straightforward if we consider the size of the integers in the machine
for instance in most machines an integer is 2 bytes = 16 bits maximum value it can hold is 2^16-1=65535 2^16=65536
0%65536=0
-1%65536=65535 which corressponds to 1111.............1 and all the bits are set to 1 (if we consider residue classes mod 65536)
hence it is much straight forward.
I guess
no if u consider this notion it is perfectly dine for unsigned ints and it actually works out
just check the following program fragment
int main()
{
unsigned int a=2;
cout<<(unsigned int)pow(double(a),double(sizeof(a)*8));
unsigned int b=-1;
cout<<"\n"<<b;
getchar();
return 0;
}
answer for b = 4294967295 whcih is -1%2^32 on 4 byte integers
hence it is perfectly valid for unsigned integers
in case of any discrepancies plzz report