How does one convert from one integer type to another safely and with setting off alarm bells in compilers and static analysis tools?
Different compilers will warn for something like:
int i = get_int();
size_t s = i;
for loss of signedness or
size_t s = get_size();
int i = s;
for narrowing.
casting can remove the warnings but don't solve the safety issue.
Is there a proper way of doing this?
You can try boost::numeric_cast<>.
boost numeric_cast returns the result of converting a value of type Source to a value of type Target. If out-of-range is detected, an exception is thrown (see bad_numeric_cast, negative_overflow and positive_overflow ).
How does one convert from one integer type to another safely and with setting off alarm bells in compilers and static analysis tools?
Control when conversion is needed. As able, only convert when there is no value change. Sometimes, then one must step back and code at a higher level. IOWs, was a lossy conversion needed or can code be re-worked to avoid conversion loss?
It is not hard to add an if(). The test just needs to be carefully formed.
Example where size_t n and int len need a compare. Note that positive values of int may exceed that of size_t - or visa-versa or the same. Note in this case, the conversion of int to unsigned only happens with non-negative values - thus no value change.
int len = snprintf(buf, n, ...);
if (len < 0 || (unsigned)len >= n) {
// Handle_error();
}
unsigned to int example when it is known that the unsigned value at this point of code is less than or equal to INT_MAX.
unsigned n = ...
int i = n & INT_MAX;
Good analysis tools see that n & INT_MAX always converts into int without loss.
There is no built-in safe narrowing conversion between int types in c++ and STL. You could implement it yourself using as an example Microsoft GSL.
Theoretically, if you want perfect safety, you shouldn't be mixing types like this at all. (And you definitely shouldn't be using explicit casts to silence warnings, as you know.) If you've got values of type size_t, it's best to always carry them around in variables of type size_t.
There is one case where I do sometimes decide I can accept less than 100.000% perfect type safety, and that is when I assign sizeof's return value, which is a size_t, to an int. For any machine I am ever going to use, the only time this conversion might lose information is when sizeof returns a value greater than 2147483647. But I am content to assume that no single object in any of my programs will ever be that big. (In particular, I will unhesitatingly write things like printf("sizeof(int) = %d\n", (int)sizeof(int)), explicit cast and all. There is no possible way that the size of a type like int will not fit in an int!)
[Footnote: Yes, it's true, on a 16-bit machine the assumption is the rather less satisfying threshold that sizeof won't return a value greater than 32767. It's more likely that a single object might have a size like that, but probably not in a program that's running on a 16-bitter.]
I'd like to assign a value to a variable like this:
double var = 0xFFFFFFFF;
As a result var gets the value 65535.0 assigned. Since the compiler assumes a 64bit target system the number literal (i.e. all respective 32 bits) is interpreted significand precision bits. However, since 0xFFFF FFFF is just a notation for a bit pattern, without any hint about the representation, it could be quite differently interpreted w.r.t. becoming a floating point value. Thus, I was wondering if there is a way to manipulate this fixed interpretation of the value. In other words, give a hint about the desired representation. (Maybe someone could also point me to part in the standard where this implicit interpretation is defined).
So far, the default precision interpretation on my system seems to be
(int)0xFFFFFFFF x 100.
Only the fraction field is getting filled1.
So maybe (here: for 16 bit cross-compilation) I want it to be a different representation like:
(int)0xFFFFFF x 10(int)0xFF
(ignoring the sign bit for a moment).
Thus my question: How can I force a custom double interpretation of the hex literal notation?
1 Even when my hex literal would be 0xFFFF FFFF FFFF FFFF the value is only interpreted as the fraction part - so clearly, bits should be used for exponent and sign field. But it seems the literal gets just cut off.
C++ doesn't specify the in-memory representation for double, moreover, it doesn't even specify the in-memory representation of integer types (and it can really be different on systems with different endings). So if you want to interpret bytes 0xFF, 0xFF as a double, you can do something like:
uint8_t bytes[sizeof(double)] = {0xFF, 0xFF};
double var;
memcpy(&var, bytes, sizeof(double));
Note that using unions or reinterpret_casting pointers is, strictly speaking, undefined behavior, though in practice also works.
"I was wondering if there is a way to manipulate this interpretation."
Yes, you can use a reinterpret_cast<double&> via address, to force type (re-)interpretation from a certain bit pattern in memory.
"Thus my question: How can I force double interpretation of the hex notation?"
You can also use a union, to make it clearer:
union uint64_2_double {
uint64_t bits;
double dValue;
};
uint64_2_double x;
x.bits = 0x000000000000FFFF;
std::cout << x.dValue << std::endl;
There does not seem to be a direct way to initialize a double variable with an hexadecimal pattern, the c-style cast is equivalent to a C++ static_cast and the reinterpret_cast will complain it can't perform the conversion. I will give you two options, one simple solution but that will not initialize directly the variable, and a complicated one. You can do the following:
double var;
*reinterpret_cast<long *>(&var) = 0xFFFF;
Note: watch out that I would expect you to want to initialize all 64 bits of the double, your constant 0xFFFF seems small, it gives 3.23786e-319
A literal value that begins with 0x is an hexadecimal number of type unsigned int. You should use the suffix ul to make it a literal of unsigned long, which in most architectures will mean a 64 bit unsigned; or, #include <stdint.h> and do for example uint64_t(0xABCDFE13)
Now for the complicated stuff: In old C++ you can program a function that converts the integral constant to a double, but it won't be constexpr.
In constexpr functions you can't make reinterpret_cast. Then, your only choice to make a constexpr converter to double is to use an union in the middle, for example:
struct longOrDouble {
union {
unsigned long asLong;
double asDouble;
};
constexpr longOrDouble(unsigned long v) noexcept: asLong(v) {}
};
constexpr double toDouble(long v) { return longOrDouble(v).asDouble; }
This is a bit complicated, but this answers your question. Now, you can write:
double var = toDouble(0xFFFF)
And this will insert the given binary pattern into the double.
Using union to write to one member and read from another is undefined behavior in C++, there is an excellent question and excellent answers on this right here:
Accessing inactive union member and undefined behavior?
I'm working on a microcontroller with only 2KB of SRAM and desperately need to conserve some memory. Trying to work out how I can put 8 0/1 values into a single byte using a bitfield but can't quite work it out.
struct Bits
{
int8_t b0:1, b1:1, b2:1, b3:1, b4:1, b5:1, b6:1, b7:1;
};
int main(){
Bits b;
b.b0 = 0;
b.b1 = 1;
cout << (int)b.b0; // outputs 0, correct
cout << (int)b.b1; // outputs -1, should be outputting 1
}
What gives?
All of your bitfield members are signed 1-bit integers. On a two's complement system, that means they can represent only either 0 or -1. Use uint8_t if you want 0 and 1:
struct Bits
{
uint8_t b0:1, b1:1, b2:1, b3:1, b4:1, b5:1, b6:1, b7:1;
};
As a word of caution - the standard doesn't really enforce an implementation scheme for bitfields. There is no guarantee that Bits will be 1 byte, and hypothetically it is entirely possible for it to be larger.
In practice however the actual implementations usually follow the obvious logic and it will "almost always" be 1 byte in size, but again, there is no requirement that it is guaranteed. Just in case you want to be sure, you could do it manually.
BTW -1 is still true but it -1 != true
As noted, these variables consist of only a sign bit, so the only available values are 0 and -1.
A more appropriate type for these bitfields would be bool. C++14 ยง9.6/4:
If the value true or false is stored into a bit-field of type bool of any size (including a one bit bit-field), the original bool value and the value of the bit-field shall compare equal.
Yes, std::uint8_t will do the job, but you might as well use the best fit. You won't need things like the cast for std::cout << (int)b.b0;.
Signed and unsigned integers are the answer.
Keep in mind that signaling is just an interpretation of bits, -1 or 1 is just the 'print' serializer interpreting the "variable type", as it was "revealed" to cout functions (look operator overloading) by compiler, the bit is the same, its value also (on/off) - since you have only 1 bit.
Don't care about that, but is a good practice to be explicit, so prefer to declare your variable with unsigned, it instructs the compiler to mount a proper code when you set or get the value to a serializer like "print" (cout).
"COUT" OPERATOR OVERLOADING:
"cout" works through a series of functions which the parameter overloading instructs the compiler which function to call. So, there are two functions, one receives an unsigned and another signed, thus they can interpret the same data differently, and you can change it, instructing the compiler to call another one using cast. See cout << myclass
My program does the common task of writing binary data to a file, conforming to a certain non-text file format. Since the data I'm writing is not already in existing chunks but instead is put together byte by byte at runtime, I use std::ostream::put() instead of write(). I assume this is normal procedure.
The program works just fine. It uses both std::stringstream::put() and std::ofstream::put() with two-digit hex integers as the arguments. But I get compiler warning C4309: "truncation of constant value" (in VC++ 2010) whenever the argument to put() is greater than 0x7f. Obviously the compiler is expecting a signed char, and the constant is out of range. But I don't think any truncation is actually happening; the byte gets written just like it's supposed to.
Compiler warnings make me think I'm not doing things in the normal, accepted way. The situation I described has to be a common one. Is there are common way to avoid such a compiler warning? Or is this an example of a pointless compiler warning that should just be ignored?
I thought of two inelegant ways to avoid it. I could use syntax like mystream.put( char(0xa4) ) on every call. Or instead of using std::stringstream I could use std::basic_stringstream< unsigned char >, but I don't think that trick would work with std::ofstream, which is not a templated type. I feel like there should be a better solution here, especially since ofstream is meant for writing binary files.
Your thoughts?
--EDIT--
Ah, I was mistaken about std::ofstream not being a templated type. It is actually std::basic_ofstream<char>, but I tried that method that and realized it won't work anyway for lack of defined methods and polymorphic incompatibility with std::ostream.
Here's a code sample:
stringstream ss;
int a, b;
/* Do stuff */
ss.put( 0 );
ss.put( 0x90 | a ); // oddly, no warning here...
ss.put( b ); // ...or here
ss.put( 0xa4 ); // C4309
I found solution that I'm happy with. It's more elegant than explicitly casting every constant to unsigned char. This is what I had:
ss.put( 0xa4 ); // C4309
I thought that the "truncation" was happening in implicitly casting unsigned char to char, but Cong Xu pointed out that integer constants are assumed to be signed, and any one greater than 0x7f gets promoted from char to int. Then it has to actually be truncated (cut down to one byte) if passed to put(). By using the suffix "u", I can specify an unsigned integer constant, and if it's no greater than 0xff, it will be an unsigned char. This is what I have now, without compiler warnings:
ss.put( 0xa4u );
std::stringstream ss;
ss.put(0x7f);
ss.put(0x80); //C4309
As you've guessed, the problem is that ostream.put() expects a char, but 0x7F is the maximum value for char, and anything greater gets promoted to int. You should cast to unsigned char, which is as wide as char so it'll store anything char does and safely, but also make truncation warnings legitimate:
ss.put(static_cast<unsigned char>(0x80)); // OK
ss.put(static_cast<unsigned char>(0xFFFF)); //C4309
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