Why weren't the contents of stdint.h the standard when it was included in the standard (no int no short no float, but int32_t, int16_t, float32_t etc.)? What advantage did/does ambiguous type sizes provide?
In objective-C, why was it decided that CGFloat, NSInteger, NSUInteger have different sizes on different platforms?
When C was designed, there were computers with different word sizes. Not just multiples of 8, but other sizes like the 18-bit word size on the PDP-7. So sometimes an int was 16 bits, but maybe it was 18 bits, or 32 bits, or some other size entirely. On a Cray-1 an int was 64 bits. As a result, int meant "whatever is convenient for this computer, but at least 16 bits".
That was about forty years ago. Computers have changed, so it certainly looks odd now.
NSInteger is used to denote the computer's word size, since it makes no sense to ask for the 5 billionth element of an array on a 32-bit system, but it makes perfect sense on a 64-bit system.
I can't speak for why CGFloat is a double on 64-bit system. That baffles me.
C is meant to be portable from enbedded devices, over your phone, to descktops, mainfraimes and beyond. These don't have the same base types, e.g the later may have uint128_t where others don't. Writing code with fixed width types would severely restrict portability in some cases.
This is why with preference you should neither use uintX_t nor int, long etc but the semantic typedefs such as size_t and ptrdiff_t. These are really the ones that make your code portable.
Related
For fun, I'm writing a bignum library in Rust. My goal (as with most bignum libraries) is to make it as efficient as I can. I'd like it to be efficient even on unusual architectures.
It seems intuitive to me that a CPU will perform arithmetic faster on integers with the native number of bits for the architecture (i.e., u64 for 64-bit machines, u16 for 16-bit machines, etc.) As such, since I want to create a library that is efficient on all architectures, I need to take the target architecture's native integer size into account. The obvious way to do this would be to use the cfg attribute target_pointer_width. For instance, to define the smallest type which will always be able to hold more than the maximum native int size:
#[cfg(target_pointer_width = "16")]
type LargeInt = u32;
#[cfg(target_pointer_width = "32")]
type LargeInt = u64;
#[cfg(target_pointer_width = "64")]
type LargeInt = u128;
However, while looking into this, I came across this comment. It gives an example of an architecture where the native int size is different from the pointer width. Thus, my solution will not work for all architectures. Another potential solution would be to write a build script which codegens a small module which defines LargeInt based on the size of a usize (which we can acquire like so: std::mem::size_of::<usize>().) However, this has the same problem as above, since usize is based on the pointer width as well. A final obvious solution is to simply keep a map of native int sizes for each architecture. However, this solution is inelegant and doesn't scale well, so I'd like to avoid it.
So, my questions: is there a way to find the target's native int size, preferably before compilation, in order to reduce runtime overhead? Is this effort even worth it? That is, is there likely to be a significant difference between using the native int size as opposed to the pointer width?
It's generally hard (or impossible) to get compilers to emit optimal code for BigNum stuff, that's why https://gmplib.org/ has its low level primitive functions (mpn_... docs) hand-written in assembly for various target architectures with tuning for different micro-architecture, e.g. https://gmplib.org/repo/gmp/file/tip/mpn/x86_64/core2/mul_basecase.asm for the general case of multi-limb * multi-limb numbers. And https://gmplib.org/repo/gmp/file/tip/mpn/x86_64/coreisbr/aors_n.asm for mpn_add_n and mpn_sub_n (Add OR Sub = aors), tuned for SandyBridge-family which doesn't have partial-flag stalls so it can loop with dec/jnz.
Understanding what kind of asm is optimal may be helpful when writing code in a higher level language. Although in practice you can't even get close to that so it sometimes makes sense to use a different technique, like only using values up to 2^30 in 32-bit integers (like CPython does internally, getting the carry-out via a right shift, see the section about Python in this). In Rust you do have access to add_overflow to get the carry-out, but using it is still hard.
For practical use, writing Rust bindings for GMP is probably your best bet, unless that already exists.
Using the largest chunks possible is very good; on all current CPUs, add reg64, reg64 has the same throughput and latency as add reg32, reg32 or reg8. So you get twice as much work done per unit. And carry propagation through 64 bits of result in 1 cycle of latency.
(There are alternate ways to store BigInteger data that can make SIMD useful; #Mysticial explains in Can long integer routines benefit from SSE?. e.g. 30 value bits per 32-bit int, allowing you to defer normalization until after a few addition steps. But every use of such numbers has to be aware of these issues so it's not an easy drop-in replacement.)
In Rust, you probably want to just use u64 regardless of the target, unless you really care about small-number (single-limb) performance on 32-bit targets. Let the compiler build u64 operations for you out of add / adc (add with carry).
The only thing that might need to be ISA-specific is if u128 is not available on some targets. You want to use 64 * 64 => 128-bit full multiply as your building block for multiplication; if the compiler can do that for you with u128 then that's great, especially if it inlines efficiently.
See also discussion in comments under the question.
One stumbling block for getting compilers to emit efficient BigInt addition loops (even inside the body of one unrolled loop) is writing an add that takes a carry input and produces a carry output. Note that x += 0xff..ff + carry=1 needs to produce a carry out even though 0xff..ff + 1 wraps to zero. So in C or Rust, x += y + carry has to check for carry out in both the y+carry and the x+= parts.
It's really hard (probably impossible) to convince compiler back-ends like LLVM to emit a chain of adc instructions. An add/adc is doable when you don't need the carry-out from adc. Or probably if the compiler is doing it for you for u128.overflowing_add
Often compilers will turn the carry flag into a 0 / 1 in a register instead of using adc. You can hopefully avoid that for at least pairs of u64 in addition by combining the input u64 values to u128 for u128.overflowing_add. That will hopefully not cost any asm instructions because a u128 already has to be stored across two separate 64-bit registers, just like two separate u64 values.
So combining up to u128 could just be a local optimization for a function that adds arrays of u64 elements, to get the compiler to suck less.
In my library ibig what I do is:
Select architecture-specific size based on target_arch.
If I don't have a value for an architecture, select 16, 32 or 64 based on target_pointer_width.
If target_pointer_width is not one of these values, use 64.
The general standard appears to use NS_ENUM with NSInteger as the base type. Why is this the case? Assuming less than 256 cases (which covers almost any enumeration), is there any reason to use that instead of uint8_t, which could use less memory space? Either imports into Swift fine.
This is different than NS_OPTIONS, where a larger type makes sense, since you shouldn't be doing any bit math with enumerations, and you can use every number representable by the base type as a value.
The answer to the question in the title:
Is there any reason to use NSInteger instead of uint8_t with NS_ENUM?
is probably not.
When declaring an enum in C if no underlying type is specified the compiler is free to choose any suitable type from char and the signed and unsigned integer types which can at least represent all the values required. The current Xcode/Clang compiler picks a 4-byte integer. One could reasonably assume the compiler writers made an informed choice - some balance of performance and storage.
Smaller types, such as uint8_t, will usually be aligned on smaller boundaries in memory (or on disc) - but that is only of benefit if the adjacent field matches the alignment e.g. if a 2-byte size typed field follows a 1-byte sized typed field then unless otherwise specified (e.g. with a #pragma packed) there will probably be an intervening unused byte.
Whether any performance or storage differences are significant will be heavily dependent on the application. Follow the usual rule of thumb - don't optimise until an issue is found.
However if you find semantic benefit in limiting the size then certainly do so - there is no general reason you shouldn't. The choice is similar to picking signed vs. unsigned integers, some programmers avoid unsigned types for values that will be ≥ 0 unless absolutely required for the extra range, while others appreciate the semantic benefit.
Summary: There is no right answer, its largely a subjective issue.
HTH
First of all: The memory footprint is close to completely meaningless. You are talking about 1 Byte vs. 4/8 Bytes. (If the memory alignment does not force the usage of 4/8 bytes whatever you chosed.) How many NS_ENUM (C) objects do you want to have in your running app?
I guess that the reason is pretty easy: NSInteger is akin of "catch all" integer type in Cocoa. That makes assignments easier, especially you do not have to care about assigning a bigger integer type to a smaller one. Without casting this would lead to warnings.
Having more than one integer type in a desktop app with a 32/64 bit model is akin of an anachronism. Nor a Mac neither a MacBook neither an iPhone is an embedded micro controller …
You can use any integer data type including uint8_t with NS_ENUM as.
typedef NS_ENUM(uint8_t, eEnumAddEditViewMode) {
eWBEnumAddMode,
eWBEnumEditMode
};
In old c style standard NSInteger is default, because NSInteger is akin of "catch all" integer type in objective c. and developer can easily type boxing and unboxing with their own variable. This is just developer friendly best practise.
What is the difference between objective-c C primitive numbers? I know what they are and how to use them (somewhat), but I'm not sure what the capabilities and uses of each one is. Could anyone clear up which ones are best for some scenarios and not others?
int
float
double
long
short
What can I store with each one? I know that some can store more precise numbers and some can only store whole numbers. Say for example I wanted to store a latitude (possibly retrieved from a CLLocation object), which one should I use to avoid loosing any data?
I also noticed that there are unsigned variants of each one. What does that mean and how is it different from a primitive number that is not unsigned?
Apple has some interesting documentation on this, however it doesn't fully satisfy my question.
Well, first off types like int, float, double, long, and short are C primitives, not Objective-C. As you may be aware, Objective-C is sort of a superset of C. The Objective-C NSNumber is a wrapper class for all of these types.
So I'll answer your question with respect to these C primitives, and how Objective-C interprets them. Basically, each numeric type can be placed in one of two categories: Integer Types and Floating-Point Types.
Integer Types
short
int
long
long long
These can only store, well, integers (whole numbers), and are characterized by two traits: size and signedness.
Size means how much physical memory in the computer a type requires for storage, that is, how many bytes. Technically, the exact memory allocated for each type is implementation-dependendant, but there are a few guarantees: (1) char will always be 1 byte (2) sizeof(short) <= sizeof(int) <= sizeof(long) <= sizeof(long long).
Signedness means, simply whether or not the type can represent negative values. So a signed integer, or int, can represent a certain range of negative or positive numbers (traditionally –2,147,483,648 to 2,147,483,647), and an unsigned integer, or unsigned int can represent the same range of numbers, but all positive (0 to 4,294,967,295).
Floating-Point Types
float
double
long double
These are used to store decimal values (aka fractions) and are also categorized by size. Again the only real guarantee you have is that sizeof(float) <= sizeof(double) <= sizeof (long double). Floating-point types are stored using a rather peculiar memory model that can be difficult to understand, and that I won't go into, but there is an excellent guide here.
There's a fantastic blog post about C primitives in an Objective-C context over at RyPress. Lots of intro CPS textbooks also have good resources.
Firstly I would like to specify the difference between au unsigned int and an int. Say that you have a very high number, and that you write a loop iterating with an unsigned int:
for(unsigned int i=0; i< N; i++)
{ ... }
If N is a number defined with #define, it may be higher that the maximum value storable with an int instead of an unsigned int. If you overflow i will start again from zero and you'll go in an infinite loop, that's why I prefer to use an int for loops.
The same happens if for mistake you iterate with an int, comparing it to a long. If N is a long you should iterate with a long, but if N is an int you can still safely iterate with a long.
Another pitfail that may occur is when using the shift operator with an integer constant, then assigning it to an int or long. Maybe you also log sizeof(long) and you notice that it returns 8 and you don't care about portability, so you think that you wouldn't lose precision here:
long i= 1 << 34;
Bit instead 1 isn't a long, so it will overflow and when you cast it to a long you have already lost precision. Instead you should type:
long i= 1l << 34;
Newer compilers will warn you about this.
Taken from this question: Converting Long 64-bit Decimal to Binary.
About float and double there is a thing to considerate: they use a mantissa and an exponent to represent the number. It's something like:
value= 2^exponent * mantissa
So the more the exponent is high, the more the floating point number doesn't have an exact representation. It may also happen that a number is too high, so that it will have a so inaccurate representation, that surprisingly if you print it you get a different number:
float f= 9876543219124567;
NSLog("%.0f",f); // On my machine it prints 9876543585124352
If I use a double it prints 9876543219124568, and if I use a long double with the .0Lf format it prints the correct value. Always be careful when using floating points numbers, unexpected things may happen.
For example it may also happen that two floating point numbers have almost the same value, that you expect they have the same value but there is a subtle difference, so that the equality comparison fails. But this has been treated hundreds of times on Stack Overflow, so I will just post this link: What is the most effective way for float and double comparison?.
I am beginning with CGAL. What I would like to do is to create point that coordinates are number ~ 2^51.
typedef CGAL::Exact_predicates_exact_constructions_kernel K;
typedef K::Point_2 P;
uint_64 x,y;
//init them somehow
P sp0(x,y);
Then I got a long template error. Someone could help?
I guess you realize that changing the kernel may have other effects on your program.
Concerning your original question, if your integer values are smaller than 2^51, then they fit exactly in doubles (with 53 bit mantissa), so one simple option is to cast them to double, as in :
P sp0((double)x,(double)y);
Otherwise, the Exact_predicates_exact_construction_kernel should have its main number type be able to read your uint64 values (maybe cast them to unsigned long long if it's OK on your platform) :
typedef K::FT FT;
P sp0((FT)x,(FT)y);
CGAL Number types are only documented to interoperate with int and double. I recently added some code so we can construct more numbers from long (required for Eigen), and your code will work in the next version of CGAL (except that you typo-ed uint64_t) on platforms where uint64_t is unsigned int or unsigned long (not windows). For long long support, since many of our number types are based on other libraries (GMP) that do not support long long themselves yet, it may have to wait a bit.
Ok. I think that I found solution. The problem was that I used exact Kernel that supports only double, switching to inexact kernel solved the problem. It was also possible to use just double. (one of the requirements was to use data type that supports intergers up to 2^48).
There's a common way to store multiple values in one variable, by using a bitmask. For example, if a user has read, write and execute privileges on an item, that can be converted to a single number by saying read = 4 (2^2), write = 2 (2^1), execute = 1 (2^0) and then add them together to get 7.
I use this technique in several web applications, where I'd usually store the variable into a field and give it a type of MEDIUMINT or whatever, depending on the number of different values.
What I'm interested in, is whether or not there is a practical limit to the number of values you can store like this? For example, if the number was over 64, you couldn't use (64 bit) integers any more. If this was the case, what would you use? How would it affect your program logic (ie: could you still use bitwise comparisons)?
I know that once you start getting really large sets of values, a different method would be the optimal solution, but I'm interested in the boundaries of this method.
Off the top of my head, I'd write a set_bit and get_bit function that could take an array of bytes and a bit offset in the array, and use some bit-twiddling to set/get the appropriate bit in the array. Something like this (in C, but hopefully you get the idea):
// sets the n-th bit in |bytes|. num_bytes is the number of bytes in the array
// result is 0 on success, non-zero on failure (offset out-of-bounds)
int set_bit(char* bytes, unsigned long num_bytes, unsigned long offset)
{
// make sure offset is valid
if(offset < 0 || offset > (num_bytes<<3)-1) { return -1; }
//set the right bit
bytes[offset >> 3] |= (1 << (offset & 0x7));
return 0; //success
}
//gets the n-th bit in |bytes|. num_bytes is the number of bytes in the array
// returns (-1) on error, 0 if bit is "off", positive number if "on"
int get_bit(char* bytes, unsigned long num_bytes, unsigned long offset)
{
// make sure offset is valid
if(offset < 0 || offset > (num_bytes<<3)-1) { return -1; }
//get the right bit
return (bytes[offset >> 3] & (1 << (offset & 0x7));
}
I've used bit masks in filesystem code where the bit mask is many times bigger than a machine word. think of it like an "array of booleans";
(journalling masks in flash memory if you want to know)
many compilers know how to do this for you. Adda bit of OO code to have types that operate senibly and then your code starts looking like it's intent, not some bit-banging.
My 2 cents.
With a 64-bit integer, you can store values up to 2^64-1, 64 is only 2^6. So yes, there is a limit, but if you need more than 64-its worth of flags, I'd be very interested to know what they were all doing :)
How many states so you need to potentially think about? If you have 64 potential states, the number of combinations they can exist in is the full size of a 64-bit integer.
If you need to worry about 128 flags, then a pair of bit vectors would suffice (2^64 * 2).
Addition: in Programming Pearls, there is an extended discussion of using a bit array of length 10^7, implemented in integers (for holding used 800 numbers) - it's very fast, and very appropriate for the task described in that chapter.
Some languages ( I believe perl does, not sure ) permit bitwise arithmetic on strings. Giving you a much greater effective range. ( (strlen * 8bit chars ) combinations )
However, I wouldn't use a single value for superimposition of more than one /type/ of data. The basic r/w/x triplet of 3-bit ints would probably be the upper "practical" limit, not for space efficiency reasons, but for practical development reasons.
( Php uses this system to control its error-messages, and I have already found that its a bit over-the-top when you have to define values where php's constants are not resident and you have to generate the integer by hand, and to be honest, if chmod didn't support the 'ugo+rwx' style syntax I'd never want to use it because i can never remember the magic numbers )
The instant you have to crack open a constants table to debug code you know you've gone too far.
Old thread, but it's worth mentioning that there are cases requiring bloated bit masks, e.g., molecular fingerprints, which are often generated as 1024-bit arrays which we have packed in 32 bigint fields (SQL Server not supporting UInt32). Bit wise operations work fine - until your table starts to grow and you realize the sluggishness of separate function calls. The binary data type would work, were it not for T-SQL's ban on bitwise operators having two binary operands.
For example .NET uses array of integers as an internal storage for their BitArray class.
Practically there's no other way around.
That being said, in SQL you will need more than one column (or use the BLOBS) to store all the states.
You tagged this question SQL, so I think you need to consult with the documentation for your database to find the size of an integer. Then subtract one bit for the sign, just to be safe.
Edit: Your comment says you're using MySQL. The documentation for MySQL 5.0 Numeric Types states that the maximum size of a NUMERIC is 64 or 65 digits. That's 212 bits for 64 digits.
Remember that your language of choice has to be able to work with those digits, so you may be limited to a 64-bit integer anyway.