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?.
Related
In Kotlin 123.456 is a valid Double value, however, 123.456F.toDouble() results in 123.45600128173828 - presumably just the way precision is handled between the two.
I want to be able to convert freely between the two, specifically for cases like this:
123.456F -> 123.456 // Float to Double
123.456 -> 123.456F // Double to Float
How can I convert a float to a double in cases like this, and maintain precision?
It's a big ugly, but you could convert your Float to a String and back out to a Double:
val myDouble: Double = 123.456f.toString().toDouble()
// 123.456d
You could always encapsulate this in an extension function:
fun Float.toExactDouble(): Double =
this.toString().toDouble()
val myDouble = 123.456f.toExactDouble()
In Kotlin 123.456 is a valid Double value
Actually, that's not quite true. There's a Double value very close to 123.456, but it's not exactly 123.456. What you're seeing is the consequences of that.
So you can't maintain precision, because you don't have that precision to start with!
Short answer:
If you need exact values, don't use floating-point!
(In particular: Never store money values in floating-point! See for example this question.)
The best alternative is usually BigDecimal which can store and calculate decimal fractions to an arbitrary precision. They're less efficient, but Kotlin's operator overloading makes them painless to use (unlike Java!).
Or if you're not going to be doing any calculations, you could store them as Strings.
Or if you'll only need a certain number of decimal places, you could scale them all up to Ints (or Longs).
Technical explanation:
Floats and Doubles use binary floating-point; they store an integer, and an integer power of 2 to multiple or divide it by. (For example, 3/4 would be stored as 3*2⁻².) This means they can store a wide range of binary fractions exactly.
However, just as you can't store 1/3 as a decimal fraction (it's 0.3333333333…, but any finite number of digits will only be an approximation), so you can't store 1/10 as a binary fraction (it's 0.000110011001100…). This means that a binary floating-point number can't store most decimal numbers exactly.
Instead, they store the nearest possible value to the number you want. And the routines which convert them to a String will try to undo that difference, by rounding appropriately. But that doesn't always give the result you expect.
Floating-point numbers are great when you need a huge range of values (e.g. in scientific and technical use), but don't care about storing them exactly.
In the math-headers we see
extern float fabsf(float);
extern double fabs(double);
extern long double fabsl(long double);
...
extern float fmodf(float, float);
extern double fmod(double, double);
extern long double fmodl(long double, long double);
Why is there one function for each type?
Isn't this a lot of duplicate code? If I where to say write a lerp-function or a clamp-function would I need to write one for each type?
Seems like we will have duplicate code where there's only one thing changing – the type.
extern float clampf(float value, float min, float max)
{
if(value > max)
return max;
if(value < min)
return min;
return value;
}
extern double clamp(double value, double min, double max)
{
if(value > max)
return max;
if(value < min)
return min;
return value;
}
Question 1: What is the historical reason for this structure?
Question 2: Should I follow the same pattern? Or should I only implement the double-kind since it is the one which is most common?
Question 3: Or should I just use macro's to overcome the type-issue altogether?
Historically (circa C89 and before), the math library contained only the double-precision versions of these functions, which is why those versions have no suffix. If you needed to compute the sine of a float, you either wrote your own implementation, or (more likely!) you simply wrote:
float x;
float y = sin(x);
However, this introduces some overhead on modern architectures. Specifically, on the most common architectures today, it is necessary for the compiler to emit code that looks something like this:
convert x to double
call sin
convert result to float
These conversions are pretty fast (about the same as an addition, usually), but they still have some cost. On top of the cost of conversion, sin needs to deliver a result that has ~53 bits of precision, more than half of which are completely wasted if the result is just going to be converted back to single precision. Between these two factors, it is possible for a dedicated single-precision sin routine to be about twice as fast; that’s a significant win for some very frequently-used library functions!
If we look at functions like fabs (and assume that the compiler does not simply inline and lower them), the situation is much, much worse. fabs, on a typical modern architecture, is a simple bitwise-and operation. So the two conversions bracketing the call (if all you have is double) are significantly more expensive than the operation itself, and can easily cause a 5x slowdown. That’s why multiple versions of these functions were added to support each FP type.
If you don’t want to keep track of all of them, you can #include <tgmath.h>, which will infer the correct function to use based on the type of the argument (meaning
sin((float)x)
will generate a call to sinf(x), whereas
sin((long double)x)
will call sinl(x)).
In your own code, you usually know a priori what the type of your arguments is, and only need to support one or maybe two types. clamp and lerp in particular are graphics operations, and almost universally are used only in single-precision variants.
Incidentally, the fact that you’re using clamp and lerp is a pretty good indication that you might want to look at writing your code in OpenCL instead of C/Obj-C; the OpenCL math library implements these operations (and many other similar operations) for you, and provides implementations that work with a wide range of basic types, including vectors.
float and double are different data types, same as int and long int. You can use the functions which operate on double on float values and implicit conversion will happen to make it work as expected in most circumstances, but if you use functions which operate on float on double values, you will almost inevitably lose precision.
There are other longer explanations available, e.g. What's the difference between a single precision and double precision floating point operation? .
I understand what the unsigned right shift operator ">>>" in Java does, but why do we need it, and why do we not need a corresponding unsigned left shift operator?
The >>> operator lets you treat int and long as 32- and 64-bit unsigned integral types, which are missing from the Java language.
This is useful when you shift something that does not represent a numeric value. For example, you could represent a black and white bit map image using 32-bit ints, where each int encodes 32 pixels on the screen. If you need to scroll the image to the right, you would prefer the bits on the left of an int to become zeros, so that you could easily put the bits from the adjacent ints:
int shiftBy = 3;
int[] imageRow = ...
int shiftCarry = 0;
// The last shiftBy bits are set to 1, the remaining ones are zero
int mask = (1 << shiftBy)-1;
for (int i = 0 ; i != imageRow.length ; i++) {
// Cut out the shiftBits bits on the right
int nextCarry = imageRow & mask;
// Do the shift, and move in the carry into the freed upper bits
imageRow[i] = (imageRow[i] >>> shiftBy) | (carry << (32-shiftBy));
// Prepare the carry for the next iteration of the loop
carry = nextCarry;
}
The code above does not pay attention to the content of the upper three bits, because >>> operator makes them
There is no corresponding << operator because left-shift operations on signed and unsigned data types are identical.
>>> is also the safe and efficient way of finding the rounded mean of two (large) integers:
int mid = (low + high) >>> 1;
If integers high and low are close to the the largest machine integer, the above will be correct but
int mid = (low + high) / 2;
can get a wrong result because of overflow.
Here's an example use, fixing a bug in a naive binary search.
Basically this has to do with sign (numberic shifts) or unsigned shifts (normally pixel related stuff).
Since the left shift, doesn't deal with the sign bit anyhow, it's the same thing (<<< and <<)...
Either way I have yet to meet anyone that needed to use the >>>, but I'm sure they are out there doing amazing things.
As you have just seen, the >> operator automatically fills the
high-order bit with its previous contents each time a shift occurs.
This preserves the sign of the value. However, sometimes this is
undesirable. For example, if you are shifting something that does not
represent a numeric value, you may not want sign extension to take
place. This situation is common when you are working with pixel-based
values and graphics. In these cases you will generally want to shift a
zero into the high-order bit no matter what its initial value was.
This is known as an unsigned shift. To accomplish this, you will use
java’s unsigned, shift-right operator,>>>, which always shifts zeros
into the high-order bit.
Further reading:
http://henkelmann.eu/2011/02/01/java_the_unsigned_right_shift_operator
http://www.java-samples.com/showtutorial.php?tutorialid=60
The signed right-shift operator is useful if one has an int that represents a number and one wishes to divide it by a power of two, rounding toward negative infinity. This can be nice when doing things like scaling coordinates for display; not only is it faster than division, but coordinates which differ by the scale factor before scaling will differ by one pixel afterward. If instead of using shifting one uses division, that won't work. When scaling by a factor of two, for example, -1 and +1 differ by two, and should thus differ by one afterward, but -1/2=0 and 1/2=0. If instead one uses signed right-shift, things work out nicely: -1>>1=-1 and 1>>1=0, properly yielding values one pixel apart.
The unsigned operator is useful either in cases where either the input is expected to have exactly one bit set and one will want the result to do so as well, or in cases where one will be using a loop to output all the bits in a word and wants it to terminate cleanly. For example:
void processBitsLsbFirst(int n, BitProcessor whatever)
{
while(n != 0)
{
whatever.processBit(n & 1);
n >>>= 1;
}
}
If the code were to use a signed right-shift operation and were passed a negative value, it would output 1's indefinitely. With the unsigned-right-shift operator, however, the most significant bit ends up being interpreted just like any other.
The unsigned right-shift operator may also be useful when a computation would, arithmetically, yield a positive number between 0 and 4,294,967,295 and one wishes to divide that number by a power of two. For example, when computing the sum of two int values which are known to be positive, one may use (n1+n2)>>>1 without having to promote the operands to long. Also, if one wishes to divide a positive int value by something like pi without using floating-point math, one may compute ((value*5468522205L) >>> 34) [(1L<<34)/pi is 5468522204.61, which rounded up yields 5468522205]. For dividends over 1686629712, the computation of value*5468522205L would yield a "negative" value, but since the arithmetically-correct value is known to be positive, using the unsigned right-shift would allow the correct positive number to be used.
A normal right shift >> of a negative number will keep it negative. I.e. the sign bit will be retained.
An unsigned right shift >>> will shift the sign bit too, replacing it with a zero bit.
There is no need to have the equivalent left shift because there is only one sign bit and it is the leftmost bit so it only interferes when shifting right.
Essentially, the difference is that one preserves the sign bit, the other shifts in zeros to replace the sign bit.
For positive numbers they act identically.
For an example of using both >> and >>> see BigInteger shiftRight.
In the Java domain most typical applications the way to avoid overflows is to use casting or Big Integer, such as int to long in the previous examples.
int hiint = 2147483647;
System.out.println("mean hiint+hiint/2 = " + ( (((long)hiint+(long)hiint)))/2);
System.out.println("mean hiint*2/2 = " + ( (((long)hiint*(long)2)))/2);
BigInteger bhiint = BigInteger.valueOf(2147483647);
System.out.println("mean bhiint+bhiint/2 = " + (bhiint.add(bhiint).divide(BigInteger.valueOf(2))));
Im looking for a list of all the scalar data types in Objective C, complete with their ranges (max/min values etc).
Sorry for the simple question, Im just really struggling to find anything like this.
int An integer value between +/– 2,147,483,647.
unsigned int An integer value between 0 and 4,294,967,296.
float A floating point value between +/– 16,777,216.
double A floating point value between +/– 2,147,483,647.
long An integer value varying in size from 32 bit to 64 bit depending on architecture.
long long A 64-bit integer.
char A single character. Technically it’s represented as an int.
BOOL A boolean value, can be either YES or NO.
NSInteger When compiling for 32-bit architecture, same as an int, when compiling for 64-bit architecture,+/– 4,294,967,296.
NSUInteger When compiling for 32-bit architecture, same as an unsigned int, when compiling for 64-bit architecture, value between 0 and 2^64
Source.
char : A character 1 byte
int :An integer — a whole number 4 bytes
float : Single precision floating point number 4 bytes
Double : Double precision floating point number 8 bytes
short : A short integer 2 bytes
long : A double short 4 bytes
long long : A double long 8 bytes
BOOL : Boolean (signed char) 1 byte
For more on sizes check this post
Integer types are signed 2's complement or unsigned and the standard C variations are provided (char, short, int, long, long long and unsigned variants of these, see C types on Wikipedia), sizes may vary dependent on 32-bit & 64-bit environments - see 64-bit computing.
BOOL is an Objective-C special and is defined as signed char, while it can take any value a signed char can the constants NO and YES are defined for use. The C9X type _Bool(aka bool) is also provided.
float & double are IEEE 32-bit & 64-bit floating point - see Wikipedia for ranges.
Standard macro contants are provided for the minimum and maximum of all the types, e.g. INT_MAX for int - again see C types on Wikipedia for these.
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.