The C standard also talks about some qualifiers for variable types. For example const means that a variable will never be modified from its original value and volatile suggests to the compiler that this value might change outside program execution flow so the compiler must be careful not to re-order access to it in any way.

signed and unsigned are probably the two most important qualifiers; and they say if a variable can take on a negative value or not. We examine this in more detail below.

Qualifiers are all intended to pass extra information about how the variable will be used to the compiler. This means two things; the compiler can check if you are violating your own rules (e.g. writing to a const value) and it can make optimisations based upon the extra knowledge (examined in later chapters).

C99 realises that all these rules, sizes and portability concerns can become very confusing very quickly. To help, it provides a series of special types which can specify the exact properties of a variable. These are defined in <stdint.h> and have the form qtypes_t where q is a qualifier, type is the base type, s is the width in bits and _t is an extension so you know you are using the C99 defined types.

So for example uint8_t is an unsigned integer exactly 8 bits wide. Many other types are defined; the complete list is detailed in C99 17.8 or (more cryptically) in the header file. ^[3]

It is up to the system implementing the C99 standard to provide these types for you by mapping them to appropriate sized types on the target system; on Linux these headers are provided by the system libraries.

Below we see an example of how types place restrictions on what operations are valid for a variable, and how the compiler can use this information to warn when variables are used in an incorrect fashion. In this code, we firstly assign an integer value into a char variable. Since the char variable is smaller, we lose the correct value of the integer. Further down, we attempt to assign a pointer to a char to memory we designated as aninteger. This operation can be done; but it is not safe. The first example is run on a 32-bit Pentium machine, and the correct value is returned. However, as shown in the second example, on a 64-bit Itanium machine a pointer is 64 bits (8 bytes) long, but an integer is only 4 bytes long. Clearly, 8 bytes can not fit into 4! We can attempt to "fool" the compiler by casting the value before assigning it; note that in this case we have shot ourselves in the foot by doing this cast and ignoring the compiler warning since the smaller variable can not hold all the information from the pointer and we end up with an invalid address.

  1 
                  $ cat types.c
    #include <stdio.h>
    #include <stdint.h>
  5 
    int main(void)
    {
            char *c;
            int i;
 10 
            i = c;
            i = (int)c;
    
            return 0;
 15 }
    
    $ uname -m
    i686
    
 20 $ gcc -Wall -o types types.c
    types.c: In function 'main':
    types.c:19: warning: assignment makes integer from pointer without a cast
    
    $ ./types
 25 i is 52
    p is 0x80484e8
    p is 0x80484e8
    
    $ uname -m
 30 ia64
    
    $ gcc -Wall  -o types types.c
    types.c: In function 'main':
    types.c:19: warning: assignment makes integer from pointer without a cast
 35 types.c:21: warning: cast from pointer to integer of different size
    types.c:22: warning: cast to pointer from integer of different size
    
    $ ./types
    i is 52
 40 p is 0x40000000000009e0
    p is 0x9e0
    
                

With our modern base 10 numeral system we indicate a negative number by placing a minus (-) sign in front of it. When using binary we need to use a different system to indicate negative numbers.

There is only one scheme in common use on modern hardware, but C99 defines three acceptable methods for negative value representation.

So far we have only discussed integer or whole numbers; the class of numbers that can represent decimal values is called floating point.

To create a decimal number, we require some way to represent the concept of the decimal place in binary. The most common scheme for this is known as the IEEE-754 floating point standard because the standard is published by the Institute of Electric and Electronics Engineers. The scheme is conceptually quite simple and is somewhat analogous to "scientific notation".

In scientific notation the value 123.45 might commonly be represented as 1.2345x102. We call 1.2345 the mantissa or significand, 10 is the radix and 2 is the exponent.

In the IEEE floating point model, we break up the available bits to represent the sign, mantissa and exponent of a decimal number. A decimal number is represented by sign × significand × 2^exponent.

The sign bit equates to either 1 or -1. Since we are working in binary, we always have the implied radix of 2.

There are differing widths for a floating point value -- we examine below at only a 32 bit value. More bits allows greater precision.

The other important factor is bias of the exponent. The exponent needs to be able to represent both positive and negative values, thus an implied value of 127 is subtracted from the exponent. For example, an exponent of 0 has an exponent field of 127, 128 would represent 1 and 126 would represent -1.

Each bit of the significand adds a little more precision to the values we can represent. Consider the scientific notation representation of the value 198765. We could write this as 1.98765x106, which corresponds to a representation below

Each additional digit allows a greater range of decimal values we can represent. In base 10, each digit after the decimal place increases the precision of our number by 10 times. For example, we can represent 0.0 through 0.9 (10 values) with one digit of decimal place, 0.00 through 0.99 (100 values) with two digits, and so on. In binary, rather than each additional digit giving us 10 times the precision, we only get two times the precision, as illustrated in the table below. This means that our binary representation does not always map in a straight-forward manner to a decimal representation.

With only one bit of precision, our fractional precision is not very big; we can only say that the fraction is either 0 or 0.5. If we add another bit of precision, we can now say that the decimal value is one of either 0,0.25,0.5,0.75. With another bit of precision we can now represent the values 0,0.125,0.25,0.375,0.5,0.625,0.75,0.875.

Increasing the number of bits therefore allows us greater and greater precision. However, since the range of possible numbers is infinite we will never have enough bits to represent any possible value.

For example, if we only have two bits of precision and need to represent the value 0.3 we can only say that it is closest to 0.25; obviously this is insufficient for most any application. With 22 bits of significand we have a much finer resolution, but it is still not enough for most applications. A double value increases the number of significand bits to 52 (it also increases the range of exponent values too). Some hardware has an 84-bit float, with a full 64 bits of significand. 64 bits allows a tremendous precision and should be suitable for all but the most demanding of applications (XXX is this sufficient to represent a length to less than the size of an atom?)

  1 
                  $ cat float.c
    #include <stdio.h>
    
  5 int main(void)
    {
            float a = 0.45;
            float b = 8.0;
    
 10         double ad = 0.45;
            double bd = 8.0;
    
            printf("float+float, 6dp    : %f\n", a+b);
            printf("double+double, 6dp  : %f\n", ad+bd);
 15         printf("float+float, 20dp   : %10.20f\n", a+b);
            printf("dobule+double, 20dp : %10.20f\n", ad+bd);
    
            return 0;
    }
 20 
    $ gcc -o float float.c
    
    $ ./float
    float+float, 6dp    : 8.450000
 25 double+double, 6dp  : 8.450000
    float+float, 20dp   : 8.44999998807907104492
    dobule+double, 20dp : 8.44999999999999928946
    
    $ python
 30 Python 2.4.4 (#2, Oct 20 2006, 00:23:25)
    [GCC 4.1.2 20061015 (prerelease) (Debian 4.1.1-16.1)] on linux2
    Type "help", "copyright", "credits" or "license" for more information.
    >>> 8.0 + 0.45
    8.4499999999999993
 35 
    
                

A practical example is illustrated above. Notice that for the default 6 decimal places of precision given by printf both answers are the same, since they are rounded up correctly. However, when asked to give the results to a larger precision, in this case 20 decimal places, we can see the results start to diverge. The code using doubles has a more accurate result, but it is still not exactly correct. We can also see that programmers not explicitly dealing with float values still have problems with precision of variables!