02-datatypes

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Scientific Programming in C

II. Data types

Susi Lehtola

30 October 2012
http://find/http://goback/


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Data types in C

The basic data types in C are

char, a single byte, capable of holding a character in thecurrent character set

int, an integer

float, single precision floating point number

double, double precision floating point number

There are also modifiers

shortand longfor integers

signed(default) or unsignedfor characters and integers

Scientific Programming in C, fall 2012 Susi Lehtola Data types 2/19


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Data types in C



int, an integer






... but what are these, really, and why do we need them?



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Data types in C



int, an integer






... but what are these, really, and why do we need them?

Lets return to that in a bit.



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Constants

1 is an integer type constant

1uor1Uis an unsigned integer

1lor1L is a long integer

1ulor1UL is an unsigned long integer

1.0is a double precision floating point constant

1.0f is a single precision floating point constant

1.0l is a long double

x is a character constant

xyz is a string constant (a constant character array)



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Representation of integers

To represent integers we need to define the maximum size of thenumber we use. For example, with 8 digits

1 xxxxxxxx

we are able to represent numbers from1 00000000

to

1 99999999

in the 10-base system.



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Binary system

Computers use the binary system, in which

000000002= 010

and

111111112= 25510

If we use the first bit to define the sign, our range is from 128 to127.

We can extend or reduce the range we span by adding or removingmore bits from the data type.



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Representation of real numbers

Extending the logic of the integer system, we can construct realnumbers by fixing a decimal point somewhere. Naturally, as thereis an infinite number of real numbers in any given finite interval,we introduce rounding errors.

For example, in the convention that the last 3 digits are decimals,the raw-data value 12957203 would correspond to the number12957.203.

This is known as the fixed-point system. Its not available in any

(standard) programming languages but it can be manuallyimplemented using integers if necessary.



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Representation of decimal numbers, contd

As practical applications often use real numbers with a huge range,usage of the fixed-point system is not computationally feasible.Computing the value of simple functions such as y=x2 would bedifficult.

In practice scientists dont write out all the zeros and the decimals,but use the scientific notation instead. For instance the Bohrradius is

a0 0.0000000000052917721 m

= 5.29177211011 m



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Floating-point numbers

Applying the same principle to represent real numbers on thecomputer, we end up with the floating-point system.

Numbers are represented in the format

x= mantissa baseexponent

Type Sign Exp. Mantissa Total bits Decimal digits

float 1 8 23 32 7.2double 1 11 52 64 15.9

80-bit double 1 15 64 80 19.2quad 1 15 112 128 34.0

Source: http://en.wikipedia.org/wiki/Floating_point

http://en.wikipedia.org/wiki/Floating_pointhttp://en.wikipedia.org/wiki/Floating_point


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Roundoff errors

Because of the floating-point system, the accuracy is not universalanymore. Whereas the result of, e.g., additions in the fixed-point

system is independent of the order of summation, in thefloating-point system the result may depend on the order theelements are summed in.

The machine epsilon is inextricably linked to this. It is defined as

the smallest number for which

1 + >1.

For example:

2+ 1 +

2= 1

2+

2+ 1 = 1 +

For float is normally around 10

7 and for doublearound 10

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Comparison of floating-point numbers

Due to the finite precision and roundoff errors, its rather rare thatfloating-point arithmetic gives you exactly the number you expect.If you expect xto be equal to y, instead of using the comparison

xy

use|xy| 10max{x, y}

to find out if this is true.



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Loops and if statements

One of the most common structures in programming are loops andif statements. The structure of these in C is the following

i n t i ;i n t x=0;f o r( i =0; i


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Loops and if statements, contdThe scope of if and foris the following statement, so if you wantto run more statements, enclose them in braces.

i n t i =0;double j =0.0 ;double k = 0 . 0 ;f o r( i =0; i


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If statementsIf you have if statements within if statements, with elsestatements, you really should use braces to be clear.

i f( i ==0)i f( j ==0)k=0;

e l s e

k=1;

Here the elsestatement refers to the last if statement (which ismade clear by the indentation). But compilers often warn aboutthese kinds of statements, since they might lead to unexpectedbehavior.

i f( i ==0) {i f( j ==0)

k=0;e l s e

k=1;

}Scientific Programming in C, fall 2012 Susi Lehtola Data types 15/19


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Loop example

Connection between Fahrenheit and centigrade temperature scale

is

F = 1

.

8

C+ 32

# i n c l u d e < s t d i o . h>

f l o a t c e l c i u s t o f a h r (f l o a t c ) {

r e t u r n 1 . 8 f c +32.0 f ;}

i n t m a i n ( v o i d ) {i n t i ;

f o r( i =0; i


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Loop example, contd

$ ./ a . out0 3 2. 00 00 0010 5 0 .0 0 00 0 020 6 8 .0 0 00 0 030 8 6 .0 0 00 0 0

40 1 0 4. 0 00 0 0050 1 2 2. 0 00 0 0060 1 4 0. 0 00 0 0070 1 5 8. 0 00 0 0080 1 7 6. 0 00 0 0090 1 9 4. 0 00 0 00100 2 1 2 . 0 00 0 0 0


f


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If example

The realization of the function

y(x) =

a, xa

x, x >a

is

double c u t o f f ( double x , double a ) {i f( x


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Operators

The operators that are available in C are

= assignment multiplication/ division+ addition- substraction% modulus division

There are also the following comparison operators

== equality

> greater than>= at least< smaller than

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