CS1061 C Programming Lecture 7: Floating Point

A. O’Riordan, 2004

A Floating Point

Floating point variable types (or floats)  allow us to store non-integer numbers (real numbers), which can have fractional parts as well as whole (integral) parts.

 for any given storage size, floating point variables can represent much larger numbers than integer variables can.

   The reason for this is that a float type is represented internally in exponential format. The exponential format consists of two parts: the mantissa and the exponent.

The mantissa contains the significant digits - that is, the digits that represent the precision (detail) of a quantity. The greater the number of mantissa digits, the greater the precision.

The second part, the exponent, merely specifies where to place a decimal point that separates the whole part from the fractional part of a number hence, the term 'floating point'.

Exponentials

The reason that floats can store larger numbers is that the size of the number is indicated by a power of ten. Actually, the size is indicated by a power of 2 since all internal values are in binary format but we use decimal numbers (base 10) in our illustrations because this is more natural.

1.2345x10

4 = 1.2345x10x10x10x10 = 12345 1.2345x10

4 is represented as 1.2345e4

or 1.2345E4

Here are example floats (all have the same value): 20.0 2e2 0.2E3

Floats can have round-off error More advanced material here (don’t worry about this too much)!

Suppose we have a hypothetical storage location that can hold four decimal digits; the largest integer that this could represent would be 9999 but we use a float representation and apportion the mantissa as three digits and the exponent as one digit. Then we could represent a much larger number within these four digits, the largest being: 999 x 10 9 = 999,000,000,000 (Here the mantissa is 999 and the exponent is 9.) Of course we can really only represent a small subset of the numbers less than 999x10 9 . Computations involving large numbers thus result in inaccuracies, called round-off error.

Floats can have round-off error (2)

The maximum value that can be represented here is: 999 x 10 length of the mantissa.

9 , but the maximum precision that can be maintained is only three digits - the For example, we could not store the number 425,735,485,001 in that format - we could only approximate it with 426e9 So floating point data types can hold larger numbers than integer types of the same length. But a floating point type offers no more precision than an integer type of the same length.

Declarations

Floating point numbers are declared in C using the float keyword. For example, the following declares a floating point variable named balance.

float balance; To maintain higher-precision numbers, we must increase the storage size, and this is the purpose of yet another data type provided by the C programming language: the double precision type.

double velocity=14354.3;

Operator

& | ^ << >> ~

Bit Manipulation

All data is represented internally as sequences of bits - C has some operators for bit manipulation Name bitwise AND bitwise OR bitwise exclusive OR left shift right shift One’s complement Description The bits in the result are set to

1

the two operands are both

1

.

if the corresponding bits in The bits in the result are set to

1

if at least one of the corresponding bits in the two operands is

1

. The bits in the result are set to

1

if exactly one of the corresponding bits in the two operands is

1

. Shifts the bits of the first operand left by the number of bits specified by the second operand; fill from right with

0

bits. Shifts the bits of the first operand right by the number of bits specified by the second operand; the method of filling from the left is machine dependent.

All

0

bits are set to

1

and all

1

bits are set to

0

.

Enumeration constants

   Set of integer constants represented by identifiers Enumeration constants are like symbolic constants whose values are automatically set  Values start at

0

and are incremented by

1

 Values can be set explicitly with

=

 Need unique constant names Example: enum Months { JAN = 1, FEB, MAR, APR, MAY, JUN, JUL, AUG, SEP, OCT, NOV, DEC}; Creates a new type enum Months in which the identifiers are set to the integers 1 to 12