FLOAT type

A FLOAT is a positive or negative number with a decimal part

• real (floating point) number
• may be scientific notation

FLOAT literals: optional sign, digits, period, digits

        123.456         
        1.23456E2
        0.0001234               
        1.234e-4                

Why use floats?

• numbers with decimal parts
• larger range of numbers than INTEGER handles

• inexact
• slower than integers; more storage

Range of FLOATs

Attributes

• FLOAT'DIGITS no of significant figures
• FLOAT'FIRST minimum on given system
• FLOAT'LAST maximum on given system
• FLOAT'SMALL smallest on given system

Example:

        PUT ("The number of digits in a float value is: ");
        PUT (FLOAT'DIGITS); NEW_LINE;

        PUT ("The lowest  float value is: ");
        PUT (FLOAT'FIRST); NEW_LINE;

        PUT ("The highest float value is: ");
        PUT (FLOAT'LAST); NEW_LINE;

        PUT ("The tiniest float value is: ");
        PUT (FLOAT'SMALL); NEW_LINE;


        The number of digits in a float value is:  15
        The lowest  float value is: -1.79769313486232E+308
        The highest float value is:  1.79769313486232E+308
        The tiniest float value is:  1.94469227433161E-62

Errors with FLOATs

Since floating point numbers are stored with only a fixed number of significant digits of accuracy, they are subject to rounding errors. Four types of errors arise from this:

• representation error (rounding error)
• cancellation error: adding a large and small number, the larger number may cancel the smaller
• arithmetic underflow: two very small numbers are multiplied, giving a result that is too small to represent
• arithmetic overflow: two very large numbers are multiplied, giving a result that is too large to represent

Operations on FLOATs

I/O: special library provides GET, PUT

        package float_io is new TEXT_IO.FLOAT_IO( FLOAT );
        use  float_io;

arithmetic

• unary minus (negation) - float_val
• absolute value abs float_val
• + - * /
• ** (exponentiation) requires integer exponent

relational:

• = /= < > <= >=
• do not test for exact "equality", because of rounding errors (an example program demonstrates this).