New Numeric Types

Introduction: Kinds of Numeric Types

Kinds of New Numeric Types

• Possible kinds of numeric types:
• Integer
• Floating point


• Fixed point


• Modular

Integer and Floating Point Types

New Integer Types

        type Temperature is Range 32 .. 212;
        type Pressure is Range 0 .. 500;

        t: Temperature;
        p: Pressure;

        t := 100;   -- valid
        p := t;     -- compile error
        

• Only valid values can be assigned to t and p
• Types cannot be mixed

• Automatically get all operations on Integers
• Need to define I/O operations

• Sometimes mixed type expressions are needed and conversions can be used.

        Result: Integer := Integer(t) * Integer(Pressure)
        

• Conversion does not change value in any
• Conversion signals compiler to allow computation

Floating Point Types

• Like integer types, we can declare new floating point types


• Example:

        type Volume is Digits 8 Range 10.0 .. 1_000.0;  -- Cubic Centimeters
        type Weight is Digits 8 Range 50.0 .. 500.0;    -- Grams

        h: Height;
        w: Weight;
        density: Float;

        h := 100.0;    -- valid
        -- w := h;     -- compile error
        w := 50.0;    

        -- Sometimes need to convert types
        density := float(h) / float(w);
        



• The digits specifier tells how many digits of precision the number will have
• Type Float and Long_Long_Float have digits 6 and 18, respectively

Alternate Notation for Integer and Floating Point Types

• New number types can specify the underlying type:

        type Temperature is new Integer Range 32 .. 212;
        type Pressure is new Integer Range 0 .. 500;  

        type Volume is new Float Range 10.0 .. 1_000.0; 
        type Weight is new Float Range 50.0 .. 500.0;  
        

• Otherwise the compiler chooses the underlyin type


• First notation is more portable: allow compiler to choose new type

Fixed Point Types

What Does Floating Point Mean?

• To learn Fixed Point Types (below) you must know floating point types


• Type Float: decimal point floats (ie it can move among the significant digits)

        x: Float;

        x := 12_345_678.9  -- 12_345_678.9 
        x := x / 10.0;     -- 12_345_67.89
        x := x / 100.0;    -- 12_345.678_9
        

• Floating point can give inexact results:

        cent: Float := 0.01;
        dollar: Float := 0.0;

        for i in 1 .. 100 loop
            dollar := dollar + cent;
        end loop;
        put(dollar);   -- 0.9999993443
        

Decimal Fixed Point Types

• Decimal fixed point types have a constant, fixed number of decimal places
• Good for problems involving money

        type Money is delta 0.01 digits 15;

        cent: Money := 0.01;
        dollar: Money := 0.0;

        annualSal := 1234567.89;
        put_line(annualSal'img);       -- 1234567.89

        annualSal := annualSal / 10;   --  Division fixed by int is okay
        put_line(annualSal'img);       --  123456.78  -- Truncates toward 0!

        annualSal := annualSal / 10;
        put_line(annualSal'img);       --   12345.67

        for i in 1 .. 100 loop
            dollar := dollar + cent;
        end loop;
        put(dollar);   --  1.00
        

• Another example - calculate missing salary:

        subtype Salary is Money digits 10;

        annualSal: Salary := 100_000.00;
        monthlySal: Salary := annualSal / 12;     --  8333.33

        missingSal := annualSal - (12 * monthlySal);  -- 0.04
        

• Shows number of cents that must be added to paycheck over the year

Fixed Point and Decimal Fixed Point Types

• Decimal Fixed point types are decimal based


• Ordinary Fixed point types are binary based
• Example: subtype Volt is delta 0.125 range 0.0 .. 255.0;
• 0.125 = 2#0.001# = (0.5)**3

Modular Types

Modular Types

• Modular types:
• Values of modular types are never negative
• Modular types use modular arithmetic


• Example 1 - Hours: values range from 0 .. 11:

    type Hour_t is mod 12;   
        

• Values always in 0 .. 11 (ie remainder mod 12)
• All operations are mod 12


• Example 1 - continued

    type Hour_t is mod 12;   -- values range from 0 to 11

    startTime: Hour_t := 8;

    breakTime: Hour_t := startTime + 4;    -- 0
    endTime: Hour_t := startTime + 6;      -- 2
    notifyTime: Hour_t := startTime - 11;  -- 9
        

• Example 2 - 32 bit unsigned value (no sign bit - useful for addresses):

	type Address is mod 2**32;
        

• Similar to C unsigned types and Java char type