6.7.1. Numeric Derived Types - JulTob/Ada GitHub Wiki

You can define your own fixed point and floating point types and — with the aid of generic packages call all the mathematical functions you need.

In that respect Ada is on par with Fortran.

If we write

type Number is new Float;

Then Number has all the operations (+,*, etc) of Float. Generally speaking, it can be considered as equivalent.

Now, suppose we transfer the program to a different context where the predefined Float is not so accurate, so we want to use Long_Float. Assuming the program has been written using Number, rather than Float, then replacing the declaration to

type Number is new Long_Float;

Is the only change necessary.

We can also improve by stating the precision and range, or minimum accuracy.

type Number is digits 7;
--  Will make a type with at least 7 decimal digits of accuracy.

type Number is digits 10 range -1.0 .. 1.0;
--  Will make a Floating-point type with AT LEAST 10 digits of accuracy.


type Number is range -10.0 .. 10.0;

Pi : constant := 3.14159_26535;
-- πτΔδ
type Angle is delta Pi/(2.0**31) range -Pi .. Pi; 
--  will generate fixed-point type of 32 bits for the values of a circle

type My_Float is digits 7 range -2.0 ** 32 .. 2.0 ** 32;

type Voltage is delta 0.125 range 0.0 .. 255.0;

type Money is delta 0.01 digits 15;


type <type-name> is delta <delta-value> digits <digits-value> range <range def>;


subtype temperature is float range 0.0 .. 100.0;

subtype result_range is float range 0.0 .. 1.0;

type Length is digits 5 range 0.0 .. 4.0E6;


type Velocity is new Float;
type Height is new Float;
-- can't accidentally mix velocities and heights without an 
-- explicit type conversion.


type Euros is digits 2 range 0.00 .. 1_000_000.00;
type Dollars is delta 0.01 digits 9;
subtype Salary is Dollars digits 6


type Number is delta System.Fine_Delta range -1.0 .. +1.0;
-- Fraction'last = 1.0 - System.Fine_Delta

The Integer numbers also can be invoked.

type Number is new Integer;

type Number is new Natural;  
--  Unsigned Integers

type Number is new Positive;  
--  Non zero Naturals.

type Number is Integer range -1_000 .. +1_000; 
--  The _ is ignored. Visual aid

type Number is range -1_000_000 .. +1_000_000; 
--  The type is interpreted in context

Type forRange is range 1 .. 10;

Type image_X is range 0 .. (1024 - 1);

Month : number := 08 --Ada allows for leading zeros

subtype result_range is range 1..10;

They come with certain methods associated.

Positive’First; --  1
Natural’First; --  0
Integer’First; --   (-2^15) +1
Integer’Last; --  2^15 -1
Number’Range;

Ada also allows modular types, as in cyclical topologies.

type Angle is mod 360; 
--  360 is 0 again
----------------
Type Byte is mod 16#10000#; --Base 16
...
Mask := 16#FF00#;
Byte := Byte and Mask; --Bitwise AND.
---------------
Type word_byte is mod 16#100#;

It provides a clear syntax for numeric bases between 2 and 16 inclusive (10 is of course the default)

Conditions

You can also define types by certain conditional attributes.

for Number’Size use 32; --Memory space: 32 Bits

Base from 2 to 16

You can also define types by certain conditional attributes.

X := 16#CAFE#; -- Hexadecimal
X := 8#127#;   -- Octal
X := 2#1101_1101_0001_1001#; -- Binary
X := 5#3420#   -- Any

The compiler is responsible for choosing an appropriately sized integer type. On a PC, it would be a 32 bit size, equivalent to long_integer. On a Unix workstation it would still be a 32 bit integer, but this would be equivalent to an integer. Letting the compiler choose frees the programmer from having to choose. Compiling it on a new host does not require changing the source code.

Range

Un rango es un subconjunto de valores de un tipo escalar especificado por un límite inferior y un límite superior. Si el límite inferior es L y el límite superior es R, el rango "L .. R" comprende todos los valores del tipo en cuestión que sean mayores o iguales que L y menores o iguales que R. Si L > R el rango es nulo.

-127 .. 128
A .. A + 10
0.0 .. 2.0
1 .. 0        --  rango nulo

-- Ejemplos de rango como range_attribute_reference
Integer'Range --  rango Integer'First .. Integer'Last
Mat'Range(1)  --  rango 1 .. 5, supuesto que:
              --  Mat : array (1 .. 5, 1 .. 10) of Integer;

--Ejemplos de restricción de rango
range -128.0 .. +128.0
range Integer'First .. Integer'Last - 1
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