Ada Programming/Types/mod

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Description

Unsigned integers in Ada have a value range from 0 to some positive number (not necessarily 1 subtracted from some power of 2). They are defined using the mod keyword because they implement a wrap-around arithmetic.

 mod Modulus

where 'First is 0 and 'Last is Modulus - 1.

Wrap-around arithmetic means that 'Last + 1 = 0 = 'First, and 'First - 1 = 'Last. Additionally to the normal arithmetic operators, bitwise and, or and xor are defined for the type (see below).

The predefined package Interfaces (RM B.2 ^[Annotated]) presents unsigned integers based on powers of 2

type Unsigned_n is mod 2**n;

for which also shift and rotate operations are defined. The values of n depend on compiler and target architecture.

You can use range to sub-range a modular type:

type Byte is mod 256;
subtype Half_Byte is Byte range 0 .. 127;

But beware: the Modulus of Half_Byte is still 256! Arithmetic with such a type is interesting to say the least.

Bitwise Operations

Be very careful with bitwise operators and, or, xor, not, when the modulus is not a power of two. An example might exemplify the problem.

type Unsigned is mod 2**5;   -- modulus 32
X: Unsigned := 2#10110#;     -- 22
not X        = 2#01001#      -- bit reversal: 9 ( = 31 - 22 ) as expected

The other operators work similarly.

Now take a modulus that is not a power of two. Naive expectations about the results may lead out of the value range. As an example take again the not operator (see the RM for the others):

type Unsigned is mod 5;
X: Unsigned := 2#001#;  -- 1, bit reversal: 2#110# = 6 leads out of range

The definition of not is therefore:

 not X = Unsigned'Last – X  -- here: 4 – 1 = 2#011#

See also

Wikibook

• Ada Programming
• Ada Programming/Types
• Ada Programming/Keywords/mod

Ada Reference Manual

• 4.4: Expressions ^[Annotated]
• 3.5.4: Integer Types ^[Annotated]