Ada Programming/Types/mod
Description
[edit | edit source]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
typeUnsigned_nismod2**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:
typeByteismod256;subtypeHalf_ByteisByterange0 .. 127;
But beware: the Modulus of Half_Byte is still 256! Arithmetic with such a type is interesting to say the least.
Bitwise Operations
[edit | edit source]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.
typeUnsignedismod2**5; -- modulus 32 X: Unsigned := 2#10110#; -- 22notX = 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):
typeUnsignedismod5; 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# 