nat

#nat

##Syntax nat

##Description The nat (natural number) type has the values 0, 1, 2, 3 � Natural numbers can be combined by various operators, such as addition (+) and multiplication (*). Natural numbers can be combined with integers (type int), in which case the result is an integer. Natural numbers can also be combined with real numbers, in which case the result is generally a real number. Natural numbers can always be assigned to real variables, with implicit conversion to real.

##Example

    var counter : nat
    var j : nat := 9

##Details See also explicitIntegerConstant. The nat type is used instead of int when the values are known to be non-negative.

The Turing operators on natural numbers are the same as those for integers: +, -, * (multiply), div (truncating integer division), mod (integer remainder), ** (exponentiation), as well as comparisons (+, not=, >, >=, <, <=). The operators and, or and xor to be applied to natural number values. The bit-wise boolean result is produced as a natural number. The shr (shift right) and shl (shift left) operators are also introduced.

In the current implementation, the range of natural numbers is from 0 to 4294967294. In other words, the maximum value of a natural number is 2**32 - 2. This range exists because natural numbers are stored in 4 bytes. The types nat1, nat2 and nat4 specify natural numbers that fit into 1, 2 or 4 bytes.

Explicit constants such as 213 and 0 are considered to be integers. As a result the type of tax in this declaration is int:

Natural number values can be used whenever integer values are expected and vice versa, given that the value does not exceed the range of the expected type.

When integer and natural numbers are combined using a binary operator such as +, the result is an integer. This means, for example, that if counter is a natural number, counter + 1 is considered to be an integer. As long as the result fits into the range that is the intersection of the ranges of int and nat, the result will be as expected. Anomalies occur when the result is (or would be) greater than the largest integer (maxint=2147483647). For example, if natural number n is greater than maxint, the expression n + 1 will overflow, because its result is an int (because 1 is an int). To avoid this problem, you must be careful that both operands are natural numbers.

Suppose we have this declaration:

We can safely compute n + natOne because both operands have type nat.

Natural numbers can be converted to real numbers using natreal, but in practice this is rarely used, because a natural value used in place of a real value will be automatically converted to real.

Natural numbers can be converted to strings and back using natstr and strnat.

In the C language, a natural number is said to be "unsigned".

    var tax := 0    % The type is int        const natOne : nat := 1

##See also maxnat.html, int.html, n, int.htmln, natstr.html, strnat.html and natreal.html.