# 4.5.6 Highest Precedence Operators

## Static Semantics

The highest precedence unary operator **abs** (absolute value) is predefined for every specific numeric type *T*, with the following specification:

```
function "abs"(Right : T) return T
```

The highest precedence unary operator **not** (logical negation) is predefined for every boolean type *T*, every modular type *T*, and for every one-dimensional array type *T* whose components are of a boolean type, with the following specification:

```
function "not"(Right : T) return T
```

The result of the operator **not** for a modular type is defined as the difference between the high bound of the base range of the type and the value of the operand. For a binary modulus, this corresponds to a bit-wise complement of the binary representation of the value of the operand.

The operator **not** that applies to a one-dimensional array of boolean components yields a one-dimensional boolean array with the same bounds; each component of the result is obtained by logical negation of the corresponding component of the operand (that is, the component that has the same index value). A check is made that each component of the result belongs to the component subtype; the exception Constraint_Error is raised if this check fails.

The highest precedence *exponentiation* operator ** is predefined for every specific integer type *T* with the following specification:

```
function "**"(Left : T; Right : Natural) return T
```

Exponentiation is also predefined for every specific floating point type as well as *root_real*, with the following specification (where *T* is *root_real* or the floating point type):

```
function "**"(Left : T; Right : Integer'Base) return T
```

The right operand of an exponentiation is the *exponent*. The expression X**N with the value of the exponent N positive is equivalent to the expression X*X*...X (with N-1 multiplications) except that the multiplications are associated in an arbitrary order. With N equal to zero, the result is one. With the value of N negative (only defined for a floating point operand), the result is the reciprocal of the result using the absolute value of N as the exponent.

## Implementation Permissions

The implementation of exponentiation for the case of a negative exponent is allowed to raise Constraint_Error if the intermediate result of the repeated multiplications is outside the safe range of the type, even though the final result (after taking the reciprocal) would not be. (The best machine approximation to the final result in this case would generally be 0.0.)

## Notes

19 As implied by the specification given above for exponentiation of an integer type, a check is made that the exponent is not negative. Constraint_Error is raised if this check fails.

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