## 4.1.1 Numeric Expressions

Numeric expressions express numeric computations, and are formed with numeric operands and numeric operators. The evaluation of a numeric operation yields a single numeric value.

The term numeric includes logical data, because logical data is treated as integer data when used in a numeric context. The default for .TRUE. is -1; .FALSE. is 0. Note that on WNT and W9* systems, the default can change if a specific compiler option is used.

Numeric operators specify computations to be performed on the values of numeric operands. The result is a scalar numeric value or an array whose elements are scalar numeric values. The following are numeric operators:

Operator | Function
--- | ---
** | Exponentiation
* | Multiplication
/ | Division
+ | Addition or unary plus (identity)
- | Subtraction or unary minus (negation)

Unary operators operate on a single operand. Binary operators operate on a pair of operands. The plus and minus operators can be unary or binary. When they are unary operators, the plus or minus operators precede a single operand and denote a positive (identity) or negative (negation) value, respectively. The exponentiation, multiplication, and division operators are binary operators.

Valid numeric operations must have results that are defined by the arithmetic used by the processor. For example, raising a negative-valued base to a real power is invalid.

Numeric expressions are evaluated in an order determined by a precedence associated with each operator, as follows (see also Section 4.1.6):

Operator | Precedence
--- | ---
** | Highest
* and / |
       .
Unary + and - |
       .
Binary + and - | Lowest

Operators with equal precedence are evaluated in left-to-right order. However, exponentiation is evaluated from right to left. For example, A**B**C is evaluated as A**(B**C). B**C is evaluated first, then A is raised to the resulting power.

Normally, two operators cannot appear together. However, Compaq Fortran allows two consecutive operators if the second operator is a plus or minus.

Examples

In the following example, the exponentiation operator is evaluated first because it takes precedence over the multiplication operator:

  `A**B*C` is evaluated as `(A**B)*C`

Ordinarily, the exponentiation operator would be evaluated first in the following example. However, because Compaq Fortran allows the combination of the exponentiation and minus operators, the exponentiation operator is not evaluated until the minus operator is evaluated:

  `A**-B*C` is evaluated as `A**(-(B*C))`

Note that the multiplication operator is evaluated first, since it takes precedence over the minus operator.

When consecutive operators are used with constants, the unary plus or minus before the constant is treated the same as any other operator. This can produce unexpected results. In the following example, the multiplication operator is evaluated first, since it takes precedence over the minus operator:

  `X/-15.0*Y` is evaluated as `X/-(15.0*Y)`

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