6. Expressions

An expression combines data with operators to produce a value (§6). FORTRAN 66 has three kinds: arithmetic (a numeric value), relational (a truth value from comparing two numbers), and logical (a truth value combined with logical operators). This chapter gives their formation and evaluation rules.

Arithmetic expressions

An arithmetic expression produces a value of type integer, real, double precision, or complex (§6.1). The arithmetic operators are:

Operator	Meaning
+	addition (and unary plus)
-	subtraction (and unary minus)
*	multiplication
/	division
**	exponentiation

      X = A + B*C - D/E
C     -> * and / bind tighter than + and -

Exponentiation binds right and tightest

** has higher precedence than * and /, and a chain of exponentiations groups right to left:

      COMMON /O/ N(1)
      N(1) = 2**3**2
C     -> 2**(3**2) = 2**9 = 512, not (2**3)**2 = 64

The standard defines ** for only a few operand combinations (§6.1):

• a primary of any type may be raised to an integer primary — the result has the base's type. This is why (-2.0)**3 is the well-defined -8.0;
• a real or double precision primary may be raised to a real or double precision primary — the result is real if both are real, otherwise double precision.

No other combinations are defined. In particular a negative value may not be raised to a real or double precision exponent (it would need a complex result), and a zero may not be raised to a zero exponent (§6.4).

Mixed-mode arithmetic

In strict FORTRAN 66 the operands of an arithmetic operator must generally be of the same type; the only cross-type combinations the standard admits are a real element with a double precision element (giving double precision) or with a complex element (giving complex) (§6.1). Notably, integer and real were not meant to be mixed in one expression.

      DOUBLE PRECISION D, R
      D = 1.0D0
      R = D + 0.5
C     -> real 0.5 combined with double precision -> double precision

Relational expressions

A relational expression compares two arithmetic expressions and yields true or false (§6.2). The relational operators are:

Operator	Meaning	Operator	Meaning
.LT.	less than	.GE.	greater than or equal
.LE.	less than or equal	.GT.	greater than
.EQ.	equal	.NE.	not equal

The standard allows the two operands to be real/double precision, or both integer; a real operand compared with a double precision one is handled as if a double precision zero were added to the real (§6.2).

      LOGICAL BIG
      BIG = X .GT. 100.0

Logical expressions

A logical expression is built from logical values and the logical operators (§6.3):

Operator	Meaning
.NOT.	logical negation
.AND.	logical conjunction
.OR.	logical disjunction

Their precedence, highest first, is .NOT. then .AND. then .OR.:

      COMMON /O/ L(1)
      LOGICAL L
      L(1) = .FALSE. .OR. .TRUE. .AND. .FALSE.
C     -> .FALSE. .OR. (.TRUE. .AND. .FALSE.) = .FALSE.

Relational expressions may appear as operands of logical operators (arithmetic binds tightest, then relational, then logical), so A+B .GT. C .AND. FLAG means ((A+B) .GT. C) .AND. FLAG.

Evaluation rules

A few rules govern how an expression is evaluated (§6.4):

• Only as much of an expression need be evaluated as is required to establish its value.
• A processor may reorder operations using the associative and commutative laws — except that the integrity of parentheses is always preserved. So (A+B)+C and A+(B+C) may differ, and you use parentheses when order matters.
• The value of an integer factor or term is the nearest integer whose magnitude does not exceed the true mathematical value — i.e. division truncates toward zero. The associative and commutative laws do not apply to integer terms containing division, which proceed left to right.

      COMMON /O/ N(2)
      N(1) = 7/2
C     -> 3 (truncated toward zero, not rounded)
      N(2) = (-7)/2
C     -> -3

forterp notes.

• forterp permits mixed integer/real arithmetic and relationals on every dialect — 2.0 + 3 evaluates to 5.0, and 2 .LT. 3.0 is true — converting to the wider type as later FORTRANs do. Strict FORTRAN 66 did not sanction this mixing, but allowing it cannot change the meaning of a program that avoids it, so forterp accepts it as a convenience.
• Exponentiation is right-associative (2**3**2 is 512) and integer division truncates toward zero, matching the standard.
• On the default NATIVE target, overflow and operations like 0.0/0.0 follow host IEEE rules (infinities and NaNs); the faithful PDP10 target reproduces the FOROTS recovery behavior instead. See Appendix C.