Fortran 77 Language Reference

Chapter 3

Expressions

This chapter discusses Fortran expressions and how they are evaluated.

Expressions, Operators, and Operands

An expression is a combination of one or more operands, zero or more operators, and zero or more pairs of parentheses.

There are three kinds of expressions:

• An arithmetic expression evaluates to a single arithmetic value.
• A character expression evaluates to a single value of type character.
• A logical or relational expression evaluates to a single logical value.

The operators indicate what action or operation to perform.

The operands indicate what items to apply the action to. An operand can be any of the following kinds of data items:

• Constant
• Variable
• Array element
• Function
• Substring
• Structured record field (if it evaluates to a scalar data item)
• An expression

Arithmetic Expressions

An arithmetic expression evaluates to a single arithmetic value, and its operands have the following types. indicates a nonstandard feature.

• BYTE
• COMPLEX
• COMPLEX*32 (SPARC only)
• DOUBLE COMPLEX
• DOUBLE PRECISION
• INTEGER
• LOGICAL
• REAL
• REAL*16 (SPARC only)

The operators for an arithmetic expression are any of the following:

TABLE 3-1   Arithmetic Operators

Operator	Meaning
** * / - +	Exponentiation Multiplication Division Subtraction or Unary Minus Addition or Unary Plus

If BYTE or LOGICAL operands are combined with arithmetic operators, they are interpreted as integer data.

Each of these operators is a binary operator in an expression of the form:

a b

where a and b are operands, and is any one of the **, *, /, -, or + operators.

Examples: Binary operators:

A-Z X*B

The operators + and - are unary operators in an expression of the form:

b

where b is an operand, and is either of the - or + operators.

Examples: Unary operators:

-Z +B

Basic Arithmetic Expressions

Each arithmetic operator is shown in its basic expression in the following table:

TABLE 3-2   Arithmetic Expressions

Expression	Meaning
a ** z a / z a * z a - z -z a + z +z	Raise a to the power z Divide a by z Multiply a by z Subtract z from a Negate z Add z to a Same as z

In the absence of parentheses, if there is more than one operator in an expression, then the operators are applied in the order of precedence. With one exception, if the operators are of equal precedence, they are applied left to right.

TABLE 3-3   Arithmetic Operator Precedence

Operator	Precedence
** * / + -	First Second Last

For the left-to-right rule, the one exception is shown by the following example:

F ** S ** Z

The above is evaluated as

F ** (S ** Z)

:

f77 allows two successive operators.

Example: Two successive operators:

X ** -A * Z

The above expression is evaluated as follows:

X ** (-(A * Z))

In the above example, the compiler starts to evaluate the **, but it needs to know what power to raise X to; so it looks at the rest of the expression and must choose between - and *. It first does the *, then the -, then the **.

Mixed Mode

Except for BYTE operands, if both operands have the same type, then the resulting value has that type. (The result of an arithmetic operation with both operands type BYTE is default integer.) If operands have different types, then the weaker of two types is promoted to the stronger type, where the weaker type is the one with less precision or fewer storage units. The ranking is summarized in the following table:

Data Type	Rank
BYTE or LOGICAL*1 LOGICAL*2 LOGICAL*4 INTEGER*2 INTEGER*4 INTEGER*8 LOGICAL*8 REAL*4 (REAL) REAL*8 (DOUBLE PRECISION) REAL*16 (QUAD PRECISION) (SPARC only) COMPLEX*8 (COMPLEX) COMPLEX*16 (DOUBLE COMPLEX) COMPLEX*32 (QUAD COMPLEX) (SPARC only)	1 (Weakest) 2 3 4 5 6 6 6 7 8 9 10 11 (Strongest)

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Note – REAL*4, INTEGER*8, and LOGICAL*8 are of the same rank, but they can be the results of different pairs of operands. For example, INTEGER*8 results if you combine INTEGER*8 and any of the types between 1-5. Likewise, REAL*4 results if one of the operands is REAL*4, and the other is any of the types between 1-5. LOGICAL*8 dictates only the 8-byte size of the result.

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Example of mixed mode: If R is real, and I is integer, then the expression:

R * I

has the type real, because first I is promoted to real, and then the multiplication is performed.

Rules

Note these rules for the data type of an expression:

• If there is more than one operator in an expression, then the type of the last operation performed becomes the type of the final value of the expression.
• Integer operators apply to only integer operands.

Example: An expression that evaluates to zero:

2/3 + 3/4

• When an INTEGER*8 operand is mixed with REAL*4 operands, the result is REAL*8.

There is one extension to this: a logical or byte operand in an arithmetic context is used as an integer.

• Real operators apply to only real operands, or to combinations of byte, logical, integer, and real operands. An integer operand mixed with a real operand is promoted to real; the fractional part of the new real number is zero. For example, if R is real, and I is integer, then R+I is real. However, (2/3)*4.0 is 0.
• Double precision operators apply to only double precision operands, and any operand of lower precision is promoted to double precision. The new least significant bits of the new double precision number are set to zero. Promoting a real operand does not increase the accuracy of the operand.
• Complex operators apply to only complex operands. Any integer operands are promoted to real, and they are then used as the real part of a complex operand, with the imaginary part set to zero.
• Numeric operations are allowed on logical variables. You can use a logical value any place where the FORTRAN Standard requires a numeric value. The numeric can be integer, real, complex, double precision, double complex, or real*16 (SPARC only). The compiler implicitly converts the logical to the appropriate numeric. If you use these features, your program may not be portable.

Example: Some combinations of both integer and logical types:

COMPLEX C1 / ( 1.0, 2.0 ) / INTEGER*2 I1, I2, I3 LOGICAL L1, L2, L3, L4, L5 REAL R1 / 1.0 / DATA I1 / 8 /, I2 / 'W' /, I3 / 0 / DATA L1/.TRUE./, L2/.TRUE./, L3/.TRUE./, L4/.TRUE./, & L5/.TRUE./ L1 = L1 + 1 I2 = .NOT. I2 L2 = I1 .AND. I3 L3 = I1 .OR. I2 L4 = L4 + C1 L5 = L5 + R1

Resultant Type

For integer operands with a logical operator, the operation is done bit by bit. The result is an integer.

If the operands are mixed integer and logical, then the logicals are converted to integers, and the result is an integer.

Arithmetic Assignment

The arithmetic assignment statement assigns a value to a variable, array element, or record field. The syntax is:

v = e
e	Arithmetic expression, a character constant, or a logical expression
v	Numeric variable, array element, or record field

Assigning logicals to numerics is allowed, but nonstandard, and may not be portable. The resultant data type is, of course, the data type of v.

Execution of an arithmetic assignment statement causes the evaluation of the expression e, and conversion to the type of v (if types differ), and assignment of v with the resulting value typed according to the table below.

Character constants can be assigned to variables of type integer or real. Such a constant can be a Hollerith constant or a string in apostrophes or quotes. The characters are transferred to the variables without any conversion of data. This practice is nonstandard and may not be portable.

Type of v	Conversion of e
INTEGER*2, INTEGER*4, or INTEGER*8 REAL REAL*8 REAL*16 (SPARC only) DOUBLE PRECISION COMPLEX*8 COMPLEX*16 COMPLEX*32 (SPARC only)	INT(e) REAL(e) DBLE(e) QREAL(e) (SPARC only) DBLE(e) CMPLX(e) DCMPLX(e) QCMPLX(e) (SPARC only)

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Note – Compiling with any of the options -i2, -dbl, -r8, or -xtypemap will have an effect on the assumed type of e. This is discussed in Chapter 2. See also the Fortran User's Guide for a description of these options.

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Example: Arithmetic assignment:

INTEGER I2*2, J2*2, I4*4 LOGICAL L1, L2 REAL R4*4, R16*16 DOUBLE PRECISION DP COMPLEX C8, C16*16 J2 = 29002 I2 = J2 I4 = (I2 * 2) + 1 DP = 6.4D0 QP = 9.8Q1 R4 = DP R16 = QP C8 = R1 C8 = ( 3.0, 5.0 ) I2 = C8 C16 = C8 C8 = L1 R4 = L2

Character Expressions

A character expression is an expression whose operands have the character type. It evaluates to a single value of type character, with a size of one or more characters. The only character operator is the concatenation operator, //.

Expression	Meaning
a // z	Concatenate a with z.

The result of concatenating two strings is a third string that contains the characters of the left operand followed immediately by the characters of the right operand. The value of a concatenation operation a//z is a character string whose value is the value of a concatenated on the right with the value of z, and whose length is the sum of the lengths of a and z.

The operands can be any of the following kinds of data items:

• Character constant
• Character variable
• Character array element
• Character function
• Substring
• Structured record field (if it evaluates to a scalar character data item)

Examples: Character expressions, assuming C, S, and R.C are characters:

'wxy' 'AB' // 'wxy' C C // S C(4:7) R.C

Note the following (nonstandard) exceptions:

n Control characters--One way to enter control characters is to hold down the Control key and press another key. Most control characters can be entered this way, but not Control-A, Control-B, Control-C, or Control-J.

Example: A valid way to enter a Control-C:

CHARACTER etx etx = CHAR(3)

n Multiple byte characters--Multiple byte characters, such as Kanji, are allowed in comments and strings.

Character String Assignment

The form of the character string assignment is:

v = e
e	Expression giving the value to be assigned
v	Variable, array element, substring, or character record field

The meaning of character assignment is to copy characters from the right to the left side.

Execution of a character assignment statement causes evaluation of the character expression and assignment of the resulting value to v.

• If e is longer than v, characters on the right are truncated.
• If e is shorter than v, blank characters are padded on the right.

Example: The following program below displays joined:

CHARACTER A*4, B*2, C*8 A = 'join' B = 'ed' C = A // B PRINT *, C END

Also, this program displays the equal string:

IF ( ('ab' // 'cd') .EQ. 'abcd' ) PRINT *, 'equal' END

Example: Character assignment:

CHARACTER BELL*1, C2*2, C3*3, C5*5, C6*6 REAL Z C2 = 'z' C3 = 'uvwxyz' C5 = 'vwxyz' C5(1:2) = 'AB' C6 = C5 // C2 I = 'abcd' Z = 'wxyz' BELL = CHAR(7) Control Character (^G)

The results are:

Variable	Receiving Value	Comment
C2	'z'	A trailing blank
C3	'uvw'
C5	'ABxyz'
C6	'ABxyzz'	The final 'z' comes from C2
I	'abcd'
Z	'wxyz'
BELL	07 hex	Control-G, a bell

Example 4: A Hollerith assignment:

CHARACTER S*4 INTEGER I2*2, I4*4 REAL R S = 4Hwxyz I2 = 2Hyz I4 = 4Hwxyz R = 4Hwxyz

Rules of Assignment

Here are the rules for character assignments:

• If the left side is longer than the right, it is padded with trailing blanks.
• If the left side is shorter than the right, trailing characters are discarded.
• The left and right sides of a character substring assignment cannot overlap. See the Substrings .

Logical Expressions

A logical expression is a sequence of one or more logical operands and logical operators. It evaluates to a single logical value. The operators can be any of the following.

TABLE 3-4   Logical Operators

Operator	Standard Name
.AND. .OR. .NEQV. .XOR. .EQV. .NOT.	Logical conjunction Logical disjunction (inclusive OR) Logical nonequivalence Logical exclusive OR Logical equivalence Logical negation

The period delimiters are necessary.

Two logical operators cannot appear consecutively, unless the second one is the .NOT. operator.

Logical operators are evaluated according to the following precedence:

TABLE 3-5   Logical Operator Precedence

Operator	Precedence
.NOT. .AND. .OR. .NEQV.,.XOR., .EQV.	Highest Lowest

If the logical operators are of equal precedence, they are evaluated left to right.

If the logical operators appear along with the various other operators in a logical expression, the precedence is as follows.

TABLE 3-6   Operator Precedence

Operator	Precedence
Arithmetic Character Relational Logical	Highest Lowest

The following table shows the meanings of simple expressions:

TABLE 3-7   Logical Expressions and Their Meanings

Expression	Meaning
X .AND. Y X .OR. Y X .NEQV. Y X .XOR. Y X .EQV. Y .NOT. X	Both X and Y are true. Either X or Y, or both, are true. X and Y are not both true and not both false. Either X or Y is true, but not both. X and Y are both true or both false. Logical negation.

Logical operations on operands of different sizes result in a logical value promoted to the size of the largest operand. For example L2.AND.L4 gives a LOGICAL*4 result if L2 is LOGICAL*2 and L4 is LOGICAL*4.

BYTE variables are treated the same as LOGICAL*1.

Logical Assignment

This is the syntax for the assignment of the value of a logical expression to a logical variable:

v = e
e	A logical expression, an integer between -128 and 127, or a single character constant
v	A logical variable, array element, or record field

Execution of a logical assignment statement causes evaluation of the logical expression e and assignment of the resulting value to v. If e is a logical expression, rather than an integer between -128 and 127, or a single character constant, then e must have a value of either true or false.

Logical expressions of any size can be assigned to logical variables of any size.

Assigning numerics to logicals is allowed. (All non-zero values are treated as .TRUE., and zero is .FALSE.) This practice is nonstandard, however, and is not portable.

Example: A logical assignment:

LOGICAL B1*1, B2*1 LOGICAL L3, L4 B2 = B1 B1 = L3 L4 = .TRUE.

Relational Operator

A relational operator compares two arithmetic expressions, or two character expressions, and evaluates to a single logical value. The operators can be any of the following:

TABLE 3-8   Relational Operators

Operator	Meaning
.LT. .LE. .EQ. .NE. .GT. .GE.	Less than Less than or equal Equal Not equal Greater than Greater than or equal

The period delimiters are necessary.

All relational operators have equal precedence. Character and arithmetic operators have higher precedence than relational operators.

For a relational expression, first each of the two operands is evaluated, and then the two values are compared. If the specified relationship holds, then the value is true; otherwise, it is false.

Example: Relational operators:

NODE .GE. 0 X .LT. Y U*V .GT. U-V M+N .GT. U-V      Mixed mode: integer M+N is promoted to real STR1 .LT. STR2    STR1 and STR2 are character type S .EQ. 'a'        S is character type

For character relational expressions:

• "Less than" means "precedes in the ASCII collating sequence."
• If one operand is shorter than the other, the shorter one is padded on the right with blanks to the length of the longer.

Constant Expressions

A constant expression is made up of explicit constants and parameters and the FORTRAN operators. Each operand is either itself another constant expression, a constant, a symbolic name of a constant, or one of the intrinsic functions called with constant arguments.

Examples: Constant expressions:

PARAMETER (L=29002), (P=3.14159), (C='along the ') PARAMETER ( I=L*2, V=4.0*P/3.0, S=C//'riverrun' ) PARAMETER ( M=MIN(I,L), IA=ICHAR('A') ) PARAMETER ( Q=6.4Q6, D=2.3D9 ) K = 66 * 80 VOLUME = V*10**3 DO I = 1, 20*3

There are a few restrictions on constant expressions:

• Constant expressions are permitted wherever a constant is allowed, except they are not allowed in DATA or standard FORMAT statements.
• Constant expressions are permitted in variable format expressions.
• Exponentiation to a floating-point power is not allowed; a warning is issued.

Example: Exponentiation to a floating-point power is not allowed:

demo% cat ConstExpr.f parameter (T=2.0*(3.0**2.5)) write(*,*) t end demo% f77 ConstExpr.f ConstExpr.f: MAIN: "ConstExpr.f", line 1: Warning: parameter t set to a nonconstant demo% a.out 31.1769 demo%

Record Assignment

The general form of record assignment is:

v = e
e	A record or record field
v	A record or record field

Both e and v must have the same structure. That is, each must have the same number of fields, and corresponding fields must be of the same type and size.

Example: A record assignment and a record-field assignment:

STRUCTURE /PRODUCT/ INTEGER*4 ID CHARACTER*16 NAME CHARACTER*8 MODEL REAL*4 COST REAL*4 PRICE END STRUCTURE RECORD /PRODUCT/ CURRENT, PRIOR, NEXT, LINE(10) ... CURRENT = NEXT LINE(1) = CURRENT WRITE ( 9 ) CURRENT NEXT.ID = 82

In the above example, the first assignment statement copies one whole record (all five fields) to another record; the second assignment statement copies a whole record into the first element of an array of records; the WRITE statement writes a whole record; and the last statement sets the ID of one record to 82.

Evaluation of Expressions

The following restrictions apply to all arithmetic, character, relational, and logical expressions:

• If you reference any one of these items in an expression, variable, array element, character substring, record field, pointer, or function, then that item must be defined at the time the reference is executed.
• An integer operand must be defined with an integer value, and not with a statement label value by an ASSIGN statement.
• All the characters of a substring that are referenced must be defined at the time the reference is executed.
• The execution of a function reference must not alter the value of any other entity within the same statement.
• The execution of a function reference must not alter the value of any entity that affects the value of any other function reference in the same statement.