COBOL Tutorial

COBOL Arithmetic Operations

Progress0 of 0 lessons

Introduction to COBOL Arithmetic

Arithmetic operations in COBOL are fundamental to business applications, providing precise mathematical calculations essential for financial, statistical, and computational tasks. COBOL's arithmetic capabilities are designed for accuracy and reliability in business environments.

COBOL provides several methods for performing arithmetic:

ADD Statement: Addition operations with multiple operands
SUBTRACT Statement: Subtraction operations
MULTIPLY Statement: Multiplication operations
DIVIDE Statement: Division operations with remainder handling
COMPUTE Statement: Complex expressions with standard operators
Intrinsic Functions: Advanced mathematical functions

Basic Arithmetic Statements

COBOL provides four basic arithmetic statements that handle the fundamental mathematical operations with built-in precision and error handling.

ADD Statement

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
IDENTIFICATION DIVISION.
PROGRAM-ID. ADD-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 NUMBERS.
   05 FIRST-NUMBER    PIC 9(5)V99 VALUE 1234.56.
   05 SECOND-NUMBER    PIC 9(5)V99 VALUE 567.89.
   05 THIRD-NUMBER     PIC 9(5)V99 VALUE 100.00.
   05 TOTAL-SUM        PIC 9(6)V99 VALUE ZERO.
   05 RUNNING-TOTAL    PIC 9(6)V99 VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== ADD Statement Demonstration ==="
    DISPLAY "First Number: " FIRST-NUMBER
    DISPLAY "Second Number: " SECOND-NUMBER
    DISPLAY "Third Number: " THIRD-NUMBER
    
    * Simple addition
    ADD FIRST-NUMBER TO RUNNING-TOTAL
    DISPLAY "After adding first number: " RUNNING-TOTAL
    
    * Addition with multiple operands
    ADD FIRST-NUMBER SECOND-NUMBER THIRD-NUMBER GIVING TOTAL-SUM
    DISPLAY "Sum of all three numbers: " TOTAL-SUM
    
    * Addition with ROUNDED option
    ADD FIRST-NUMBER TO RUNNING-TOTAL ROUNDED
    DISPLAY "Running total with rounding: " RUNNING-TOTAL
    
    STOP RUN.

SUBTRACT Statement

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
IDENTIFICATION DIVISION.
PROGRAM-ID. SUBTRACT-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 CALCULATIONS.
   05 GROSS-AMOUNT     PIC 9(6)V99 VALUE 5000.00.
   05 DISCOUNT         PIC 9(4)V99 VALUE 250.00.
   05 TAX-AMOUNT       PIC 9(4)V99 VALUE 300.00.
   05 NET-AMOUNT       PIC 9(6)V99 VALUE ZERO.
   05 FINAL-AMOUNT     PIC 9(6)V99 VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== SUBTRACT Statement Demonstration ==="
    DISPLAY "Gross Amount: $" GROSS-AMOUNT
    DISPLAY "Discount: $" DISCOUNT
    DISPLAY "Tax Amount: $" TAX-AMOUNT
    
    * Simple subtraction
    SUBTRACT DISCOUNT FROM GROSS-AMOUNT GIVING NET-AMOUNT
    DISPLAY "Amount after discount: $" NET-AMOUNT
    
    * Multiple subtractions
    SUBTRACT DISCOUNT TAX-AMOUNT FROM GROSS-AMOUNT GIVING FINAL-AMOUNT
    DISPLAY "Final amount after all deductions: $" FINAL-AMOUNT
    
    STOP RUN.

MULTIPLY Statement

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
IDENTIFICATION DIVISION.
PROGRAM-ID. MULTIPLY-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 CALCULATIONS.
   05 BASE-PRICE       PIC 9(5)V99 VALUE 100.00.
   05 QUANTITY         PIC 9(3) VALUE 25.
   05 DISCOUNT-RATE    PIC 9V99 VALUE 0.15.
   05 TOTAL-COST       PIC 9(6)V99 VALUE ZERO.
   05 DISCOUNTED-PRICE PIC 9(5)V99 VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== MULTIPLY Statement Demonstration ==="
    DISPLAY "Base Price: $" BASE-PRICE
    DISPLAY "Quantity: " QUANTITY
    DISPLAY "Discount Rate: " DISCOUNT-RATE
    
    * Simple multiplication
    MULTIPLY BASE-PRICE BY QUANTITY GIVING TOTAL-COST
    DISPLAY "Total cost: $" TOTAL-COST
    
    * Multiplication with decimal
    MULTIPLY BASE-PRICE BY DISCOUNT-RATE GIVING DISCOUNTED-PRICE
    DISPLAY "Discount amount: $" DISCOUNTED-PRICE
    
    STOP RUN.

DIVIDE Statement

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
IDENTIFICATION DIVISION.
PROGRAM-ID. DIVIDE-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 CALCULATIONS.
   05 DIVIDEND         PIC 9(6)V99 VALUE 1000.00.
   05 DIVISOR          PIC 9(3)V99 VALUE 3.00.
   05 QUOTIENT         PIC 9(6)V99 VALUE ZERO.
   05 REMAINDER        PIC 9(3)V99 VALUE ZERO.
   05 AVERAGE          PIC 9(5)V99 VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== DIVIDE Statement Demonstration ==="
    DISPLAY "Dividend: " DIVIDEND
    DISPLAY "Divisor: " DIVISOR
    
    * Simple division
    DIVIDE DIVIDEND BY DIVISOR GIVING QUOTIENT
    DISPLAY "Quotient: " QUOTIENT
    
    * Division with remainder
    DIVIDE DIVIDEND BY DIVISOR GIVING QUOTIENT REMAINDER REMAINDER
    DISPLAY "Quotient: " QUOTIENT
    DISPLAY "Remainder: " REMAINDER
    
    * Division with ROUNDED
    DIVIDE DIVIDEND BY DIVISOR GIVING AVERAGE ROUNDED
    DISPLAY "Rounded average: " AVERAGE
    
    STOP RUN.

COMPUTE Statement

The COMPUTE statement provides the most flexible way to perform arithmetic operations, allowing complex expressions with standard mathematical operators.

Basic COMPUTE Operations

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
IDENTIFICATION DIVISION.
PROGRAM-ID. COMPUTE-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 CALCULATIONS.
   05 PRINCIPAL        PIC 9(6)V99 VALUE 10000.00.
   05 INTEREST-RATE    PIC 9V9999 VALUE 0.0750.
   05 TIME-YEARS       PIC 9(2) VALUE 5.
   05 SIMPLE-INTEREST  PIC 9(6)V99 VALUE ZERO.
   05 COMPOUND-INTEREST PIC 9(8)V99 VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== COMPUTE Statement Demonstration ==="
    DISPLAY "Principal: $" PRINCIPAL
    DISPLAY "Interest Rate: " INTEREST-RATE
    DISPLAY "Time (years): " TIME-YEARS
    
    * Simple interest calculation
    COMPUTE SIMPLE-INTEREST = PRINCIPAL * INTEREST-RATE * TIME-YEARS
    DISPLAY "Simple Interest: $" SIMPLE-INTEREST
    
    * Compound interest calculation
    COMPUTE COMPOUND-INTEREST = PRINCIPAL * 
                                (1 + INTEREST-RATE) ** TIME-YEARS - PRINCIPAL
    DISPLAY "Compound Interest: $" COMPOUND-INTEREST
    
    STOP RUN.

Complex COMPUTE Expressions

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
IDENTIFICATION DIVISION.
PROGRAM-ID. COMPLEX-COMPUTE-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 BUSINESS-CALCULATIONS.
   05 REVENUE          PIC 9(7)V99 VALUE 50000.00.
   05 COST-OF-GOODS    PIC 9(6)V99 VALUE 20000.00.
   05 OPERATING-COSTS  PIC 9(6)V99 VALUE 15000.00.
   05 GROSS-PROFIT     PIC 9(7)V99 VALUE ZERO.
   05 OPERATING-PROFIT PIC 9(7)V99 VALUE ZERO.
   05 PROFIT-MARGIN    PIC 9V9999 VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== Complex COMPUTE Expressions ==="
    DISPLAY "Revenue: $" REVENUE
    DISPLAY "Cost of Goods: $" COST-OF-GOODS
    DISPLAY "Operating Costs: $" OPERATING-COSTS
    
    * Multiple calculations with parentheses
    COMPUTE GROSS-PROFIT = REVENUE - COST-OF-GOODS
    DISPLAY "Gross Profit: $" GROSS-PROFIT
    
    COMPUTE OPERATING-PROFIT = REVENUE - COST-OF-GOODS - OPERATING-COSTS
    DISPLAY "Operating Profit: $" OPERATING-PROFIT
    
    * Complex expression with division
    COMPUTE PROFIT-MARGIN = (REVENUE - COST-OF-GOODS - OPERATING-COSTS) / REVENUE
    DISPLAY "Profit Margin: " PROFIT-MARGIN
    
    STOP RUN.

Mathematical Intrinsic Functions

COBOL provides intrinsic functions for advanced mathematical operations, extending the language's computational capabilities.

Common Mathematical Functions

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
IDENTIFICATION DIVISION.
PROGRAM-ID. MATH-FUNCTIONS-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 MATH-CALCULATIONS.
   05 INPUT-VALUE      PIC S9(5)V99 VALUE -123.45.
   05 ABSOLUTE-VALUE   PIC 9(5)V99 VALUE ZERO.
   05 SQUARE-ROOT      PIC 9(5)V99 VALUE ZERO.
   05 ROUNDED-VALUE    PIC 9(5)V99 VALUE ZERO.
   05 LOGARITHM        PIC 9(5)V99 VALUE ZERO.
 
01 TRIGONOMETRIC-CALC.
   05 ANGLE-DEGREES    PIC 9(3)V99 VALUE 45.00.
   05 ANGLE-RADIANS    PIC 9(5)V99 VALUE ZERO.
   05 SINE-VALUE       PIC S9V9999 VALUE ZERO.
   05 COSINE-VALUE     PIC S9V9999 VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== Mathematical Intrinsic Functions ==="
    DISPLAY "Input Value: " INPUT-VALUE
    
    * Absolute value
    COMPUTE ABSOLUTE-VALUE = FUNCTION ABS(INPUT-VALUE)
    DISPLAY "Absolute Value: " ABSOLUTE-VALUE
    
    * Square root
    COMPUTE SQUARE-ROOT = FUNCTION SQRT(ABSOLUTE-VALUE)
    DISPLAY "Square Root: " SQUARE-ROOT
    
    * Rounding
    COMPUTE ROUNDED-VALUE = FUNCTION ROUND(INPUT-VALUE, 1)
    DISPLAY "Rounded Value: " ROUNDED-VALUE
    
    * Logarithm
    COMPUTE LOGARITHM = FUNCTION LOG(ABSOLUTE-VALUE)
    DISPLAY "Natural Logarithm: " LOGARITHM
    
    DISPLAY " "
    DISPLAY "=== Trigonometric Functions ==="
    DISPLAY "Angle (degrees): " ANGLE-DEGREES
    
    * Convert degrees to radians
    COMPUTE ANGLE-RADIANS = ANGLE-DEGREES * 3.14159 / 180
    
    * Trigonometric functions
    COMPUTE SINE-VALUE = FUNCTION SIN(ANGLE-RADIANS)
    COMPUTE COSINE-VALUE = FUNCTION COS(ANGLE-RADIANS)
    
    DISPLAY "Sine: " SINE-VALUE
    DISPLAY "Cosine: " COSINE-VALUE
    
    STOP RUN.

Decimal Arithmetic and Precision

COBOL's strength in decimal arithmetic makes it ideal for financial calculations where precision is critical.

Precision Control

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
IDENTIFICATION DIVISION.
PROGRAM-ID. DECIMAL-PRECISION-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 FINANCIAL-CALCULATIONS.
   05 PRINCIPAL        PIC 9(8)V99 VALUE 100000.00.
   05 INTEREST-RATE    PIC 9V999999 VALUE 0.075000.
   05 MONTHLY-PAYMENT  PIC 9(6)V99 VALUE ZERO.
   05 TOTAL-PAYMENTS   PIC 9(8)V99 VALUE ZERO.
   05 INTEREST-PAID    PIC 9(8)V99 VALUE ZERO.
 
01 PRECISION-CONTROL.
   05 MONTHLY-RATE     PIC 9V999999 VALUE ZERO.
   05 PAYMENT-FACTOR   PIC 9(6)V999999 VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== Decimal Precision Control ==="
    DISPLAY "Principal: $" PRINCIPAL
    DISPLAY "Annual Interest Rate: " INTEREST-RATE
    
    * Calculate monthly interest rate with high precision
    COMPUTE MONTHLY-RATE = INTEREST-RATE / 12
    DISPLAY "Monthly Interest Rate: " MONTHLY-RATE
    
    * Calculate payment factor with precision
    COMPUTE PAYMENT-FACTOR = MONTHLY-RATE * (1 + MONTHLY-RATE) ** 360 / 
                             ((1 + MONTHLY-RATE) ** 360 - 1)
    
    * Calculate monthly payment
    COMPUTE MONTHLY-PAYMENT = PRINCIPAL * PAYMENT-FACTOR ROUNDED
    DISPLAY "Monthly Payment: $" MONTHLY-PAYMENT
    
    * Calculate total payments
    COMPUTE TOTAL-PAYMENTS = MONTHLY-PAYMENT * 360
    DISPLAY "Total Payments: $" TOTAL-PAYMENTS
    
    * Calculate total interest
    COMPUTE INTEREST-PAID = TOTAL-PAYMENTS - PRINCIPAL
    DISPLAY "Total Interest Paid: $" INTEREST-PAID
    
    STOP RUN.

Performance Optimization

Optimizing arithmetic operations is crucial for high-performance applications, especially those processing large volumes of data.

Efficient Arithmetic Techniques

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
IDENTIFICATION DIVISION.
PROGRAM-ID. PERFORMANCE-OPTIMIZATION-DEMO.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 OPTIMIZED-CALCULATIONS.
   05 BASE-AMOUNT      PIC S9(8)V99 USAGE COMP-3 VALUE 1000.00.
   05 MULTIPLIER       PIC S9(3)V99 USAGE COMP-3 VALUE 1.15.
   05 RESULT-AMOUNT    PIC S9(8)V99 USAGE COMP-3 VALUE ZERO.
   05 WORK-AMOUNT      PIC S9(8)V99 USAGE COMP-3 VALUE ZERO.
 
01 PERFORMANCE-COUNTERS.
   05 CALCULATION-COUNT PIC 9(6) VALUE 100000.
   05 LOOP-INDEX       PIC 9(6) VALUE ZERO.
 
PROCEDURE DIVISION.
    DISPLAY "=== Performance Optimization Demo ==="
    DISPLAY "Performing " CALCULATION-COUNT " calculations"
    
    * Optimized arithmetic using COMP-3 for better performance
    PERFORM VARYING LOOP-INDEX FROM 1 BY 1
       UNTIL LOOP-INDEX > CALCULATION-COUNT
       
       * Use COMPUTE for complex calculations
       COMPUTE WORK-AMOUNT = BASE-AMOUNT * MULTIPLIER
       
       * Accumulate results efficiently
       ADD WORK-AMOUNT TO RESULT-AMOUNT
       
       * Increment base amount for next iteration
       ADD 1.00 TO BASE-AMOUNT
    END-PERFORM
    
    DISPLAY "Final result: " RESULT-AMOUNT
    DISPLAY "Performance optimization completed"
    
    STOP RUN.

Error Handling in Arithmetic

Proper error handling ensures arithmetic operations complete successfully and handle exceptional conditions gracefully.

Arithmetic Error Handling

cobol

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
IDENTIFICATION DIVISION.
PROGRAM-ID. ARITHMETIC-ERROR-HANDLING.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 ERROR-CONTROL.
   05 DIVIDEND         PIC 9(6)V99 VALUE 1000.00.
   05 DIVISOR          PIC 9(3)V99 VALUE 0.00.
   05 RESULT           PIC 9(6)V99 VALUE ZERO.
   05 ERROR-FLAG       PIC X(1) VALUE 'N'.
 
01 ERROR-MESSAGES.
   05 DIV-ZERO-MSG     PIC X(30) VALUE "Error: Division by zero".
   05 OVERFLOW-MSG     PIC X(30) VALUE "Error: Arithmetic overflow".
   05 UNDERFLOW-MSG    PIC X(30) VALUE "Error: Arithmetic underflow".
 
PROCEDURE DIVISION.
    DISPLAY "=== Arithmetic Error Handling Demo ==="
    
    PERFORM TEST-DIVISION-BY-ZERO
    PERFORM TEST-OVERFLOW-CONDITION
    PERFORM TEST-UNDERFLOW-CONDITION
    
    STOP RUN.
 
TEST-DIVISION-BY-ZERO.
    DISPLAY "Testing division by zero..."
    MOVE 0.00 TO DIVISOR
    
    DIVIDE DIVIDEND BY DIVISOR GIVING RESULT
       ON SIZE ERROR
          DISPLAY DIV-ZERO-MSG
          MOVE 'Y' TO ERROR-FLAG
       NOT ON SIZE ERROR
          DISPLAY "Division successful: " RESULT
    END-DIVIDE.
 
TEST-OVERFLOW-CONDITION.
    DISPLAY "Testing overflow condition..."
    MOVE 999999.99 TO DIVIDEND
    MOVE 0.01 TO DIVISOR
    
    MULTIPLY DIVIDEND BY 1000 GIVING RESULT
       ON SIZE ERROR
          DISPLAY OVERFLOW-MSG
       NOT ON SIZE ERROR
          DISPLAY "Multiplication successful: " RESULT
    END-MULTIPLY.
 
TEST-UNDERFLOW-CONDITION.
    DISPLAY "Testing underflow condition..."
    MOVE 0.001 TO DIVIDEND
    MOVE 1000.00 TO DIVISOR
    
    DIVIDE DIVIDEND BY DIVISOR GIVING RESULT
       ON SIZE ERROR
          DISPLAY UNDERFLOW-MSG
       NOT ON SIZE ERROR
          DISPLAY "Division successful: " RESULT
    END-DIVIDE.

Best Practices for Arithmetic Operations

Following best practices ensures accurate, efficient, and maintainable arithmetic operations in COBOL applications.

Design Guidelines

Use appropriate PICTURE clauses for precision requirements
Choose optimal USAGE clauses for performance
Implement proper error handling for all operations
Use COMPUTE for complex expressions
Validate input data before calculations

Performance Tips

Use COMP-3 for decimal arithmetic when possible
Minimize data movement between fields
Use ROUNDED only when necessary
Avoid unnecessary conversions
Profile arithmetic-intensive code sections

FAQ

What are the basic arithmetic operations in COBOL?

COBOL provides four basic arithmetic operations: ADD (addition), SUBTRACT (subtraction), MULTIPLY (multiplication), and DIVIDE (division). These operations can be used with multiple operands and support various data types including numeric literals and data items.

What is the COMPUTE statement in COBOL?

The COMPUTE statement allows complex mathematical expressions using standard arithmetic operators (+, -, *, /, **). It provides more flexibility than individual ADD, SUBTRACT, MULTIPLY, and DIVIDE statements and supports parentheses for grouping operations.

How do you handle decimal arithmetic in COBOL?

COBOL handles decimal arithmetic using PICTURE clauses with V (implied decimal point) and appropriate USAGE clauses. The language automatically handles decimal alignment and precision, making it ideal for financial calculations.

What are COBOL intrinsic functions for mathematics?

COBOL provides intrinsic functions like FUNCTION ABS (absolute value), FUNCTION SQRT (square root), FUNCTION SIN/COS/TAN (trigonometric functions), FUNCTION LOG (logarithm), and FUNCTION ROUND (rounding) for advanced mathematical operations.

How do you optimize arithmetic performance in COBOL?

Arithmetic performance optimization includes using appropriate USAGE clauses (COMP-3, COMP-5), minimizing data movement, using COMPUTE for complex expressions, avoiding unnecessary conversions, and choosing efficient data types for calculations.

COBOL Tutorial

COBOL Arithmetic Operations

Introduction to COBOL Arithmetic

Basic Arithmetic Statements

ADD Statement

SUBTRACT Statement

MULTIPLY Statement

DIVIDE Statement

COMPUTE Statement

Basic COMPUTE Operations

Complex COMPUTE Expressions

Mathematical Intrinsic Functions

Common Mathematical Functions

Decimal Arithmetic and Precision

Precision Control

Performance Optimization

Efficient Arithmetic Techniques

Error Handling in Arithmetic

Arithmetic Error Handling

Best Practices for Arithmetic Operations

Design Guidelines

Performance Tips

FAQ

What are the basic arithmetic operations in COBOL?

What is the COMPUTE statement in COBOL?

How do you handle decimal arithmetic in COBOL?

What are COBOL intrinsic functions for mathematics?

How do you optimize arithmetic performance in COBOL?

Data Types

Picture Clause

Usage Clause

Performance Optimization