Arbitrary Precision Calculator (APC)

A command-line calculator written in C that performs arithmetic operations — addition, subtraction, multiplication, and division — on integers of any size, far beyond the 64-bit limit of standard C data types.

Each number is stored digit-by-digit in a Doubly Linked List, enabling precise computation through manual digit-level arithmetic.

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✨ Features

• Addition of arbitrarily large integers
• Subtraction with correct sign and borrow handling
• Multiplication using long-multiplication with partial products
• Division using repeated subtraction (returns integer quotient)
• Full support for negative numbers (- sign prefix)
• Division-by-zero detection with error message
• Leading zero removal from results
• Complete memory cleanup after every operation

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🔗 Data Structure

Doubly Linked List (Dlist)

head → [d1] ↔ [d2] ↔ [d3] ↔ ... ↔ [dn] ← tail
        MSB                            LSB

• Each node stores ONE digit
• Arithmetic traversal goes tail → head (LSB to MSB)
• Result digits are inserted at front to maintain correct order

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🗂️ Project Structure

apc/
├── apc.h             # Dlist struct definition + all function prototypes
├── main.c            # CLI argument parsing, sign detection, operator dispatch
├── apc.c             # Core list utilities: insert, delete, compare, print
├── addition.c        # Tail-to-head addition with carry
├── subtraction.c     # Tail-to-head subtraction with borrow
├── multiplication.c  # Long multiplication with partial product accumulation
├── division.c        # Repeated subtraction-based integer division
└── Makefile

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⚙️ Build & Run

Compile

make

Usage

./apc <operand1> <operator> <operand2>

Symbol	Operation
+	Addition
-	Subtraction
*	Multiplication
x	Multiplication (alternate)
/	Division

⚠️ Wrap * in quotes to prevent shell expansion: ./apc 99 '*' 99

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🧪 Sample Test Cases

Addition

./apc 10 + 20           # → 30
./apc 999 + 1           # → 1000
./apc -10 + -20         # → -30
./apc -10 + 5           # → -5
./apc 0 + 0             # → 0

Subtraction

./apc 50 - 20           # → 30
./apc 1000 - 1          # → 999
./apc 20 - 50           # → -30
./apc 123 - 123         # → 0
./apc -50 - 20          # → -70

Multiplication

./apc 5 '*' 4           # → 20
./apc 99 '*' 99         # → 9801
./apc 0 '*' 123         # → 0
./apc -10 '*' 5         # → -50
./apc -10 '*' -5        # → 50

Division

./apc 100 / 5           # → 20
./apc 7 / 2             # → 3
./apc 5 / 10            # → 0
./apc -20 / 5           # → -4
./apc 10 / 0            # → Division failed

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🧠 How Each Operation Works

Addition

• Traverse both lists from tail → head (LSB first)
• At each step: sum = d1 + d2 + carry, store sum % 10, update carry = sum / 10
• Insert each result digit at the front of the result list
• Loop continues while either list has digits OR carry is non-zero (handles 999 + 1 → 1000)

Subtraction

• Assumes head1 >= head2 (caller ensures this via compare_list())
• Traverse from tail → head with borrow tracking
• If d1 < d2: borrow from next digit (d1 += 10, borrow = 1)

Multiplication

• For each digit of operand2 (tail → head), multiply against all digits of operand1
• Each partial product gets positional zero-padding (place value)
• Partial products are accumulated using the addition function

Division

• Checks for zero divisor before starting
• If dividend < divisor: quotient is 0
• Repeatedly subtracts divisor from dividend, counting iterations
• Count is converted to a digit list as the quotient

Sign Handling

• Signs are detected from the leading - character before list conversion
• Result sign is negative only if signs differ (for * and /) or as computed (for + and -)
• -0 is printed as 0

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🧹 Memory Management

Every code path (including error paths like division by zero) calls delete_list() on all lists before returning. No memory leaks.

make clean

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👩‍💻 Author

Suchithra S
B.E. ECE — Gopalan College of Engineering & Management, VTU (2025)
Advanced Embedded Systems Training — Emertxe Information Technologies, Bengaluru
GitHub: github.com/suchithrasr
LinkedIn: linkedin.com/in/suchithrasr