92 lines
No EOL
4.4 KiB
NASM
92 lines
No EOL
4.4 KiB
NASM
; ========================================================================================
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; GCD.asm - Greatest Common Divisor Using Euclidean Algorithm
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; ========================================================================================
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; This program implements the Euclidean algorithm to find the Greatest Common
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; Divisor (GCD) of two numbers. The Euclidean algorithm is based on the principle
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; that GCD(a, b) = GCD(b, a mod b), and it repeats this process until b = 0.
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; When b = 0, the GCD is the value of a.
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AREA RESET, DATA, READONLY ; Define a read-only data section for the vector table
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EXPORT __Vectors ; Export the vector table for external linking
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__Vectors ; Start of the vector table
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DCD 0x10001000 ; Stack pointer initial value (points to top of stack)
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DCD Reset_Handler ; Address of the reset handler (program entry point)
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ALIGN ; Ensure proper alignment for the next section
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AREA MYCODE, CODE, READONLY ; Define the code section as read-only
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ENTRY ; Mark the entry point of the program
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EXPORT Reset_Handler ; Export the reset handler function
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; ========================================================================================
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; Reset_Handler - Main program execution
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; ========================================================================================
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; Algorithm Overview:
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; 1. Initialize two numbers in registers R0 and R1 (48 and 18 in this example)
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; 2. Enter the Euclidean algorithm loop:
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; a. Compare the two numbers
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; b. If equal, GCD is found (algorithm complete)
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; c. If R0 > R1, subtract R1 from R0 (replace larger with difference)
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; d. If R0 < R1, subtract R0 from R1 (replace larger with difference)
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; e. Repeat until both numbers are equal
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; 3. Store the GCD result to memory
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; 4. Enter infinite loop for program termination
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Reset_Handler
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; Step 1: Initialize the two numbers for GCD calculation
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; R0 and R1 hold the two numbers to find GCD of
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MOV r0, #48 ; R0 = 48 (first number)
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MOV r1, #18 ; R1 = 18 (second number)
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; Step 2: Main Euclidean algorithm loop
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GCD_Loop
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; Compare the two numbers to determine which is larger
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CMP r0, r1 ; Compare R0 and R1, set condition flags
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; If R0 == R1, we have found the GCD
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BEQ GCD_Done ; Branch to GCD_Done if R0 == R1
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; If R0 > R1 (GT condition), subtract R1 from R0
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BGT GT_A_B ; Branch to GT_A_B if R0 > R1
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; If R0 < R1, subtract R0 from R1 (replace larger with difference)
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SUB r1, r1, r0 ; R1 = R1 - R0 (R1 was larger, now smaller)
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B GCD_Loop ; Branch back to GCD_Loop
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; Handle case where R0 > R1
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GT_A_B
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SUB r0, r0, r1 ; R0 = R0 - R1 (R0 was larger, now smaller)
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B GCD_Loop ; Branch back to GCD_Loop
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; Step 3: GCD calculation complete
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; When we reach here, R0 == R1 and contains the GCD
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GCD_Done
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; Load address of result storage into R2
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LDR r2, =result ; R2 = address of result storage
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; Store the GCD (in R0) to memory
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STR r0, [r2] ; Store GCD value to [R2]
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; Step 4: Program termination
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; Enter infinite loop to stop program execution
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LoopForever
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B LoopForever ; Branch to LoopForever (infinite loop)
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ALIGN ; Ensure proper alignment for data section
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AREA MYDATA, DATA, READWRITE ; Define a read-write data section
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; ========================================================================================
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; Data Section - Input Numbers and Result Storage
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; ========================================================================================
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; numA: First number for GCD calculation (48 in this example)
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; numB: Second number for GCD calculation (18 in this example)
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; GCD(48, 18) = 6, as calculated by the Euclidean algorithm:
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; GCD(48, 18) -> GCD(18, 48-18=30) -> GCD(30, 18) -> GCD(18, 30-18=12)
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; -> GCD(12, 18) -> GCD(18, 12) -> GCD(12, 18-12=6) -> GCD(6, 12)
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; -> GCD(12, 6) -> GCD(6, 12-6=0) -> GCD(6, 0) = 6
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numA DCD 48 ; First number for GCD
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numB DCD 18 ; Second number for GCD
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result DCD 0 ; Storage for the GCD result
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END ; End of the assembly program |