Recursive Power Calculator for MIPS

Calculator

Formula Used

Base case: x⁰ = 1

Simple recursive case: xⁿ = x × x^{n - 1}, when n > 0

Negative exponent: x^-n = 1 / xⁿ, when x is not zero

Fast recursive case: xⁿ = x^n/2 × x^n/2, when n is even

Odd fast case: xⁿ = x × x^floor(n/2) × x^floor(n/2)

How to Use This Calculator

1. Enter the base value in the x field.
2. Enter an integer exponent in the n field.
3. Select simple recursion for classic MIPS practice.
4. Select squaring recursion for fewer calls.
5. Choose the decimal precision for the final output.
6. Press the calculate button.
7. Review the result, trace, calls, depth, and stack estimate.
8. Use CSV or PDF export for records.

Example Data Table

MIPS Recursive Function Pattern

This sample shows a classic integer routine for non-negative exponents. For negative exponents, use a floating point design or reciprocal logic outside this integer routine.

# Recursive integer power: pow_rec(x, n)
# Input:  $a0 = x, $a1 = n
# Output: $v0 = x^n
# Note: this version handles n >= 0.

pow_rec:
    addiu $sp, $sp, -12
    sw    $ra, 8($sp)
    sw    $a0, 4($sp)
    sw    $a1, 0($sp)

    beq   $a1, $zero, pow_base

    addiu $a1, $a1, -1
    jal   pow_rec

    lw    $a0, 4($sp)
    mul   $v0, $a0, $v0
    j     pow_done

pow_base:
    li    $v0, 1

pow_done:
    lw    $a1, 0($sp)
    lw    $a0, 4($sp)
    lw    $ra, 8($sp)
    addiu $sp, $sp, 12
    jr    $ra

Learning Article

Understanding Recursive Power

Recursive power logic is a core topic in assembly study. It shows how a small rule can repeat until a base case stops the process. This calculator turns that idea into a clear conversion tool. It converts a base and integer exponent into a final power value, while also showing the recursive path.

How the Rule Works

The standard rule is simple. When n equals zero, the result is one. When n is positive, the function multiplies x by the answer for n minus one. When n is negative, the tool first solves the positive exponent. Then it returns the reciprocal. This mirrors the thinking used before writing a MIPS routine.

Why Stack Frames Matter

MIPS recursion needs careful stack handling. A function should save the return address. It may also save arguments and temporary values. After the recursive call returns, the function restores saved data. Then it completes the pending multiplication. Missing one save or restore step can break the program. The trace helps you see those frames before coding.

Fast Recursion Option

The squaring option reduces calls. It splits the exponent in half. If n is even, it squares the half result. If n is odd, it multiplies one extra x. This method is faster for large exponents. It is useful when you want fewer recursive calls and fewer stack frames.

Practical Study Use

Use the calculator during homework checks, lab planning, and code reviews. Try small numbers first. Compare the trace with your assembly comments. Then test negative and zero exponents. Results are rounded with your selected precision. CSV and PDF exports help you save examples for reports.

Important Limits

This page also highlights limits. Floating point values can lose tiny precision. Very large powers can overflow normal numeric ranges. MIPS integer registers have stricter limits. Treat the output as a learning guide. For exact arbitrary precision work, use a library designed for big numbers. For assembly practice, the steps and formulas are the most important parts. It can also support teaching. Instructors may create repeatable test cases. Students may compare simple recursion with faster recursion. Each case exposes a different stack shape. That makes debugging easier. It also builds confidence before moving into registers, labels, jumps, and return paths during lab time.

FAQs