Toom-Cook Multiplication Calculator
Multiply large integers using the Toom-Cook (Toom-3) algorithm.
Enter Numbers
Toom-3 Overview
1. Split each number into 3 parts
2. Evaluate polynomials at 5 points
3. Multiply pointwise (5 multiplications)
4. Interpolate to get result coefficients
5. Combine with appropriate powers
Evaluation Points
t = 0, 1, -1, 2, and infinity
These 5 points determine a degree-4 polynomial uniquely.
123456 × 789012
= 102,427,763,472
Complexity Comparison
Traditional O(n²)36
Karatsuba O(n^1.58)17.1
Toom-3 O(n^1.46)13.8
Step 1: Split (k=2)
x = 12·B² + 34·B + 56
y = 78·B² + 90·B + 12
where B = 10^2 = 100
Step 2: Evaluate & Multiply
| t | p(t) | q(t) | r(t) |
|---|---|---|---|
| 0 | 56 | 12 | 672 |
| 1 | 102 | 180 | 18360 |
| -1 | 34 | 0 | 0 |
| 2 | 172 | 504 | 86688 |
| inf | 12 | 78 | 936 |
Step 3: Interpolate
r₀ = 672
r₁ = 428
r₂ = 7572
r₃ = 8752
r₄ = 936
Step 4: Combine
Result = 102,427,763,472
Verification
Direct: 97,408,265,472
Results differ!