Hacker's Delight
1. Optimal Base = e
- Cost = log_b(M+1)*b since we assume costs is proportional to
the number of bits needed to express a different number. Then
just solve the derivative of this for 0 to obtain the minimum.
2. Newton's Method Family of Approximations
- x_(n+1) = x_n + f(x_n)/f'(x_n)
- To find sqrt(a), find roots of f(x) = x^2 - a
- Also can solve for 1/a, log(a), ...
3. Recursive Function Theory ("Formula Functions")
- Cutland Computability: An Introduction to
Recursive Function Theory
4. Willans' and Wormell's Prime Formulas
- Willans' utilizes Willson's Theorem