Number Theory
Algorithms for number theoretical calculations are studied in computational number theory.
Operation | Input | Output | Algorithm | Complexity |
---|---|---|---|---|
Greatest common divisor | Two n-digit numbers | One number with at most n digits | Euclidean algorithm | O(n2) |
Binary GCD algorithm | O(n2) | |||
Left/right k-ary binary GCD algorithm | O(n2/ log n) | |||
Stehlé–Zimmermann algorithm | O(log n M(n)) | |||
Schönhage controlled Euclidean descent algorithm | O(log n M(n)) | |||
Jacobi symbol | Two n-digit numbers | 0, −1, or 1 | ||
Schönhage controlled Euclidean descent algorithm | O(log n M(n)) | |||
Stehlé–Zimmermann algorithm | O(log n M(n)) | |||
Factorial | A fixed-size number m | One O(m log m)-digit number | Bottom-up multiplication | O(m2 log m) |
Binary splitting | O(log m M(m log m)) | |||
Exponentiation of the prime factors of m | O(log log m M(m log m)), O(M(m log m)) |
Read more about this topic: Computational Complexity Of Mathematical Operations
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