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Fast exponentiation by squaring with modular reduction:
let rec pow_mod base exp m =
if exp = 0 then 1
else if exp mod 2 = 0 then
let half = pow_mod base (exp / 2) m in
(half * half) mod m
else
(base * pow_mod base (exp - 1) m) mod m
Even exponent halves and squares (O(log n)); odd decrements and
multiplies. mod-reduction at each step keeps intermediates bounded.
pow_mod 2 30 1000003 + pow_mod 3 20 13 + pow_mod 5 17 100 = 738639
84 baseline programs total.
12 lines
259 B
OCaml
12 lines
259 B
OCaml
let rec pow_mod base exp m =
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if exp = 0 then 1
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else if exp mod 2 = 0 then
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let half = pow_mod base (exp / 2) m in
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(half * half) mod m
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else
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(base * pow_mod base (exp - 1) m) mod m
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;;
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pow_mod 2 30 1000003 + pow_mod 3 20 13 + pow_mod 5 17 100
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