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scalable power

This commit is contained in:
Aurelien Rebourg 2020-01-17 07:18:19 +01:00
parent bd2b51628e
commit 1593431898
1 changed files with 30 additions and 4 deletions
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34
Source/scalable/scalable_power.ml
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@ -11,13 +11,25 @@ open Scalable_basic_arithmetics
@param x base, a bitarray
@param n exponent, a non-negative bitarray
*)
let pow x n = []
let pow x n =
let rec pow_rec x1 n =
match n with
[] -> x1
| n -> pow_rec (mult_b x1 x) (diff_b n [0;1])
in pow_rec [0;1] n;;
(** Fast bitarray exponentiation function. Logarithmic complexity.
@param x base, a bitarray
@param n exponent, a non-negative bitarray
*)
let power x n = []
let power x n =
if n = [] then [0;1] else
let rec power_rec x1 n =
match n with
[0;1] -> x1
| n when mod_b n [0;0;1] = [] -> power_rec (mult_b x1 x1) (quot_b n [0;0;1])
| n -> mult_b x1 (power_rec (mult_b x1 x1) (quot_b (diff_b n [0;1]) [0;0;1]))
in power_rec x n;;
(* Modular expnonentiation ; modulo a given natural (bitarray without
sign bits).
@ -28,7 +40,17 @@ let power x n = []
@param n exponent, a non-negative bitarray
@param m modular base, a positive bitarray
*)
let mod_power x n m = []
let mod_power x n m =
if n = [] then
[0;1]
else
let rec mod_power_rec c e =
let c = mod_b (mult_b x c) m
in if (<<) e n then
mod_power_rec c (add_b e [0;1])
else
c
in mod_power_rec [0;1] [0;1];;
(* Making use of Fermat Little Theorem for very quick exponentation
modulo prime number.
@ -40,4 +62,8 @@ let mod_power x n m = []
@param n exponent, a non-negative bitarray
@param p prime modular base, a positive bitarray
*)
let prime_mod_power x n p = []
let prime_mod_power x n p =
if x = [] then
[]
else
mod_power x (mod_b n (diff_b p [0;1])) p;;