96 lines
2.6 KiB
C
96 lines
2.6 KiB
C
#pragma once
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#include "funconfig.h"
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#include <stdbool.h>
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#include <stdint.h>
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/**
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* @brief Calculates greatest common divider of two integers using the euclidean
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* algorithm
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*
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* @param a First number
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* @param b Second number
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* @return The greatest common divider
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*/
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u64 gcd(u64 a, u64 b);
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/**
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* @brief Computes Euler's Totient function φ(n), which counts the number of
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* integers from 1 to n that are coprime to n.
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*
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* @param n The input number.
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* @return The number of integers from 1 to n that are coprime to n.
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*/
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u64 totient(u64 n);
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/**
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* @brief Computes (a * b) % m safely without overflow.
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*
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* Uses repeated addition and bit shifting to handle large values,
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* ensuring correctness even on 32-bit microcontrollers.
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*
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* @param a The first operand.
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* @param b The second operand.
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* @param m The modulus.
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* @return (a * b) % m computed safely.
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*/
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u64 mulmod(u64 a, u64 b, u64 m);
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/**
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* @brief Modular exponentiation (a^b) mod m
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*
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* @param a The base
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* @param b The exponent
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* @param m The modulus
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*/
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u64 modexp(u64 a, u64 b, u64 m);
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/**
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* @brief Computes the modular inverse of a modulo m.
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*
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* @param a The integer whose modular inverse is to be found.
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* @param m The modulus.
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* @return The modular inverse of a modulo m, or -1 if no inverse exists.
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*/
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u64 mod_inverse(u64 a, u64 m);
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/**
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* @brief Generates a random prime number within the given range.
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*
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* @param min The lower bound (inclusive).
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* @param max The upper bound (inclusive).
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* @return A prime number in the range [min, max].
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*/
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u64 gen_prime(u64 min, u64 max);
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/**
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* @brief Checks if a number is prime.
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*
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* @param n The number to check.
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* @return true if n is prime, false otherwise.
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*/
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bool is_prime(u64 n);
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/**
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* @brief Performs the Miller-Rabin primality test to check if a number is
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* probably prime.
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*
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* @param n The number to test for primality.
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* @param k The number of rounds of testing to perform.
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* @return true if n is probably prime, false if n is composite.
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*/
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bool miller_rabin(u64 n, u64 k);
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/**
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* @brief Computes the greatest common divisor (GCD) of two integers a and b
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* using the Extended Euclidean Algorithm. Also finds coefficients x and y such
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* that ax + by = gcd(a, b).
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*
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* @param a The first integer.
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* @param b The second integer.
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* @param x Pointer to an integer to store the coefficient x in the equation ax
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* + by = gcd(a, b).
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* @param y Pointer to an integer to store the coefficient y in the equation ax
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* + by = gcd(a, b).
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* @return The greatest common divisor (gcd) of a and b.
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*/
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u64 extended_euclid(u64 a, u64 b, u64 *x, u64 *y);
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