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Added requirements for Karatsuba's algorithm

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Marco Cetica
2025-11-11 14:51:03 +01:00
parent 119ed5c33f
commit 87cae7d2be
1 changed files with 271 additions and 3 deletions
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274
src/bignum.c
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@@ -21,6 +21,9 @@ static bigint_result_t bigint_trim_zeros(bigint_t *number);
static bigint_result_t bigint_compare_abs(const bigint_t *x, const bigint_t *y);
static bigint_result_t bigint_add_abs(const bigint_t *x, const bigint_t *y);
static bigint_result_t bigint_sub_abs(const bigint_t *x, const bigint_t *y);
static bigint_result_t bigint_shift_left(const bigint_t *num, size_t n);
static bigint_result_t bigint_split(const bigint_t *num, size_t m, bigint_t **high, bigint_t **low);
static bigint_result_t bigint_karatsuba(const bigint_t *x, const bigint_t *y);
/**
* bigint_from_int
@@ -158,9 +161,9 @@ static bigint_result_t bigint_trim_zeros(bigint_t *number) {
* @y: a non-null big integer
*
* Compares absolute value of two big integers
* if |x| < |y| => -1
* if |x| < |y| => -1
* if |x| == |y| => 0
* if |x| > |y| => 1
* if |x| > |y| => 1
*
* Returns a bigint_result_t data type
*/
@@ -583,6 +586,272 @@ bigint_result_t bigint_sub(const bigint_t *x, const bigint_t *y) {
return result;
}
/**
* bigint_shift_left
* @num: a non-null big integer
* @n: number of digits to shift
*
* Shift left by @n digits (i.e., multiply by BASE^n)
*
* Returns a bigint_result_t data type
*/
bigint_result_t bigint_shift_left(const bigint_t *num, size_t n) {
bigint_result_t result = {0};
if (n == 0) {
return bigint_clone(num);
}
bigint_t *shifted = malloc(sizeof(bigint_t));
if (shifted == NULL) {
result.status = BIGNUM_ERR_ALLOCATE;
SET_MSG(result, "Failed to allocate memory for big integer");
return result;
}
vector_result_t vec_res = vector_new(vector_size(num->digits) + n, sizeof(int));
if (vec_res.status != VECTOR_OK) {
free(shifted);
result.status = BIGNUM_ERR_ALLOCATE;
COPY_MSG(result, vec_res.message);
return result;
}
shifted->digits = vec_res.value.vector;
shifted->is_negative = num->is_negative;
// Add 'n' zeros by starting from the LSB
int zero = 0;
for (size_t idx = 0; idx < n; idx++) {
vector_result_t push_res = vector_push(shifted->digits, &zero);
if (push_res.status != VECTOR_OK) {
vector_destroy(shifted->digits);
free(shifted);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, push_res.message);
return result;
}
}
// Copy back original digits
for (size_t idx = 0; idx < vector_size(num->digits); idx++) {
vector_result_t get_res = vector_get(num->digits, idx);
if (get_res.status != VECTOR_OK) {
vector_destroy(shifted->digits);
free(shifted);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, get_res.message);
return result;
}
int *digit = (int*)get_res.value.element;
vector_result_t push_res = vector_push(shifted->digits, digit);
if (push_res.status != VECTOR_OK) {
vector_destroy(shifted->digits);
free(shifted);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, push_res.message);
return result;
}
}
result.value.number = shifted;
result.status = BIGNUM_OK;
SET_MSG(result, "Big integer shifted successfully");
return result;
}
/**
* bigint_split
* @num: a non-null big integers
* @m: the pivot/position where to split
* @high: digits \in [0, m)
* @low: digits \in [m, size)
*
* Splits number into @high and @low parts at position @m
*
* Returns a bigint_result_t data type
*/
bigint_result_t bigint_split(const bigint_t *num, size_t m, bigint_t **high, bigint_t **low) {
bigint_result_t result = {0};
const size_t size = vector_size(num->digits);
// Low part: digits \in [0, m)
*low = malloc(sizeof(bigint_t));
if (low == NULL) {
result.status = BIGNUM_ERR_ALLOCATE;
SET_MSG(result, "Failed to allocate memory for big integer");
return result;
}
vector_result_t low_res = vector_new(m, sizeof(int));
if (low_res.status != VECTOR_OK) {
free(low);
result.status = BIGNUM_ERR_ALLOCATE;
COPY_MSG(result, low_res.message);
return result;
}
(*low)->digits = low_res.value.vector;
(*low)->is_negative = false;
for (size_t idx = 0; idx < m && idx < size; idx++) {
vector_result_t get_res = vector_get(num->digits, idx);
if (get_res.status != VECTOR_OK) {
vector_destroy((*low)->digits);
free(low);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, get_res.message);
return result;
}
int *digit = (int*)get_res.value.element;
vector_result_t push_res = vector_push((*low)->digits, digit);
if (push_res.status != VECTOR_OK) {
vector_destroy((*low)->digits);
free(low);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, push_res.message);
return result;
}
}
if (vector_size((*low)->digits) == 0) {
int zero = 0;
vector_result_t push_res = vector_push((*low)->digits, &zero);
if (push_res.status != VECTOR_OK) {
vector_destroy((*low)->digits);
free(low);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, push_res.message);
return result;
}
}
// First pass of zero trimming
bigint_result_t first_trim_res = bigint_trim_zeros(*low);
if (first_trim_res.status != BIGNUM_OK) {
vector_destroy((*low)->digits);
free(low);
return first_trim_res;
}
// High part: digits \in [m, size)
*high = malloc(sizeof(bigint_t));
if (low == NULL) {
vector_destroy((*low)->digits);
free(low);
result.status = BIGNUM_ERR_ALLOCATE;
SET_MSG(result, "Failed to allocate memory for big integer");
return result;
}
vector_result_t high_res = vector_new(size > m ? (size - m) : 1, sizeof(int));
if (high_res.status != VECTOR_OK) {
vector_destroy((*low)->digits);
free(low);
free(high);
result.status = BIGNUM_ERR_ALLOCATE;
COPY_MSG(result, low_res.message);
return result;
}
(*high)->digits = high_res.value.vector;
(*high)->is_negative = false;
if (size > m) {
for (size_t idx = m; idx < size; idx++) {
vector_result_t get_res = vector_get(num->digits, idx);
if (get_res.status != VECTOR_OK) {
vector_destroy((*low)->digits);
vector_destroy((*high)->digits);
free(low);
free(high);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, get_res.message);
return result;
}
int *digit = (int*)get_res.value.element;
vector_result_t push_res = vector_push((*high)->digits, digit);
if (push_res.status != VECTOR_OK) {
vector_destroy((*low)->digits);
vector_destroy((*high)->digits);
free(low);
free(high);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, push_res.message);
return result;
}
}
} else {
int zero = 0;
vector_result_t push_res = vector_push((*high)->digits, &zero);
if (push_res.status != VECTOR_OK) {
vector_destroy((*low)->digits);
vector_destroy((*high)->digits);
free(low);
free(high);
result.status = BIGNUM_ERR_INVALID;
COPY_MSG(result, push_res.message);
return result;
}
}
// Second pass of zero trimming
bigint_result_t second_trim_res = bigint_trim_zeros(*high);
if (second_trim_res.status != BIGNUM_OK) {
vector_destroy((*low)->digits);
vector_destroy((*high)->digits);
free(low);
free(high);
return second_trim_res;
}
result.status = BIGNUM_OK;
SET_MSG(result, "Big number successfully splitted");
return result;
}
/**
* bigint_karatusba
* @x: a non-null big integer
* @y: a non-null big integer
*
* Perform a multiplication using Karatsuba recursive algorithm
* in O(n^{\log_2 3}) \approx O(n^{1.585})
*/
bigint_result_t bigint_karatsuba(const bigint_t *x, const bigint_t *y) {
const size_t x_size = vector_size(x->digits);
const size_t y_size = vector_size(y->digits);
// TODO: enough for today!
}
/**
* bigint_from_string
* @string_num: an array of chars representing a number
@@ -611,7 +880,6 @@ bigint_result_t bigint_from_string(const char *string_num) {
vector_result_t vec_res = vector_new(4, sizeof(int));
if (vec_res.status != VECTOR_OK) {
vector_destroy(number->digits);
free(number);
result.status = BIGNUM_ERR_ALLOCATE;
COPY_MSG(result, vec_res.message);