Added requirements for division and fixed critical bugs

README.md

@@ -119,7 +119,7 @@ int main(void) {
         fact = partial_fact;
     }
 
-    printf("%ld! = ", n);
+    printf("%d! = ", n);
     bigint_print(fact);
     printf("\n");
 

src/bigint.c

@@ -11,14 +11,6 @@
 
 #define IS_DIGIT(c) ((c) >= '0') && ((c) <= '9')
 
-#define DESTROY_IF(p) \
-    do { \
-        if ((p) && (p) != result.value.number) { \
-            bigint_destroy((p)); \
-            (p) = NULL; \
-        } \
-    } while (0)
-
 #include <stdio.h>
 #include <string.h>
 #include <stdlib.h>
@@ -35,6 +27,8 @@ 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_base(const bigint_t *x, const bigint_t *y);
 static bigint_result_t bigint_karatsuba(const bigint_t *x, const bigint_t *y);
+static bigint_result_t bigint_shift_right(const bigint_t *num, size_t n);
+static bigint_result_t bigint_reciprocal(const bigint_t *num, size_t precision);
 
 /**
  * bigint_from_int
@@ -882,6 +876,116 @@ bigint_result_t bigint_prod(const bigint_t *x, const bigint_t *y) {
     return result;
 }
 
+/**
+ * bigint_divmod
+ *  @x: a valid non-null big integer
+ *  @y: a valid non-null big integer
+ * 
+ *  Computes division with remainder
+ *  
+ *  Returns a bigint_result_t data type
+ */
+bigint_result_t bigint_divmod(const bigint_t *x, const bigint_t *y) {
+    bigint_result_t result = {0};
+    bigint_result_t tmp_res = {0};
+
+    // Intermediate results
+    bigint_t *quotient = NULL;
+    bigint_t *y_times_q = NULL;
+    bigint_t *remainder = NULL;
+
+    if (x == NULL || y == NULL) {
+        result.status = BIGINT_ERR_INVALID;
+        SET_MSG(result, "Invalid big numbers");
+
+        return result;
+    }
+
+    // Check for division by zero
+    const size_t y_size = vector_size(y->digits);
+    if (y_size == 0) {
+        result.status = BIGINT_ERR_DIV_BY_ZERO;
+        SET_MSG(result, "Division by zero");
+
+        return result;
+    }
+
+    if (y_size == 1) {
+        vector_result_t y_val_res = vector_get(y->digits, 0);
+        if (y_val_res.status != VECTOR_OK) {
+            result.status = BIGINT_ERR_INVALID;
+            COPY_MSG(result, y_val_res.message);
+
+            return result;
+        }
+
+        int *y_val = (int*)y_val_res.value.element;
+        if (*y_val == 0) {
+            result.status = BIGINT_ERR_DIV_BY_ZERO;
+            SET_MSG(result, "Division by zero");
+
+            return result;
+        }
+    }
+
+    // |x| < |y| then quotient is 0 and remainder is x
+    tmp_res = bigint_compare_abs(x, y);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+
+    if (tmp_res.value.compare_status < 0) {
+        tmp_res = bigint_from_int(0);
+        if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+        quotient = tmp_res.value.number;
+
+        tmp_res = bigint_clone(x);
+        if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+        remainder = tmp_res.value.number;
+
+        result.value.division.quotient = quotient;
+        result.value.division.remainder = remainder;
+        result.status = BIGINT_OK;
+        SET_MSG(result, "Division between big integers was successful");
+
+        return result;
+    }
+
+    tmp_res = bigint_div(x, y);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+    quotient = tmp_res.value.number;
+
+    // Computed r = x - y * q
+    tmp_res = bigint_prod(y, quotient);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+    y_times_q = tmp_res.value.number;
+
+    tmp_res = bigint_sub(x, y_times_q);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+    remainder = tmp_res.value.number;
+
+    // Ensure that remainder has correct sign (i.e., same as dividend x)
+    // In C-style division, sign(remainder) = sign(dividend)
+    remainder->is_negative = x->is_negative;
+
+    tmp_res = bigint_trim_zeros(remainder);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+    
+    result.value.division.quotient = quotient;
+    result.value.division.remainder = remainder;
+    result.status = BIGINT_OK;
+    SET_MSG(result, "Division between big integers was successful");
+
+    bigint_destroy(y_times_q);
+    
+    return result;
+
+cleanup:
+    if (quotient) { bigint_destroy(quotient); }
+    if (y_times_q) { bigint_destroy(y_times_q); }
+    if (remainder) { bigint_destroy(remainder); }
+
+    return result;
+}
+
 /**
  * bigint_shift_left
  *  @num: a non-null big integer
@@ -1255,6 +1359,14 @@ bigint_result_t bigint_karatsuba_base(const bigint_t *x, const bigint_t *y) {
  */
 bigint_result_t bigint_karatsuba(const bigint_t *x, const bigint_t *y) {
     bigint_result_t result = {0};
+    bigint_result_t tmp_res = {0};
+
+    if (x == NULL || y == NULL) {
+        result.status = BIGINT_ERR_INVALID;
+        SET_MSG(result, "Invalid big integers");
+
+        return result;
+    }
 
     const size_t x_size = vector_size(x->digits);
     const size_t y_size = vector_size(y->digits);
@@ -1276,14 +1388,12 @@ bigint_result_t bigint_karatsuba(const bigint_t *x, const bigint_t *y) {
     bigint_t *z2_shifted = NULL, *z1_shifted = NULL;
     bigint_t *temp = NULL, *product = NULL;
 
-    bigint_result_t tmp_res = {0};
-
     // Split x = x1 * BASE^pivot + x0
     tmp_res = bigint_split(x, pivot, &x1, &x0);
     if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
 
     // Split y = y1 * BASE^pivot + y0
-    tmp_res = bigint_split(x, pivot, &y1, &y0);
+    tmp_res = bigint_split(y, pivot, &y1, &y0);
     if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
 
     // Perform karatsuba's trick
@@ -1332,18 +1442,251 @@ bigint_result_t bigint_karatsuba(const bigint_t *x, const bigint_t *y) {
     if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
     product = tmp_res.value.number;
 
+    // Destroy intermediate allocations except for the product
+    bigint_destroy(x1); bigint_destroy(x0);
+    bigint_destroy(y1); bigint_destroy(y0);
+    bigint_destroy(z0); bigint_destroy(z2);
+    bigint_destroy(x_sum); bigint_destroy(y_sum);
+    bigint_destroy(z1_temp); bigint_destroy(z1_sub1);
+    bigint_destroy(z1); bigint_destroy(z2_shifted);
+    bigint_destroy(z1_shifted); bigint_destroy(temp);
+
     result.value.number = product;
     result.status = BIGINT_OK;
     SET_MSG(result, "Product between big integers was successful");
 
-cleanup: // Destroy intermediate allocations except for the product
-    DESTROY_IF(x1); DESTROY_IF(x0);
-    DESTROY_IF(y1); DESTROY_IF(y0);
-    DESTROY_IF(z0); DESTROY_IF(z2);
-    DESTROY_IF(x_sum); DESTROY_IF(y_sum);
-    DESTROY_IF(z1_temp); DESTROY_IF(z1_sub1); DESTROY_IF(z1);
-    DESTROY_IF(z2_shifted); DESTROY_IF(z1_shifted);
-    DESTROY_IF(temp);
+cleanup: // Destroy intermediate allocations on error
+    if (x1) { bigint_destroy(x1); }
+    if (x0) { bigint_destroy(x0); }
+    if (y1) { bigint_destroy(y1); }
+    if (y0) { bigint_destroy(y0); }
+    if (z0) { bigint_destroy(z0); }
+    if (z2) { bigint_destroy(z2); }
+    if (x_sum) { bigint_destroy(x_sum); }
+    if (y_sum) { bigint_destroy(y_sum); }
+    if (z1_temp) { bigint_destroy(z1_temp); }
+    if (z1_sub1) { bigint_destroy(z1_sub1); }
+    if (z1) { bigint_destroy(z1); }
+    if (z2_shifted) { bigint_destroy(z2_shifted); }
+    if (z1_shifted) { bigint_destroy(z1_shifted); }
+    if (temp) { bigint_destroy(temp); }
+    if (product) { bigint_destroy(product); }
+
+    return result;
+}
+
+/**
+ * bigint_shift_right
+ *  @num: a valid non-null big integer
+ *  @n: number of digits to shift
+ * 
+ *  Shifts right by @n digits (i.e., divide by BASE^n)
+ *
+ *  Returns a bigint_result_t data type
+ */
+bigint_result_t bigint_shift_right(const bigint_t *num, size_t n) {
+    bigint_result_t result = {0};
+
+    const size_t size = vector_size(num->digits);
+
+    if (n >= size) return bigint_from_int(0);
+    if (n == 0) return bigint_clone(num);
+
+    bigint_t *shifted = malloc(sizeof(bigint_t));
+    if (shifted == NULL) {
+        result.status = BIGINT_ERR_ALLOCATE;
+        SET_MSG(result, "Failed to allocate memory for big integer");
+
+        return result;
+    }
+
+    vector_result_t vec_res = vector_new(size - n, sizeof(int));
+    if (vec_res.status != VECTOR_OK) {
+        free(shifted);
+        result.status = BIGINT_ERR_INVALID;
+        COPY_MSG(result, vec_res.message);
+
+        return result;
+    }
+
+    shifted->digits = vec_res.value.vector;
+    shifted->is_negative = num->is_negative;
+
+    // Copy digits from position 'n' onwards
+    for (size_t idx = n; idx < size; idx++) {
+        vector_result_t vec_res = vector_get(num->digits, idx);
+        if (vec_res.status != VECTOR_OK) {
+            vector_destroy(shifted->digits);
+            free(shifted);
+            result.status = BIGINT_ERR_INVALID;
+            COPY_MSG(result, vec_res.message);
+
+            return result;
+        }
+
+        int *digit = (int*)vec_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 = BIGINT_ERR_INVALID;
+            COPY_MSG(result, push_res.message);
+
+            return result;
+        }
+    }
+
+    bigint_result_t trim_res = bigint_trim_zeros(shifted);
+    if (trim_res.status != BIGINT_OK) {
+        vector_destroy(shifted->digits);
+        free(shifted);
+
+        return trim_res;
+    }
+
+    result.value.number = shifted;
+    result.status = BIGINT_OK;
+    SET_MSG(result, "Big integer shifted successfully");
+
+    return result;
+}
+
+/**
+ * bigint_reciprocal
+ *  @num: a valid non-null big integer
+ *  @precision: the precision of the computation
+ * 
+ *  Compute the reciprocal using Newton-Raphson algorithm.
+ *  It calculates 1/num with precision @precision, returning
+ *  floor(BASE^(2 * @precision) / num)
+ * 
+ *  Returns a bigint_result_t data type
+ */
+bigint_result_t bigint_reciprocal(const bigint_t *num, size_t precision) {
+    bigint_result_t result = {0};
+    bigint_result_t tmp_res = {0};
+
+    // Results of each steps
+    bigint_t *x = NULL;
+    bigint_t *scale = NULL;
+    bigint_t *two = NULL;
+    bigint_t *two_scaled = NULL;
+    bigint_t *dx = NULL;
+    bigint_t *two_minus_dx = NULL;
+    bigint_t *x_new_tmp = NULL;
+    bigint_t *x_new = NULL;
+    
+    if (num == NULL) {
+        result.status = BIGINT_ERR_INVALID;
+        SET_MSG(result, "Invalid big integer");
+
+        return result;
+    }
+
+    const size_t num_size = vector_size(num->digits);
+    // Get most significant digit
+    vector_result_t msd_res = vector_get(num->digits, num_size - 1);
+    if (msd_res.status != VECTOR_OK) {
+        result.status = BIGINT_ERR_INVALID;
+        COPY_MSG(result, msd_res.message);
+
+        return result;
+    }
+
+    int *msd = (int*)msd_res.value.element;
+
+    // x = floor(BASE^2 / (msd + 1))
+    const long long initial_val = ((long long)BIGINT_BASE * (long long)BIGINT_BASE) / ((long long)(*msd) + 1LL);
+    tmp_res = bigint_from_int(initial_val);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+    x = tmp_res.value.number;
+
+    tmp_res = bigint_from_int(1);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+    scale = tmp_res.value.number;
+
+    // Scale to proper precision. That is scale x by BASE^(2 * precision - 2)
+    // in order to reach BASE^(2 * precision) magnitude
+    if (precision > 1) {
+        tmp_res = bigint_shift_left(scale, 2 * precision - 2);
+        if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+        bigint_destroy(scale);
+        scale = tmp_res.value.number;
+
+        tmp_res = bigint_prod(x, scale);
+        if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+        bigint_destroy(x);
+        x = tmp_res.value.number;
+    }
+
+    // two_scaled = 2 * BASE^(2 * precision)
+    tmp_res = bigint_from_int(2);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+    two = tmp_res.value.number;
+
+    tmp_res = bigint_shift_left(two, 2 * precision);
+    if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+
+    bigint_destroy(two);
+    two = NULL;
+    two_scaled = tmp_res.value.number;
+
+    // Determine the number of Newton-Raphson iterations
+    size_t iterations = 0;
+    size_t target = precision;
+    while ((1ULL << iterations) < target) { iterations++; }
+    iterations += 2; // Add a few more just to be sure
+
+    // x_{n+1} = x_n * (2 * BASE^(2P) - d * x_n) / BASE^(2P)
+    for (size_t it = 0; it < iterations; it++) {
+        // dx = d * x
+        tmp_res = bigint_prod(num, x);
+        if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+        dx = tmp_res.value.number;
+
+        // two_minus_dx = 2 * BASE^(2P) - dx
+        tmp_res = bigint_sub(two_scaled, dx);
+        if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+        two_minus_dx = tmp_res.value.number;
+
+        // x_new_temp = x * (two_minus_dx)
+        tmp_res = bigint_prod(x, two_minus_dx);
+        if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+        x_new_tmp = tmp_res.value.number;
+
+        // x_new = x_new_temp >> (2 * precision)
+        tmp_res = bigint_shift_right(x_new_tmp, 2 * precision);
+        if (tmp_res.status != BIGINT_OK) { result = tmp_res; goto cleanup; }
+        x_new = tmp_res.value.number;
+
+        // Rotation pass: replace x with x_new and free intermediates
+        bigint_destroy(x);
+        x = x_new;
+        x_new = NULL;
+
+        bigint_destroy(dx); dx = NULL;
+        bigint_destroy(two_minus_dx); two_minus_dx = NULL;
+        bigint_destroy(x_new_tmp); x_new_tmp = NULL;
+    }
+
+    bigint_destroy(scale);
+    bigint_destroy(two_scaled);
+
+    result.value.number = x;
+    result.status = BIGINT_OK;
+    SET_MSG(result, "Reciprocal computed successfully");
+    return result;
+
+cleanup:
+    if (x) { bigint_destroy(x); }
+    if (scale) { bigint_destroy(scale); }
+    if (two) { bigint_destroy(two); }
+    if (two_scaled) { bigint_destroy(two_scaled); }
+    if (dx) { bigint_destroy(dx); }
+    if (two_minus_dx) { bigint_destroy(two_minus_dx); }
+    if (x_new_tmp) { bigint_destroy(x_new_tmp); }
+    if (x_new) { bigint_destroy(x_new); }
 
     return result;
 }

src/bigint.h

@@ -24,11 +24,17 @@ typedef struct {
     bool is_negative;
 } bigint_t;
 
+typedef struct {
+    bigint_t *quotient;
+    bigint_t *remainder;
+} div_result_t;
+
 typedef struct {
     bigint_status_t status;
     uint8_t message[RESULT_MSG_SIZE];
     union {
         bigint_t *number;
+        div_result_t division;
         int8_t compare_status;
         char *string_num;
     } value;
@@ -46,6 +52,7 @@ bigint_result_t bigint_compare(const bigint_t *x, const bigint_t *y);
 bigint_result_t bigint_add(const bigint_t *x, const bigint_t *y);
 bigint_result_t bigint_sub(const bigint_t *x, const bigint_t *y);
 bigint_result_t bigint_prod(const bigint_t *x, const bigint_t *y);
+bigint_result_t bigint_divmod(const bigint_t *x, const bigint_t *y);
 bigint_result_t bigint_destroy(bigint_t *number);
 bigint_result_t bigint_print(const bigint_t *number);