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-rw-r--r--prism/util/pm_integer.c332
1 files changed, 167 insertions, 165 deletions
diff --git a/prism/util/pm_integer.c b/prism/util/pm_integer.c
index 5bcb508c1c..4caedc4121 100644
--- a/prism/util/pm_integer.c
+++ b/prism/util/pm_integer.c
@@ -1,20 +1,14 @@
#include "prism/util/pm_integer.h"
/**
- * Bigint with arbitary base. In practice, base is 1<<32 or 10**9.
- * When base is 10**9, it acts as bigdecimal.
+ * Adds two positive pm_integer_t with the given base.
+ * Return pm_integer_t with values allocated. Not normalized.
*/
-typedef struct {
- size_t length;
- uint32_t *values;
-} bigint_t;
-
-/**
- * Adds two bigint_t with the given base.
- */
-static bigint_t
-big_add(bigint_t left, bigint_t right, uint64_t base) {
- size_t length = (left.length < right.length ? right.length : left.length);
+static pm_integer_t
+big_add(pm_integer_t left_, pm_integer_t right_, uint64_t base) {
+ pm_integer_t left = left_.values ? left_ : (pm_integer_t) { 0, 1, &left_.value, false };
+ pm_integer_t right = right_.values ? right_ : (pm_integer_t) { 0, 1, &right_.value, false };
+ size_t length = left.length < right.length ? right.length : left.length;
uint32_t *values = (uint32_t*) malloc(sizeof(uint32_t) * (length + 1));
uint64_t carry = 0;
for (size_t i = 0; i < length; i++) {
@@ -26,15 +20,19 @@ big_add(bigint_t left, bigint_t right, uint64_t base) {
values[length] = (uint32_t) carry;
length++;
}
- return (bigint_t) { length, values };
+ return (pm_integer_t) { 0, length, values, false };
}
/**
- * Calculates `a - b - c` with the given base.
- * Result is assumed to be positive value. Internal use for karatsuba_multiply.
+ * Internal use for karatsuba_multiply. Calculates `a - b - c` with the given
+ * base. Assume a, b, c, a - b - c all to be poitive.
+ * Return pm_integer_t with values allocated. Not normalized.
*/
-static bigint_t
-big_sub2(bigint_t a, bigint_t b, bigint_t c, uint64_t base) {
+static pm_integer_t
+big_sub2(pm_integer_t a_, pm_integer_t b_, pm_integer_t c_, uint64_t base) {
+ pm_integer_t a = a_.values ? a_ : (pm_integer_t) { 0, 1, &a_.value, false };
+ pm_integer_t b = b_.values ? b_ : (pm_integer_t) { 0, 1, &b_.value, false };
+ pm_integer_t c = c_.values ? c_ : (pm_integer_t) { 0, 1, &c_.value, false };
size_t length = a.length;
uint32_t *values = (uint32_t*) malloc(sizeof(uint32_t) * length);
int64_t carry = 0;
@@ -50,16 +48,19 @@ big_sub2(bigint_t a, bigint_t b, bigint_t c, uint64_t base) {
}
}
while (length > 1 && values[length - 1] == 0) length--;
- return (bigint_t) { length, values };
+ return (pm_integer_t) { 0, length, values, false };
}
/**
- * Multiply two bigint_t with the given base using karatsuba algorithm.
+ * Multiply two positive integers with the given base using karatsuba algorithm.
+ * Return pm_integer_t with values allocated. Not normalized.
*/
-static bigint_t
-karatsuba_multiply(bigint_t left, bigint_t right, uint64_t base) {
+static pm_integer_t
+karatsuba_multiply(pm_integer_t left_, pm_integer_t right_, uint64_t base) {
+ pm_integer_t left = left_.values ? left_ : (pm_integer_t) { 0, 1, &left_.value, false };
+ pm_integer_t right = right_.values ? right_ : (pm_integer_t) { 0, 1, &right_.value, false };
if (left.length > right.length) {
- bigint_t temp = left;
+ pm_integer_t temp = left;
left = right;
right = temp;
}
@@ -76,40 +77,40 @@ karatsuba_multiply(bigint_t left, bigint_t right, uint64_t base) {
values[i + right.length] = carry;
}
while (length > 1 && values[length - 1] == 0) length--;
- return (bigint_t) { length, values };
+ return (pm_integer_t) { 0, length, values, false };
}
if (left.length * 2 <= right.length) {
uint32_t *values = (uint32_t*) calloc(left.length + right.length, sizeof(uint32_t));
for (size_t start_offset = 0; start_offset < right.length; start_offset += left.length) {
size_t end_offset = start_offset + left.length;
if (end_offset > right.length) end_offset = right.length;
- bigint_t sliced_right = { end_offset - start_offset, right.values + start_offset };
- bigint_t v = karatsuba_multiply(left, sliced_right, base);
+ pm_integer_t sliced_right = { 0, end_offset - start_offset, right.values + start_offset, false };
+ pm_integer_t v = karatsuba_multiply(left, sliced_right, base);
uint32_t carry = 0;
for (size_t i = 0; i < v.length; i++) {
uint64_t sum = (uint64_t) values[start_offset + i] + v.values[i] + carry;
values[start_offset + i] = (uint32_t) (sum % base);
carry = (uint32_t) (sum / base);
}
- free(v.values);
- values[start_offset + v.length] += carry;
+ if (carry > 0) values[start_offset + v.length] += carry;
+ pm_integer_free(&v);
}
- return (bigint_t) { left.length + right.length, values };
+ return (pm_integer_t) { 0, left.length + right.length, values, false };
}
size_t half = left.length / 2;
- bigint_t x0 = { half, left.values };
- bigint_t x1 = { left.length - half, left.values + half };
- bigint_t y0 = { half, right.values };
- bigint_t y1 = { right.length - half, right.values + half };
- bigint_t z0 = karatsuba_multiply(x0, y0, base);
- bigint_t z2 = karatsuba_multiply(x1, y1, base);
+ pm_integer_t x0 = { 0, half, left.values, false };
+ pm_integer_t x1 = { 0, left.length - half, left.values + half, false };
+ pm_integer_t y0 = { 0, half, right.values, false };
+ pm_integer_t y1 = { 0, right.length - half, right.values + half, false };
+ pm_integer_t z0 = karatsuba_multiply(x0, y0, base);
+ pm_integer_t z2 = karatsuba_multiply(x1, y1, base);
// For simplicity to avoid considering negative values,
// use `z1 = (x0 + x1) * (y0 + y1) - z0 - z2` instead of original karatsuba algorithm.
- bigint_t x01 = big_add(x0, x1, base);
- bigint_t y01 = big_add(y0, y1, base);
- bigint_t xy = karatsuba_multiply(x01, y01, base);
- bigint_t z1 = big_sub2(xy, z0, z2, base);
+ pm_integer_t x01 = big_add(x0, x1, base);
+ pm_integer_t y01 = big_add(y0, y1, base);
+ pm_integer_t xy = karatsuba_multiply(x01, y01, base);
+ pm_integer_t z1 = big_sub2(xy, z0, z2, base);
size_t length = left.length + right.length;
uint32_t *values = (uint32_t*) calloc(length, sizeof(uint32_t));
@@ -127,13 +128,13 @@ karatsuba_multiply(bigint_t left, bigint_t right, uint64_t base) {
carry = (uint32_t) (sum / base);
}
while (length > 1 && values[length - 1] == 0) length--;
- free(z0.values);
- free(z1.values);
- free(z2.values);
- free(x01.values);
- free(y01.values);
- free(xy.values);
- return (bigint_t) { length, values };
+ pm_integer_free(&z0);
+ pm_integer_free(&z1);
+ pm_integer_free(&z2);
+ pm_integer_free(&x01);
+ pm_integer_free(&y01);
+ pm_integer_free(&xy);
+ return (pm_integer_t) { 0, length, values, false };
}
/**
@@ -163,67 +164,95 @@ pm_integer_parse_digit(const uint8_t character) {
}
/**
- * Create a bigint_t from uint64_t with the given base.
+ * Create a pm_integer_t from uint64_t with the given base.
*/
-static bigint_t
-uint64_to_bigint(uint64_t value, uint64_t base) {
+static pm_integer_t
+pm_integer_from_uint64(uint64_t value, uint64_t base) {
+ if (value < base) {
+ return (pm_integer_t) { (uint32_t) value, 0, NULL, false };
+ }
uint64_t v = value;
size_t len = 0;
while (value > 0) { len++; value /= base; }
- if (len == 0) len = 1;
uint32_t *values = (uint32_t*) malloc(sizeof(uint32_t) * len);
for (size_t i = 0; i < len; i++) {
values[i] = (uint32_t) (v % base);
v /= base;
}
- return (bigint_t) { len, values };
+ return (pm_integer_t) { 0, len, values, false };
}
/**
- * Convert base of bigint.
+ * Normalize pm_integer_t.
+ * Heading zero values will be removed. If the integer fits into uint32_t,
+ * values is set to NULL, length is set to 0, and value field will be used.
+ */
+static void
+pm_integer_normalize(pm_integer_t *integer) {
+ if (integer->values == NULL) {
+ return;
+ }
+ while (integer->length > 1 && integer->values[integer->length - 1] == 0) {
+ integer->length--;
+ }
+ if (integer->length > 1) {
+ return;
+ }
+
+ uint32_t value = integer->values[0];
+ bool negative = integer->negative && value != 0;
+ pm_integer_free(integer);
+ *integer = (pm_integer_t) { value, 0, NULL, negative };
+}
+
+/**
+ * Convert base of the integer.
* In practice, it converts 10**9 to 1<<32 or 1<<32 to 10**9.
*/
-static bigint_t
-karatsuba_convert_base(bigint_t source, uint64_t base_from, uint64_t base_to) {
+static pm_integer_t
+pm_integer_convert_base(pm_integer_t source_, uint64_t base_from, uint64_t base_to) {
+ pm_integer_t source = source_.values ? source_ : (pm_integer_t) { 0, 1, &source_.value, source_.negative };
size_t bigints_length = (source.length + 1) / 2;
- bigint_t *bigints = (bigint_t*) malloc(sizeof(bigint_t) * bigints_length);
+ pm_integer_t *bigints = (pm_integer_t*) malloc(sizeof(pm_integer_t) * bigints_length);
for (size_t i = 0; i < source.length; i += 2) {
uint64_t v = source.values[i] + base_from * (i + 1 < source.length ? source.values[i + 1] : 0);
- bigints[i / 2] = uint64_to_bigint(v, base_to);
+ bigints[i / 2] = pm_integer_from_uint64(v, base_to);
}
- bigint_t base = uint64_to_bigint(base_from, base_to);
+ pm_integer_t base = pm_integer_from_uint64(base_from, base_to);
while (bigints_length > 1) {
size_t new_length = (bigints_length + 1) / 2;
- bigint_t new_base = karatsuba_multiply(base, base, base_to);
- free(base.values);
+ pm_integer_t new_base = karatsuba_multiply(base, base, base_to);
+ pm_integer_free(&base);
base = new_base;
- bigint_t *new_bigints = (bigint_t*) malloc(sizeof(bigint_t) * new_length);
+ pm_integer_t *new_bigints = (pm_integer_t*) malloc(sizeof(pm_integer_t) * new_length);
for (size_t i = 0; i < bigints_length; i += 2) {
if (i + 1 == bigints_length) {
new_bigints[i / 2] = bigints[i];
} else {
- bigint_t multiplied = karatsuba_multiply(base, bigints[i + 1], base_to);
+ pm_integer_t multiplied = karatsuba_multiply(base, bigints[i + 1], base_to);
new_bigints[i / 2] = big_add(bigints[i], multiplied, base_to);
- free(bigints[i].values);
- free(bigints[i + 1].values);
- free(multiplied.values);
+ pm_integer_free(&bigints[i]);
+ pm_integer_free(&bigints[i + 1]);
+ pm_integer_free(&multiplied);
}
}
free(bigints);
bigints = new_bigints;
bigints_length = new_length;
}
- free(base.values);
- bigint_t result = bigints[0];
+ pm_integer_free(&base);
+ pm_integer_t result = bigints[0];
+ result.negative = source.negative;
free(bigints);
+ pm_integer_normalize(&result);
return result;
}
/**
- * Convert digits to bigint_t with the given power-of-two base.
+ * Convert digits to integer with the given power-of-two base.
*/
-static bigint_t
-big_parse_powof2(uint32_t base, const uint8_t *digits, size_t digits_length) {
+static void
+pm_integer_parse_powof2(pm_integer_t *integer, uint32_t base, const uint8_t *digits, size_t digits_length) {
size_t bit = 1;
while (base > (uint32_t) (1 << bit)) bit++;
size_t length = (digits_length * bit + 31) / 32;
@@ -237,32 +266,31 @@ big_parse_powof2(uint32_t base, const uint8_t *digits, size_t digits_length) {
if (32 - shift < bit) values[index + 1] |= value >> (32 - shift);
}
while (length > 1 && values[length - 1] == 0) length--;
- return (bigint_t) { length, values };
+ *integer = (pm_integer_t) { 0, length, values, false };
+ pm_integer_normalize(integer);
}
/**
- * Convert decimal digits to bigint.
+ * Convert decimal digits to pm_integer_t.
*/
-static bigint_t
-big_parse_decimal(const uint8_t *digits, size_t digits_length) {
- // Construct a bigdecimal from the digits.
+static void
+pm_integer_parse_decimal(pm_integer_t *integer, const uint8_t *digits, size_t digits_length) {
+ // Construct a bigdecimal with base = 10**9 from the digits
const size_t batch = 9;
- const uint64_t batch_base = 1000000000;
size_t values_length = (digits_length + batch - 1) / batch;
- bigint_t bigint = { values_length, (uint32_t*) calloc(values_length, sizeof(uint32_t)) };
+ pm_integer_t decimal = { 0, values_length, (uint32_t*) calloc(values_length, sizeof(uint32_t)), false };
uint32_t v = 0;
for (size_t i = 0; i < digits_length; i++) {
v = v * 10 + digits[i];
size_t reverse_index = digits_length - i - 1;
if (reverse_index % batch == 0) {
- bigint.values[reverse_index / batch] = v;
+ decimal.values[reverse_index / batch] = v;
v = 0;
}
}
- // Convert bigint base from 10**9 to 1<<32.
- bigint_t converted = karatsuba_convert_base(bigint, batch_base, ((uint64_t) 1 << 32));
- free(bigint.values);
- return converted;
+ // Convert base from 10**9 to 1<<32.
+ *integer = pm_integer_convert_base(decimal, 1000000000, ((uint64_t) 1 << 32));
+ pm_integer_free(&decimal);
}
/**
@@ -277,22 +305,12 @@ pm_integer_parse_big(pm_integer_t *integer, uint32_t multiplier, const uint8_t *
if (*start == '_') continue;
digits[digits_length++] = (uint8_t) pm_integer_parse_digit(*start);
}
- // Construct bigint_t from the digits.
- bigint_t bigint =
- multiplier == 10 ? big_parse_decimal(digits, digits_length) : big_parse_powof2(multiplier, digits, digits_length);
-
- // Pack bigint_t to pm_integer_t.
- integer->length = bigint.length - 1;
- integer->head.value = bigint.values[0];
- pm_integer_word_t *current = &integer->head;
- for (size_t i = 1; i < bigint.length; i++) {
- current->next = malloc(sizeof(pm_integer_word_t));
- current = current->next;
- current->value = bigint.values[i];
- current->next = NULL;
+ // Construct pm_integer_t from the digits.
+ if (multiplier == 10) {
+ pm_integer_parse_decimal(integer, digits, digits_length);
+ } else {
+ pm_integer_parse_powof2(integer, multiplier, digits, digits_length);
}
-
- free(bigint.values);
free(digits);
}
@@ -351,13 +369,13 @@ pm_integer_parse(pm_integer_t *integer, pm_integer_base_t base, const uint8_t *s
if (*ptr == '_') continue;
value = value * multiplier + pm_integer_parse_digit(*ptr);
if (value > UINT32_MAX) {
- // If the integer is too large to fit into a single node, then we'll
+ // If the integer is too large to fit into a single uint32_t, then we'll
// parse it as a big integer.
pm_integer_parse_big(integer, multiplier, start, end);
return;
}
}
- integer->head.value = (uint32_t) value;
+ integer->value = (uint32_t) value;
}
/**
@@ -365,7 +383,7 @@ pm_integer_parse(pm_integer_t *integer, pm_integer_base_t base, const uint8_t *s
*/
size_t
pm_integer_memsize(const pm_integer_t *integer) {
- return sizeof(pm_integer_t) + integer->length * sizeof(pm_integer_word_t);
+ return sizeof(pm_integer_t) + integer->length * sizeof(uint32_t);
}
/**
@@ -378,16 +396,21 @@ pm_integer_compare(const pm_integer_t *left, const pm_integer_t *right) {
if (left->negative != right->negative) return left->negative ? -1 : 1;
int negative = left->negative ? -1 : 1;
- if (left->length < right->length) return -1 * negative;
- if (left->length > right->length) return 1 * negative;
+ if (left->values == right->values) {
+ if (left->value < right->value) return -1 * negative;
+ if (left->value > right->value) return 1 * negative;
+ return 0;
+ }
+
+ if (left->values == NULL || left->length < right->length) return -1 * negative;
+ if (right->values == NULL || left->length > right->length) return 1 * negative;
- for (
- const pm_integer_word_t *left_word = &left->head, *right_word = &right->head;
- left_word != NULL && right_word != NULL;
- left_word = left_word->next, right_word = right_word->next
- ) {
- if (left_word->value < right_word->value) return -1 * negative;
- if (left_word->value > right_word->value) return 1 * negative;
+ for (size_t i = 0; i < left->length; i++) {
+ size_t index = left->length - i - 1;
+ uint32_t l = left->values[index];
+ uint32_t r = right->values[index];
+ if (l < r) return -1 * negative;
+ if (l > r) return 1 * negative;
}
return 0;
@@ -402,75 +425,54 @@ pm_integer_string(pm_buffer_t *buffer, const pm_integer_t *integer) {
pm_buffer_append_byte(buffer, '-');
}
- switch (integer->length) {
- case 0: {
- const uint32_t value = integer->head.value;
- pm_buffer_append_format(buffer, "%" PRIu32, value);
- return;
- }
- case 1: {
- const uint64_t value = ((uint64_t) integer->head.value) | (((uint64_t) integer->head.next->value) << 32);
- pm_buffer_append_format(buffer, "%" PRIu64, value);
- return;
- }
- default: {
- // Pack pm_integer_t to bigint_t.
- size_t length = integer->length + 1;
- uint32_t *values = calloc(length, sizeof(uint32_t));
- const pm_integer_word_t *current = &(integer->head);
- for (size_t i = 0; i < length; i++) {
- values[i] = current->value;
- current = current->next;
- }
- bigint_t bigint = { length, values };
- // Convert bigint base from 1<<32 to 10**9.
- bigint_t converted = karatsuba_convert_base(bigint, (uint64_t) 1 << 32, 1000000000);
- free(values);
-
- // Allocate a buffer that we'll copy the decimal digits into.
- size_t char_length = converted.length * 9;
- char *digits = calloc(char_length, sizeof(char));
- if (digits == NULL) return;
+ if (integer->values == NULL) {
+ pm_buffer_append_format(buffer, "%" PRIu32, integer->value);
+ return;
+ }
+ if (integer->length == 2) {
+ const uint64_t value = ((uint64_t) integer->values[0]) | ((uint64_t) integer->values[1] << 32);
+ pm_buffer_append_format(buffer, "%" PRIu64, value);
+ return;
+ }
- // Pack bigdecimal to digits.
- for (size_t i = 0; i < converted.length; i++) {
- uint32_t v = converted.values[i];
- for (size_t j = 0; j < 9; j++) {
- digits[char_length - 9 * i - j - 1] = (char) ('0' + v % 10);
- v /= 10;
- }
- }
- size_t start_offset = 0;
- while (start_offset < char_length - 1 && digits[start_offset] == '0') start_offset++;
+ // Convert base from 1<<32 to 10**9.
+ pm_integer_t converted = pm_integer_convert_base(*integer, (uint64_t) 1 << 32, 1000000000);
- // Finally, append the string to the buffer and free the digits.
- pm_buffer_append_string(buffer, digits + start_offset, char_length - start_offset);
- free(digits);
- free(converted.values);
- return;
- }
+ if (converted.values == NULL) {
+ pm_buffer_append_format(buffer, "%" PRIu32, converted.value);
+ pm_integer_free(&converted);
+ return;
}
-}
-/**
- * Recursively destroy the linked list of an integer.
- */
-static void
-pm_integer_word_destroy(pm_integer_word_t *integer) {
- if (integer->next != NULL) {
- pm_integer_word_destroy(integer->next);
+ // Allocate a buffer that we'll copy the decimal digits into.
+ size_t char_length = converted.length * 9;
+ char *digits = calloc(char_length, sizeof(char));
+ if (digits == NULL) return;
+
+ // Pack bigdecimal to digits.
+ for (size_t i = 0; i < converted.length; i++) {
+ uint32_t v = converted.values[i];
+ for (size_t j = 0; j < 9; j++) {
+ digits[char_length - 9 * i - j - 1] = (char) ('0' + v % 10);
+ v /= 10;
+ }
}
+ size_t start_offset = 0;
+ while (start_offset < char_length - 1 && digits[start_offset] == '0') start_offset++;
- xfree(integer);
+ // Finally, append the string to the buffer and free the digits.
+ pm_buffer_append_string(buffer, digits + start_offset, char_length - start_offset);
+ free(digits);
+ pm_integer_free(&converted);
}
/**
* Free the internal memory of an integer. This memory will only be allocated if
- * the integer exceeds the size of a single node in the linked list.
+ * the integer exceeds the size of a single uint32_t.
*/
PRISM_EXPORTED_FUNCTION void
pm_integer_free(pm_integer_t *integer) {
- if (integer->head.next) {
- pm_integer_word_destroy(integer->head.next);
+ if (integer->values) {
+ free(integer->values);
}
}
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