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ruby/prism/util/pm_integer.c

671 строка
23 KiB
C
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#include "prism/util/pm_integer.h"
/**
* Pull out the length and values from the integer, regardless of the form in
* which the length/values are stored.
*/
#define INTEGER_EXTRACT(integer, length_variable, values_variable) \
if ((integer)->values == NULL) { \
length_variable = 1; \
values_variable = &(integer)->value; \
} else { \
length_variable = (integer)->length; \
values_variable = (integer)->values; \
}
/**
* Adds two positive pm_integer_t with the given base.
* Return pm_integer_t with values allocated. Not normalized.
*/
static void
big_add(pm_integer_t *destination, pm_integer_t *left, pm_integer_t *right, uint64_t base) {
size_t left_length;
uint32_t *left_values;
INTEGER_EXTRACT(left, left_length, left_values)
size_t right_length;
uint32_t *right_values;
INTEGER_EXTRACT(right, right_length, right_values)
size_t length = left_length < right_length ? right_length : left_length;
uint32_t *values = (uint32_t *) xmalloc(sizeof(uint32_t) * (length + 1));
if (values == NULL) return;
uint64_t carry = 0;
for (size_t index = 0; index < length; index++) {
uint64_t sum = carry + (index < left_length ? left_values[index] : 0) + (index < right_length ? right_values[index] : 0);
values[index] = (uint32_t) (sum % base);
carry = sum / base;
}
if (carry > 0) {
values[length] = (uint32_t) carry;
length++;
}
*destination = (pm_integer_t) { length, values, 0, false };
}
/**
* Internal use for karatsuba_multiply. Calculates `a - b - c` with the given
* base. Assume a, b, c, a - b - c all to be positive.
* Return pm_integer_t with values allocated. Not normalized.
*/
static void
big_sub2(pm_integer_t *destination, pm_integer_t *a, pm_integer_t *b, pm_integer_t *c, uint64_t base) {
size_t a_length;
uint32_t *a_values;
INTEGER_EXTRACT(a, a_length, a_values)
size_t b_length;
uint32_t *b_values;
INTEGER_EXTRACT(b, b_length, b_values)
size_t c_length;
uint32_t *c_values;
INTEGER_EXTRACT(c, c_length, c_values)
uint32_t *values = (uint32_t*) xmalloc(sizeof(uint32_t) * a_length);
int64_t carry = 0;
for (size_t index = 0; index < a_length; index++) {
int64_t sub = (
carry +
a_values[index] -
(index < b_length ? b_values[index] : 0) -
(index < c_length ? c_values[index] : 0)
);
if (sub >= 0) {
values[index] = (uint32_t) sub;
carry = 0;
} else {
sub += 2 * (int64_t) base;
values[index] = (uint32_t) ((uint64_t) sub % base);
carry = sub / (int64_t) base - 2;
}
}
while (a_length > 1 && values[a_length - 1] == 0) a_length--;
*destination = (pm_integer_t) { a_length, values, 0, false };
}
/**
* Multiply two positive integers with the given base using karatsuba algorithm.
* Return pm_integer_t with values allocated. Not normalized.
*/
static void
karatsuba_multiply(pm_integer_t *destination, pm_integer_t *left, pm_integer_t *right, uint64_t base) {
size_t left_length;
uint32_t *left_values;
INTEGER_EXTRACT(left, left_length, left_values)
size_t right_length;
uint32_t *right_values;
INTEGER_EXTRACT(right, right_length, right_values)
if (left_length > right_length) {
size_t temporary_length = left_length;
left_length = right_length;
right_length = temporary_length;
uint32_t *temporary_values = left_values;
left_values = right_values;
right_values = temporary_values;
}
if (left_length <= 10) {
size_t length = left_length + right_length;
uint32_t *values = (uint32_t *) xcalloc(length, sizeof(uint32_t));
if (values == NULL) return;
for (size_t left_index = 0; left_index < left_length; left_index++) {
uint32_t carry = 0;
for (size_t right_index = 0; right_index < right_length; right_index++) {
uint64_t product = (uint64_t) left_values[left_index] * right_values[right_index] + values[left_index + right_index] + carry;
values[left_index + right_index] = (uint32_t) (product % base);
carry = (uint32_t) (product / base);
}
values[left_index + right_length] = carry;
}
while (length > 1 && values[length - 1] == 0) length--;
*destination = (pm_integer_t) { length, values, 0, false };
return;
}
if (left_length * 2 <= right_length) {
uint32_t *values = (uint32_t *) xcalloc(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;
pm_integer_t sliced_left = {
.length = left_length,
.values = left_values,
.value = 0,
.negative = false
};
pm_integer_t sliced_right = {
.length = end_offset - start_offset,
.values = right_values + start_offset,
.value = 0,
.negative = false
};
pm_integer_t product;
karatsuba_multiply(&product, &sliced_left, &sliced_right, base);
uint32_t carry = 0;
for (size_t index = 0; index < product.length; index++) {
uint64_t sum = (uint64_t) values[start_offset + index] + product.values[index] + carry;
values[start_offset + index] = (uint32_t) (sum % base);
carry = (uint32_t) (sum / base);
}
if (carry > 0) values[start_offset + product.length] += carry;
pm_integer_free(&product);
}
*destination = (pm_integer_t) { left_length + right_length, values, 0, false };
return;
}
size_t half = left_length / 2;
pm_integer_t x0 = { half, left_values, 0, false };
pm_integer_t x1 = { left_length - half, left_values + half, 0, false };
pm_integer_t y0 = { half, right_values, 0, false };
pm_integer_t y1 = { right_length - half, right_values + half, 0, false };
pm_integer_t z0 = { 0 };
karatsuba_multiply(&z0, &x0, &y0, base);
pm_integer_t z2 = { 0 };
karatsuba_multiply(&z2, &x1, &y1, base);
// For simplicity to avoid considering negative values,
// use `z1 = (x0 + x1) * (y0 + y1) - z0 - z2` instead of original karatsuba algorithm.
pm_integer_t x01 = { 0 };
big_add(&x01, &x0, &x1, base);
pm_integer_t y01 = { 0 };
big_add(&y01, &y0, &y1, base);
pm_integer_t xy = { 0 };
karatsuba_multiply(&xy, &x01, &y01, base);
pm_integer_t z1;
big_sub2(&z1, &xy, &z0, &z2, base);
size_t length = left_length + right_length;
uint32_t *values = (uint32_t*) xcalloc(length, sizeof(uint32_t));
assert(z0.values != NULL);
memcpy(values, z0.values, sizeof(uint32_t) * z0.length);
assert(z2.values != NULL);
memcpy(values + 2 * half, z2.values, sizeof(uint32_t) * z2.length);
uint32_t carry = 0;
for(size_t index = 0; index < z1.length; index++) {
uint64_t sum = (uint64_t) carry + values[index + half] + z1.values[index];
values[index + half] = (uint32_t) (sum % base);
carry = (uint32_t) (sum / base);
}
for(size_t index = half + z1.length; carry > 0; index++) {
uint64_t sum = (uint64_t) carry + values[index];
values[index] = (uint32_t) (sum % base);
carry = (uint32_t) (sum / base);
}
while (length > 1 && values[length - 1] == 0) length--;
pm_integer_free(&z0);
pm_integer_free(&z1);
pm_integer_free(&z2);
pm_integer_free(&x01);
pm_integer_free(&y01);
pm_integer_free(&xy);
*destination = (pm_integer_t) { length, values, 0, false };
}
/**
* The values of a hexadecimal digit, where the index is the ASCII character.
* Note that there's an odd exception here where _ is mapped to 0. This is
* because it's possible for us to end up trying to parse a number that has
* already had an error attached to it, and we want to provide _something_ to
* the user.
*/
static const int8_t pm_integer_parse_digit_values[256] = {
// 0 1 2 3 4 5 6 7 8 9 A B C D E F
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // 0x
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // 1x
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // 2x
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, -1, -1, -1, -1, -1, // 3x
-1, 10, 11, 12, 13, 14, 15, -1, -1, -1, -1, -1, -1, -1, -1, -1, // 4x
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, // 5x
-1, 10, 11, 12, 13, 14, 15, -1, -1, -1, -1, -1, -1, -1, -1, -1, // 6x
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // 7x
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // 8x
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // 9x
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // Ax
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // Bx
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // Cx
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // Dx
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // Ex
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, // Fx
};
/**
* Return the value of a hexadecimal digit in a uint8_t.
*/
static uint8_t
pm_integer_parse_digit(const uint8_t character) {
int8_t value = pm_integer_parse_digit_values[character];
assert(value != -1 && "invalid digit");
return (uint8_t) value;
}
/**
* Create a pm_integer_t from uint64_t with the given base. It is assumed that
* the memory for the pm_integer_t pointer has been zeroed.
*/
static void
pm_integer_from_uint64(pm_integer_t *integer, uint64_t value, uint64_t base) {
if (value < base) {
integer->value = (uint32_t) value;
return;
}
size_t length = 0;
uint64_t length_value = value;
while (length_value > 0) {
length++;
length_value /= base;
}
uint32_t *values = (uint32_t *) xmalloc(sizeof(uint32_t) * length);
if (values == NULL) return;
for (size_t value_index = 0; value_index < length; value_index++) {
values[value_index] = (uint32_t) (value % base);
value /= base;
}
integer->length = length;
integer->values = values;
}
/**
* 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) { .values = NULL, .value = value, .length = 0, .negative = negative };
}
/**
* Convert base of the integer.
* In practice, it converts 10**9 to 1<<32 or 1<<32 to 10**9.
*/
static void
pm_integer_convert_base(pm_integer_t *destination, const pm_integer_t *source, uint64_t base_from, uint64_t base_to) {
size_t source_length;
const uint32_t *source_values;
INTEGER_EXTRACT(source, source_length, source_values)
size_t bigints_length = (source_length + 1) / 2;
assert(bigints_length > 0);
pm_integer_t *bigints = (pm_integer_t *) xcalloc(bigints_length, sizeof(pm_integer_t));
if (bigints == NULL) return;
for (size_t index = 0; index < source_length; index += 2) {
uint64_t value = source_values[index] + base_from * (index + 1 < source_length ? source_values[index + 1] : 0);
pm_integer_from_uint64(&bigints[index / 2], value, base_to);
}
pm_integer_t base = { 0 };
pm_integer_from_uint64(&base, base_from, base_to);
while (bigints_length > 1) {
pm_integer_t next_base;
karatsuba_multiply(&next_base, &base, &base, base_to);
pm_integer_free(&base);
base = next_base;
size_t next_length = (bigints_length + 1) / 2;
pm_integer_t *next_bigints = (pm_integer_t *) xcalloc(next_length, sizeof(pm_integer_t));
for (size_t bigints_index = 0; bigints_index < bigints_length; bigints_index += 2) {
if (bigints_index + 1 == bigints_length) {
next_bigints[bigints_index / 2] = bigints[bigints_index];
} else {
pm_integer_t multiplied = { 0 };
karatsuba_multiply(&multiplied, &base, &bigints[bigints_index + 1], base_to);
big_add(&next_bigints[bigints_index / 2], &bigints[bigints_index], &multiplied, base_to);
pm_integer_free(&bigints[bigints_index]);
pm_integer_free(&bigints[bigints_index + 1]);
pm_integer_free(&multiplied);
}
}
xfree(bigints);
bigints = next_bigints;
bigints_length = next_length;
}
*destination = bigints[0];
destination->negative = source->negative;
pm_integer_normalize(destination);
xfree(bigints);
pm_integer_free(&base);
}
#undef INTEGER_EXTRACT
/**
* Convert digits to integer with the given power-of-two base.
*/
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;
uint32_t *values = (uint32_t *) xcalloc(length, sizeof(uint32_t));
for (size_t digit_index = 0; digit_index < digits_length; digit_index++) {
size_t bit_position = bit * (digits_length - digit_index - 1);
uint32_t value = digits[digit_index];
size_t index = bit_position / 32;
size_t shift = bit_position % 32;
values[index] |= value << shift;
if (32 - shift < bit) values[index + 1] |= value >> (32 - shift);
}
while (length > 1 && values[length - 1] == 0) length--;
*integer = (pm_integer_t) { .length = length, .values = values, .value = 0, .negative = false };
pm_integer_normalize(integer);
}
/**
* Convert decimal digits to pm_integer_t.
*/
static void
pm_integer_parse_decimal(pm_integer_t *integer, const uint8_t *digits, size_t digits_length) {
const size_t batch = 9;
size_t length = (digits_length + batch - 1) / batch;
uint32_t *values = (uint32_t *) xcalloc(length, sizeof(uint32_t));
uint32_t value = 0;
for (size_t digits_index = 0; digits_index < digits_length; digits_index++) {
value = value * 10 + digits[digits_index];
size_t reverse_index = digits_length - digits_index - 1;
if (reverse_index % batch == 0) {
values[reverse_index / batch] = value;
value = 0;
}
}
// Convert base from 10**9 to 1<<32.
pm_integer_convert_base(integer, &((pm_integer_t) { .length = length, .values = values, .value = 0, .negative = false }), 1000000000, ((uint64_t) 1 << 32));
xfree(values);
}
/**
* Parse a large integer from a string that does not fit into uint32_t.
*/
static void
pm_integer_parse_big(pm_integer_t *integer, uint32_t multiplier, const uint8_t *start, const uint8_t *end) {
// Allocate an array to store digits.
uint8_t *digits = xmalloc(sizeof(uint8_t) * (size_t) (end - start));
size_t digits_length = 0;
for (; start < end; start++) {
if (*start == '_') continue;
digits[digits_length++] = pm_integer_parse_digit(*start);
}
// 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);
}
xfree(digits);
}
/**
* Parse an integer from a string. This assumes that the format of the integer
* has already been validated, as internal validation checks are not performed
* here.
*/
void
pm_integer_parse(pm_integer_t *integer, pm_integer_base_t base, const uint8_t *start, const uint8_t *end) {
// Ignore unary +. Unary - is parsed differently and will not end up here.
// Instead, it will modify the parsed integer later.
if (*start == '+') start++;
// Determine the multiplier from the base, and skip past any prefixes.
uint32_t multiplier = 10;
switch (base) {
case PM_INTEGER_BASE_DEFAULT:
while (*start == '0') start++; // 01 -> 1
break;
case PM_INTEGER_BASE_BINARY:
start += 2; // 0b
multiplier = 2;
break;
case PM_INTEGER_BASE_OCTAL:
start++; // 0
if (*start == '_' || *start == 'o' || *start == 'O') start++; // o
multiplier = 8;
break;
case PM_INTEGER_BASE_DECIMAL:
if (*start == '0' && (end - start) > 1) start += 2; // 0d
break;
case PM_INTEGER_BASE_HEXADECIMAL:
start += 2; // 0x
multiplier = 16;
break;
case PM_INTEGER_BASE_UNKNOWN:
if (*start == '0' && (end - start) > 1) {
switch (start[1]) {
case '_': start += 2; multiplier = 8; break;
case '0': case '1': case '2': case '3': case '4': case '5': case '6': case '7': start++; multiplier = 8; break;
case 'b': case 'B': start += 2; multiplier = 2; break;
case 'o': case 'O': start += 2; multiplier = 8; break;
case 'd': case 'D': start += 2; break;
case 'x': case 'X': start += 2; multiplier = 16; break;
default: assert(false && "unreachable"); break;
}
}
break;
}
// It's possible that we've consumed everything at this point if there is an
// invalid integer. If this is the case, we'll just return 0.
if (start >= end) return;
const uint8_t *cursor = start;
uint64_t value = (uint64_t) pm_integer_parse_digit(*cursor++);
for (; cursor < end; cursor++) {
if (*cursor == '_') continue;
value = value * multiplier + (uint64_t) pm_integer_parse_digit(*cursor);
if (value > UINT32_MAX) {
// 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->value = (uint32_t) value;
}
/**
* Compare two integers. This function returns -1 if the left integer is less
* than the right integer, 0 if they are equal, and 1 if the left integer is
* greater than the right integer.
*/
int
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->values == NULL && right->values == NULL) {
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 (size_t index = 0; index < left->length; index++) {
size_t value_index = left->length - index - 1;
uint32_t left_value = left->values[value_index];
uint32_t right_value = right->values[value_index];
if (left_value < right_value) return -1 * negative;
if (left_value > right_value) return 1 * negative;
}
return 0;
}
/**
* Reduce a ratio of integers to its simplest form.
*/
void pm_integers_reduce(pm_integer_t *numerator, pm_integer_t *denominator) {
// If either the numerator or denominator do not fit into a 32-bit integer,
// then this function is a no-op. In the future, we may consider reducing
// even the larger numbers, but for now we're going to keep it simple.
if (
// If the numerator doesn't fit into a 32-bit integer, return early.
numerator->length != 0 ||
// If the denominator doesn't fit into a 32-bit integer, return early.
denominator->length != 0 ||
// If the numerator is 0, then return early.
numerator->value == 0 ||
// If the denominator is 1, then return early.
denominator->value == 1
) return;
// Find the greatest common divisor of the numerator and denominator.
uint32_t divisor = numerator->value;
uint32_t remainder = denominator->value;
while (remainder != 0) {
uint32_t temporary = remainder;
remainder = divisor % remainder;
divisor = temporary;
}
// Divide the numerator and denominator by the greatest common divisor.
numerator->value /= divisor;
denominator->value /= divisor;
}
/**
* Convert an integer to a decimal string.
*/
PRISM_EXPORTED_FUNCTION void
pm_integer_string(pm_buffer_t *buffer, const pm_integer_t *integer) {
if (integer->negative) {
pm_buffer_append_byte(buffer, '-');
}
// If the integer fits into a single uint32_t, then we can just append the
// value directly to the buffer.
if (integer->values == NULL) {
pm_buffer_append_format(buffer, "%" PRIu32, integer->value);
return;
}
// If the integer is two uint32_t values, then we can | them together and
// append the result to the buffer.
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;
}
// Otherwise, first we'll convert the base from 1<<32 to 10**9.
pm_integer_t converted = { 0 };
pm_integer_convert_base(&converted, integer, (uint64_t) 1 << 32, 1000000000);
if (converted.values == NULL) {
pm_buffer_append_format(buffer, "%" PRIu32, converted.value);
pm_integer_free(&converted);
return;
}
// Allocate a buffer that we'll copy the decimal digits into.
size_t digits_length = converted.length * 9;
char *digits = xcalloc(digits_length, sizeof(char));
if (digits == NULL) return;
// Pack bigdecimal to digits.
for (size_t value_index = 0; value_index < converted.length; value_index++) {
uint32_t value = converted.values[value_index];
for (size_t digit_index = 0; digit_index < 9; digit_index++) {
digits[digits_length - 9 * value_index - digit_index - 1] = (char) ('0' + value % 10);
value /= 10;
}
}
size_t start_offset = 0;
while (start_offset < digits_length - 1 && digits[start_offset] == '0') start_offset++;
// Finally, append the string to the buffer and free the digits.
pm_buffer_append_string(buffer, digits + start_offset, digits_length - start_offset);
xfree(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 uint32_t.
*/
PRISM_EXPORTED_FUNCTION void
pm_integer_free(pm_integer_t *integer) {
if (integer->values) {
xfree(integer->values);
}
}
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