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2165 lines
49 KiB
C
2165 lines
49 KiB
C
// Copyright (c) 2019 Christoffer Lerno. All rights reserved.
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// Use of this source code is governed by the GNU LGPLv3.0 license
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// a copy of which can be found in the LICENSE file.
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#include "bigint.h"
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#include "../utils/lib.h"
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#include <inttypes.h>
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static inline uint32_t u32_min(uint32_t a, uint32_t b)
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{
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return a < b ? a : b;
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}
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static inline size_t size_max(size_t a, size_t b)
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{
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return a > b ? a : b;
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}
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static inline unsigned unsigned_max(unsigned a, unsigned b)
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{
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return a > b ? a : b;
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}
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static inline const uint64_t *bigint_ptr(const BigInt *big_int)
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{
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return big_int->digit_count == 1 ? &big_int->digit : big_int->digits;
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}
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#define alloc_digits(_digits) ((_digits) ? malloc_arena(sizeof(uint64_t) * (_digits)) : NULL)
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static void normalize(BigInt *big_int)
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{
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const uint64_t *digits = bigint_ptr(big_int);
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unsigned last_non_zero = UINT32_MAX;
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for (unsigned i = 0; i < big_int->digit_count; i++)
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{
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if (digits[i] != 0)
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{
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last_non_zero = i;
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}
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}
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if (last_non_zero == UINT32_MAX)
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{
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big_int->is_negative = false;
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big_int->digit_count = 0;
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return;
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}
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big_int->digit_count = last_non_zero + 1;
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if (!last_non_zero)
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{
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big_int->digit = digits[0];
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}
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}
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static char digit_to_char(uint8_t digit, bool upper)
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{
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if (digit <= 9)
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{
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return (char) (digit + '0');
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}
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if (digit <= 35)
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{
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return (char) (digit + (upper ? 'A' : 'a') - 10);
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}
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FATAL_ERROR("Can't reach");
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}
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static bool bit_at_index(const BigInt *big_int, size_t index)
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{
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size_t digit_index = index / 64;
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if (digit_index >= big_int->digit_count)
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{
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return false;
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}
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size_t digit_bit_index = index % 64;
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const uint64_t *digits = bigint_ptr(big_int);
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uint64_t digit = digits[digit_index];
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return ((digit >> digit_bit_index) & 0x1U) == 0x1U;
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}
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uint32_t bigint_hash(BigInt x)
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{
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if (x.digit_count == 0)
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{
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return 0;
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}
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else
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{
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return (uint32_t) bigint_ptr(&x)[0];
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}
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}
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static size_t bigint_bits_needed(const BigInt *big_int)
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{
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size_t full_bits = big_int->digit_count * 64;
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size_t leading_zero_count = bigint_clz(big_int, full_bits);
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size_t bits_needed = full_bits - leading_zero_count;
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return bits_needed + big_int->is_negative;
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}
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void bigint_init_unsigned(BigInt *big_int, uint64_t value)
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{
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if (value == 0)
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{
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big_int->digit_count = 0;
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big_int->is_negative = false;
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return;
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}
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big_int->digit_count = 1;
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big_int->digit = value;
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big_int->is_negative = false;
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}
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void bigint_init_signed(BigInt *dest, int64_t value)
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{
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if (value >= 0)
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{
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return bigint_init_unsigned(dest, (uint64_t)value);
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}
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dest->is_negative = true;
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dest->digit_count = 1;
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dest->digit = ((uint64_t) (-(value + 1))) + 1;
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}
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void bigint_init_bigint(BigInt *dest, const BigInt *src)
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{
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if (src->digit_count == 0)
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{
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return bigint_init_unsigned(dest, 0);
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}
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if (src->digit_count == 1)
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{
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dest->digit_count = 1;
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dest->digit = src->digit;
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dest->is_negative = src->is_negative;
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return;
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}
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dest->is_negative = src->is_negative;
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dest->digit_count = src->digit_count;
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dest->digits = alloc_digits(dest->digit_count);
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memcpy(dest->digits, src->digits, sizeof(uint64_t) * dest->digit_count);
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}
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void bigint_negate(BigInt *dest, const BigInt *source)
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{
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bigint_init_bigint(dest, source);
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dest->is_negative = !dest->is_negative;
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normalize(dest);
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}
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static void to_twos_complement(BigInt *dest, const BigInt *source, size_t bit_count)
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{
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if (bit_count == 0 || source->digit_count == 0)
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{
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bigint_init_unsigned(dest, 0);
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return;
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}
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if (source->is_negative)
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{
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BigInt negated = { 0 };
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bigint_negate(&negated, source);
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BigInt inverted = { 0 };
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bigint_not(&inverted, &negated, bit_count, false);
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BigInt one = { 0 };
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bigint_init_unsigned(&one, 1);
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bigint_add(dest, &inverted, &one);
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return;
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}
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dest->is_negative = false;
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const uint64_t *source_digits = bigint_ptr(source);
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if (source->digit_count == 1)
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{
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dest->digit = source_digits[0];
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if (bit_count < 64)
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{
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dest->digit &= (1ULL << bit_count) - 1;
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}
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dest->digit_count = 1;
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normalize(dest);
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return;
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}
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unsigned digits_to_copy = (unsigned int) (bit_count / 64);
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unsigned leftover_bits = (unsigned int) (bit_count % 64);
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dest->digit_count = digits_to_copy + ((leftover_bits == 0) ? 0 : 1);
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if (dest->digit_count == 1 && leftover_bits == 0)
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{
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dest->digit = source_digits[0];
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if (dest->digit == 0) dest->digit_count = 0;
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return;
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}
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dest->digits = malloc_arena(dest->digit_count * sizeof(u_int64_t));
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for (size_t i = 0; i < digits_to_copy; i += 1)
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{
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uint64_t digit = (i < source->digit_count) ? source_digits[i] : 0;
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dest->digits[i] = digit;
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}
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if (leftover_bits != 0)
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{
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uint64_t digit = (digits_to_copy < source->digit_count) ? source_digits[digits_to_copy] : 0;
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dest->digits[digits_to_copy] = digit & ((1ULL << leftover_bits) - 1);
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}
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normalize(dest);
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}
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size_t bigint_clz(const BigInt *big_int, size_t bit_count)
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{
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if (big_int->is_negative || bit_count == 0)
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{
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return 0;
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}
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if (big_int->digit_count == 0)
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{
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return bit_count;
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}
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size_t count = 0;
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for (size_t i = bit_count - 1;;)
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{
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if (bit_at_index(big_int, i))
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{
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return count;
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}
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count++;
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if (i == 0) break;
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i--;
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}
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return count;
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}
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bool bigint_eql(BigInt a, BigInt b)
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{
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return bigint_cmp(&a, &b) == CMP_EQ;
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}
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static void from_twos_complement(BigInt *dest, const BigInt *src, size_t bit_count, bool is_signed)
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{
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assert(!src->is_negative);
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if (bit_count == 0 || src->digit_count == 0)
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{
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bigint_init_unsigned(dest, 0);
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return;
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}
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if (is_signed && bit_at_index(src, bit_count - 1))
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{
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BigInt negative_one = { 0 };
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bigint_init_signed(&negative_one, -1);
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BigInt minus_one = { 0 };
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bigint_add(&minus_one, src, &negative_one);
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BigInt inverted = { 0 };
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bigint_not(&inverted, &minus_one, bit_count, false);
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bigint_negate(dest, &inverted);
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return;
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}
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bigint_init_bigint(dest, src);
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}
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void bigint_init_data(BigInt *dest, const uint64_t *digits, unsigned int digit_count, bool is_negative)
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{
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if (digit_count == 0)
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{
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return bigint_init_unsigned(dest, 0);
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}
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else if (digit_count == 1)
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{
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dest->digit_count = 1;
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dest->digit = digits[0];
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dest->is_negative = is_negative;
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normalize(dest);
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return;
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}
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dest->digit_count = digit_count;
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dest->is_negative = is_negative;
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dest->digits = alloc_digits(digit_count);
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memcpy(dest->digits, digits, sizeof(uint64_t) * digit_count);
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normalize(dest);
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}
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/* TODO
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void bigint_init_bigfloat(BigInt *dest, const BigFloat *op) {
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float128_t zero;
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ui32_to_f128M(0, &zero);
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dest->is_negative = f128M_lt(&op->value, &zero);
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float128_t abs_val;
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if (dest->is_negative) {
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f128M_sub(&zero, &op->value, &abs_val);
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} else {
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memcpy(&abs_val, &op->value, sizeof(float128_t));
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}
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float128_t max_u64;
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ui64_to_f128M(UINT64_MAX, &max_u64);
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if (f128M_le(&abs_val, &max_u64)) {
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dest->digit_count = 1;
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dest->data.digit = f128M_to_ui64(&op->value, softfloat_round_minMag, false);
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bigint_normalize(dest);
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return;
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}
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float128_t amt;
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f128M_div(&abs_val, &max_u64, &amt);
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float128_t remainder;
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f128M_rem(&abs_val, &max_u64, &remainder);
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dest->digit_count = 2;
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dest->data.digits = allocate_nonzero<uint64_t>(dest->digit_count);
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dest->data.digits[0] = f128M_to_ui64(&remainder, softfloat_round_minMag, false);
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dest->data.digits[1] = f128M_to_ui64(&amt, softfloat_round_minMag, false);
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bigint_normalize(dest);
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}
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*/
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bool bigint_fits_in_bits(const BigInt *big_int, size_t bit_count, bool is_signed)
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{
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assert(big_int->digit_count != 1 || big_int->digit != 0);
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if (bit_count == 0)
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{
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return bigint_cmp_zero(big_int) == CMP_EQ;
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}
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if (big_int->digit_count == 0)
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{
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return true;
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}
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if (!is_signed)
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{
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size_t full_bits = big_int->digit_count * 64;
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size_t leading_zero_count = bigint_clz(big_int, full_bits);
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return bit_count >= full_bits - leading_zero_count;
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}
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BigInt one = { 0 };
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bigint_init_unsigned(&one, 1);
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BigInt shl_amt = { 0 };
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bigint_init_unsigned(&shl_amt, bit_count - 1);
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BigInt max_value_plus_one = { 0 };
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bigint_shl(&max_value_plus_one, &one, &shl_amt);
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BigInt max_value = { 0 };
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bigint_sub(&max_value, &max_value_plus_one, &one);
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BigInt min_value = { 0 };
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bigint_negate(&min_value, &max_value_plus_one);
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CmpRes min_cmp = bigint_cmp(big_int, &min_value);
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CmpRes max_cmp = bigint_cmp(big_int, &max_value);
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return (min_cmp == CMP_GT || min_cmp == CMP_EQ) && (max_cmp == CMP_LT || max_cmp == CMP_EQ);
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}
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void bigint_write_twos_complement(const BigInt *big_int, uint8_t *buf, size_t bit_count, bool is_big_endian)
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{
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if (bit_count == 0)
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{
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return;
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}
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BigInt twos_comp = { 0 };
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to_twos_complement(&twos_comp, big_int, bit_count);
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const uint64_t *twos_comp_digits = bigint_ptr(&twos_comp);
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size_t bits_in_last_digit = bit_count % 64;
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if (bits_in_last_digit == 0) bits_in_last_digit = 64;
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size_t bytes_in_last_digit = (bits_in_last_digit + 7) / 8;
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size_t unwritten_byte_count = 8 - bytes_in_last_digit;
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if (is_big_endian)
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{
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size_t last_digit_index = (bit_count - 1) / 64;
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size_t digit_index = last_digit_index;
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size_t buf_index = 0;
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for (;;)
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{
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uint64_t x = (digit_index < twos_comp.digit_count) ? twos_comp_digits[digit_index] : 0;
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for (size_t byte_index = 7;;)
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{
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uint8_t byte = (uint8_t) (x & 0xffU);
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if (digit_index == last_digit_index)
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{
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buf[buf_index + byte_index - unwritten_byte_count] = byte;
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if (byte_index == unwritten_byte_count) break;
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}
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else
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{
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buf[buf_index + byte_index] = byte;
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}
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if (byte_index == 0) break;
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byte_index -= 1;
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x >>= 8U;
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}
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if (digit_index == 0) break;
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digit_index -= 1;
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if (digit_index == last_digit_index)
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{
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buf_index += bytes_in_last_digit;
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}
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else
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{
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buf_index += 8;
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}
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}
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}
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else
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{
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size_t digit_count = (bit_count + 63) / 64;
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size_t buf_index = 0;
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for (size_t digit_index = 0; digit_index < digit_count; digit_index += 1)
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{
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uint64_t x = (digit_index < twos_comp.digit_count) ? twos_comp_digits[digit_index] : 0;
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for (size_t byte_index = 0;
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byte_index < 8 && (digit_index + 1 < digit_count || byte_index < bytes_in_last_digit);
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byte_index += 1)
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{
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uint8_t byte = (uint8_t) (x & 0xffU);
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buf[buf_index] = byte;
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buf_index += 1;
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x >>= 8U;
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}
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}
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}
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}
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uint64_t bigint_as_unsigned(const BigInt *bigint)
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{
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assert(!bigint->is_negative);
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if (bigint->digit_count == 0)
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{
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return 0;
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}
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if (bigint->digit_count != 1)
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{
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FATAL_ERROR("Bigint exceeds u64");
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}
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return bigint->digit;
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}
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void bigint_read_twos_complement(BigInt *dest, const uint8_t *buf, size_t bit_count, bool is_big_endian,
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bool is_signed)
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{
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if (bit_count == 0)
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{
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bigint_init_unsigned(dest, 0);
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return;
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}
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dest->digit_count = (unsigned int) ((bit_count + 63) / 64);
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uint64_t *digits;
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if (dest->digit_count == 1)
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{
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digits = &dest->digit;
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}
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else
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{
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digits = alloc_digits(dest->digit_count);
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dest->digits = digits;
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}
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size_t bits_in_last_digit = bit_count % 64;
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if (bits_in_last_digit == 0)
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{
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bits_in_last_digit = 64;
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}
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size_t bytes_in_last_digit = (bits_in_last_digit + 7) / 8;
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size_t unread_byte_count = 8 - bytes_in_last_digit;
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if (is_big_endian)
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{
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size_t buf_index = 0;
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uint64_t digit = 0;
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for (size_t byte_index = unread_byte_count; byte_index < 8; byte_index += 1)
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{
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uint8_t byte = buf[buf_index];
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buf_index += 1;
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digit <<= 8U;
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digit |= byte;
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}
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digits[dest->digit_count - 1] = digit;
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for (size_t digit_index = 1; digit_index < dest->digit_count; digit_index += 1)
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{
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digit = 0;
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for (size_t byte_index = 0; byte_index < 8; byte_index += 1)
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{
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uint8_t byte = buf[buf_index];
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buf_index += 1;
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digit <<= 8;
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digit |= byte;
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}
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digits[dest->digit_count - 1 - digit_index] = digit;
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}
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}
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else
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{
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size_t buf_index = 0;
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for (size_t digit_index = 0; digit_index < dest->digit_count; digit_index += 1)
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{
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uint64_t digit = 0;
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|
size_t end_byte_index = (digit_index == dest->digit_count - 1) ? bytes_in_last_digit : 8;
|
|
for (size_t byte_index = 0; byte_index < end_byte_index; byte_index += 1)
|
|
{
|
|
uint64_t byte = buf[buf_index];
|
|
buf_index += 1;
|
|
|
|
digit |= byte << (8 * byte_index);
|
|
}
|
|
digits[digit_index] = digit;
|
|
}
|
|
}
|
|
|
|
if (is_signed)
|
|
{
|
|
normalize(dest);
|
|
BigInt tmp = { 0 };
|
|
bigint_init_bigint(&tmp, dest);
|
|
from_twos_complement(dest, &tmp, bit_count, true);
|
|
}
|
|
else
|
|
{
|
|
dest->is_negative = false;
|
|
normalize(dest);
|
|
}
|
|
}
|
|
|
|
#if defined(_MSC_VER)
|
|
|
|
static bool add_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result)
|
|
{
|
|
*result = op1 + op2;
|
|
return *result < op1 || *result < op2;
|
|
}
|
|
|
|
static bool sub_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result)
|
|
{
|
|
*result = op1 - op2;
|
|
return *result > op1;
|
|
}
|
|
|
|
bool mul_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result)
|
|
{
|
|
*result = op1 * op2;
|
|
|
|
if (op1 == 0 || op2 == 0) return false;
|
|
if (op1 > UINT64_MAX / op2) return true;
|
|
if (op2 > UINT64_MAX / op1) return true;
|
|
return false;
|
|
}
|
|
|
|
#else
|
|
|
|
static bool add_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result)
|
|
{
|
|
return __builtin_uaddll_overflow((unsigned long long) op1, (unsigned long long) op2,
|
|
(unsigned long long *) result);
|
|
}
|
|
|
|
static bool sub_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result)
|
|
{
|
|
return __builtin_usubll_overflow((unsigned long long) op1, (unsigned long long) op2,
|
|
(unsigned long long *) result);
|
|
}
|
|
|
|
bool mul_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result)
|
|
{
|
|
return __builtin_umulll_overflow((unsigned long long) op1, (unsigned long long) op2,
|
|
(unsigned long long *) result);
|
|
}
|
|
|
|
#endif
|
|
|
|
void bigint_add(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
if (op1->digit_count == 0)
|
|
{
|
|
return bigint_init_bigint(dest, op2);
|
|
}
|
|
if (op2->digit_count == 0)
|
|
{
|
|
return bigint_init_bigint(dest, op1);
|
|
}
|
|
if (op1->is_negative == op2->is_negative)
|
|
{
|
|
dest->is_negative = op1->is_negative;
|
|
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
const uint64_t *op2_digits = bigint_ptr(op2);
|
|
bool overflow = add_u64_overflow(op1_digits[0], op2_digits[0], &dest->digit);
|
|
if (overflow == 0 && op1->digit_count == 1 && op2->digit_count == 1)
|
|
{
|
|
dest->digit_count = 1;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
unsigned i = 1;
|
|
uint64_t first_digit = dest->digit;
|
|
dest->digits = alloc_digits(unsigned_max(op1->digit_count, op2->digit_count) + 1);
|
|
dest->digits[0] = first_digit;
|
|
|
|
for (;;)
|
|
{
|
|
bool found_digit = false;
|
|
uint64_t x = (uint64_t) overflow;
|
|
overflow = 0;
|
|
|
|
if (i < op1->digit_count)
|
|
{
|
|
found_digit = true;
|
|
uint64_t digit = op1_digits[i];
|
|
overflow += add_u64_overflow(x, digit, &x);
|
|
}
|
|
|
|
if (i < op2->digit_count)
|
|
{
|
|
found_digit = true;
|
|
uint64_t digit = op2_digits[i];
|
|
overflow += add_u64_overflow(x, digit, &x);
|
|
}
|
|
|
|
dest->digits[i] = x;
|
|
i += 1;
|
|
|
|
if (!found_digit)
|
|
{
|
|
dest->digit_count = i;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
const BigInt *op_pos;
|
|
const BigInt *op_neg;
|
|
if (op1->is_negative)
|
|
{
|
|
op_neg = op1;
|
|
op_pos = op2;
|
|
}
|
|
else
|
|
{
|
|
op_pos = op1;
|
|
op_neg = op2;
|
|
}
|
|
|
|
BigInt op_neg_abs = { 0 };
|
|
bigint_negate(&op_neg_abs, op_neg);
|
|
const BigInt *bigger_op;
|
|
const BigInt *smaller_op;
|
|
switch (bigint_cmp(op_pos, &op_neg_abs))
|
|
{
|
|
case CMP_EQ:
|
|
bigint_init_unsigned(dest, 0);
|
|
return;
|
|
case CMP_LT:
|
|
bigger_op = &op_neg_abs;
|
|
smaller_op = op_pos;
|
|
dest->is_negative = true;
|
|
break;
|
|
case CMP_GT:
|
|
bigger_op = op_pos;
|
|
smaller_op = &op_neg_abs;
|
|
dest->is_negative = false;
|
|
break;
|
|
default:
|
|
FATAL_ERROR("UNREACHABLE");
|
|
}
|
|
const uint64_t *bigger_op_digits = bigint_ptr(bigger_op);
|
|
const uint64_t *smaller_op_digits = bigint_ptr(smaller_op);
|
|
uint64_t overflow = (uint64_t)sub_u64_overflow(bigger_op_digits[0], smaller_op_digits[0], &dest->digit);
|
|
if (overflow == 0 && bigger_op->digit_count == 1 && smaller_op->digit_count == 1)
|
|
{
|
|
dest->digit_count = 1;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
uint64_t first_digit = dest->digit;
|
|
dest->digits = alloc_digits(bigger_op->digit_count);
|
|
dest->digits[0] = first_digit;
|
|
unsigned i = 1;
|
|
|
|
for (;;)
|
|
{
|
|
bool found_digit = false;
|
|
uint64_t x = bigger_op_digits[i];
|
|
uint64_t prev_overflow = overflow;
|
|
overflow = 0;
|
|
|
|
if (i < smaller_op->digit_count)
|
|
{
|
|
found_digit = true;
|
|
uint64_t digit = smaller_op_digits[i];
|
|
overflow += sub_u64_overflow(x, digit, &x);
|
|
}
|
|
if (sub_u64_overflow(x, prev_overflow, &x))
|
|
{
|
|
found_digit = true;
|
|
overflow += 1;
|
|
}
|
|
dest->digits[i] = x;
|
|
i += 1;
|
|
|
|
if (!found_digit || i >= bigger_op->digit_count)
|
|
{
|
|
break;
|
|
}
|
|
}
|
|
assert(overflow == 0);
|
|
dest->digit_count = i;
|
|
normalize(dest);
|
|
}
|
|
|
|
void bigint_add_wrap(BigInt *dest, const BigInt *op1, const BigInt *op2, size_t bit_count, bool is_signed)
|
|
{
|
|
BigInt unwrapped = { 0 };
|
|
bigint_add(&unwrapped, op1, op2);
|
|
bigint_truncate(dest, &unwrapped, bit_count, is_signed);
|
|
}
|
|
|
|
void bigint_sub(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
BigInt op2_negated = { 0 };
|
|
bigint_negate(&op2_negated, op2);
|
|
return bigint_add(dest, op1, &op2_negated);
|
|
}
|
|
|
|
void bigint_sub_wrap(BigInt *dest, const BigInt *op1, const BigInt *op2, size_t bit_count, bool is_signed)
|
|
{
|
|
BigInt op2_negated = { 0 };
|
|
bigint_negate(&op2_negated, op2);
|
|
return bigint_add_wrap(dest, op1, &op2_negated, bit_count, is_signed);
|
|
}
|
|
|
|
static void mul_overflow(uint64_t op1, uint64_t op2, uint64_t *lo, uint64_t *hi)
|
|
{
|
|
uint64_t u1 = (op1 & 0xffffffff);
|
|
uint64_t v1 = (op2 & 0xffffffff);
|
|
uint64_t t = (u1 * v1);
|
|
uint64_t w3 = (t & 0xffffffff);
|
|
uint64_t k = (t >> 32);
|
|
|
|
op1 >>= 32;
|
|
t = (op1 * v1) + k;
|
|
k = (t & 0xffffffff);
|
|
uint64_t w1 = (t >> 32);
|
|
|
|
op2 >>= 32;
|
|
t = (u1 * op2) + k;
|
|
k = (t >> 32);
|
|
|
|
*hi = (op1 * op2) + w1 + k;
|
|
*lo = (t << 32) + w3;
|
|
}
|
|
|
|
static void mul_scalar(BigInt *dest, const BigInt *op, uint64_t scalar)
|
|
{
|
|
bigint_init_unsigned(dest, 0);
|
|
|
|
BigInt bi_64;
|
|
bigint_init_unsigned(&bi_64, 64);
|
|
|
|
const uint64_t *op_digits = bigint_ptr(op);
|
|
size_t i = op->digit_count - 1;
|
|
|
|
while (1)
|
|
{
|
|
BigInt shifted;
|
|
bigint_shl(&shifted, dest, &bi_64);
|
|
|
|
uint64_t result_scalar;
|
|
uint64_t carry_scalar;
|
|
mul_overflow(scalar, op_digits[i], &result_scalar, &carry_scalar);
|
|
|
|
BigInt result;
|
|
bigint_init_unsigned(&result, result_scalar);
|
|
|
|
BigInt carry;
|
|
bigint_init_unsigned(&carry, carry_scalar);
|
|
|
|
BigInt carry_shifted;
|
|
bigint_shl(&carry_shifted, &carry, &bi_64);
|
|
|
|
BigInt tmp;
|
|
bigint_add(&tmp, &shifted, &carry_shifted);
|
|
|
|
bigint_add(dest, &tmp, &result);
|
|
|
|
if (i == 0)
|
|
{
|
|
break;
|
|
}
|
|
i -= 1;
|
|
}
|
|
}
|
|
|
|
void bigint_mul(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
if (op1->digit_count == 0 || op2->digit_count == 0)
|
|
{
|
|
return bigint_init_unsigned(dest, 0);
|
|
}
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
const uint64_t *op2_digits = bigint_ptr(op2);
|
|
|
|
uint64_t carry;
|
|
mul_overflow(op1_digits[0], op2_digits[0], &dest->digit, &carry);
|
|
if (carry == 0 && op1->digit_count == 1 && op2->digit_count == 1)
|
|
{
|
|
dest->is_negative = (op1->is_negative != op2->is_negative);
|
|
dest->digit_count = 1;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
|
|
bigint_init_unsigned(dest, 0);
|
|
|
|
BigInt bi_64;
|
|
bigint_init_unsigned(&bi_64, 64);
|
|
|
|
size_t i = op2->digit_count - 1;
|
|
for (;;)
|
|
{
|
|
BigInt shifted;
|
|
bigint_shl(&shifted, dest, &bi_64);
|
|
|
|
BigInt scalar_result;
|
|
mul_scalar(&scalar_result, op1, op2_digits[i]);
|
|
|
|
bigint_add(dest, &scalar_result, &shifted);
|
|
|
|
if (i == 0)
|
|
{
|
|
break;
|
|
}
|
|
i -= 1;
|
|
}
|
|
|
|
dest->is_negative = (op1->is_negative != op2->is_negative);
|
|
normalize(dest);
|
|
}
|
|
|
|
void bigint_mul_wrap(BigInt *dest, const BigInt *op1, const BigInt *op2, size_t bit_count, bool is_signed)
|
|
{
|
|
BigInt unwrapped = { 0 };
|
|
bigint_mul(&unwrapped, op1, op2);
|
|
bigint_truncate(dest, &unwrapped, bit_count, is_signed);
|
|
}
|
|
|
|
unsigned countLeadingZeros(uint32_t val)
|
|
{
|
|
if (val == 0) return 32;
|
|
|
|
#if defined(_MSC_VER)
|
|
unsigned long Index;
|
|
_BitScanReverse(&Index, Val);
|
|
return Index ^ 31;
|
|
#else
|
|
return __builtin_clz(val);
|
|
#endif
|
|
}
|
|
|
|
/// Make a 64-bit integer from a high / low pair of 32-bit integers.
|
|
static inline uint64_t make_64(uint32_t hi, uint32_t lo)
|
|
{
|
|
return (((uint64_t) hi) << 32) | ((uint64_t) lo);
|
|
}
|
|
|
|
/// Return the high 32 bits of a 64 bit value.
|
|
static inline uint32_t hi_32(uint64_t value)
|
|
{
|
|
return (uint32_t) (value >> 32);
|
|
}
|
|
|
|
/// Return the low 32 bits of a 64 bit value.
|
|
static inline uint32_t lo_32(uint64_t val)
|
|
{
|
|
return (uint32_t) val;
|
|
}
|
|
|
|
/// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
|
|
/// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
|
|
/// variables here have the same names as in the algorithm. Comments explain
|
|
/// the algorithm and any deviation from it.
|
|
static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t *r, unsigned m, unsigned n)
|
|
{
|
|
assert(u && "Must provide dividend");
|
|
assert(v && "Must provide divisor");
|
|
assert(q && "Must provide quotient");
|
|
assert(u != v && u != q && v != q && "Must use different memory");
|
|
assert(n > 1 && "n must be > 1");
|
|
|
|
// b denotes the base of the number system. In our case b is 2^32.
|
|
const uint64_t b = ((uint64_t) 1) << 32;
|
|
|
|
// D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
|
|
// u and v by d. Note that we have taken Knuth's advice here to use a power
|
|
// of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
|
|
// 2 allows us to shift instead of multiply and it is easy to determine the
|
|
// shift amount from the leading zeros. We are basically normalizing the u
|
|
// and v so that its high bits are shifted to the top of v's range without
|
|
// overflow. Note that this can require an extra word in u so that u must
|
|
// be of length m+n+1.
|
|
unsigned shift = countLeadingZeros(v[n - 1]);
|
|
uint32_t v_carry = 0;
|
|
uint32_t u_carry = 0;
|
|
if (shift)
|
|
{
|
|
for (unsigned i = 0; i < m + n; ++i)
|
|
{
|
|
uint32_t u_tmp = u[i] >> (32 - shift);
|
|
u[i] = (u[i] << shift) | u_carry;
|
|
u_carry = u_tmp;
|
|
}
|
|
for (unsigned i = 0; i < n; ++i)
|
|
{
|
|
uint32_t v_tmp = v[i] >> (32 - shift);
|
|
v[i] = (v[i] << shift) | v_carry;
|
|
v_carry = v_tmp;
|
|
}
|
|
}
|
|
u[m + n] = u_carry;
|
|
|
|
// D2. [Initialize j.] Set j to m. This is the loop counter over the places.
|
|
int j = (int)m;
|
|
do
|
|
{
|
|
// D3. [Calculate q'.].
|
|
// Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
|
|
// Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
|
|
// Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
|
|
// qp by 1, increase rp by v[n-1], and repeat this test if rp < b. The test
|
|
// on v[n-2] determines at high speed most of the cases in which the trial
|
|
// value qp is one too large, and it eliminates all cases where qp is two
|
|
// too large.
|
|
uint64_t dividend = make_64(u[j + n], u[j + n - 1]);
|
|
uint64_t qp = dividend / v[n - 1];
|
|
uint64_t rp = dividend % v[n - 1];
|
|
if (qp == b || qp * v[n - 2] > b * rp + u[j + n - 2])
|
|
{
|
|
qp--;
|
|
rp += v[n - 1];
|
|
if (rp < b && (qp == b || qp * v[n - 2] > b * rp + u[j + n - 2]))
|
|
{
|
|
qp--;
|
|
}
|
|
}
|
|
|
|
// D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
|
|
// (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
|
|
// consists of a simple multiplication by a one-place number, combined with
|
|
// a subtraction.
|
|
// The digits (u[j+n]...u[j]) should be kept positive; if the result of
|
|
// this step is actually negative, (u[j+n]...u[j]) should be left as the
|
|
// true value plus b**(n+1), namely as the b's complement of
|
|
// the true value, and a "borrow" to the left should be remembered.
|
|
int64_t borrow = 0;
|
|
for (unsigned i = 0; i < n; ++i)
|
|
{
|
|
uint64_t p = ((uint64_t) qp) * ((uint64_t) (v[i]));
|
|
int64_t subres = ((int64_t) (u[j + i])) - borrow - lo_32(p);
|
|
u[j + i] = lo_32((uint64_t) subres);
|
|
borrow = hi_32(p) - hi_32((uint64_t) subres);
|
|
}
|
|
bool is_neg = u[j + n] < borrow;
|
|
u[j + n] -= lo_32((uint64_t) borrow);
|
|
|
|
// D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
|
|
// negative, go to step D6; otherwise go on to step D7.
|
|
q[j] = lo_32(qp);
|
|
if (is_neg)
|
|
{
|
|
// D6. [Add back]. The probability that this step is necessary is very
|
|
// small, on the order of only 2/b. Make sure that test data accounts for
|
|
// this possibility. Decrease q[j] by 1
|
|
q[j]--;
|
|
// and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
|
|
// A carry will occur to the left of u[j+n], and it should be ignored
|
|
// since it cancels with the borrow that occurred in D4.
|
|
bool carry = false;
|
|
for (unsigned i = 0; i < n; i++)
|
|
{
|
|
uint32_t limit = u32_min(u[j + i], v[i]);
|
|
u[j + i] += v[i] + carry;
|
|
carry = u[j + i] < limit || (carry && u[j + i] == limit);
|
|
}
|
|
u[j + n] += carry;
|
|
}
|
|
|
|
// D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
|
|
} while (--j >= 0);
|
|
|
|
// D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
|
|
// remainder may be obtained by dividing u[...] by d. If r is non-null we
|
|
// compute the remainder (urem uses this).
|
|
if (r)
|
|
{
|
|
// The value d is expressed by the "shift" value above since we avoided
|
|
// multiplication by d by using a shift left. So, all we have to do is
|
|
// shift right here.
|
|
if (shift)
|
|
{
|
|
uint32_t carry = 0;
|
|
for (int i = (int)n - 1; i >= 0; i--)
|
|
{
|
|
r[i] = (u[i] >> shift) | carry;
|
|
carry = u[i] << (32 - shift);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (int i = (int)n - 1; i >= 0; i--)
|
|
{
|
|
r[i] = u[i];
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
static void bigint_unsigned_division(const BigInt *op1, const BigInt *op2, BigInt *Quotient, BigInt *Remainder)
|
|
{
|
|
CmpRes cmp = bigint_cmp(op1, op2);
|
|
if (cmp == CMP_LT)
|
|
{
|
|
if (!Quotient)
|
|
{
|
|
bigint_init_unsigned(Quotient, 0);
|
|
}
|
|
if (!Remainder)
|
|
{
|
|
bigint_init_bigint(Remainder, op1);
|
|
}
|
|
return;
|
|
}
|
|
if (cmp == CMP_EQ)
|
|
{
|
|
if (!Quotient)
|
|
{
|
|
bigint_init_unsigned(Quotient, 1);
|
|
}
|
|
if (!Remainder)
|
|
{
|
|
bigint_init_unsigned(Remainder, 0);
|
|
}
|
|
return;
|
|
}
|
|
|
|
const uint64_t *LHS = bigint_ptr(op1);
|
|
const uint64_t *RHS = bigint_ptr(op2);
|
|
unsigned lhsWords = op1->digit_count;
|
|
unsigned rhsWords = op2->digit_count;
|
|
|
|
// First, compose the values into an array of 32-bit words instead of
|
|
// 64-bit words. This is a necessity of both the "short division" algorithm
|
|
// and the Knuth "classical algorithm" which requires there to be native
|
|
// operations for +, -, and * on an m bit value with an m*2 bit result. We
|
|
// can't use 64-bit operands here because we don't have native results of
|
|
// 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
|
|
// work on large-endian machines.
|
|
unsigned n = rhsWords * 2;
|
|
unsigned m = (lhsWords * 2) - n;
|
|
|
|
// Allocate space for the temporary values we need either on the stack, if
|
|
// it will fit, or on the heap if it won't.
|
|
uint32_t SPACE[128];
|
|
uint32_t *U = NULL;
|
|
uint32_t *V = NULL;
|
|
uint32_t *Q = NULL;
|
|
uint32_t *R = NULL;
|
|
if ((Remainder ? 4 : 3) * n + 2 * m + 1 <= 128)
|
|
{
|
|
U = &SPACE[0];
|
|
V = &SPACE[m + n + 1];
|
|
Q = &SPACE[(m + n + 1) + n];
|
|
if (Remainder)
|
|
{
|
|
R = &SPACE[(m + n + 1) + n + (m + n)];
|
|
}
|
|
}
|
|
else
|
|
{
|
|
U = malloc_arena(sizeof(uint32_t) * (m + n + 1));
|
|
V = malloc_arena(sizeof(uint32_t) * n);
|
|
Q = malloc_arena(sizeof(uint32_t) * (m + n));
|
|
if (Remainder)
|
|
{
|
|
R = malloc_arena(sizeof(uint32_t) * n);
|
|
}
|
|
}
|
|
|
|
// Initialize the dividend
|
|
memset(U, 0, (m + n + 1) * sizeof(uint32_t));
|
|
for (unsigned i = 0; i < lhsWords; ++i)
|
|
{
|
|
uint64_t tmp = LHS[i];
|
|
U[i * 2] = lo_32(tmp);
|
|
U[i * 2 + 1] = hi_32(tmp);
|
|
}
|
|
U[m + n] = 0; // this extra word is for "spill" in the Knuth algorithm.
|
|
|
|
// Initialize the divisor
|
|
memset(V, 0, (n) * sizeof(uint32_t));
|
|
for (unsigned i = 0; i < rhsWords; ++i)
|
|
{
|
|
uint64_t tmp = RHS[i];
|
|
V[i * 2] = lo_32(tmp);
|
|
V[i * 2 + 1] = hi_32(tmp);
|
|
}
|
|
|
|
// initialize the quotient and remainder
|
|
memset(Q, 0, (m + n) * sizeof(uint32_t));
|
|
if (Remainder) memset(R, 0, n * sizeof(uint32_t));
|
|
|
|
// Now, adjust m and n for the Knuth division. n is the number of words in
|
|
// the divisor. m is the number of words by which the dividend exceeds the
|
|
// divisor (i.e. m+n is the length of the dividend). These sizes must not
|
|
// contain any zero words or the Knuth algorithm fails.
|
|
for (unsigned i = n; i > 0 && V[i - 1] == 0; i--)
|
|
{
|
|
n--;
|
|
m++;
|
|
}
|
|
for (unsigned i = m + n; i > 0 && U[i - 1] == 0; i--)
|
|
{
|
|
m--;
|
|
}
|
|
|
|
// If we're left with only a single word for the divisor, Knuth doesn't work
|
|
// so we implement the short division algorithm here. This is much simpler
|
|
// and faster because we are certain that we can divide a 64-bit quantity
|
|
// by a 32-bit quantity at hardware speed and short division is simply a
|
|
// series of such operations. This is just like doing short division but we
|
|
// are using base 2^32 instead of base 10.
|
|
assert(n != 0 && "Divide by zero?");
|
|
if (n == 1)
|
|
{
|
|
uint32_t divisor = V[0];
|
|
uint32_t rem = 0;
|
|
for (int i = (int)m; i >= 0; i--)
|
|
{
|
|
uint64_t partial_dividend = make_64(rem, U[i]);
|
|
if (partial_dividend == 0)
|
|
{
|
|
Q[i] = 0;
|
|
rem = 0;
|
|
}
|
|
else if (partial_dividend < divisor)
|
|
{
|
|
Q[i] = 0;
|
|
rem = lo_32(partial_dividend);
|
|
}
|
|
else if (partial_dividend == divisor)
|
|
{
|
|
Q[i] = 1;
|
|
rem = 0;
|
|
}
|
|
else
|
|
{
|
|
Q[i] = lo_32(partial_dividend / divisor);
|
|
rem = lo_32(partial_dividend - (Q[i] * divisor));
|
|
}
|
|
}
|
|
if (R)
|
|
{
|
|
R[0] = rem;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
// Now we're ready to invoke the Knuth classical divide algorithm. In this
|
|
// case n > 1.
|
|
KnuthDiv(U, V, Q, R, m, n);
|
|
}
|
|
|
|
// If the caller wants the quotient
|
|
if (Quotient)
|
|
{
|
|
Quotient->is_negative = false;
|
|
Quotient->digit_count = lhsWords;
|
|
if (lhsWords == 1)
|
|
{
|
|
Quotient->digit = make_64(Q[1], Q[0]);
|
|
}
|
|
else
|
|
{
|
|
Quotient->digits = alloc_digits(lhsWords);
|
|
for (size_t i = 0; i < lhsWords; i += 1)
|
|
{
|
|
Quotient->digits[i] = make_64(Q[i * 2 + 1], Q[i * 2]);
|
|
}
|
|
}
|
|
}
|
|
|
|
// If the caller wants the remainder
|
|
if (Remainder)
|
|
{
|
|
Remainder->is_negative = false;
|
|
Remainder->digit_count = rhsWords;
|
|
if (rhsWords == 1)
|
|
{
|
|
Remainder->digit = make_64(R[1], R[0]);
|
|
}
|
|
else
|
|
{
|
|
Remainder->digits = alloc_digits(rhsWords);
|
|
for (size_t i = 0; i < rhsWords; i += 1)
|
|
{
|
|
Remainder->digits[i] = make_64(R[i * 2 + 1], R[i * 2]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
void bigint_div_trunc(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
assert(op2->digit_count != 0); // division by zero
|
|
if (op1->digit_count == 0)
|
|
{
|
|
bigint_init_unsigned(dest, 0);
|
|
return;
|
|
}
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
const uint64_t *op2_digits = bigint_ptr(op2);
|
|
if (op1->digit_count == 1 && op2->digit_count == 1)
|
|
{
|
|
dest->digit = op1_digits[0] / op2_digits[0];
|
|
dest->digit_count = 1;
|
|
dest->is_negative = op1->is_negative != op2->is_negative;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
if (op2->digit_count == 1 && op2_digits[0] == 1)
|
|
{
|
|
// X / 1 == X
|
|
bigint_init_bigint(dest, op1);
|
|
dest->is_negative = op1->is_negative != op2->is_negative;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
|
|
const BigInt *op1_positive;
|
|
BigInt op1_positive_data;
|
|
if (op1->is_negative)
|
|
{
|
|
bigint_negate(&op1_positive_data, op1);
|
|
op1_positive = &op1_positive_data;
|
|
}
|
|
else
|
|
{
|
|
op1_positive = op1;
|
|
}
|
|
|
|
const BigInt *op2_positive;
|
|
BigInt op2_positive_data;
|
|
if (op2->is_negative)
|
|
{
|
|
bigint_negate(&op2_positive_data, op2);
|
|
op2_positive = &op2_positive_data;
|
|
}
|
|
else
|
|
{
|
|
op2_positive = op2;
|
|
}
|
|
|
|
bigint_unsigned_division(op1_positive, op2_positive, dest, NULL);
|
|
dest->is_negative = op1->is_negative != op2->is_negative;
|
|
normalize(dest);
|
|
}
|
|
|
|
void bigint_div_floor(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
if (op1->is_negative != op2->is_negative)
|
|
{
|
|
bigint_div_trunc(dest, op1, op2);
|
|
BigInt mult_again = { 0 };
|
|
bigint_mul(&mult_again, dest, op2);
|
|
mult_again.is_negative = op1->is_negative;
|
|
if (bigint_cmp(&mult_again, op1) != CMP_EQ)
|
|
{
|
|
BigInt tmp = { 0 };
|
|
bigint_init_bigint(&tmp, dest);
|
|
BigInt neg_one = { 0 };
|
|
bigint_init_signed(&neg_one, -1);
|
|
bigint_add(dest, &tmp, &neg_one);
|
|
}
|
|
normalize(dest);
|
|
}
|
|
else
|
|
{
|
|
bigint_div_trunc(dest, op1, op2);
|
|
}
|
|
}
|
|
|
|
void bigint_rem(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
assert(op2->digit_count != 0); // division by zero
|
|
if (op1->digit_count == 0)
|
|
{
|
|
bigint_init_unsigned(dest, 0);
|
|
return;
|
|
}
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
const uint64_t *op2_digits = bigint_ptr(op2);
|
|
|
|
if (op1->digit_count == 1 && op2->digit_count == 1)
|
|
{
|
|
dest->digit = op1_digits[0] % op2_digits[0];
|
|
dest->digit_count = 1;
|
|
dest->is_negative = op1->is_negative;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
if (op2->digit_count == 2 && op2_digits[0] == 0 && op2_digits[1] == 1)
|
|
{
|
|
// special case this divisor
|
|
bigint_init_unsigned(dest, op1_digits[0]);
|
|
dest->is_negative = op1->is_negative;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
|
|
if (op2->digit_count == 1 && op2_digits[0] == 1)
|
|
{
|
|
// X % 1 == 0
|
|
bigint_init_unsigned(dest, 0);
|
|
return;
|
|
}
|
|
|
|
const BigInt *op1_positive;
|
|
BigInt op1_positive_data;
|
|
if (op1->is_negative)
|
|
{
|
|
bigint_negate(&op1_positive_data, op1);
|
|
op1_positive = &op1_positive_data;
|
|
}
|
|
else
|
|
{
|
|
op1_positive = op1;
|
|
}
|
|
|
|
const BigInt *op2_positive;
|
|
BigInt op2_positive_data;
|
|
if (op2->is_negative)
|
|
{
|
|
bigint_negate(&op2_positive_data, op2);
|
|
op2_positive = &op2_positive_data;
|
|
}
|
|
else
|
|
{
|
|
op2_positive = op2;
|
|
}
|
|
|
|
bigint_unsigned_division(op1_positive, op2_positive, NULL, dest);
|
|
dest->is_negative = op1->is_negative;
|
|
normalize(dest);
|
|
}
|
|
|
|
void bigint_mod(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
if (op1->is_negative)
|
|
{
|
|
BigInt first_rem;
|
|
bigint_rem(&first_rem, op1, op2);
|
|
first_rem.is_negative = !op2->is_negative;
|
|
BigInt op2_minus_rem;
|
|
bigint_add(&op2_minus_rem, op2, &first_rem);
|
|
bigint_rem(dest, &op2_minus_rem, op2);
|
|
dest->is_negative = false;
|
|
}
|
|
else
|
|
{
|
|
bigint_rem(dest, op1, op2);
|
|
dest->is_negative = false;
|
|
}
|
|
}
|
|
|
|
void bigint_or(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
if (op1->digit_count == 0)
|
|
{
|
|
return bigint_init_bigint(dest, op2);
|
|
}
|
|
if (op2->digit_count == 0)
|
|
{
|
|
return bigint_init_bigint(dest, op1);
|
|
}
|
|
if (op1->is_negative || op2->is_negative)
|
|
{
|
|
size_t big_bit_count = size_max(bigint_bits_needed(op1), bigint_bits_needed(op2));
|
|
|
|
BigInt twos_comp_op1 = { 0 };
|
|
to_twos_complement(&twos_comp_op1, op1, big_bit_count);
|
|
|
|
BigInt twos_comp_op2 = { 0 };
|
|
to_twos_complement(&twos_comp_op2, op2, big_bit_count);
|
|
|
|
BigInt twos_comp_dest = { 0 };
|
|
bigint_or(&twos_comp_dest, &twos_comp_op1, &twos_comp_op2);
|
|
|
|
from_twos_complement(dest, &twos_comp_dest, big_bit_count, true);
|
|
}
|
|
else
|
|
{
|
|
dest->is_negative = false;
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
const uint64_t *op2_digits = bigint_ptr(op2);
|
|
if (op1->digit_count == 1 && op2->digit_count == 1)
|
|
{
|
|
dest->digit_count = 1;
|
|
dest->digit = op1_digits[0] | op2_digits[0];
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
dest->digit_count = unsigned_max(op1->digit_count, op2->digit_count);
|
|
dest->digits = alloc_digits(dest->digit_count);
|
|
for (size_t i = 0; i < dest->digit_count; i += 1)
|
|
{
|
|
uint64_t digit = 0;
|
|
if (i < op1->digit_count)
|
|
{
|
|
digit |= op1_digits[i];
|
|
}
|
|
if (i < op2->digit_count)
|
|
{
|
|
digit |= op2_digits[i];
|
|
}
|
|
dest->digits[i] = digit;
|
|
}
|
|
normalize(dest);
|
|
}
|
|
}
|
|
|
|
void bigint_and(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
if (op1->digit_count == 0 || op2->digit_count == 0)
|
|
{
|
|
return bigint_init_unsigned(dest, 0);
|
|
}
|
|
if (op1->is_negative || op2->is_negative)
|
|
{
|
|
size_t big_bit_count = size_max(bigint_bits_needed(op1), bigint_bits_needed(op2));
|
|
|
|
BigInt twos_comp_op1 = { 0 };
|
|
to_twos_complement(&twos_comp_op1, op1, big_bit_count);
|
|
|
|
BigInt twos_comp_op2 = { 0 };
|
|
to_twos_complement(&twos_comp_op2, op2, big_bit_count);
|
|
|
|
BigInt twos_comp_dest = { 0 };
|
|
bigint_and(&twos_comp_dest, &twos_comp_op1, &twos_comp_op2);
|
|
|
|
from_twos_complement(dest, &twos_comp_dest, big_bit_count, true);
|
|
}
|
|
else
|
|
{
|
|
dest->is_negative = false;
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
const uint64_t *op2_digits = bigint_ptr(op2);
|
|
if (op1->digit_count == 1 && op2->digit_count == 1)
|
|
{
|
|
dest->digit_count = 1;
|
|
dest->digit = op1_digits[0] & op2_digits[0];
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
|
|
dest->digit_count = unsigned_max(op1->digit_count, op2->digit_count);
|
|
dest->digits = alloc_digits(dest->digit_count);
|
|
|
|
size_t i = 0;
|
|
for (; i < op1->digit_count && i < op2->digit_count; i += 1)
|
|
{
|
|
dest->digits[i] = op1_digits[i] & op2_digits[i];
|
|
}
|
|
for (; i < dest->digit_count; i += 1)
|
|
{
|
|
dest->digits[i] = 0;
|
|
}
|
|
normalize(dest);
|
|
}
|
|
}
|
|
|
|
void bigint_xor(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
if (op1->digit_count == 0)
|
|
{
|
|
return bigint_init_bigint(dest, op2);
|
|
}
|
|
if (op2->digit_count == 0)
|
|
{
|
|
return bigint_init_bigint(dest, op1);
|
|
}
|
|
if (op1->is_negative || op2->is_negative)
|
|
{
|
|
size_t big_bit_count = size_max(bigint_bits_needed(op1), bigint_bits_needed(op2));
|
|
|
|
BigInt twos_comp_op1 = { 0 };
|
|
to_twos_complement(&twos_comp_op1, op1, big_bit_count);
|
|
|
|
BigInt twos_comp_op2 = { 0 };
|
|
to_twos_complement(&twos_comp_op2, op2, big_bit_count);
|
|
|
|
BigInt twos_comp_dest = { 0 };
|
|
bigint_xor(&twos_comp_dest, &twos_comp_op1, &twos_comp_op2);
|
|
|
|
from_twos_complement(dest, &twos_comp_dest, big_bit_count, true);
|
|
}
|
|
else
|
|
{
|
|
dest->is_negative = false;
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
const uint64_t *op2_digits = bigint_ptr(op2);
|
|
|
|
assert(op1->digit_count > 0 && op2->digit_count > 0);
|
|
if (op1->digit_count == 1 && op2->digit_count == 1)
|
|
{
|
|
dest->digit_count = 1;
|
|
dest->digit = op1_digits[0] ^ op2_digits[0];
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
dest->digit_count = unsigned_max(op1->digit_count, op2->digit_count);
|
|
dest->digits = alloc_digits(dest->digit_count);
|
|
size_t i = 0;
|
|
for (; i < op1->digit_count && i < op2->digit_count; i += 1)
|
|
{
|
|
dest->digits[i] = op1_digits[i] ^ op2_digits[i];
|
|
}
|
|
for (; i < dest->digit_count; i += 1)
|
|
{
|
|
if (i < op1->digit_count)
|
|
{
|
|
dest->digits[i] = op1_digits[i];
|
|
}
|
|
else if (i < op2->digit_count)
|
|
{
|
|
dest->digits[i] = op2_digits[i];
|
|
}
|
|
else
|
|
{
|
|
FATAL_ERROR("Unreachable");
|
|
}
|
|
}
|
|
normalize(dest);
|
|
}
|
|
}
|
|
|
|
void bigint_shl(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
assert(!op2->is_negative);
|
|
|
|
if (op2->digit_count != 1)
|
|
{
|
|
FATAL_ERROR("Unsupported: shift left by amount greater than 64 bit integer");
|
|
}
|
|
bigint_shl_int(dest, op1, bigint_as_unsigned(op2));
|
|
}
|
|
|
|
void bigint_shl_int(BigInt *dest, const BigInt *op1, uint64_t shift)
|
|
{
|
|
if (shift == 0)
|
|
{
|
|
bigint_init_bigint(dest, op1);
|
|
return;
|
|
}
|
|
|
|
if (op1->digit_count == 0)
|
|
{
|
|
bigint_init_unsigned(dest, 0);
|
|
return;
|
|
}
|
|
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
|
|
if (op1->digit_count == 1 && shift < 64)
|
|
{
|
|
dest->digit = op1_digits[0] << shift;
|
|
if (dest->digit > op1_digits[0])
|
|
{
|
|
dest->digit_count = 1;
|
|
dest->is_negative = op1->is_negative;
|
|
return;
|
|
}
|
|
}
|
|
|
|
uint64_t digit_shift_count = shift / 64;
|
|
uint64_t leftover_shift_count = shift % 64;
|
|
|
|
dest->digits = alloc_digits(op1->digit_count + digit_shift_count + 1);
|
|
dest->digit_count = digit_shift_count;
|
|
uint64_t carry = 0;
|
|
for (size_t i = 0; i < op1->digit_count; i += 1)
|
|
{
|
|
uint64_t digit = op1_digits[i];
|
|
dest->digits[dest->digit_count] = carry | (digit << leftover_shift_count);
|
|
dest->digit_count++;
|
|
if (leftover_shift_count > 0)
|
|
{
|
|
carry = digit >> (64 - leftover_shift_count);
|
|
}
|
|
else
|
|
{
|
|
carry = 0;
|
|
}
|
|
}
|
|
dest->digits[dest->digit_count] = carry;
|
|
dest->digit_count += 1;
|
|
dest->is_negative = op1->is_negative;
|
|
normalize(dest);
|
|
}
|
|
|
|
void bigint_shl_trunc(BigInt *dest, const BigInt *op1, const BigInt *op2, size_t bit_count, bool is_signed)
|
|
{
|
|
BigInt unwrapped = { 0 };
|
|
bigint_shl(&unwrapped, op1, op2);
|
|
bigint_truncate(dest, &unwrapped, bit_count, is_signed);
|
|
}
|
|
|
|
void bigint_shr(BigInt *dest, const BigInt *op1, const BigInt *op2)
|
|
{
|
|
assert(!op2->is_negative);
|
|
|
|
if (op1->digit_count == 0)
|
|
{
|
|
return bigint_init_unsigned(dest, 0);
|
|
}
|
|
|
|
if (op2->digit_count == 0)
|
|
{
|
|
return bigint_init_bigint(dest, op1);
|
|
}
|
|
|
|
if (op2->digit_count != 1)
|
|
{
|
|
FATAL_ERROR("Unsupported: shift right by amount greater than 64 bit integer");
|
|
}
|
|
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
uint64_t shift_amt = bigint_as_unsigned(op2);
|
|
|
|
if (op1->digit_count == 1)
|
|
{
|
|
dest->digit = shift_amt < 64 ? op1_digits[0] >> shift_amt : 0;
|
|
dest->digit_count = 1;
|
|
dest->is_negative = op1->is_negative;
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
|
|
uint64_t digit_shift_count = shift_amt / 64;
|
|
uint64_t leftover_shift_count = shift_amt % 64;
|
|
|
|
if (digit_shift_count >= op1->digit_count)
|
|
{
|
|
return bigint_init_unsigned(dest, 0);
|
|
}
|
|
|
|
dest->digit_count = op1->digit_count - digit_shift_count;
|
|
uint64_t *digits;
|
|
if (dest->digit_count == 1)
|
|
{
|
|
digits = &dest->digit;
|
|
}
|
|
else
|
|
{
|
|
digits = alloc_digits(dest->digit_count);
|
|
dest->digits = digits;
|
|
}
|
|
|
|
uint64_t carry = 0;
|
|
for (size_t op_digit_index = op1->digit_count - 1;;)
|
|
{
|
|
uint64_t digit = op1_digits[op_digit_index];
|
|
size_t dest_digit_index = op_digit_index - digit_shift_count;
|
|
digits[dest_digit_index] = carry | (digit >> leftover_shift_count);
|
|
carry = digit << (64 - leftover_shift_count);
|
|
|
|
if (dest_digit_index == 0) break;
|
|
op_digit_index -= 1;
|
|
}
|
|
dest->is_negative = op1->is_negative;
|
|
normalize(dest);
|
|
}
|
|
|
|
|
|
void bigint_negate_wrap(BigInt *dest, const BigInt *op, size_t bit_count)
|
|
{
|
|
BigInt zero;
|
|
bigint_init_unsigned(&zero, 0);
|
|
bigint_sub_wrap(dest, &zero, op, bit_count, true);
|
|
}
|
|
|
|
void bigint_not(BigInt *dest, const BigInt *op, size_t bit_count, bool is_signed)
|
|
{
|
|
if (bit_count == 0)
|
|
{
|
|
bigint_init_unsigned(dest, 0);
|
|
return;
|
|
}
|
|
|
|
if (is_signed)
|
|
{
|
|
BigInt twos_comp = { 0 };
|
|
to_twos_complement(&twos_comp, op, bit_count);
|
|
|
|
BigInt inverted = { 0 };
|
|
bigint_not(&inverted, &twos_comp, bit_count, false);
|
|
|
|
from_twos_complement(dest, &inverted, bit_count, true);
|
|
return;
|
|
}
|
|
|
|
assert(!op->is_negative);
|
|
|
|
dest->is_negative = false;
|
|
const uint64_t *op_digits = bigint_ptr(op);
|
|
if (bit_count <= 64)
|
|
{
|
|
dest->digit_count = 1;
|
|
if (op->digit_count == 0)
|
|
{
|
|
if (bit_count == 64)
|
|
{
|
|
dest->digit = UINT64_MAX;
|
|
}
|
|
else
|
|
{
|
|
dest->digit = (1ULL << bit_count) - 1;
|
|
}
|
|
}
|
|
else if (op->digit_count == 1)
|
|
{
|
|
dest->digit = ~op_digits[0];
|
|
if (bit_count != 64)
|
|
{
|
|
uint64_t
|
|
mask = (1ULL << bit_count) - 1;
|
|
dest->digit &= mask;
|
|
}
|
|
}
|
|
normalize(dest);
|
|
return;
|
|
}
|
|
dest->digit_count = (unsigned int) ((bit_count + 63) / 64);
|
|
assert(dest->digit_count >= op->digit_count);
|
|
dest->digits = alloc_digits(dest->digit_count);
|
|
size_t i = 0;
|
|
for (; i < op->digit_count; i += 1)
|
|
{
|
|
dest->digits[i] = ~op_digits[i];
|
|
}
|
|
for (; i < dest->digit_count; i += 1)
|
|
{
|
|
dest->digits[i] = 0xffffffffffffffffULL;
|
|
}
|
|
size_t digit_index = dest->digit_count - 1;
|
|
size_t digit_bit_index = bit_count % 64;
|
|
if (digit_bit_index != 0)
|
|
{
|
|
uint64_t
|
|
mask = (1ULL << digit_bit_index) - 1;
|
|
dest->digits[digit_index] &= mask;
|
|
}
|
|
normalize(dest);
|
|
}
|
|
|
|
void bigint_truncate(BigInt *dst, const BigInt *op, size_t bit_count, bool is_signed)
|
|
{
|
|
BigInt twos_comp;
|
|
to_twos_complement(&twos_comp, op, bit_count);
|
|
from_twos_complement(dst, &twos_comp, bit_count, is_signed);
|
|
}
|
|
|
|
CmpRes bigint_cmp(const BigInt *op1, const BigInt *op2)
|
|
{
|
|
if (op1->is_negative && !op2->is_negative)
|
|
{
|
|
return CMP_LT;
|
|
}
|
|
else if (!op1->is_negative && op2->is_negative)
|
|
{
|
|
return CMP_GT;
|
|
}
|
|
else if (op1->digit_count > op2->digit_count)
|
|
{
|
|
return op1->is_negative ? CMP_LT : CMP_GT;
|
|
}
|
|
else if (op2->digit_count > op1->digit_count)
|
|
{
|
|
return op1->is_negative ? CMP_GT : CMP_LT;
|
|
}
|
|
else if (op1->digit_count == 0)
|
|
{
|
|
return CMP_EQ;
|
|
}
|
|
const uint64_t *op1_digits = bigint_ptr(op1);
|
|
const uint64_t *op2_digits = bigint_ptr(op2);
|
|
for (unsigned i = op1->digit_count - 1;; i--)
|
|
{
|
|
uint64_t op1_digit = op1_digits[i];
|
|
uint64_t op2_digit = op2_digits[i];
|
|
|
|
if (op1_digit > op2_digit)
|
|
{
|
|
return op1->is_negative ? CMP_LT : CMP_GT;
|
|
}
|
|
if (op1_digit < op2_digit)
|
|
{
|
|
return op1->is_negative ? CMP_GT : CMP_LT;
|
|
}
|
|
if (i == 0)
|
|
{
|
|
return CMP_EQ;
|
|
}
|
|
}
|
|
}
|
|
|
|
void bigint_print(BigInt *bigint, uint64_t base)
|
|
{
|
|
if (bigint->digit_count == 0)
|
|
{
|
|
printf("0");
|
|
return;
|
|
}
|
|
if (bigint->is_negative)
|
|
{
|
|
printf("-");
|
|
}
|
|
if (bigint->digit_count == 1 && base == 10)
|
|
{
|
|
printf("%" PRIu64, bigint->digit);
|
|
return;
|
|
}
|
|
size_t len = bigint->digit_count * 64;
|
|
char *start = malloc_arena(len);
|
|
char *buf = start;
|
|
|
|
BigInt digit_bi = { 0 };
|
|
BigInt a1 = { 0 };
|
|
BigInt a2 = { 0 };
|
|
|
|
BigInt *a = &a1;
|
|
BigInt *other_a = &a2;
|
|
bigint_init_bigint(a, bigint);
|
|
|
|
BigInt base_bi = { 0 };
|
|
bigint_init_unsigned(&base_bi, base);
|
|
|
|
for (;;)
|
|
{
|
|
bigint_rem(&digit_bi, a, &base_bi);
|
|
uint8_t digit = (uint8_t)bigint_as_unsigned(&digit_bi);
|
|
*(buf++) = digit_to_char(digit, false);
|
|
bigint_div_trunc(other_a, a, &base_bi);
|
|
{
|
|
BigInt *tmp = a;
|
|
a = other_a;
|
|
other_a = tmp;
|
|
}
|
|
if (bigint_cmp_zero(a) == CMP_EQ)
|
|
{
|
|
break;
|
|
}
|
|
}
|
|
|
|
// reverse
|
|
|
|
for (char *ptr = buf - 1; ptr >= start; ptr--)
|
|
{
|
|
printf("%c", *ptr);
|
|
}
|
|
}
|
|
|
|
const char *bigint_to_error_string(const BigInt *bigint, uint64_t base)
|
|
{
|
|
if (bigint->digit_count == 0)
|
|
{
|
|
return "0";
|
|
}
|
|
if (bigint->digit_count == 1 && base == 10)
|
|
{
|
|
char *res = NULL;
|
|
asprintf(&res, "%" PRIu64, bigint->digit);
|
|
return res;
|
|
}
|
|
size_t len = bigint->digit_count * 64;
|
|
char *start = malloc_arena(len);
|
|
char *buf = start;
|
|
|
|
BigInt digit_bi = { 0 };
|
|
BigInt a1 = { 0 };
|
|
BigInt a2 = { 0 };
|
|
|
|
BigInt *a = &a1;
|
|
BigInt *other_a = &a2;
|
|
bigint_init_bigint(a, bigint);
|
|
|
|
BigInt base_bi = { 0 };
|
|
bigint_init_unsigned(&base_bi, base);
|
|
|
|
for (;;)
|
|
{
|
|
bigint_rem(&digit_bi, a, &base_bi);
|
|
uint8_t digit = (uint8_t)bigint_as_unsigned(&digit_bi);
|
|
*(buf++) = digit_to_char(digit, false);
|
|
bigint_div_trunc(other_a, a, &base_bi);
|
|
{
|
|
BigInt *tmp = a;
|
|
a = other_a;
|
|
other_a = tmp;
|
|
}
|
|
if (bigint_cmp_zero(a) == CMP_EQ)
|
|
{
|
|
break;
|
|
}
|
|
}
|
|
|
|
// reverse
|
|
char *out = malloc_arena(buf - start + 2);
|
|
char *current = out;
|
|
if (bigint->is_negative)
|
|
{
|
|
*(current++) = '-';
|
|
}
|
|
for (char *ptr = buf - 1; ptr >= start; ptr--)
|
|
{
|
|
*(current++) = *ptr;
|
|
}
|
|
*(current++) = '\0';
|
|
return out;
|
|
}
|
|
|
|
void bigint_fprint(FILE *file, BigInt *bigint, uint64_t base)
|
|
{
|
|
if (bigint->digit_count == 0)
|
|
{
|
|
fprintf(file, "0");
|
|
return;
|
|
}
|
|
if (bigint->is_negative)
|
|
{
|
|
fprintf(file, "-");
|
|
}
|
|
if (bigint->digit_count == 1 && base == 10)
|
|
{
|
|
fprintf(file, "%" PRIu64, bigint->digit);
|
|
return;
|
|
}
|
|
size_t len = bigint->digit_count * 64;
|
|
char *start = malloc_arena(len);
|
|
char *buf = start;
|
|
|
|
BigInt digit_bi = { 0 };
|
|
BigInt a1 = { 0 };
|
|
BigInt a2 = { 0 };
|
|
|
|
BigInt *a = &a1;
|
|
BigInt *other_a = &a2;
|
|
bigint_init_bigint(a, bigint);
|
|
|
|
BigInt base_bi = { 0 };
|
|
bigint_init_unsigned(&base_bi, base);
|
|
|
|
for (;;)
|
|
{
|
|
bigint_rem(&digit_bi, a, &base_bi);
|
|
uint8_t digit = (uint8_t)bigint_as_unsigned(&digit_bi);
|
|
*(buf++) = digit_to_char(digit, false);
|
|
bigint_div_trunc(other_a, a, &base_bi);
|
|
{
|
|
BigInt *tmp = a;
|
|
a = other_a;
|
|
other_a = tmp;
|
|
}
|
|
if (bigint_cmp_zero(a) == CMP_EQ)
|
|
{
|
|
break;
|
|
}
|
|
}
|
|
|
|
// reverse
|
|
|
|
for (char *ptr = buf - 1; ptr >= start; ptr--)
|
|
{
|
|
fprintf(file, "%c", *ptr);
|
|
}
|
|
}
|
|
size_t bigint_popcount_unsigned(const BigInt *big_int)
|
|
{
|
|
assert(!big_int->is_negative);
|
|
if (big_int->digit_count == 0)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
unsigned count = 0;
|
|
size_t bit_count = big_int->digit_count * 64;
|
|
for (size_t i = 0; i < bit_count; i++)
|
|
{
|
|
if (bit_at_index(big_int, i))
|
|
{
|
|
count += 1;
|
|
}
|
|
}
|
|
return count;
|
|
}
|
|
|
|
size_t bigint_popcount_signed(const BigInt *bi, size_t bit_count)
|
|
{
|
|
if (bit_count == 0)
|
|
{
|
|
return 0;
|
|
}
|
|
if (bi->digit_count == 0)
|
|
{
|
|
return 0;
|
|
}
|
|
|
|
BigInt twos_comp = { 0 };
|
|
to_twos_complement(&twos_comp, bi, bit_count);
|
|
|
|
size_t count = 0;
|
|
for (size_t i = 0; i < bit_count; i += 1)
|
|
{
|
|
if (bit_at_index(&twos_comp, i))
|
|
{
|
|
count += 1;
|
|
}
|
|
}
|
|
return count;
|
|
}
|
|
|
|
size_t bigint_ctz(const BigInt *bi, size_t bit_count)
|
|
{
|
|
if (bit_count == 0)
|
|
{
|
|
return 0;
|
|
}
|
|
if (bi->digit_count == 0)
|
|
{
|
|
return bit_count;
|
|
}
|
|
|
|
BigInt twos_comp = { 0 };
|
|
to_twos_complement(&twos_comp, bi, bit_count);
|
|
|
|
size_t count = 0;
|
|
for (size_t i = 0; i < bit_count; i += 1)
|
|
{
|
|
if (bit_at_index(&twos_comp, i))
|
|
{
|
|
return count;
|
|
}
|
|
count += 1;
|
|
}
|
|
return count;
|
|
}
|
|
|
|
|
|
int64_t bigint_as_signed(const BigInt *bigint)
|
|
{
|
|
if (bigint->digit_count == 0) return 0;
|
|
if (bigint->digit_count != 1)
|
|
{
|
|
FATAL_ERROR("BigInt larger than i64");
|
|
}
|
|
|
|
if (bigint->is_negative)
|
|
{
|
|
// TODO this code path is untested
|
|
if (bigint->digit <= 9223372036854775808ULL)
|
|
{
|
|
return (-((int64_t) (bigint->digit - 1))) - 1;
|
|
}
|
|
else
|
|
{
|
|
FATAL_ERROR("BigInt does not fit in i64");
|
|
}
|
|
}
|
|
return bigint->digit;
|
|
}
|
|
|
|
CmpRes bigint_cmp_zero(const BigInt *op)
|
|
{
|
|
if (op->digit_count == 0)
|
|
{
|
|
return CMP_EQ;
|
|
}
|
|
return op->is_negative ? CMP_LT : CMP_GT;
|
|
}
|
|
|
|
|
|
void bigint_incr(BigInt *x)
|
|
{
|
|
if (!x->digit_count)
|
|
{
|
|
bigint_init_unsigned(x, 1);
|
|
return;
|
|
}
|
|
|
|
if (x->digit_count == 1)
|
|
{
|
|
if (x->is_negative && x->digit != 0)
|
|
{
|
|
x->digit -= 1;
|
|
return;
|
|
}
|
|
else if (!x->is_negative && x->digit != UINT64_MAX)
|
|
{
|
|
x->digit += 1;
|
|
return;
|
|
}
|
|
}
|
|
|
|
BigInt copy;
|
|
bigint_init_bigint(©, x);
|
|
|
|
BigInt one;
|
|
bigint_init_unsigned(&one, 1);
|
|
|
|
bigint_add(x, ©, &one);
|
|
}
|
|
|
|
long double bigint_as_float(const BigInt *bigint)
|
|
{
|
|
if (bigint_fits_in_bits(bigint, 64, bigint->is_negative))
|
|
{
|
|
return bigint->is_negative ? bigint_as_signed(bigint) : bigint_as_unsigned(bigint);
|
|
}
|
|
BigInt div;
|
|
uint64_t mult = 0x100000000000ULL;
|
|
long double mul = 1;
|
|
bigint_init_unsigned(&div, mult);
|
|
BigInt current;
|
|
bigint_init_bigint(¤t, bigint);
|
|
long double f = 0;
|
|
do
|
|
{
|
|
BigInt temp;
|
|
bigint_mod(&temp, ¤t, &div);
|
|
f += bigint_as_signed(&temp) * mul;
|
|
mul *= mult;
|
|
bigint_div_trunc(&temp, ¤t, &div);
|
|
current = temp;
|
|
}
|
|
while (current.digit_count > 0);
|
|
return f;
|
|
}
|