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479 lines (358 loc) · 19.3 KB
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////////////////////////////////////////////////////////////////////////////////////////////////////
//
// Simple Long Integer Math for C++
// version 2.0
//
////////////////////////////////////////////////////////////////////////////////////////////////////
//
// Licensed under the MIT License <http://opensource.org/licenses/MIT>.
// SPDX-License-Identifier: MIT
//
// Copyright (c) 2020-2026 Yury Kalmykov <y_kalmykov@mail.ru>.
//
////////////////////////////////////////////////////////////////////////////////////////////////////
#include "type_sets.h"
#include <gtest/gtest.h>
#include <cstddef>
#include <tuple>
namespace slim
{
template<typename uint_t>
constexpr size_t total_bits = word_bits<uint_t> * word_count<uint_t>;
////////////////////////////////////////////////////////////////////////////////////////////////////
// standalone functions
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename uint_t, typename int_t>
void run_128_compound_assignment_tests()
{
// += and -= on 128-bit unsigned family
uint_t add_target = 0xdeadbeef00000000ull;
add_target += 0x0000000100000000ull;
ASSERT_EQ(add_target, uint_t(0xdeadbef000000000ull));
uint_t sub_target = 0xdeadbef000000000ull;
sub_target -= 0x0000000100000000ull;
ASSERT_EQ(sub_target, uint_t(0xdeadbeef00000000ull));
// += with carry into high word
uint_t carry_add_target = uint_t(native_word_t<uint_t>(-1));
carry_add_target += 1;
ASSERT_EQ(carry_add_target.digits[0], 0ull);
ASSERT_EQ(carry_add_target.digits[1], 1ull);
// *= and /= on 128-bit signed family
int_t mul_target = 100;
mul_target *= -7;
ASSERT_EQ(mul_target, int_t(-700));
mul_target /= 7;
ASSERT_EQ(mul_target, int_t(-100));
// %= on 128-bit signed family
int_t rem_target = -7;
rem_target %= 3;
ASSERT_EQ(rem_target, int_t(-1));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename uint_t>
void run_256_compound_assignment_tests()
{
// &=, |=, ^= on 256-bit unsigned family
constexpr uint_t pattern = uint_t(0xaaaaaaaaaaaaaaaaull);
uint_t bitand_target = uint_t(-1);
bitand_target &= pattern;
ASSERT_EQ(bitand_target, pattern);
uint_t bitor_target = uint_t(0);
bitor_target |= pattern;
ASSERT_EQ(bitor_target, pattern);
uint_t bitxor_target = pattern;
bitxor_target ^= pattern;
ASSERT_EQ(bitxor_target, uint_t(0));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename uint_t>
void run_128_bit_shift_edge_case_tests()
{
// shift by 0 is identity
constexpr uint_t shift_identity_val = (uint_t(native_word_t<uint_t>(0x12345678u)) << word_bits<uint_t>) + uint_t(native_word_t<uint_t>(0xdeadbeefu));
static_assert((shift_identity_val << 0) == shift_identity_val);
static_assert((shift_identity_val >> 0) == shift_identity_val);
const uint_t shift_identity_val_r = shift_identity_val;
ASSERT_EQ(shift_identity_val_r << 0, shift_identity_val_r);
ASSERT_EQ(shift_identity_val_r >> 0, shift_identity_val_r);
// shift by exactly one native word
constexpr uint_t one = 1;
static_assert((one << word_bits<uint_t>).digits[0] == 0);
static_assert((one << word_bits<uint_t>).digits[1] == 1);
static_assert(((one << word_bits<uint_t>) >> word_bits<uint_t>) == 1);
ASSERT_EQ((uint_t(1) << word_bits<uint_t>).digits[0], native_word_t<uint_t>(0));
ASSERT_EQ((uint_t(1) << word_bits<uint_t>).digits[1], native_word_t<uint_t>(1));
ASSERT_EQ((uint_t(1) << word_bits<uint_t>) >> word_bits<uint_t>, uint_t(1));
// shift by the highest bit position
static_assert((one << (total_bits<uint_t> - 1)).digits[0] == 0);
static_assert((one << (total_bits<uint_t> - 1)).digits[word_count<uint_t> - 1] == (native_word_t<uint_t>(1) << (word_bits<uint_t> - 1)));
static_assert(((one << (total_bits<uint_t> - 1)) >> (total_bits<uint_t> - 1)) == 1);
ASSERT_EQ((uint_t(1) << (total_bits<uint_t> - 1)).digits[0], native_word_t<uint_t>(0));
ASSERT_EQ((uint_t(1) << (total_bits<uint_t> - 1)).digits[word_count<uint_t> - 1], (native_word_t<uint_t>(1) << (word_bits<uint_t> - 1)));
ASSERT_EQ((uint_t(1) << (total_bits<uint_t> - 1)) >> (total_bits<uint_t> - 1), uint_t(1));
// logical right shift of all ones
constexpr uint_t all_ones = uint_t(-1);
static_assert((all_ones >> (total_bits<uint_t> - 1)) == 1);
ASSERT_EQ(uint_t(-1) >> (total_bits<uint_t> - 1), uint_t(1));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename int_t>
void run_128_signed_shift_tests()
{
// signed type uses the same logical shift
constexpr int_t neg_one = int_t(-1);
static_assert((neg_one >> (total_bits<int_t> - 1)) == 1);
ASSERT_EQ(int_t(-1) >> (total_bits<int_t> - 1), int_t(1));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename int_t>
void run_256_signed_shift_tests()
{
// signed type uses the same logical shift
constexpr int_t neg_one = int_t(-1);
static_assert((neg_one >> (total_bits<int_t> - 1)) == 1);
ASSERT_EQ(int_t(-1) >> (total_bits<int_t> - 1), int_t(1));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename uint_t>
void run_256_bit_shift_edge_case_tests()
{
// shift of zero value stays zero
static_assert((uint_t(0) << 200) == 0);
static_assert((uint_t(0) >> 200) == 0);
ASSERT_EQ(uint_t(0) << 200, uint_t(0));
ASSERT_EQ(uint_t(0) >> 200, uint_t(0));
// shifts at word boundaries
constexpr uint_t one = 1;
static_assert((one << word_bits<uint_t>).digits[0] == 0 && (one << word_bits<uint_t>).digits[1] == 1 &&
(one << word_bits<uint_t>).digits[2] == 0 && (one << word_bits<uint_t>).digits[3] == 0);
static_assert((one << (2 * word_bits<uint_t>)).digits[2] == 1 && (one << (2 * word_bits<uint_t>)).digits[3] == 0);
static_assert((one << (3 * word_bits<uint_t>)).digits[3] == 1);
const uint_t one_r = 1;
ASSERT_EQ((one_r << word_bits<uint_t>).digits[0], native_word_t<uint_t>(0));
ASSERT_EQ((one_r << word_bits<uint_t>).digits[1], native_word_t<uint_t>(1));
ASSERT_EQ((one_r << word_bits<uint_t>).digits[2], native_word_t<uint_t>(0));
ASSERT_EQ((one_r << word_bits<uint_t>).digits[3], native_word_t<uint_t>(0));
ASSERT_EQ((one_r << (2 * word_bits<uint_t>)).digits[2], native_word_t<uint_t>(1));
ASSERT_EQ((one_r << (2 * word_bits<uint_t>)).digits[3], native_word_t<uint_t>(0));
ASSERT_EQ((one_r << (3 * word_bits<uint_t>)).digits[3], native_word_t<uint_t>(1));
// round-trips at word boundaries
static_assert(((one << word_bits<uint_t>) >> word_bits<uint_t>) == 1);
static_assert(((one << (2 * word_bits<uint_t>)) >> (2 * word_bits<uint_t>)) == 1);
static_assert(((one << (3 * word_bits<uint_t>)) >> (3 * word_bits<uint_t>)) == 1);
ASSERT_EQ((one_r << word_bits<uint_t>) >> word_bits<uint_t>, uint_t(1));
ASSERT_EQ((one_r << (2 * word_bits<uint_t>)) >> (2 * word_bits<uint_t>), uint_t(1));
ASSERT_EQ((one_r << (3 * word_bits<uint_t>)) >> (3 * word_bits<uint_t>), uint_t(1));
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename uint_t>
void run_256_multiword_carry_borrow_tests()
{
// {MAX, 0, 0, 0} + 1 -> carry into word 1 only
constexpr uint_t word0_max = uint_t(native_word_t<uint_t>(-1));
static_assert((word0_max + 1).digits[0] == 0);
static_assert((word0_max + 1).digits[1] == 1);
static_assert((word0_max + 1).digits[2] == 0);
static_assert((word0_max + 1).digits[3] == 0);
const uint_t word0_max_r = word0_max;
ASSERT_EQ((word0_max_r + 1).digits[0], 0ull);
ASSERT_EQ((word0_max_r + 1).digits[1], 1ull);
ASSERT_EQ((word0_max_r + 1).digits[2], 0ull);
ASSERT_EQ((word0_max_r + 1).digits[3], 0ull);
// {MAX, MAX, 0, 0} + 1 -> carry ripples through words 0 and 1
constexpr uint_t words01_max = (uint_t(1) << (2 * word_bits<uint_t>)) - 1;
static_assert((words01_max + 1).digits[0] == 0);
static_assert((words01_max + 1).digits[1] == 0);
static_assert((words01_max + 1).digits[2] == 1);
static_assert((words01_max + 1).digits[3] == 0);
const uint_t words01_max_r = words01_max;
ASSERT_EQ((words01_max_r + 1).digits[0], 0ull);
ASSERT_EQ((words01_max_r + 1).digits[1], 0ull);
ASSERT_EQ((words01_max_r + 1).digits[2], 1ull);
ASSERT_EQ((words01_max_r + 1).digits[3], 0ull);
// {0, 0, 1, 0} - 1 -> borrow through words 1 and 0
constexpr uint_t word2_one = uint_t(1) << (2 * word_bits<uint_t>);
static_assert((word2_one - 1).digits[0] == native_word_t<uint_t>(-1));
static_assert((word2_one - 1).digits[1] == native_word_t<uint_t>(-1));
static_assert((word2_one - 1).digits[2] == 0);
static_assert((word2_one - 1).digits[3] == 0);
const uint_t word2_one_r = word2_one;
ASSERT_EQ((word2_one_r - 1).digits[0], native_word_t<uint_t>(-1));
ASSERT_EQ((word2_one_r - 1).digits[1], native_word_t<uint_t>(-1));
ASSERT_EQ((word2_one_r - 1).digits[2], 0ull);
ASSERT_EQ((word2_one_r - 1).digits[3], 0ull);
// {0, 0, 0, 1} - 1 -> borrow through all three words
constexpr uint_t word3_one = uint_t(1) << (3 * word_bits<uint_t>);
static_assert((word3_one - 1).digits[0] == native_word_t<uint_t>(-1));
static_assert((word3_one - 1).digits[1] == native_word_t<uint_t>(-1));
static_assert((word3_one - 1).digits[2] == native_word_t<uint_t>(-1));
static_assert((word3_one - 1).digits[3] == 0);
const uint_t word3_one_r = word3_one;
ASSERT_EQ((word3_one_r - 1).digits[0], native_word_t<uint_t>(-1));
ASSERT_EQ((word3_one_r - 1).digits[1], native_word_t<uint_t>(-1));
ASSERT_EQ((word3_one_r - 1).digits[2], native_word_t<uint_t>(-1));
ASSERT_EQ((word3_one_r - 1).digits[3], 0ull);
// carry from word 1 to word 2
constexpr uint_t word1_max = uint_t(native_word_t<uint_t>(-1)) << word_bits<uint_t>;
constexpr uint_t word1_one = uint_t(1) << word_bits<uint_t>;
static_assert((word1_max + word1_one).digits[0] == 0);
static_assert((word1_max + word1_one).digits[1] == 0);
static_assert((word1_max + word1_one).digits[2] == 1);
static_assert((word1_max + word1_one).digits[3] == 0);
const uint_t word1_max_r = word1_max;
const uint_t word1_one_r = word1_one;
ASSERT_EQ((word1_max_r + word1_one_r).digits[0], 0ull);
ASSERT_EQ((word1_max_r + word1_one_r).digits[1], 0ull);
ASSERT_EQ((word1_max_r + word1_one_r).digits[2], 1ull);
ASSERT_EQ((word1_max_r + word1_one_r).digits[3], 0ull);
// multiplication with carry from word 0 to word 1
constexpr uint_t mul_carry_base = uint_t(native_word_t<uint_t>(-1));
static_assert((mul_carry_base * 2).digits[0] == native_word_t<uint_t>(native_word_t<uint_t>(-1) - 1));
static_assert((mul_carry_base * 2).digits[1] == 1);
static_assert((mul_carry_base * 2).digits[2] == 0);
static_assert((mul_carry_base * 2).digits[3] == 0);
const uint_t mul_carry_base_r = mul_carry_base;
ASSERT_EQ((mul_carry_base_r * 2).digits[0], native_word_t<uint_t>(native_word_t<uint_t>(-1) - 1));
ASSERT_EQ((mul_carry_base_r * 2).digits[1], 1ull);
ASSERT_EQ((mul_carry_base_r * 2).digits[2], 0ull);
ASSERT_EQ((mul_carry_base_r * 2).digits[3], 0ull);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename uint_t>
void run_256_shift_at_or_beyond_width_noop_tests()
{
// shifts at or beyond the total bit width keep the value unchanged
constexpr uint_t value = uint_t(native_word_t<uint_t>(0x11223344u))
+ (uint_t(native_word_t<uint_t>(0x55667788u)) << word_bits<uint_t>)
+ (uint_t(native_word_t<uint_t>(0x99aabbccu)) << (2 * word_bits<uint_t>))
+ (uint_t(native_word_t<uint_t>(0xddeeff00u)) << (3 * word_bits<uint_t>));
static_assert((value << total_bits<uint_t>) == value);
static_assert((value >> total_bits<uint_t>) == value);
static_assert((value << (total_bits<uint_t> + 1)) == value);
static_assert((value >> (total_bits<uint_t> + 1)) == value);
static_assert((value << (total_bits<uint_t> + 44)) == value);
static_assert((value >> (total_bits<uint_t> + 44)) == value);
const uint_t value_r = value;
ASSERT_EQ(value_r << total_bits<uint_t>, value_r);
ASSERT_EQ(value_r >> total_bits<uint_t>, value_r);
ASSERT_EQ(value_r << (total_bits<uint_t> + 1), value_r);
ASSERT_EQ(value_r >> (total_bits<uint_t> + 1), value_r);
ASSERT_EQ(value_r << (total_bits<uint_t> + 44), value_r);
ASSERT_EQ(value_r >> (total_bits<uint_t> + 44), value_r);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename int_t>
void run_256_signed_shift_at_or_beyond_width_noop_tests()
{
// shifts at or beyond the total bit width keep the value unchanged
constexpr int_t int_value = -int_t(0x12345678u);
static_assert((int_value << total_bits<int_t>) == int_value);
static_assert((int_value >> total_bits<int_t>) == int_value);
static_assert((int_value << (total_bits<int_t> + 1)) == int_value);
static_assert((int_value >> (total_bits<int_t> + 1)) == int_value);
static_assert((int_value << (total_bits<int_t> + 17)) == int_value);
static_assert((int_value >> (total_bits<int_t> + 17)) == int_value);
const int_t int_value_r = int_value;
ASSERT_EQ(int_value_r << total_bits<int_t>, int_value_r);
ASSERT_EQ(int_value_r >> total_bits<int_t>, int_value_r);
ASSERT_EQ(int_value_r << (total_bits<int_t> + 1), int_value_r);
ASSERT_EQ(int_value_r >> (total_bits<int_t> + 1), int_value_r);
ASSERT_EQ(int_value_r << (total_bits<int_t> + 17), int_value_r);
ASSERT_EQ(int_value_r >> (total_bits<int_t> + 17), int_value_r);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename uint_t, typename int_t>
void run_128_shift_at_or_beyond_width_noop_tests()
{
// unsigned shifts at or beyond the total bit width keep the value unchanged
constexpr uint_t uint_value = uint_t(native_word_t<uint_t>(0xdeadbeefu))
+ (uint_t(native_word_t<uint_t>(0xcafebabeu)) << word_bits<uint_t>);
static_assert((uint_value << total_bits<uint_t>) == uint_value);
static_assert((uint_value >> total_bits<uint_t>) == uint_value);
static_assert((uint_value << (total_bits<uint_t> + 1)) == uint_value);
static_assert((uint_value >> (total_bits<uint_t> + 1)) == uint_value);
static_assert((uint_value << (total_bits<uint_t> + 17)) == uint_value);
static_assert((uint_value >> (total_bits<uint_t> + 17)) == uint_value);
const uint_t uint_value_r = uint_value;
ASSERT_EQ(uint_value_r << total_bits<uint_t>, uint_value_r);
ASSERT_EQ(uint_value_r >> total_bits<uint_t>, uint_value_r);
ASSERT_EQ(uint_value_r << (total_bits<uint_t> + 1), uint_value_r);
ASSERT_EQ(uint_value_r >> (total_bits<uint_t> + 1), uint_value_r);
ASSERT_EQ(uint_value_r << (total_bits<uint_t> + 17), uint_value_r);
ASSERT_EQ(uint_value_r >> (total_bits<uint_t> + 17), uint_value_r);
// signed shifts at or beyond the total bit width follow the same no-op rule
constexpr int_t int_value = -int_t(0x12345678u);
static_assert((int_value << total_bits<int_t>) == int_value);
static_assert((int_value >> total_bits<int_t>) == int_value);
static_assert((int_value << (total_bits<int_t> + 1)) == int_value);
static_assert((int_value >> (total_bits<int_t> + 1)) == int_value);
static_assert((int_value << (total_bits<int_t> + 17)) == int_value);
static_assert((int_value >> (total_bits<int_t> + 17)) == int_value);
const int_t int_value_r = int_value;
ASSERT_EQ(int_value_r << total_bits<int_t>, int_value_r);
ASSERT_EQ(int_value_r >> total_bits<int_t>, int_value_r);
ASSERT_EQ(int_value_r << (total_bits<int_t> + 1), int_value_r);
ASSERT_EQ(int_value_r >> (total_bits<int_t> + 1), int_value_r);
ASSERT_EQ(int_value_r << (total_bits<int_t> + 17), int_value_r);
ASSERT_EQ(int_value_r >> (total_bits<int_t> + 17), int_value_r);
}
////////////////////////////////////////////////////////////////////////////////////////////////////
// compound_shift_tests
////////////////////////////////////////////////////////////////////////////////////////////////////
TEST(compound_shift_tests, family_128_signed_and_unsigned_compound_assignment_operators)
{
run_128_compound_assignment_tests<uint128_t, int128_t>();
run_128_compound_assignment_tests<uint32x4_t, int32x4_t>();
}
////////////////////////////////////////////////////////////////////////////////////////////////////
TEST(compound_shift_tests, family_256_unsigned_compound_assignment_operators)
{
run_256_compound_assignment_tests<uint256_t>();
run_256_compound_assignment_tests<uint32x8_t>();
run_256_compound_assignment_tests<uint64x4_t>();
}
////////////////////////////////////////////////////////////////////////////////////////////////////
TEST(compound_shift_tests, family_128_signed_and_unsigned_bit_shift_edge_cases)
{
run_128_bit_shift_edge_case_tests<uint128_t>();
run_128_bit_shift_edge_case_tests<uint32x4_t>();
run_128_signed_shift_tests<int128_t>();
run_128_signed_shift_tests<int32x4_t>();
}
////////////////////////////////////////////////////////////////////////////////////////////////////
TEST(compound_shift_tests, family_256_signed_and_unsigned_bit_shift_edge_cases)
{
run_256_bit_shift_edge_case_tests<uint256_t>();
run_256_bit_shift_edge_case_tests<uint32x8_t>();
run_256_bit_shift_edge_case_tests<uint64x4_t>();
run_256_signed_shift_tests<int256_t>();
run_256_signed_shift_tests<int32x8_t>();
run_256_signed_shift_tests<int64x4_t>();
}
////////////////////////////////////////////////////////////////////////////////////////////////////
TEST(compound_shift_tests, family_256_unsigned_multiword_carry_borrow)
{
run_256_multiword_carry_borrow_tests<uint256_t>();
run_256_multiword_carry_borrow_tests<uint32x8_t>();
run_256_multiword_carry_borrow_tests<uint64x4_t>();
}
////////////////////////////////////////////////////////////////////////////////////////////////////
TEST(compound_shift_tests, family_128_signed_and_unsigned_shift_at_or_beyond_width_is_noop)
{
run_128_shift_at_or_beyond_width_noop_tests<uint128_t, int128_t>();
run_128_shift_at_or_beyond_width_noop_tests<uint32x4_t, int32x4_t>();
}
////////////////////////////////////////////////////////////////////////////////////////////////////
TEST(compound_shift_tests, family_256_signed_and_unsigned_shift_at_or_beyond_width_is_noop)
{
run_256_shift_at_or_beyond_width_noop_tests<uint256_t>();
run_256_shift_at_or_beyond_width_noop_tests<uint32x8_t>();
run_256_shift_at_or_beyond_width_noop_tests<uint64x4_t>();
run_256_signed_shift_at_or_beyond_width_noop_tests<int256_t>();
run_256_signed_shift_at_or_beyond_width_noop_tests<int32x8_t>();
run_256_signed_shift_at_or_beyond_width_noop_tests<int64x4_t>();
}
} // namespace slim
////////////////////////////////////////////////////////////////////////////////////////////////////
// compound_shift_tests.cpp
////////////////////////////////////////////////////////////////////////////////////////////////////