// Copyright 2018 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "absl/strings/internal/charconv_bigint.h"
#include <string>
#include "gtest/gtest.h"
namespace absl {
ABSL_NAMESPACE_BEGIN
namespace strings_internal {
TEST(BigUnsigned, ShiftLeft) {
{
// Check that 3 * 2**100 is calculated correctly
BigUnsigned<4> num(3u);
num.ShiftLeft(100);
EXPECT_EQ(num, BigUnsigned<4>("3802951800684688204490109616128"));
}
{
// Test that overflow is truncated properly.
// 15 is 4 bits long, and BigUnsigned<4> is a 128-bit bigint.
// Shifting left by 125 bits should truncate off the high bit, so that
// 15 << 125 == 7 << 125
// after truncation.
BigUnsigned<4> a(15u);
BigUnsigned<4> b(7u);
BigUnsigned<4> c(3u);
a.ShiftLeft(125);
b.ShiftLeft(125);
c.ShiftLeft(125);
EXPECT_EQ(a, b);
EXPECT_NE(a, c);
}
{
// Same test, larger bigint:
BigUnsigned<84> a(15u);
BigUnsigned<84> b(7u);
BigUnsigned<84> c(3u);
a.ShiftLeft(84 * 32 - 3);
b.ShiftLeft(84 * 32 - 3);
c.ShiftLeft(84 * 32 - 3);
EXPECT_EQ(a, b);
EXPECT_NE(a, c);
}
{
// Check that incrementally shifting has the same result as doing it all at
// once (attempting to capture corner cases.)
const std::string seed = "1234567890123456789012345678901234567890";
BigUnsigned<84> a(seed);
for (int i = 1; i <= 84 * 32; ++i) {
a.ShiftLeft(1);
BigUnsigned<84> b(seed);
b.ShiftLeft(i);
EXPECT_EQ(a, b);
}
// And we should have fully rotated all bits off by now:
EXPECT_EQ(a, BigUnsigned<84>(0u));
}
{
// Bit shifting large and small numbers by large and small offsets.
// Intended to exercise bounds-checking corner on ShiftLeft() (directly
// and under asan).
// 2**(32*84)-1
const BigUnsigned<84> all_bits_one(
"1474444211396924248063325089479706787923460402125687709454567433186613"
"6228083464060749874845919674257665016359189106695900028098437021384227"
"3285029708032466536084583113729486015826557532750465299832071590813090"
"2011853039837649252477307070509704043541368002938784757296893793903797"
"8180292336310543540677175225040919704702800559606097685920595947397024"
"8303316808753252115729411497720357971050627997031988036134171378490368"
"6008000778741115399296162550786288457245180872759047016734959330367829"
"5235612397427686310674725251378116268607113017720538636924549612987647"
"5767411074510311386444547332882472126067840027882117834454260409440463"
"9345147252664893456053258463203120637089916304618696601333953616715125"
"2115882482473279040772264257431663818610405673876655957323083702713344"
"4201105427930770976052393421467136557055");
const BigUnsigned<84> zero(0u);
const BigUnsigned<84> one(1u);
// in bounds shifts
for (int i = 1; i < 84*32; ++i) {
// shifting all_bits_one to the left should result in a smaller number,
// since the high bits rotate off and the low bits are replaced with
// zeroes.
BigUnsigned<84> big_shifted = all_bits_one;
big_shifted.ShiftLeft(i);
EXPECT_GT(all_bits_one, big_shifted);
// Shifting 1 to the left should instead result in a larger number.
BigUnsigned<84> small_shifted = one;
small_shifted.ShiftLeft(i);
EXPECT_LT(one, small_shifted);
}
// Shifting by zero or a negative number has no effect
for (int no_op_shift : {0, -1, -84 * 32, std::numeric_limits<int>::min()}) {
BigUnsigned<84> big_shifted = all_bits_one;
big_shifted.ShiftLeft(no_op_shift);
EXPECT_EQ(all_bits_one, big_shifted);
BigUnsigned<84> small_shifted = one;
big_shifted.ShiftLeft(no_op_shift);
EXPECT_EQ(one, small_shifted);
}
// Shifting by an amount greater than the number of bits should result in
// zero.
for (int out_of_bounds_shift :
{84 * 32, 84 * 32 + 1, std::numeric_limits<int>::max()}) {
BigUnsigned<84> big_shifted = all_bits_one;
big_shifted.ShiftLeft(out_of_bounds_shift);
EXPECT_EQ(zero, big_shifted);
BigUnsigned<84> small_shifted = one;
small_shifted.ShiftLeft(out_of_bounds_shift);
EXPECT_EQ(zero, small_shifted);
}
}
}
TEST(BigUnsigned, MultiplyByUint32) {
const BigUnsigned<84> factorial_100(
"933262154439441526816992388562667004907159682643816214685929638952175999"
"932299156089414639761565182862536979208272237582511852109168640000000000"
"00000000000000");
BigUnsigned<84> a(1u);
for (uint32_t i = 1; i <= 100; ++i) {
a.MultiplyBy(i);
}
EXPECT_EQ(a, BigUnsigned<84>(factorial_100));
}
TEST(BigUnsigned, MultiplyByBigUnsigned) {
{
// Put the terms of factorial_200 into two bigints, and multiply them
// together.
const BigUnsigned<84> factorial_200(
"7886578673647905035523632139321850622951359776871732632947425332443594"
"4996340334292030428401198462390417721213891963883025764279024263710506"
"1926624952829931113462857270763317237396988943922445621451664240254033"
"2918641312274282948532775242424075739032403212574055795686602260319041"
"7032406235170085879617892222278962370389737472000000000000000000000000"
"0000000000000000000000000");
BigUnsigned<84> evens(1u);
BigUnsigned<84> odds(1u);
for (uint32_t i = 1; i < 200; i += 2) {
odds.MultiplyBy(i);
evens.MultiplyBy(i + 1);
}
evens.MultiplyBy(odds);
EXPECT_EQ(evens, factorial_200);
}
{
// Multiply various powers of 10 together.
for (int a = 0 ; a < 700; a += 25) {
SCOPED_TRACE(a);
BigUnsigned<84> a_value("3" + std::string(a, '0'));
for (int b = 0; b < (700 - a); b += 25) {
SCOPED_TRACE(b);
BigUnsigned<84> b_value("2" + std::string(b, '0'));
BigUnsigned<84> expected_product("6" + std::string(a + b, '0'));
b_value.MultiplyBy(a_value);
EXPECT_EQ(b_value, expected_product);
}
}
}
}
TEST(BigUnsigned, MultiplyByOverflow) {
{
// Check that multiplcation overflow predictably truncates.
// A big int with all bits on.
BigUnsigned<4> all_bits_on("340282366920938463463374607431768211455");
// Modulo 2**128, this is equal to -1. Therefore the square of this,
// modulo 2**128, should be 1.
all_bits_on.MultiplyBy(all_bits_on);
EXPECT_EQ(all_bits_on, BigUnsigned<4>(1u));
}
{
// Try multiplying a large bigint by 2**50, and compare the result to
// shifting.
BigUnsigned<4> value_1("12345678901234567890123456789012345678");
BigUnsigned<4> value_2("12345678901234567890123456789012345678");
BigUnsigned<4> two_to_fiftieth(1u);
two_to_fiftieth.ShiftLeft(50);
value_1.ShiftLeft(50);
value_2.MultiplyBy(two_to_fiftieth);
EXPECT_EQ(value_1, value_2);
}
}
TEST(BigUnsigned, FiveToTheNth) {
{
// Sanity check that MultiplyByFiveToTheNth gives consistent answers, up to
// and including overflow.
for (int i = 0; i < 1160; ++i) {
SCOPED_TRACE(i);
BigUnsigned<84> value_1(123u);
BigUnsigned<84> value_2(123u);
value_1.MultiplyByFiveToTheNth(i);
for (int j = 0; j < i; j++) {
value_2.MultiplyBy(5u);
}
EXPECT_EQ(value_1, value_2);
}
}
{
// Check that the faster, table-lookup-based static method returns the same
// result that multiplying in-place would return, up to and including
// overflow.
for (int i = 0; i < 1160; ++i) {
SCOPED_TRACE(i);
BigUnsigned<84> value_1(1u);
value_1.MultiplyByFiveToTheNth(i);
BigUnsigned<84> value_2 = BigUnsigned<84>::FiveToTheNth(i);
EXPECT_EQ(value_1, value_2);
}
}
}
TEST(BigUnsigned, TenToTheNth) {
{
// Sanity check MultiplyByTenToTheNth.
for (int i = 0; i < 800; ++i) {
SCOPED_TRACE(i);
BigUnsigned<84> value_1(123u);
BigUnsigned<84> value_2(123u);
value_1.MultiplyByTenToTheNth(i);
for (int j = 0; j < i; j++) {
value_2.MultiplyBy(10u);
}
EXPECT_EQ(value_1, value_2);
}
}
{
// Alternate testing approach, taking advantage of the decimal parser.
for (int i = 0; i < 200; ++i) {
SCOPED_TRACE(i);
BigUnsigned<84> value_1(135u);
value_1.MultiplyByTenToTheNth(i);
BigUnsigned<84> value_2("135" + std::string(i, '0'));
EXPECT_EQ(value_1, value_2);
}
}
}
} // namespace strings_internal
ABSL_NAMESPACE_END
} // namespace absl
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