1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
|
// 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));
}
}
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
|
