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