5ht / unsigned-bigint

An efficient big integer C++ library.

bigint

这是一个大数运算库。

要求

• 编译时要求Visual Studio 2017
• 运行时要求支持ADX、BMI2、RDRAND指令集
• 运行时支持Intel Haswell或更新，AMD Ryzen或更新

使用

声明

unsigned_bigint<16> foo;    // 16表示这个数有16*64=1024位二进制位

输入输出

unsigned_bigint<16> a, b;
std::cin >> std::hex >> a >> b;                     // 十六进制输入
std::cout << std::hex << "a = " << a << std::endl;  // 十六进制输出
std::cin >> std::dec >> a >> b;                     // 十进制输入
std::cout << std::dec << "a = " << a << std::endl;  // 十进制输出
std::cin >> std::oct >> a >> b;                     // 八进制输入
std::cout << std::oct << "a = " << a << std::endl;  // 八进制输出

赋值

unsigned_bigint<16> a;
a = 65535;
std::cout << std::hex << "a = " << a << std::endl;

但如果要赋值为大数，由于C++常量不支持大整数（要支持的话我还写这个库做什么），请使用字符串进行赋值：

unsigned_bigint<16> a;
a = unsigned_bigint<16>("0x0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF");
std::cout << std::hex << "a = " << a << std::endl;

四则运算等

unsigned_bigint<16> a, b;
std::cin >> std::hex >> a >> b;
std::cout << std::hex << "a + b = " << a + b << std::endl
                      << "a - b = " << a - b << std::endl
                      << "a * b = " << a * b << std::endl
                      << "a / b = " << a / b << std::endl
                      << "a % b = " << a % b << std::endl;

模运算

foo = fast_pow_mod(a, n, m); // foo = (a ^ n) % m
bar = multiply_mod(a, b, m); // foo = (b * b) % m

比较操作及位运算

unsigned_bigint<16> a, b;
std::cin >> std::hex >> a >> b;
std::cout << std::hex << "(a > 0) = " << (a > 0) << std::endl
                      << "(a == b) = " << (a == b) << std::endl
                      << "(a != b) = " << (a != b) << std::endl
                      << "(a < b) = " << (a < b) << std::endl
                      << "(a <= b) = " << (a <= b) << std::endl
                      << "(a > b) = " << (a > b) << std::endl
                      << "(a >= b) = " << (a >= b) << std::endl
                      << "(a | b) = " << (a | b) << std::endl
                      << "(a & b) = " << (a & b) << std::endl
                      << "(a ^ b) = " << (a ^ b) << std::endl;

获取及修改某一位的值

unsigned_bigint<16> a;
std::cin >> std::hex >> a;
a.bit(0) = 1;                        // 最低位置1
std::cout << a.bit(0) << std::endl;  // 输出最低位

随机数生成器

unsigned_bigint<16> a, b;
std::cin >> std::hex >> a >> b;
// 使用Intel CPU中的指令获得真随机数，仅在Intel CPU上可用
std::cout << std::hex << "unsigned_bigint<16>::randIntel() = "
                      << unsigned_bigint<16>::randIntel() << std::endl;
// 生成伪随机数
std::cout << std::hex << "unsigned_bigint<16>::rand() = "
                      << unsigned_bigint<16>::rand() << std::endl;

质数判断

unsigned_bigint<16> a;
std::cin >> std::hex >> a;
std::cout << "a " << (a.is_prime_number() ? "is" : "isn't")
          << " a prime number" << std::endl;

性能对比

与Boost比较如下。（数据为运行时间，越小越好）

其中四则运算运算次数为500000次，模幂运算次数为1000次。

操作	256位		512位		1024位		2048位		4096位
	Unsigned Bigint	boost	Unsigned Bigint	boost	Unsigned Bigint	boost	Unsigned Bigint	boost	Unsigned Bigint	boost
加	0.0060686	0.0083953	0.0064107	0.0115023	0.0091979	0.0212813	0.0151207	0.0388485	0.0315682	0.0767778
减	0.0052497	0.0079826	0.0062715	0.0123272	0.0095903	0.0280378	0.0165817	0.0494003	0.0354999	0.0785873
乘	0.019142	0.0335125	0.063854	0.2700601	0.111633	0.3944791	0.3698449	1.4607164	1.2972828	5.5994093
除	0.9787682	0.2175322	1.6977481	0.3206437	2.571229	0.6465876	5.7703808	4.6256008	11.174972	10.216111
模幂	0.0675292	0.2627964	0.2580181	1.6192191	1.2872345	10.114824	7.361546	76.14449	52.701681	445.34939

boost自己进行的性能测试可以在这里找到。