c语言实现1024bit大数乘法(3)

记录大数相乘的一般思路，乘法只是正数的大数相乘，数组第0位代表数组长度。
z[1]=x[1]*y[1]
z[2]=x[1]*y[2] +x[2]*y[1]
z[3]=x[1]*y[3] +x[2]*y[2]+x[3]*y[1]
…
因此可得z[i]=x[i-j+1]*y[j], for j=1到 y[0]， x[0]> i-j>=0
考虑到进为问题，得到如下程序

          Init(t);
		t[0] = x[0] + y[0] - 1;
		for (i = 1; i <= t[0]; i++)
		{
			sum = carry;
			carry = 0;
			for (j = 1; j <= y[0]; j++)
			{
				if ((i - j) >= 0 && (i - j) < x[0])
				{
					mul = x[i - j + 1];
					mul = (unsigned long long)mul * y[j];
					carry = carry + mul / 0x100000000;
					mul = mul & 0xffffffff;
					sum = sum + mul;
				}
			}
			carry = carry + sum / 0x100000000;
			t[i] = (unsigned int)sum;
		}

全部代码如下

/****************************************************************************************************
大数相乘
调用方式Mul(x,y,z)
返回值，z=x*y
*****************************************************************************************************/
void Mul_Long(unsigned int x[], unsigned long long y, unsigned int *z)
{
	unsigned int t[34];
	unsigned long long mul;
	unsigned int carry = 0;
	int i;
	Init(t);
	Mov_Big(x, t);
	for (i = 1; i <= x[0]; i++)
	{
		mul = x[i];
		mul = mul * y + carry;
		t[i] = (unsigned int)mul;
		carry = (unsigned int)(mul >> 32);
	}
	if (carry != 0)
	{
		t[0]++;
		t[t[0]] = carry;
	}
	i = t[0];
	while (t[i] == 0 && i > 1)     //这里有改动i>1 
	{
		t[0]--;
		i--;
	}
	Mov_Big(t, z);
}


void Mul_Big(unsigned int x[], unsigned int y[], unsigned int *z)
{
	unsigned int t[100];
	unsigned long long sum, mul = 0, carry = 0;
	unsigned int i, j;
	if (y[0] == 1)
		Mul_Long(x, y[1], z);
	else
	{
		Init(t);
		t[0] = x[0] + y[0] - 1;
		for (i = 1; i <= t[0]; i++)
		{
			sum = carry;
			carry = 0;
			for (j = 1; j <= y[0]; j++)
			{
				if ((i - j) >= 0 && (i - j) < x[0])
				{
					mul = x[i - j + 1];
					mul = (unsigned long long)mul * y[j];
					carry = carry + mul / 0x100000000;
					mul = mul & 0xffffffff;
					sum = sum + mul;
				}
			}
			carry = carry + sum / 0x100000000;
			t[i] = (unsigned int)sum;
		}
		if (carry != 0)
		{
			t[0]++;
			t[t[0]] = (unsigned int)carry;
		}
		i = t[0];
		while (t[i] == 0 && i > 1)//这里有改动 
		{
			t[0]--;
			i--;
		}
		Mov_Big(t, z);

	}

}