/// <summary>
/// /重载：一个高精度数除以一个高精度数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator /(BigNumber a, BigNumber b)
{
BigNumber c = new BigNumber();
BigNumber temp = new BigNumber();
if (Comparer(a, Trans(0)))
{
return(c);
}
c.positive = a.positive * b.positive;
a.positive = 1;
b.positive = 1;
temp = a;
int times = 0, add = 0;
int i, t, s, p;
for (s = 0; a.value[s] == 0; s++)
{
;
}
for (t = 0; b.value[t] == 0; t++)
{
;
}
if (t - s > 0)
{
times = t - s;
for (i = 59 - times; i >= 0; i--)
{
temp.value[i + times] = temp.value[i];
}
for (i = 0; i < times; i++)
{
temp.value[i] = 0;
}
}
p = 19 - t;
for (i = t; p + i < 60; i++)
{
int k = 9;
while ((temp - b * k).positive == -1 && k >= 0)
{
k--;
}
c.value[p + i] = k;
temp = (temp - b * k) * 10;
}
c = (c + Trans(add)) * Math.Pow(10.0, times);
if (c.zero(c))
{
c.positive = 1;
}
return(c);
}
/// <summary>
/// 减半Taylor
/// </summary>
/// <param name="a"></param>
/// <returns></returns>
public BigNumber Taylor(BigNumber a)
{
int i = 0, count = 0;
BigNumber two = new BigNumber();
//Trans(2);
two.value[19] = 2;
BigNumber ln2 = new BigNumber();
//0.69314 71805 59945 30941 72321 21458 17656 80718
// 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59
ln2.value[23] = ln2.value[26] = ln2.value[39] = ln2.value[44] = ln2.value[46] = ln2.value[50] = ln2.value[58] = 1;
ln2.value[41] = ln2.value[43] = ln2.value[45] = 2;
ln2.value[22] = ln2.value[35] = ln2.value[42] = 3;
ln2.value[24] = ln2.value[33] = ln2.value[38] = ln2.value[47] = 4;
ln2.value[29] = ln2.value[30] = ln2.value[34] = ln2.value[48] = ln2.value[53] = 5;
ln2.value[20] = ln2.value[52] = ln2.value[54] = 6;
ln2.value[25] = ln2.value[40] = ln2.value[51] = ln2.value[57] = 7;
ln2.value[27] = ln2.value[49] = ln2.value[55] = ln2.value[59] = 8;
ln2.value[21] = ln2.value[31] = ln2.value[32] = ln2.value[37] = 9;
if (!(a < two))
{
do
{
a = a / 2;
i++;
} while (!(a < two));
}
a = a - 1;
BigNumber x = copy(a);
BigNumber lnx = new BigNumber();
BigNumber temp1 = new BigNumber();
int n = 1;
BigNumber temp = x / n;
do
{
lnx = lnx + temp;
count++;
temp1 = x * a;
x = invert(temp1);
n++;
temp = x / n;
} while (!(temp.zero(temp)));
BigNumber result = new BigNumber();
result = lnx + (ln2 * i);
return(result);
}
/// <summary>
/// *重载：两个高精度数相乘
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator *(BigNumber a, BigNumber b)
{
BigNumber c = new BigNumber();
if (a.zero(a) || b.zero(b))
{
return(c);
}
int positive = a.positive * b.positive;
a.positive = 1;
b.positive = 1;
BigNumber d = copy(b);
int i, j;
for (i = 59; i >= 0; i--)
{
if (i >= 20) //处理小数部分
{
for (j = 0; j < i - 19; j++)
{
d.value[j] = 0;
}
for (j = i - 19; j < 60; j++)
{
d.value[j] = b.value[j - i + 19];
}
c = c + (d * a.value[i]);
}
else //处理整数部分
{
for (j = 0; j < 60 - 19 + i; j++)
{
d.value[j] = b.value[j + 19 - i];
}
c = c + (d * a.value[i]);
}
}
c.positive = positive;
if (c.zero(c))
{
c.positive = 1;
}
return(c);
}
/// <summary>
/// 迭代开根号
/// </summary>
/// <param name="a"></param>
/// <returns></returns>
public BigNumber sqrt(BigNumber a)
{
BigNumber one = new BigNumber();
one.value[19] = 1;
BigNumber x1 = new BigNumber();
BigNumber x2 = new BigNumber();
if (a.zero(a))
{
return(a);
}
else
{
if (a > one)
{
x2 = a / 2;
}
else
{
x2 = a * 2;
}
do
{
x1 = copy(x2);
x2 = (x1 + (a / x1)) / 2;
} while (!(x2 - x1).zero(x2 - x1));
for (int i = 0; i < 60; i++)
{
if (x2.value[i] > 9)
{
x2.value[i] -= 10;
x2.value[i + 1] += 1;
}
}
return(x2);
}
}
/// <summary>
/// +重载:两个高精度数相加
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator +(BigNumber a, BigNumber b)
{
BigNumber c = new BigNumber();
int flag = a.positive * b.positive;
if (flag == 1)
{
c.positive = a.positive;
int carry = 0;
for (int i = 59; i >= 0; i--)
{
c.value[i] = a.value[i] + b.value[i] + carry;
if (c.value[i] > 9)
{
c.value[i] = c.value[i] - 10;
carry = 1;
}
else
{
carry = 0;
}
}
}
else
{
if (abs(a) > abs(b))
{
c.positive = a.positive;
int borrow = 0;
for (int i = 59; i >= 0; i--)
{
c.value[i] = a.value[i] - b.value[i] - borrow;
if (c.value[i] >= 0)
{
borrow = 0;
}
else
{
c.value[i] += 10;
borrow = 1;
}
}
}
else
{
c.positive = b.positive;
int borrow = 0;
for (int i = 59; i >= 0; i--)
{
c.value[i] = b.value[i] - a.value[i] - borrow;
if (c.value[i] >= 0)
{
borrow = 0;
}
else
{
c.value[i] += 10;
borrow = 1;
}
}
}
}
if (c.zero(c))
{
c.positive = 1;
}
return(c);
}
/// <summary>
/// e^x高精度运算
/// </summary>
/// <param name="a"></param>
/// <returns></returns>
public BigNumber exp(BigNumber a)
{
BigNumber e = new BigNumber();
int i;
for (i = 0; i < 18; i++)
{
e.value[i] = 0;
}
e.value[32] = e.value[40] = 0;
e.value[21] = e.value[25] = e.value[46] = 1;
e.value[19] = e.value[23] = e.value[27] = e.value[35] = e.value[41] = e.value[49] = e.value[52] = e.value[59] = 2;
e.value[36] = e.value[38] = e.value[47] = 3;
e.value[29] = e.value[33] = e.value[44] = e.value[53] = 4;
e.value[30] = e.value[34] = e.value[37] = e.value[48] = e.value[57] = 5;
e.value[39] = e.value[50] = e.value[51] = 6;
e.value[20] = e.value[43] = e.value[45] = e.value[55] = e.value[56] = e.value[58] = 7;
e.value[22] = e.value[24] = e.value[26] = e.value[28] = e.value[42] = 8;
e.value[31] = e.value[54] = 9;
//Trans(2.7182818284590452353602874713526624977572);
BigNumber Integer = new BigNumber();
BigNumber Decimal = new BigNumber();
for (i = 0; i < 20; i++)
{
Integer.value[i] = a.value[i];
}
for (i = 20; i < 60; i++)
{
Decimal.value[i] = a.value[i];
}
BigNumber temp = Trans(1);
BigNumber temp1 = copy(Decimal);
BigNumber result = Trans(1);
i = 1;
if (a.zero(a))
{
return(Trans(1));
}
else if (a.positive == 1)
{
while (!Integer.zero(Integer))
{
temp = temp * e;
Integer = Integer - 1;
}
while (!temp1.zero(temp1))
{
result = result + temp1;
i++;
temp1 = temp1 * Decimal / i;
}
result = result * temp;
return(result);
}
else
{
while (!Integer.zero(Integer))
{
temp = temp * e;
Integer = Integer - 1;
}
while (!temp1.zero(temp1))
{
result = result + temp1;
i++;
temp1 = temp1 * Decimal / i;
}
result = 1 / (temp * result);
return(result);
}
}