/// <summary>
/// 把string转化为高精度数
/// </summary>
/// <param name="a"></param>
/// <returns></returns>
public BigNumber StringToBn(string a)
{
BigNumber b = new BigNumber();
bool Decimal = false;
int i, dot = 0;
for (i = 0; i < a.Length; i++)
{
if (a[i] == '.')
{
dot = i;
Decimal = true;
break;
}
}
if (a[0] == '-')
{
b.positive = -1;
if (Decimal)
{
for (i = dot - 1; i > 0; i--)
{
b.value[i + 20 - dot] = a[i] - 48;
}
for (i = dot + 1; i < a.Length; i++)
{
b.value[i + 19 - dot] = a[i] - 48;
}
}
else
{
for (i = 1; i < a.Length; i++)
{
b.value[20 + i - a.Length] = a[i] - 48;
}
}
return(b);
}
else
{
b.positive = 1;
if (Decimal)
{
for (i = dot - 1; i >= 0; i--)
{
b.value[i + 20 - dot] = a[i] - 48;
}
for (i = dot + 1; i < a.Length; i++)
{
b.value[i + 19 - dot] = a[i] - 48;
}
}
else
{
for (i = 0; i < a.Length; i++)
{
b.value[20 + i - a.Length] = a[i] - 48;
}
}
return(b);
}
}
/// <summary>
/// 求平方
/// </summary>
/// <param name="a"></param>
/// <returns></returns>
public static BigNumber square(BigNumber a)
{
return(copy(a * a));
}
/// <summary>
/// /重载：一个高精度数除以一个double型的数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator /(BigNumber a, double b)
{
BigNumber c = Trans(b);
return(a / c);
}
/// <summary>
/// /重载：一个double型的数除以一个高精度数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator /(double a, BigNumber b)
{
BigNumber c = Trans(a);
return(c / b);
}
/// <summary>
/// -重载：一个int型减一个高精度数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator -(int a, BigNumber b)
{
BigNumber c = Trans(a);
return(c - b);
}
/// <summary>
/// *重载：一个double型乘一个高精度数
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator *(double a, BigNumber b)
{
BigNumber c = Trans(a);
return(b * c);
}
/// <summary>
/// +重载：一个高精度数加一个int型
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator +(BigNumber a, int b)
{
BigNumber c = Trans(b);
return(a + c);
}
/// <summary>
/// -重载:两个高精度数相减
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
public static BigNumber operator -(BigNumber a, BigNumber b)
{
BigNumber c = invert(b);
return(a + c);
}
/// <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);
}
}
/// <summary>
/// 经典四阶R-K算法
/// </summary>
/// <param name="a"></param>
/// <returns></returns>
public BigNumber RK(BigNumber a)
{
int i = 0;
BigNumber two = new BigNumber();
two.value[19] = 2;
if (!(a < two))
{
do
{
a = a / 2;
i++;
} while (!(a < two));
}
BigNumber an = a;
BigNumber yn = new BigNumber();
BigNumber xn = new BigNumber();
//Trans(1);
xn.value[19] = 1;
BigNumber one = new BigNumber();
one.value[19] = 1;
BigNumber h = new BigNumber();
//Trans(0.000005);
h.value[25] = 5;
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 > one)
{
while (xn < an)
{
yn += ((((1 / xn) + (4 / (xn + (h / 2))) + (1 / (xn + h))) * h) / 6);
xn += h;
}
}
else
{
bool flag = false;
set(h, flag);
while (xn > an)
{
yn = yn + ((((1 / xn) + (4 / (xn + (h / 2))) + (1 / (xn + h))) * h) / 6);
xn += h;
}
}
BigNumber result = new BigNumber();
result = yn + (ln2 * i);
return(result);
}