public MainWindow()
{
InitializeComponent();
calc.times = new int[3];
//初始化，存1、2、4、根号2的大数表示
calc.one = new bigNum("1");
calc.two = new bigNum("2");
calc.four = new bigNum("4");
calc.sqrt2 = bigNum.sqrt(2);
//calc.sqrt2.show();
/*
* 计算ln2
*/
bigNum sqrt2_1 = calc.sqrt2 - calc.one;
calc.ln2 = new bigNum("0");
bigNum an = new bigNum(sqrt2_1);
for (int i = 1; i <= 300; ++i)
{
calc.ln2 = calc.ln2 + an / (new bigNum(i.ToString()));
an = an * sqrt2_1;
an.neg = (i % 2 == 1 ? true : false);
}
calc.ln2 = calc.ln2 * calc.two;
//calc.ln2.show();
}
/*
* 大数数字加法
*/
private static bigNum plus(bigNum b1, bigNum b2)
{
bigNum bn1 = new bigNum(b1), bn2 = new bigNum(b2), ans = new bigNum();
if (bn1.dot > bn2.dot)
{
for (int i = bn2.cnt - 1; i >= 0; --i)
{
bn2.num[i + bn1.dot - bn2.dot] = bn2.num[i];
bn2.num[i] = 0;
}
bn2.cnt += bn1.dot - bn2.dot;
bn2.dot = bn1.dot;
}
else if (bn1.dot < bn2.dot)
{
for (int i = bn1.cnt - 1; i >= 0; --i)
{
bn1.num[i + bn2.dot - bn1.dot] = bn1.num[i];
bn1.num[i] = 0;
}
bn1.cnt += bn2.dot - bn1.dot;
bn1.dot = bn2.dot;
}
else
{
}
ans.cnt = bn1.cnt > bn2.cnt ? bn1.cnt : bn2.cnt;
ans.dot = bn1.dot;
for (int i = 0; i < ans.cnt; ++i)
{
ans.num[i] = bn1.num[i] + bn2.num[i];
}
//进位
for (int i = 0; i < ans.cnt; ++i)
{
if (ans.num[i] >= mod)
{
ans.num[i + 1] += ans.num[i] / mod;
ans.num[i] %= mod;
if (i == ans.cnt - 1)
{
++ans.cnt;
}
}
}
if (ans.cnt > maxlen)
{
int delta = ans.cnt - maxlen;
for (int i = 0; i < maxlen; ++i)
{
ans.num[i] = ans.num[i + delta];
ans.num[i + delta] = 0;
}
ans.dot -= delta;
ans.cnt = maxlen;
}
return(ans);
}
/*
* 大数除法
*/
public static bigNum operator /(bigNum b1, bigNum b2)
{
bigNum ans = new bigNum("0");
bigNum bn1 = new bigNum(b1), bn2 = new bigNum(b2);
int[] num_a = bn1.num, num_b = bn2.num;
int len1 = bn1.cnt, len2 = bn2.cnt;
for (int i = len1 - 1; i >= 0; --i)
{
num_a[i + maxlen * 2 - len1] = num_a[i];
num_a[i] = 0;
}
len1 = maxlen * 2;
int nTimes = len1 - len2;
for (int i = len2 - 1; i >= 0; --i)
{
num_b[i + nTimes] = num_b[i];
num_b[i] = 0;
}
len2 = len1;
int nTemp;
for (int i = 0; i <= nTimes; ++i)
{
while ((nTemp = SubStract(num_a, num_b, len1, len2, i)) >= 0)
{
len1 = nTemp;
ans.num[nTimes - i]++;
}
if (len1 == len2 - i && num_a[len1 - 1] == 0)
{
len1--;
}
}
ans.dot = 2 * maxlen - (bn1.cnt - bn1.dot) - bn2.dot;
ans.cnt = len2;
while (ans.num[ans.cnt - 1] == 0 && ans.cnt > ans.dot + 1)
{
ans.cnt--;
}
if (ans.cnt > maxlen)
{
int delta = ans.cnt - maxlen;
for (int i = 0; i < maxlen; ++i)
{
ans.num[i] = ans.num[i + delta];
ans.num[i + delta] = 0;
}
ans.dot -= delta;
ans.cnt = maxlen;
}
ans.neg = bn1.neg ^ bn2.neg;
return(ans);
}
public bigNum(bigNum bn)//由大数初始化
{
neg = bn.neg;
cnt = bn.cnt;
dot = bn.dot;
num = new int[1010];
for (int i = 0; i < cnt; ++i)
{
num[i] = bn.num[i];
}
}
/*
* 整数开根号
*/
public static bigNum sqrt(int xx)
{
if (xx > 0)
{
bool flag = false;
bigNum x = new bigNum(xx.ToString());
bigNum[] a = new bigNum[2];
a[1] = new bigNum("1");
bigNum delta;
bool loop = true;
while (loop)
{
loop = false;
if (!flag)
{
a[0] = (a[1] + x / a[1]) / calc.two;
}
else
{
a[1] = (a[0] + x / a[0]) / calc.two;
}
flag = !flag;
delta = a[1] - a[0];
for (int j = delta.cnt - 1; j >= delta.dot; --j)
{
if (delta.num[j] != 0)
{
loop = true;
break;
}
}
if (!loop)
{
for (int j = delta.dot - 1; j >= delta.dot - 500 && j >= 0; --j)
{
if (delta.num[j] != 0)
{
loop = true;
break;
}
}
}
}
return(flag ? a[1] : a[0]);
}
return(new bigNum("0"));
}
/*
* 根据要求精度四舍五入
*/
public bigNum round(bigNum bn, int acc)
{
bigNum ans = new bigNum(bn);
if (ans.dot <= acc)
{
for (int i = ans.cnt - 1; i >= 0; --i)
{
ans.num[i + acc - ans.dot] = ans.num[i];
ans.num[i] = 0;
}
ans.cnt += acc - ans.dot;
ans.dot = acc;
}
else
{
if (ans.num[ans.dot - acc - 1] >= 5)
{
ans.num[ans.dot - acc] += 1;
}
for (int i = ans.dot - acc; i < ans.cnt; ++i)
{
if (ans.num[i] >= mod)
{
ans.num[i + 1] += ans.num[i] / mod;
ans.num[i] %= mod;
if (i == ans.cnt - 1)
{
ans.cnt++;
}
}
else
{
break;
}
}
}
return(ans);
}
/*
* 大数乘法
*/
public static bigNum operator *(bigNum b1, bigNum b2)
{
bigNum ans = new bigNum();
for (int i = 0; i < b1.cnt; ++i)
{
for (int j = 0; j < b2.cnt; ++j)
{
ans.num[i + j] += b1.num[i] * b2.num[j];
}
}
ans.cnt = b1.cnt + b2.cnt - 1;
ans.dot = b1.dot + b2.dot;
for (int i = 0; i < ans.cnt; ++i)
{
if (ans.num[i] >= mod)
{
ans.num[i + 1] += ans.num[i] / mod;
ans.num[i] %= mod;
if (i == ans.cnt - 1)
{
++ans.cnt;
}
}
}
if (ans.cnt > maxlen)
{
int delta = ans.cnt - maxlen;
for (int i = 0; i < maxlen; ++i)
{
ans.num[i] = ans.num[i + delta];
ans.num[i + delta] = 0;
}
ans.dot -= delta;
ans.cnt = maxlen;
}
return(ans);
}
/*
* 大数带符号减法
*/
public static bigNum operator -(bigNum b1, bigNum b2)
{
bigNum ans = new bigNum();
if ((b1.neg ^ b2.neg))//符号不同，数字相加，符号跟随被减数
{
ans = plus(b1, b2);
ans.neg = b1.neg;
}
else//符号相同，数字相减，
{
if (b1 >= b2)
{
ans = minus(b1, b2);
ans.neg = b1.neg;
}
else
{
ans = minus(b2, b1);
ans.neg = !b1.neg;
}
}
if (ans.cnt > maxlen)
{
int delta = ans.cnt - maxlen;
for (int i = 0; i < maxlen; ++i)
{
ans.num[i] = ans.num[i + delta];
ans.num[i + delta] = 0;
}
ans.dot -= delta;
ans.cnt = maxlen;
}
return(ans);
}
/*
* 大数数字减法
*/
private static bigNum minus(bigNum b1, bigNum b2)
{
bigNum bn1 = new bigNum(b1), bn2 = new bigNum(b2), ans = new bigNum();
if (bn1.dot > bn2.dot)
{
for (int i = bn2.cnt - 1; i >= 0; --i)
{
bn2.num[i + bn1.dot - bn2.dot] = bn2.num[i];
bn2.num[i] = 0;
}
bn2.cnt += bn1.dot - bn2.dot;
bn2.dot = bn1.dot;
}
else if (bn1.dot < bn2.dot)
{
for (int i = bn1.cnt - 1; i >= 0; --i)
{
bn1.num[i + bn2.dot - bn1.dot] = bn1.num[i];
bn1.num[i] = 0;
}
bn1.cnt += bn2.dot - bn1.dot;
bn1.dot = bn2.dot;
}
else
{
}
ans.cnt = bn1.cnt > bn2.cnt ? bn1.cnt : bn2.cnt;
ans.dot = bn1.dot;
for (int i = 0; i < ans.cnt; ++i)
{
ans.num[i] = bn1.num[i] - bn2.num[i];
}
//借位
for (int i = 0; i < ans.cnt; ++i)
{
if (ans.num[i] < 0)
{
ans.num[i + 1] += ans.num[i] / mod;
ans.num[i] %= mod;
if (ans.num[i] < 0)
{
ans.num[i + 1]--;
ans.num[i] += mod;
}
}
}
while (ans.num[ans.cnt - 1] == 0 && ans.cnt > ans.dot + 1)
{
ans.cnt--;
}
if (ans.cnt > maxlen)
{
int delta = ans.cnt - maxlen;
for (int i = 0; i < maxlen; ++i)
{
ans.num[i] = ans.num[i + delta];
ans.num[i + delta] = 0;
}
ans.dot -= delta;
ans.cnt = maxlen;
}
return(ans);
}
/*
* a. Taylor展开（最佳或近似最佳逼近）；
* b. 数值积分；
* c. 非Taylor展开的函数逼近方法（选作）；
*/
private void button_Click(object sender, RoutedEventArgs e)
{
if (accuracy.Text == "")
{
MessageBox.Show("请输入精度");
return;
}
if (num.Text == "")
{
MessageBox.Show("请输入x");
return;
}
Stopwatch stopwatch = new Stopwatch();
for (int i = 0; i < accuracy.Text.Length; ++i)
{
if (accuracy.Text[i] < '0' || accuracy.Text[i] > '9')
{
MessageBox.Show("精度请输入有效正整数");
return;
}
}
acc = Convert.ToInt32(accuracy.Text);
if (acc >= 50)
{
MessageBox.Show("精度建议小于50");
return;
}
if (acc < 0)
{
MessageBox.Show("结果小数位数大于等于0");
return;
}
int cntdot = 0;
for (int i = 0; i < num.Text.Length; ++i)
{
if (num.Text[i] < '0' || num.Text[i] > '9')
{
if (num.Text[i] == '.')
{
cntdot++;
if (cntdot > 1)
{
MessageBox.Show("请输入有效x");
return;
}
}
else
{
MessageBox.Show("请输入有效x");
return;
}
}
}
bigNum input = new bigNum(num.Text);
if (input < calc.one)
{
MessageBox.Show("请输入不小于1的x");
return;
}
/*
* Taylor展开段
*/
stopwatch.Reset();
stopwatch.Start();
bigNum halfTaylorAns = calc.halfTaylor(num.Text, acc);
halfTaylor.Text = (calc.round(halfTaylorAns, acc)).show(acc);
stopwatch.Stop();
halfTaylorTime.Text = stopwatch.ElapsedMilliseconds.ToString() + "ms";
halfTaylorTimes.Text = calc.times[0].ToString();
/*
* Romberg数值积分段
*/
stopwatch.Reset();
stopwatch.Start();
bigNum rombergAns = calc.romberg(num.Text, acc);
romberg.Text = (calc.round(rombergAns, acc)).show(acc);
stopwatch.Stop();
rombergTime.Text = stopwatch.ElapsedMilliseconds.ToString() + "ms";
rombergTimes.Text = calc.times[1].ToString();
/*
* 有理逼近段
*/
stopwatch.Reset();
stopwatch.Start();
bigNum rationalAns = calc.rational(num.Text, acc);
rational.Text = (calc.round(rationalAns, acc)).show(acc);
stopwatch.Stop();
rationalTime.Text = stopwatch.ElapsedMilliseconds.ToString() + "ms";
rationalTimes.Text = calc.times[2].ToString();
//MessageBox.Show("Done!");
}
