关于圆周率，可参阅“维基百科-圆周率”。我前天在博客园也发表了一篇随笔：“计算圆周率的C程序” 。这个C#版的计算圆周率程序就是在C程序的基础上改写的。C#版的程序必须使用C#2.0编译，算法和C程序是一样的，都是利用圆周率的反正切展式的泰勒级数来计算，但C#程序充分使用面象对象的编程方法，并且程序中有适当的注释，比C程序容易理解多了。C#程序从配置文件中读取计算所用的公式，允许自己增加计算公式。
using System; using System.IO; using System.Text.RegularExpressions; using System.Collections.Generic; using System.Diagnostics; namespace Skyiv.Util 
{ 
// 用反正切展式计算圆周率 // 例如: pi= + 16 * arctan(1/5) - 4 * arctan(1/239) [Machin] sealed class ThePi 
{ 
// 表示 (positive ? + : -) coefficient * arctan(1/denominator) public sealed class Term { bool positive; // 系数是否正数 int coefficient; // 系数 int denominator; // 分母 public bool Positive { get { return positive; } } public int Coefficient { get { return coefficient; } } public int Denominator { get { return denominator; } } public Term(bool positive, int coefficient, int denominator) { this.positive = positive; this.coefficient = coefficient; this.denominator = denominator; 
} public override string ToString() { return string.Format("{0} {1} * arctan(1/{2}) ", positive ? "+" : "-", coefficient, denominator); } } const int overDigits = 3; // 额外计算的位数，以消除误差 List<Term> list = new List<Term>(); // 反正切展式 string name; // 反正切展式的发现者 public ThePi(string name) { this.name = name; } public void Add(Term term) { list.Add(term); } // 返回反正切展式，例如: pi= + 16 * arctan(1/5) - 4 * arctan(1/239) [Machin] public override string ToString() { string s = "pi= "; foreach (Term term in list) s += term.ToString(); return s + "[" + name + "]"; } // 将圆周率精确到小数点后 digits 位的值以及所用时间输出到 tw public void Out(TextWriter tw, int digits) { const int digitsPerGroup = 5; const int groupsPerLine = 13; const int digitsPerLine = groupsPerLine * digitsPerGroup; tw.WriteLine(this); TimeSpan elapsed; int [] piValue = Compute(digits, out elapsed); tw.Write("pi= {0}.", piValue[piValue.Length - 1]); int position = 6; for (int i = piValue.Length - 2; i >= overDigits; i--, position++) { tw.Write(piValue[i]); if (position % digitsPerLine == 0) tw.WriteLine(); else if (position % digitsPerGroup == 0) tw.Write(" "); } if ((position - 1) % digitsPerLine != 0) tw.WriteLine(); tw.WriteLine("[{0}] DIGITS:{1:N0} ELAPSED:{2}", name, digits, elapsed); } // 计算圆周率到小数点后 digits 位, 并统计所用时间 elapsed int [] Compute(int digits, out TimeSpan elapsed) { Stopwatch stopWatch = new Stopwatch(); stopWatch.Start(); int [] piValue = Compute(digits + overDigits); Format(piValue); stopWatch.Stop(); elapsed = stopWatch.Elapsed; return piValue; } // 计算圆周率到小数点后 digits 位, 结果未格式化 int [] Compute(int digits) { int [] pi = new int [digits + 1]; // 圆周率的值, 反序存放，如: 
951413 int [] tmp = new int [digits + 1]; // 中间计算结果，也是反序存放 foreach (Term term in list) { // arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - x^11/11 + .. int validDigits = digits; int divisor = term.Denominator; bool positive = term.Positive; Array.Clear(tmp, 0, tmp.Length); tmp[digits] = term.Coefficient; Divide(true, positive, true, ref validDigits, pi, tmp, divisor); positive = !positive; divisor *= divisor; for (int step = 3; validDigits > 0; positive = !positive, step += 2) { Divide(false, true, true, ref validDigits, null, tmp, divisor); Divide(true, positive, false, ref validDigits, pi, tmp, step); } } return pi; } // 计算 sum += 或 -= (dividend /= 或 / divisor) void Divide( bool updateSum, // 是否更新sum bool positive, // 系数是否正数 bool updateDividend, // 是否更新被除数 ref int digits, // 被除数的有效位数 int [] sum, // 和数 int [] dividend, // 被除数 int divisor // 除数 ) { for (int remainder = 0, i = digits; i >= 0; i--) { int quotient = 10 * remainder + dividend[i]; remainder = quotient % divisor; quotient /= divisor; if (updateDividend) dividend[i] = quotient; if (!updateSum) continue; if (positive) sum[i] += quotient; else sum[i] -= quotient; } if (updateDividend) while (digits > 0 && dividend[digits] == 0) digits--; } // 将 pi 数据组中的每个元素格式化为个位数 void Format(int [] pi) { for (int quotient = 0, i = 0; i < pi.Length; i++) {