定义PI到36位小数

Question

有可能在C++但是要做到这一点

ifndef M_PI 
define M_PI   3.141592653589793238462643383279502884 
endif 

在C＃中，我试图声明一个双var和36位小数分配给它的PI值。 这不起作用，因为双精度数据存储最多为16位小数（MSDN docx）。我尝试创建一个隐式类型局部变量，但编译器只是宣布它为双精度，然后我又回到原点。也许我可以在C＃中包含cmath？

我如何在C＃中定义PI 36个小数点

Answer 1

Here is an article about calculating pi to 1 million digit in C#，您可以缩小它下降到36位

这里是一个示例代码，我建议阅读完整的文章和背后的逻辑。

public static HighPrecision GetPi(int digits) 
{ 
    HighPrecision.Precision = digits; 
    HighPrecision first = 4 * Atan(5); 
    HighPrecision second = Atan(239); 
    return 4 * (first - second); 
} 

，如果你只是想存储PI（不计算它），你可以将值从here复制，并存储在HighPrecision变量。

Answer 2

据我知道C＃在typedecimal精度最高，但它仅达28-29显著十进制数字。我不认为您可以在不使用自定义库的情况下在C＃中覆盖最多36位十进制数字。

Answer 3

如果你真的需要那么多的精度，可以使用任意精度的C库像GNU MPC或GNU MPFR。由于他们是C函数库，所以你可能需要使用interop使用它们......但是，这会限制你的高精度pi使用使用你选择的套餐...

Answer 4

你可以在C++中做什么，而不能在C＃中做的是为文字创建一个别名。在C++ #define M_PI 3.141592653589793238462643383279502884中写入不会将PI定义为36个地方。它只是将字面量化。

#define M_PI 3.141592653589793238462643383279502884 
double pi = M_PI; 

这是完全一样的写作

double pi = 3.141592653589793238462643383279502884; 

这将工作在C++和C＃几乎相同。在C++中，该值与C＃中的精度相同，因为文字将被解释为double，我相信这两者在两者中基本相同。

M_PI被宣布为高达36位的原因是因为这是quad double的最大精度。遗憾的是，在C＃中没有如此精确的本机类型。在C++中，除非您将它用作quad double，否则您不会从M_PI获得任何特别的东西。

已经别名文字没有太大的帮助，它只是允许这样写：

float pif = M_PI; 
    int pii = M_PI; 
    double pid = M_PI; 
    quad double piq = M_PI; 

不幸的是，你需要使用自定义类型。

Answer 5

我发现这个问题很有趣，所以这里是我的2美分。

我把Machin的公式implementation，应用到大整数的IntXLib实现（它已经对Discrete Hartley transform进行了优化乘除运算符）。

最后，我将结果与Pi value posted here进行了比较。

这里，在i7 920 @ 2.66 Ghz上计算138 ms中的2500个小数。现在

static void Main(string[] args) 
{ 
    String referencePi = "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125"; 
    Stopwatch watch = new Stopwatch(); 
    watch.Restart(); 
    DecimalX calculatedPi = PiHelper.Calculate(2500); 
    watch.Stop(); 
    Console.WriteLine("Pi with 2500 decimals in " + watch.ElapsedMilliseconds + " ms"); 
    String hmmmmm = calculatedPi.ToString(); 
    if (hmmmmm == referencePi) 
     Console.WriteLine("Pi approximation found"); 
} 

public class DecimalX 
{ 
    /// Integer represatation of the decimal 
    private readonly IntX _integerPart; 
    /// Power of 10 (10^X) 
    private readonly uint _scale; 
    public DecimalX(IntX integerPart, uint scale) 
    { 
     _integerPart = integerPart; 
     _scale = scale; 
    } 
    public override string ToString() 
    { 
     IntX afterPoint = null; 
     IntX beforePoint = IntX.DivideModulo(_integerPart, IntX.Pow(10, _scale, MultiplyMode.AutoFht), out afterPoint, DivideMode.AutoNewton); 
     return beforePoint.ToString() + "." + afterPoint.ToString(); 
    } 
} 

public class PiHelper 
{ 
    public static IntX InverseTan(int denominator, int numberOfDigitsRequired) 
    { 
     int demonimatorSquared = denominator * denominator; 
     int degreeNeeded = GetDegreeOfPrecisionNeeded(demonimatorSquared, numberOfDigitsRequired); 
     IntX tenToNumberPowerOfDigitsRequired = IntX.Pow(10, (uint)numberOfDigitsRequired, MultiplyMode.AutoFht); 
     IntX s = IntX.Divide(tenToNumberPowerOfDigitsRequired, new IntX(2 * degreeNeeded + 1), DivideMode.AutoNewton); // s = (10^N)/c 
     int c = 2 * degreeNeeded + 1; 
     for (int i = 0; i < degreeNeeded; i++) 
     { 
      c = c - 2; 
      var temp1 = IntX.Divide(tenToNumberPowerOfDigitsRequired, new IntX(c), DivideMode.AutoNewton); 
      var temp2 = IntX.Divide(s, new IntX(demonimatorSquared), DivideMode.AutoNewton); 
      s = temp1 - temp2; 
     } 
     return IntX.Divide(s, new IntX(denominator), DivideMode.AutoNewton); 
    } 

    private static int GetDegreeOfPrecisionNeeded(int demonimatorSquared, int numberOfDigitsRequired) 
    { 
     int degreeNeeded = 0; 
     while ((Math.Log(2 * degreeNeeded + 3) + (degreeNeeded + 1) * Math.Log10(demonimatorSquared)) <= numberOfDigitsRequired * Math.Log(10)) 
      degreeNeeded++; 
     return degreeNeeded; 
    } 

    public static DecimalX Calculate(int numberOfDigitsRequired) 
    { 
     int max = numberOfDigitsRequired + 8; // To be safe, compute 8 extra digits, to be dropped at end. The 8 is arbitrary 
     var a = IntX.Multiply(InverseTan(5, max), new IntX(16), MultiplyMode.AutoFht); //16 x arctan(1/5) 
     var b = IntX.Multiply(InverseTan(239, max), new IntX(4), MultiplyMode.AutoFht); //4 x arctan(1/239) 
     return new DecimalX(IntX.Divide(a - b, IntX.Pow(10, (uint)8), DivideMode.AutoNewton), (uint)numberOfDigitsRequired); 
    } 
} 

，你只需要实现对DecimalX类型与“正常”类型的所有运营商（如浮点/双/ INT /等..），但我认为这将是容易的！