在 C++ 中可以做而在 C# 中不能做的是为文字创建别名。用 c++ 编写#define M_PI 3.141592653589793238462643383279502884并没有定义PI为 36 个位置。它只是给文字起别名。
#define M_PI 3.141592653589793238462643383279502884
double pi = M_PI;
和写的完全一样
double pi = 3.141592653589793238462643383279502884;
这在 c++ 和 C# 中的工作方式几乎相同。在 c++ 中，该值将具有与 C# 中相同的精度，因为字面量将被解释为double我认为两者基本相同的 a。
声明最多 36 位的原因M_PI是因为这是quad double. 遗憾的是，在 C# 中没有具有如此精确度的本机类型。在 c++ 中，M_PI除非您将其用作quad double.
具有别名文字并没有多大帮助，它只允许编写：
float pif = M_PI;
int pii = M_PI;
double pid = M_PI;
quad double piq = M_PI;
不幸的是，您需要使用自定义类型。
据我所知，C# 的类型 decimal精度最高，但只有 28-29 位有效十进制数字。如果不使用自定义库，我认为您无法在 C# 中覆盖多达 36 个十进制数字。
我发现这个问题很有趣，所以这是我的 2 美分。
我采用 Machin 的公式实现，并将其应用于大整数的IntXLib实现（它使用离散哈特利变换优化了乘法和除法运算符）。
最后，我将结果与此处发布的 Pi 值进行了比较。
在这里，2500 个小数在 i7 920 @2.66 Ghz 上以 138 毫秒计算。
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);
}
}
现在，您只需使用“普通”类型（如 float / double / int / 等）在 DecimalX 类型上实现所有运算符，但我认为这很容易！
这是一篇关于在 C# 中将 pi 计算为 100 万位的文章，您可以将其缩小到 36 位
这是一个示例代码，我建议阅读全文及其背后的逻辑。
public static HighPrecision GetPi(int digits)
{
HighPrecision.Precision = digits;
HighPrecision first = 4 * Atan(5);
HighPrecision second = Atan(239);
return 4 * (first - second);
}
如果您只想存储 pi（不计算它），您可以从此处复制值并将其存储在HighPrecision变量中。