本文整理汇总了C#中Rational.Divide方法的典型用法代码示例。如果您正苦于以下问题：C# Rational.Divide方法的具体用法？C# Rational.Divide怎么用？C# Rational.Divide使用的例子？那么恭喜您, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类Rational的用法示例。
在下文中一共展示了Rational.Divide方法的3个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的C#代码示例。
示例1: BroadhurstBbp
private static BigDecimal BroadhurstBbp(int n, int p, int[] a, MathContext mc)
{
/* Explore the actual magnitude of the result first with a quick estimate.
*/
double x = 0.0;
for (int k = 1; k < 10; k++)
x += a[(k - 1)%8]/System.Math.Pow(2d, p*(k + 1)/2d)/System.Math.Pow(k, n);
/* Convert the relative precision and estimate of the result into an absolute precision.
*/
double eps = PrecisionToError(x, mc.Precision);
/* Divide this through the number of terms in the sum to account for error accumulation
* The divisor 2^(p(k+1)/2) means that on the average each 8th term in k has shrunk by
* relative to the 8th predecessor by 1/2^(4p). 1/2^(4pc) = 10^(-precision) with c the 8term
* cycles yields c=log_2( 10^precision)/4p = 3.3*precision/4p with k=8c
*/
var kmax = (int) (6.6*mc.Precision/p);
/* Now eps is the absolute error in each term */
eps /= kmax;
BigDecimal res = BigDecimal.Zero;
for (int c = 0;; c++) {
var r = new Rational();
for (int k = 0; k < 8; k++) {
var tmp = new Rational(BigInteger.ValueOf(a[k]), (BigInteger.ValueOf((1 + 8*c + k))).Pow(n));
/* floor( (pk+p)/2)
*/
int pk1h = p*(2 + 8*c + k)/2;
tmp = tmp.Divide(BigInteger.One.ShiftLeft(pk1h));
r = r.Add(tmp);
}
if (System.Math.Abs(r.ToDouble()) < eps)
break;
var mcloc = new MathContext(1 + ErrorToPrecision(r.ToDouble(), eps));
res = res.Add(r.ToBigDecimal(mcloc));
}
return res.Round(mc);
}示例2: Log
public static BigDecimal Log(int n, MathContext mc)
{
/* the value is undefined if x is negative.
*/
if (n <= 0)
throw new ArithmeticException("Cannot take log of negative " + n);
if (n == 1)
return BigDecimal.Zero;
if (n == 2) {
if (mc.Precision < Log2.Precision)
return Log2.Round(mc);
/* Broadhurst <a href="http://arxiv.org/abs/math/9803067">arXiv:math/9803067</a>
* Error propagation: the error in log(2) is twice the error in S(2,-5,...).
*/
int[] a = {2, -5, -2, -7, -2, -5, 2, -3};
BigDecimal S = BroadhurstBbp(2, 1, a, new MathContext(1 + mc.Precision));
S = S.Multiply(new BigDecimal(8));
S = Sqrt(DivideRound(S, 3));
return S.Round(mc);
}
if (n == 3) {
/* summation of a series roughly proportional to (7/500)^k. Estimate count
* of terms to estimate the precision (drop the favorable additional
* 1/k here): 0.013^k <= 10^(-precision), so k*log10(0.013) <= -precision
* so k>= precision/1.87.
*/
var kmax = (int) (mc.Precision/1.87);
var mcloc = new MathContext(mc.Precision + 1 + (int) (System.Math.Log10(kmax*0.693/1.098)));
BigDecimal log3 = MultiplyRound(Log(2, mcloc), 19);
/* log3 is roughly 1, so absolute and relative error are the same. The
* result will be divided by 12, so a conservative error is the one
* already found in mc
*/
double eps = PrecisionToError(1.098, mc.Precision)/kmax;
var r = new Rational(7153, 524288);
var pk = new Rational(7153, 524288);
for (int k = 1;; k++) {
Rational tmp = pk.Divide(k);
if (tmp.ToDouble() < eps)
break;
/* how many digits of tmp do we need in the sum?
*/
mcloc = new MathContext(ErrorToPrecision(tmp.ToDouble(), eps));
BigDecimal c = pk.Divide(k).ToBigDecimal(mcloc);
if (k%2 != 0)
log3 = log3.Add(c);
else
log3 = log3.Subtract(c);
pk = pk.Multiply(r);
}
log3 = DivideRound(log3, 12);
return log3.Round(mc);
}
if (n == 5) {
/* summation of a series roughly proportional to (7/160)^k. Estimate count
* of terms to estimate the precision (drop the favorable additional
* 1/k here): 0.046^k <= 10^(-precision), so k*log10(0.046) <= -precision
* so k>= precision/1.33.
*/
var kmax = (int) (mc.Precision/1.33);
var mcloc = new MathContext(mc.Precision + 1 + (int) (System.Math.Log10(kmax*0.693/1.609)));
BigDecimal log5 = MultiplyRound(Log(2, mcloc), 14);
/* log5 is roughly 1.6, so absolute and relative error are the same. The
* result will be divided by 6, so a conservative error is the one
* already found in mc
*/
double eps = PrecisionToError(1.6, mc.Precision)/kmax;
var r = new Rational(759, 16384);
var pk = new Rational(759, 16384);
for (int k = 1;; k++) {
Rational tmp = pk.Divide(k);
if (tmp.ToDouble() < eps)
break;
/* how many digits of tmp do we need in the sum?
*/
mcloc = new MathContext(ErrorToPrecision(tmp.ToDouble(), eps));
BigDecimal c = pk.Divide(k).ToBigDecimal(mcloc);
log5 = log5.Subtract(c);
pk = pk.Multiply(r);
}
log5 = DivideRound(log5, 6);
return log5.Round(mc);
}
if (n == 7) {
/* summation of a series roughly proportional to (1/8)^k. Estimate count
* of terms to estimate the precision (drop the favorable additional
* 1/k here): 0.125^k <= 10^(-precision), so k*log10(0.125) <= -precision
* so k>= precision/0.903.
*/
var kmax = (int) (mc.Precision/0.903);
var mcloc = new MathContext(mc.Precision + 1 + (int) (System.Math.Log10(kmax*3*0.693/1.098)));
BigDecimal log7 = MultiplyRound(Log(2, mcloc), 3);
/* log7 is roughly 1.9, so absolute and relative error are the same.
*/
double eps = PrecisionToError(1.9, mc.Precision)/kmax;
//.........这里部分代码省略.........
示例3: Zeta
public static BigDecimal Zeta(int n, MathContext mc)
{
if (n <= 0)
throw new NotSupportedException("Zeta at negative argument " + n + " not supported");
if (n == 1)
throw new ArithmeticException("Pole at zeta(1) ");
if (n%2 == 0) {
/* Even indices. Abramowitz-Stegun 23.2.16. Start with 2^(n-1)*B(n)/n!
*/
Rational b = Bernoulli.Default[n].Abs();
b = b.Divide(Factorial.Default[n]);
b = b.Multiply(BigInteger.One.ShiftLeft(n - 1));
/* to be multiplied by pi^n. Absolute error in the result of pi^n is n times
* error in pi times pi^(n-1). Relative error is n*error(pi)/pi, requested by mc.
* Need one more digit in pi if n=10, two digits if n=100 etc, and add one extra digit.
*/
var mcpi = new MathContext(mc.Precision + (int) (System.Math.Log10(10.0*n)));
BigDecimal piton = PiRound(mcpi).Pow(n, mc);
return MultiplyRound(piton, b);
}
if (n == 3) {
/* Broadhurst BBP <a href="http://arxiv.org/abs/math/9803067">arXiv:math/9803067</a>
* Error propagation: S31 is roughly 0.087, S33 roughly 0.131
*/
int[] a31 = {1, -7, -1, 10, -1, -7, 1, 0};
int[] a33 = {1, 1, -1, -2, -1, 1, 1, 0};
BigDecimal S31 = BroadhurstBbp(3, 1, a31, mc);
BigDecimal S33 = BroadhurstBbp(3, 3, a33, mc);
S31 = S31.Multiply(new BigDecimal(48));
S33 = S33.Multiply(new BigDecimal(32));
return S31.Add(S33).Divide(new BigDecimal(7), mc);
}
if (n == 5) {
/* Broadhurst BBP <a href=http://arxiv.org/abs/math/9803067">arXiv:math/9803067</a>
* Error propagation: S51 is roughly -11.15, S53 roughly 22.165, S55 is roughly 0.031
* 9*2048*S51/6265 = -3.28. 7*2038*S53/61651= 5.07. 738*2048*S55/61651= 0.747.
* The result is of the order 1.03, so we add 2 digits to S51 and S52 and one digit to S55.
*/
int[] a51 = {31, -1614, -31, -6212, -31, -1614, 31, 74552};
int[] a53 = {173, 284, -173, -457, -173, 284, 173, -111};
int[] a55 = {1, 0, -1, -1, -1, 0, 1, 1};
BigDecimal S51 = BroadhurstBbp(5, 1, a51, new MathContext(2 + mc.Precision));
BigDecimal S53 = BroadhurstBbp(5, 3, a53, new MathContext(2 + mc.Precision));
BigDecimal S55 = BroadhurstBbp(5, 5, a55, new MathContext(1 + mc.Precision));
S51 = S51.Multiply(new BigDecimal(18432));
S53 = S53.Multiply(new BigDecimal(14336));
S55 = S55.Multiply(new BigDecimal(1511424));
return S51.Add(S53).Subtract(S55).Divide(new BigDecimal(62651), mc);
}
/* Cohen et al Exp Math 1 (1) (1992) 25
*/
var betsum = new Rational();
var bern = new Bernoulli();
var fact = new Factorial();
for (int npr = 0; npr <= (n + 1)/2; npr++) {
Rational b = bern[2*npr].Multiply(bern[n + 1 - 2*npr]);
b = b.Divide(fact[2*npr]).Divide(fact[n + 1 - 2*npr]);
b = b.Multiply(1 - 2*npr);
if (npr%2 == 0)
betsum = betsum.Add(b);
else
betsum = betsum.Subtract(b);
}
betsum = betsum.Divide(n - 1);
/* The first term, including the facor (2pi)^n, is essentially most
* of the result, near one. The second term below is roughly in the range 0.003 to 0.009.
* So the precision here is matching the precisionn requested by mc, and the precision
* requested for 2*pi is in absolute terms adjusted.
*/
var mcloc = new MathContext(2 + mc.Precision + (int) (System.Math.Log10(n)));
BigDecimal ftrm = PiRound(mcloc).Multiply(new BigDecimal(2));
ftrm = ftrm.Pow(n);
ftrm = MultiplyRound(ftrm, betsum.ToBigDecimal(mcloc));
var exps = new BigDecimal(0);
/* the basic accuracy of the accumulated terms before multiplication with 2
*/
double eps = System.Math.Pow(10d, -mc.Precision);
if (n%4 == 3) {
/* since the argument n is at least 7 here, the drop
* of the terms is at rather constant pace at least 10^-3, for example
* 0.0018, 0.2e-7, 0.29e-11, 0.74e-15 etc for npr=1,2,3.... We want 2 times these terms
* fall below eps/10.
*/
int kmax = mc.Precision/3;
eps /= kmax;
/* need an error of eps for 2/(exp(2pi)-1) = 0.0037
* The absolute error is 4*exp(2pi)*err(pi)/(exp(2pi)-1)^2=0.0075*err(pi)
*/
BigDecimal exp2p = PiRound(new MathContext(3 + ErrorToPrecision(3.14, eps/0.0075)));
exp2p = Exp(exp2p.Multiply(new BigDecimal(2)));
BigDecimal c = exp2p.Subtract(BigDecimal.One);
exps = DivideRound(1, c);
for (int npr = 2; npr <= kmax; npr++) {
/* the error estimate above for npr=1 is the worst case of
* the absolute error created by an error in 2pi. So we can
* safely re-use the exp2p value computed above without
//.........这里部分代码省略.........