public void Adding_0_to_a_rational_returns_the_same_value(Rational x) { Assert.Equal(x, x + Rational.Zero); Assert.Equal(x, Rational.Zero + x); Assert.Equal(x, Rational.Add(x, Rational.Zero)); Assert.Equal(x, Rational.Add(Rational.Zero, x)); }
static void Main(string[] args) { Console.WriteLine("Enter two integers (numerator and denominator): "); int num = int.Parse(Console.ReadLine()); int denom = int.Parse(Console.ReadLine()); var rationalOne = new Rational(); rationalOne.SetFraction(num, denom); Console.WriteLine("Enter two more integers: "); num = int.Parse(Console.ReadLine()); denom = int.Parse(Console.ReadLine()); var rationalTwo = new Rational(); rationalTwo.SetFraction(num, denom); Console.WriteLine("\nHow many digits to you want to display in past the decimal?"); int digits = int.Parse(Console.ReadLine()); Console.WriteLine("\nReduced first fraction: "); Console.WriteLine($"{rationalOne.ToRationalString()}"); Console.WriteLine("Reduced second fraction: "); Console.WriteLine($"{rationalTwo.ToRationalString()}"); Console.WriteLine($"Added rational numbers = {Rational.Add(rationalOne.ToFloat(), rationalTwo.ToFloat())}"); Console.WriteLine($"Subtracted rational numbers = {Rational.Subtract(rationalOne.ToFloat(), rationalTwo.ToFloat())}"); Console.WriteLine($"Multiplied rational numbers = {Rational.Multiply(rationalOne.ToFloat(), rationalTwo.ToFloat())}"); Console.WriteLine($"Divided rational numbers = {Rational.Divide(rationalOne.ToFloat(), rationalTwo.ToFloat())}"); Console.WriteLine("\nPress any key to end program."); Console.ReadKey(); }
public void Case1() { // The statement: // Rational number = Int64.MaxValue + Int32.MaxValue; // produces compiler error CS0220: The operation overflows at compile time in checked mode. // The alternative: Rational number = Rational.Add(Int64.MaxValue, Int32.MaxValue); }
public void Case1() { byte byteValue = 254; Rational number = byteValue; number = Rational.Add(number, byteValue); Console.WriteLine(number > byteValue); // Displays True }
public void Add(Rational r1, Rational r2) { RationalBase result = r1.Add(r2); Assert.True(r1 != result && r2 != result); int n1 = r1.Numerator, d1 = r1.Denominator, n2 = r2.Numerator, d2 = r2.Denominator; Assert.Equal(new Rational(n1 * d2 + n2 * d1, d1 * d2), result); }
static void Main(string[] args) { Rational a = new Rational(3, 4); Rational b = new Rational(4, 5); Rational c = a.Add(b); Console.WriteLine(c.StrVal()); c = b.Subtract(a); Console.WriteLine(c.StrVal()); }
public void NumbersAreZero() { var num1 = new Rational { Numerator = 0, Denominator = 1 }; var num2 = num1; var result = num1.Add(num2); Assert.AreEqual(0, result.Numerator); Assert.AreEqual(1, result.Denominator); }
public void DifferentDenominators() { var num1 = new Rational { Numerator = 1, Denominator = 2 }; var num2 = new Rational { Numerator = 2, Denominator = 3 }; var result = num1.Add(num2); Assert.AreEqual(7, result.Numerator); Assert.AreEqual(6, result.Denominator); }
public void SameDenominators() { var num1 = new Rational { Numerator = 1, Denominator = 2 }; var num2 = new Rational { Numerator = 2, Denominator = 2 }; var result = num1.Add(num2); Assert.AreEqual(3, result.Numerator); Assert.AreEqual(2, result.Denominator); }
static void Main() { Rational a = new Rational(3, 4); Rational b = new Rational(4, 5); Rational c = a.Add(b); Console.WriteLine(c.StrVal()); c = a.Subtract(b); Console.WriteLine(c.StrVal()); }
public void Case1() { // Initialize a Rational value. Rational value = Rational.Add(UInt64.MaxValue, 1024); // Display value using the default ToString method. Console.WriteLine(value.ToString()); // Display value using some standard format specifiers. Console.WriteLine(value.ToString("G")); Console.WriteLine(value.ToString("C")); Console.WriteLine(value.ToString("D")); Console.WriteLine(value.ToString("F")); Console.WriteLine(value.ToString("N")); // The example displays the following output on a system whose current // culture is en-US: // 18446744073709552639 // 18446744073709552639 // $18,446,744,073,709,552,639.00 // 18446744073709552639 // 18446744073709552639.00 // 18,446,744,073,709,552,639.00 }
internal override Rational Op(Rational lhs, Rational rhs) { return(lhs.Add(rhs)); }
public void Dividing_the_sum_is_the_same_as_dividing_each_and_then_adding_the_result(NonZeroRational x, Rational y, Rational z) { Assert.Equal((y + z) / x, (y / x) + (z / x)); Assert.Equal(Rational.Divide(Rational.Add(y, z), x), Rational.Add(Rational.Divide(y, x), Rational.Divide(z, x))); }
public void Substracting_y_to_x_is_the_same_as_adding_opposite_of_y_to_x(Rational x, Rational y) { Assert.Equal(x - y, x + (-y)); Assert.Equal(Rational.Subtract(x, y), Rational.Add(x, Rational.Negate(y))); }
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); }
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 * reassessment of its error. */ c = PowRound(exp2p, npr).Subtract(BigDecimal.One); c = MultiplyRound(c, (BigInteger.ValueOf(npr)).Pow(n)); c = DivideRound(1, c); exps = exps.Add(c); } } else { /* since the argument n is at least 9 here, the drop * of the terms is at rather constant pace at least 10^-3, for example * 0.0096, 0.5e-7, 0.3e-11, 0.6e-15 etc. We want these terms * fall below eps/10. */ int kmax = (1 + mc.Precision)/3; eps /= kmax; /* need an error of eps for 2/(exp(2pi)-1)*(1+4*Pi/8/(1-exp(-2pi)) = 0.0096 * at k=7 or = 0.00766 at k=13 for example. * The absolute error is 0.017*err(pi) at k=9, 0.013*err(pi) at k=13, 0.012 at k=17 */ BigDecimal twop = PiRound(new MathContext(3 + ErrorToPrecision(3.14, eps/0.017))); twop = twop.Multiply(new BigDecimal(2)); BigDecimal exp2p = Exp(twop); BigDecimal c = exp2p.Subtract(BigDecimal.One); exps = DivideRound(1, c); c = BigDecimal.One.Subtract(DivideRound(1, exp2p)); c = DivideRound(twop, c).Multiply(new BigDecimal(2)); c = DivideRound(c, n - 1).Add(BigDecimal.One); exps = MultiplyRound(exps, c); for (int npr = 2; npr <= kmax; npr++) { c = PowRound(exp2p, npr).Subtract(BigDecimal.One); c = MultiplyRound(c, (BigInteger.ValueOf(npr)).Pow(n)); BigDecimal d = DivideRound(1, exp2p.Pow(npr)); d = BigDecimal.One.Subtract(d); d = DivideRound(twop, d).Multiply(new BigDecimal(2*npr)); d = DivideRound(d, n - 1).Add(BigDecimal.One); d = DivideRound(d, c); exps = exps.Add(d); } } exps = exps.Multiply(new BigDecimal(2)); return ftrm.Subtract(exps, mc); }
public void Multiplying_the_sum_is_the_same_as_multiplying_each_one_and_then_adding_the_result(Rational x, Rational y, Rational z) { Assert.Equal((y + z) * x, y * x + z * x); Assert.Equal(Rational.Multiply(Rational.Add(y, z), x), Rational.Add(Rational.Multiply(y, x), Rational.Multiply(z, x))); }
public void Case1() { Rational number1 = Rational.Add(Int64.MaxValue, Int32.MaxValue); Rational number2 = Math.Pow(Byte.MaxValue, 10); Rational result = number1 & number2; }
public void Adding_the_opposite_returns_0(Rational x) { Assert.Equal(Rational.Zero, x + (-x)); Assert.Equal(Rational.Zero, Rational.Add(x, Rational.Negate(x))); }
public void Adding_NaN_returns_NaN(Rational x) { Assert.Equal(Rational.NaN, x + Rational.NaN); Assert.Equal(Rational.NaN, Rational.Add(x, Rational.NaN)); }
public void Adding_3_rationals_in_any_order_returns_the_same_result(Rational x, Rational y, Rational z) { Assert.Equal(x + y + z, x + (y + z)); Assert.Equal(Rational.Add(Rational.Add(x, y), z), Rational.Add(x, Rational.Add(y, z))); }
public void AddFail(Rational r, int n, int d) { Assert.Throws <InvalidOperationException>(() => r.Add(null)); }
public void Case1() { Rational number1 = Rational.Add(Int64.MaxValue, Int32.MaxValue); Rational number2 = Math.Pow(Byte.MaxValue, 10); Rational result = Rational.BitwiseAnd(number1, number2); }
public void Adding_x_to_y_is_the_same_as_adding_y_to_x(Rational x, Rational y) { Assert.Equal(x + y, y + x); Assert.Equal(Rational.Add(x, y), Rational.Add(y, x)); }