Implement big float, transition to molarity

33 files changed, 7540 insertions, 49 deletions

diff --git a/src/main/java/ch/obermuhlner/math/big/BigComplex.java b/src/main/java/ch/obermuhlner/math/big/BigComplex.java
new file mode 100644
index 0000000000..a4620ff53b
--- /dev/null
+++ b/src/main/java/ch/obermuhlner/math/big/BigComplex.java
@@ -0,0 +1,556 @@
+package ch.obermuhlner.math.big;
+
+import java.math.BigDecimal;
+import java.math.MathContext;
+import java.util.Objects;
+
+/**
+ * Represents a complex number consisting of a real and an imaginary {@link BigDecimal} part in the form {@code a + bi}.
+ *
+ * <p>It generally follows the design of {@link BigDecimal} with some convenience improvements like overloaded operator methods.</p>
+ *
+ * <p>The biggest difference to {@link BigDecimal} is that {@link BigComplex#equals(Object) BigComplex.equals(Object)} implements the <strong>mathematical</strong> equality
+ * and <strong>not</strong> the strict technical equality.
+ * This was a difficult decision because it means that {@code BigComplex} behaves slightly different than {@link BigDecimal}
+ * but considering that the strange equality of {@link BigDecimal} is a major source of bugs we
+ * decided it was worth the slight inconsistency.
+ * If you need the strict equality use {@link BigComplex#strictEquals(Object)}`.</p>
+ *
+ * <p>This class is immutable and therefore inherently thread safe.</p>
+ */
+public final class BigComplex {
+
+	/**
+	 * Zero represented as complex number.
+	 */
+	public static final BigComplex ZERO = new BigComplex(BigDecimal.ZERO, BigDecimal.ZERO);
+
+	/**
+	 * Real 1 represented as complex number.
+	 */
+	public static final BigComplex ONE = new BigComplex(BigDecimal.ONE, BigDecimal.ZERO);
+
+	/**
+	 * Imaginary 1 represented as complex number.
+	 */
+	public static final BigComplex I = new BigComplex(BigDecimal.ZERO, BigDecimal.ONE);
+
+	/**
+	 * The real {@link BigDecimal} part of this complex number.
+	 */
+	public final BigDecimal re;
+
+	/**
+	 * The imaginary {@link BigDecimal} part of this complex number.
+	 */
+	public final BigDecimal im;
+
+	private BigComplex(BigDecimal re, BigDecimal im) {
+		this.re = re;
+		this.im = im;
+	}
+
+	/**
+	 * Calculates the addition of the given complex value to this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@link BigComplex} value to add
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex add(BigComplex value) {
+		return valueOf(
+				re.add(value.re),
+				im.add(value.im));
+	}
+
+	/**
+	 * Calculates the addition of the given complex value to this complex number using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@link BigComplex} value to add
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex add(BigComplex value, MathContext mathContext) {
+		return valueOf(
+				re.add(value.re, mathContext),
+				im.add(value.im, mathContext));
+	}
+
+	/**
+	 * Calculates the addition of the given real {@link BigDecimal} value to this complex number using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@link BigDecimal} value to add
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex add(BigDecimal value, MathContext mathContext) {
+		return valueOf(
+				re.add(value, mathContext),
+				im);
+	}
+
+	/**
+	 * Calculates the addition of the given real {@link BigDecimal} value to this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@link BigDecimal} value to add
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex add(BigDecimal value) {
+		return valueOf(
+				re.add(value),
+				im);
+	}
+
+	/**
+	 * Calculates the addition of the given real {@code double} value to this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@code double} value to add
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex add(double value) {
+		return add(BigDecimal.valueOf(value));
+	}
+
+	/**
+	 * Calculates the subtraction of the given complex value from this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@link BigComplex} value to subtract
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex subtract(BigComplex value) {
+		return valueOf(
+				re.subtract(value.re),
+				im.subtract(value.im));
+	}
+
+	/**
+	 * Calculates the subtraction of the given complex value from this complex number using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@link BigComplex} value to subtract
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex subtract(BigComplex value, MathContext mathContext) {
+		return valueOf(
+				re.subtract(value.re, mathContext),
+				im.subtract(value.im, mathContext));
+	}
+
+	/**
+	 * Calculates the subtraction of the given real {@link BigDecimal} value from this complex number using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@link BigDecimal} value to add
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex subtract(BigDecimal value, MathContext mathContext) {
+		return valueOf(
+				re.subtract(value, mathContext),
+				im);
+	}
+
+	/**
+	 * Calculates the subtraction of the given real {@link BigDecimal} value from this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@link BigDecimal} value to subtract
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex subtract(BigDecimal value) {
+		return valueOf(
+				re.subtract(value),
+				im);
+	}
+
+	/**
+	 * Calculates the subtraction of the given real {@code double} value from this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@code double} value to subtract
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex subtract(double value) {
+		return subtract(BigDecimal.valueOf(value));
+	}
+
+	/**
+	 * Calculates the multiplication of the given complex value to this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@link BigComplex} value to multiply
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex multiply(BigComplex value) {
+		return valueOf(
+				re.multiply(value.re).subtract(im.multiply(value.im)),
+				re.multiply(value.im).add(im.multiply(value.re)));
+	}
+
+	/**
+	 * Calculates the multiplication of the given complex value with this complex number using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@link BigComplex} value to multiply
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex multiply(BigComplex value, MathContext mathContext) {
+		return valueOf(
+				re.multiply(value.re, mathContext).subtract(im.multiply(value.im, mathContext), mathContext),
+				re.multiply(value.im, mathContext).add(im.multiply(value.re, mathContext), mathContext));
+	}
+
+	/**
+	 * Calculates the multiplication of the given real {@link BigDecimal} value with this complex number using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@link BigDecimal} value to multiply
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex multiply(BigDecimal value, MathContext mathContext) {
+		return valueOf(
+				re.multiply(value, mathContext),
+				im.multiply(value, mathContext));
+	}
+
+	/**
+	 * Calculates the multiplication of the given real {@link BigDecimal} value with this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@link BigDecimal} value to multiply
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex multiply(BigDecimal value) {
+		return valueOf(
+				re.multiply(value),
+				im.multiply(value));
+	}
+
+	/**
+	 * Calculates the multiplication of the given real {@code double} value with this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the real {@code double} value to multiply
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex multiply(double value) {
+		return multiply(BigDecimal.valueOf(value));
+	}
+
+	/**
+	 * Calculates this complex number divided by the given complex value using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@link BigComplex} value to divide by
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex divide(BigComplex value, MathContext mathContext) {
+		return multiply(value.reciprocal(mathContext), mathContext);
+	}
+
+	/**
+	 * Calculates this complex number divided by the given real {@link BigDecimal} value using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@link BigDecimal} value to divide by
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex divide(BigDecimal value, MathContext mathContext) {
+		return valueOf(
+				re.divide(value, mathContext),
+				im.divide(value, mathContext));
+	}
+
+	/**
+	 * Calculates this complex number divided by the given real {@code double} value using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param value the {@code double} value to divide by
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex divide(double value, MathContext mathContext) {
+		return divide(BigDecimal.valueOf(value), mathContext);
+	}
+
+	/**
+	 * Calculates the reciprocal of this complex number using the specified {@link MathContext}.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex reciprocal(MathContext mathContext) {
+		BigDecimal scale = absSquare(mathContext);
+		return valueOf(
+				re.divide(scale, mathContext),
+				im.negate().divide(scale, mathContext));
+	}
+
+	/**
+	 * Calculates the conjugate {@code a - bi} of this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex conjugate() {
+		return valueOf(re, im.negate());
+	}
+
+	/**
+	 * Calculates the negation {@code -a - bi} of this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigComplex negate() {
+		return valueOf(re.negate(), im.negate());
+	}
+
+	/**
+	 * Calculates the absolute value (also known as magnitude, length or radius) of this complex number.
+	 *
+	 * <p>This method is slower than {@link #absSquare(MathContext)} since it needs to calculate the {@link BigDecimalMath#sqrt(BigDecimal, MathContext)}.</p>
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 * @see #absSquare(MathContext)
+	 */
+	public BigDecimal abs(MathContext mathContext) {
+		return BigDecimalMath.sqrt(absSquare(mathContext), mathContext);
+	}
+
+	/**
+	 * Calculates the angle in radians (also known as argument) of this complex number.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 */
+	public BigDecimal angle(MathContext mathContext) {
+		return BigDecimalMath.atan2(im, re, mathContext);
+	}
+
+	/**
+	 * Calculates the square of the absolute value of this complex number.
+	 *
+	 * <p>This method is faster than {@link #abs(MathContext)} since it does not need to calculate the {@link BigDecimalMath#sqrt(BigDecimal, MathContext)}.</p>
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 * @see #abs(MathContext)
+	 */
+	public BigDecimal absSquare(MathContext mathContext) {
+		return re.multiply(re, mathContext).add(im.multiply(im, mathContext), mathContext);
+	}
+
+	/**
+	 * Returns whether this complex number only has a real part (the imaginary part is 0).
+	 *
+	 * @return {@code true} if this complex number only has a real part, {@code false} if the imaginary part is not 0
+	 */
+	public boolean isReal() {
+		return im.signum() == 0;
+	}
+
+	/**
+	 * Returns the real part of this complex number as {@link BigComplex} number.
+	 *
+	 * @return the real part as as {@link BigComplex} number
+	 */
+	public BigComplex re() {
+		return valueOf(re, BigDecimal.ZERO);
+	}
+
+	/**
+	 * Returns the imaginary part of this complex number as {@link BigComplex} number.
+	 *
+	 * @return the imaginary part as as {@link BigComplex} number
+	 */
+	public BigComplex im() {
+		return valueOf(BigDecimal.ZERO, im);
+	}
+
+	/**
+	 * Returns this complex nuber rounded to the specified precision.
+	 *
+	 * <p>This methods <strong>does not</strong> modify this instance.</p>
+	 *
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the rounded {@link BigComplex} result
+	 */
+	public BigComplex round(MathContext mathContext) {
+		return valueOf(re.round(mathContext), im.round(mathContext));
+	}
+
+	@Override
+	public int hashCode() {
+		return Objects.hash(re, im);
+	}
+
+	/**
+	 * {@inheritDoc}
+	 *
+	 * <p>Contrary to {@link BigDecimal#equals(Object)} this method implements <strong>mathematical</strong> equality
+	 * (by calling {@link BigDecimal#compareTo(BigDecimal)} on the real and imaginary parts)
+	 * instead of strict equality.</p>
+	 *
+	 * @see #strictEquals(Object)
+	 */
+	@Override
+	public boolean equals(Object obj) {
+		if (this == obj)
+			return true;
+		if (obj == null)
+			return false;
+		if (getClass() != obj.getClass())
+			return false;
+		BigComplex other = (BigComplex) obj;
+
+		return re.compareTo(other.re) == 0 && im.compareTo(other.im) == 0;
+	}
+
+	/**
+	 * Returns whether the real and imaginary parts of this complex number are strictly equal.
+	 *
+	 * <p>This method uses the strict equality as defined by {@link BigDecimal#equals(Object)} on the real and imaginary parts.</p>
+	 * <p>Please note that {@link #equals(Object) BigComplex.equals(Object)} implements <strong>mathematical</strong> equality instead
+	 * (by calling {@link BigDecimal#compareTo(BigDecimal) on the real and imaginary parts}).</p>
+	 *
+	 * @param obj the object to compare for strict equality
+	 * @return {@code true} if the specified object is strictly equal to this complex number
+	 * @see #equals(Object)
+	 */
+	public boolean strictEquals(Object obj) {
+		if (this == obj)
+			return true;
+		if (obj == null)
+			return false;
+		if (getClass() != obj.getClass())
+			return false;
+		BigComplex other = (BigComplex) obj;
+
+		return re.equals(other.re) && im.equals(other.im);
+	}
+
+	@Override
+	public String toString() {
+		if (im.signum() >= 0) {
+			return "(" + re + " + " + im + " i)";
+		} else {
+			return "(" + re + " - " + im.negate() + " i)";
+		}
+	}
+
+	/**
+	 * Returns a complex number with the specified real {@link BigDecimal} part.
+	 *
+	 * @param real the real {@link BigDecimal} part
+	 * @return the complex number
+	 */
+	public static BigComplex valueOf(BigDecimal real) {
+		return valueOf(real, BigDecimal.ZERO);
+	}
+
+	/**
+	 * Returns a complex number with the specified real {@code double} part.
+	 *
+	 * @param real the real {@code double} part
+	 * @return the complex number
+	 */
+	public static BigComplex valueOf(double real) {
+		return valueOf(BigDecimal.valueOf(real), BigDecimal.ZERO);
+	}
+
+	/**
+	 * Returns a complex number with the specified real and imaginary {@code double} parts.
+	 *
+	 * @param real the real {@code double} part
+	 * @param imaginary the imaginary {@code double} part
+	 * @return the complex number
+	 */
+	public static BigComplex valueOf(double real, double imaginary) {
+		return valueOf(BigDecimal.valueOf(real), BigDecimal.valueOf(imaginary));
+	}
+
+	/**
+	 * Returns a complex number with the specified real and imaginary {@link BigDecimal} parts.
+	 *
+	 * @param real the real {@link BigDecimal} part
+	 * @param imaginary the imaginary {@link BigDecimal} part
+	 * @return the complex number
+	 */
+	public static BigComplex valueOf(BigDecimal real, BigDecimal imaginary) {
+		if (real.signum() == 0) {
+			if (imaginary.signum() == 0) {
+				return ZERO;
+			}
+			if (imaginary.compareTo(BigDecimal.ONE) == 0) {
+				return I;
+			}
+		}
+		if (imaginary.signum() == 0 && real.compareTo(BigDecimal.ONE) == 0) {
+			return ONE;
+		}
+
+		return new BigComplex(real, imaginary);
+	}
+
+	/**
+	 * Returns a complex number with the specified polar {@link BigDecimal} radius and angle using the specified {@link MathContext}.
+	 *
+	 * @param radius the {@link BigDecimal} radius of the polar representation
+	 * @param angle the {@link BigDecimal} angle in radians of the polar representation
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the complex number
+	 */
+	public static BigComplex valueOfPolar(BigDecimal radius, BigDecimal angle, MathContext mathContext) {
+		if (radius.signum() == 0) {
+			return ZERO;
+		}
+
+		return valueOf(
+				radius.multiply(BigDecimalMath.cos(angle, mathContext), mathContext),
+				radius.multiply(BigDecimalMath.sin(angle, mathContext), mathContext));
+	}
+
+	public static BigComplex valueOfPolar(double radius, double angle, MathContext mathContext) {
+		return valueOfPolar(BigDecimal.valueOf(radius), BigDecimal.valueOf(angle), mathContext);
+	}
+}
diff --git a/src/main/java/ch/obermuhlner/math/big/BigComplexMath.java b/src/main/java/ch/obermuhlner/math/big/BigComplexMath.java
new file mode 100644
index 0000000000..a73d9bccdd
--- /dev/null
+++ b/src/main/java/ch/obermuhlner/math/big/BigComplexMath.java
@@ -0,0 +1,413 @@
+package ch.obermuhlner.math.big;
+
+import java.math.BigDecimal;
+import java.math.MathContext;
+import java.util.List;
+
+import static ch.obermuhlner.math.big.BigComplex.I;
+
+/**
+ * Provides advanced functions operating on {@link BigComplex}s.
+ */
+public class BigComplexMath {
+
+	private static final BigDecimal TWO = BigDecimal.valueOf(2);
+
+	/**
+	 * Calculates the reciprocal of the given complex number using the specified {@link MathContext}.
+	 *
+	 * @param x the complex number to calculate the reciprocal
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 * @see BigComplex#reciprocal(MathContext)
+	 */
+	public static BigComplex reciprocal(BigComplex x, MathContext mathContext) {
+		return x.reciprocal(mathContext);
+	}
+
+	/**
+	 * Calculates the conjugate of the given complex number using the specified {@link MathContext}.
+	 *
+	 * @param x the complex number to calculate the conjugate
+	 * @return the calculated {@link BigComplex} result
+	 * @see BigComplex#conjugate()
+	 */
+	public static BigComplex conjugate(BigComplex x) {
+		return x.conjugate();
+	}
+
+	/**
+	 * Calculates the absolute value (also known as magnitude, length or radius) of the given complex number using the specified {@link MathContext}.
+	 *
+	 * @param x the complex number to calculate the absolute value
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 * @see BigComplex#abs(MathContext)
+	 */
+	public static BigDecimal abs(BigComplex x, MathContext mathContext) {
+		return x.abs(mathContext);
+	}
+
+	/**
+	 * Calculates the square of the absolute value (also known as magnitude, length or radius) of the given complex number using the specified {@link MathContext}.
+	 *
+	 * @param x the complex number to calculate the square of the absolute value
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} result
+	 * @see BigComplex#absSquare(MathContext)
+	 */
+	public static BigDecimal absSquare(BigComplex x, MathContext mathContext) {
+		return x.absSquare(mathContext);
+	}
+
+	/**
+	 * Calculates the angle in radians of the given complex number using the specified {@link MathContext}.
+	 *
+	 * @param x the complex number to calculate the angle
+	 * @param mathContext the {@link MathContext} used to calculate the result
+	 * @return the calculated {@link BigComplex} angle in radians
+	 * @see BigComplex#angle(MathContext)
+	 */
+	public static BigDecimal angle(BigComplex x, MathContext mathContext) {
+		return x.angle(mathContext);
+	}
+
+	/**
+	 * Calculates the factorial of the specified {@link BigComplex}.
+	 *
+	 * <p>This implementation uses
+	 * <a href="https://en.wikipedia.org/wiki/Spouge%27s_approximation">Spouge's approximation</a>
+	 * to calculate the factorial for non-integer values.</p>
+	 *
+	 * <p>This involves calculating a series of constants that depend on the desired precision.
+	 * Since this constant calculation is quite expensive (especially for higher precisions),
+	 * the constants for a specific precision will be cached
+	 * and subsequent calls to this method with the same precision will be much faster.</p>
+	 *
+	 * <p>It is therefore recommended to do one call to this method with the standard precision of your application during the startup phase
+	 * and to avoid calling it with many different precisions.</p>
+	 *
+	 * <p>See: <a href="https://en.wikipedia.org/wiki/Factorial#Extension_of_factorial_to_non-integer_values_of_argument">Wikipedia: Factorial - Extension of factorial to non-integer values of argument</a></p>
+	 *
+	 * @param x the {@link BigComplex}
+	 * @param mathContext the {@link MathContext} used for the result
+	 * @return the factorial {@link BigComplex}
+	 * @throws ArithmeticException if x is a negative integer value (-1, -2, -3, ...)
+	 * @see BigDecimalMath#factorial(BigDecimal, MathContext)
+	 * @see #gamma(BigComplex, MathContext)
+	 */
+	public static BigComplex factorial(BigComplex x, MathContext mathContext) {
+		if (x.isReal() && BigDecimalMath.isIntValue(x.re)) {
+			return BigComplex.valueOf(BigDecimalMath.factorial(x.re.intValueExact()).round(mathContext));
+		}
+
+		// https://en.wikipedia.org/wiki/Spouge%27s_approximation
+		MathContext mc = new MathContext(mathContext.getPrecision() * 2, mathContext.getRoundingMode());
+
+		int a = mathContext.getPrecision() * 13 / 10;
+		List<BigDecimal> constants = BigDecimalMath.getSpougeFactorialConstants(a);
+
+		BigDecimal bigA = BigDecimal.valueOf(a);
+
+		boolean negative = false;
+		BigComplex factor = BigComplex.valueOf(constants.get(0));
+		for (int k = 1; k < a; k++) {
+			BigDecimal bigK = BigDecimal.valueOf(k);
+			factor = factor.add(BigComplex.valueOf(constants.get(k)).divide(x.add(bigK), mc), mc);
+			negative = !negative;
+		}
+
+		BigComplex result = pow(x.add(bigA, mc), x.add(BigDecimal.valueOf(0.5), mc), mc);
+		result = result.multiply(exp(x.negate().subtract(bigA, mc), mc), mc);