/**
* Compute the <a href="http://mathworld.wolfram.com/HyperbolicSine.html" TARGET="_top">
* hyperbolic sine</a> of this complex number. Implements the formula:
*
* <pre>
* <code>
* sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i
* </code>
* </pre>
*
* where the (real) functions on the right-hand side are {@link java.lang.Math#sin}, {@link
* java.lang.Math#cos}, {@link FastMath#cosh} and {@link FastMath#sinh}. <br>
* Returns {@link Complex#NaN} if either real or imaginary part of the input argument is {@code
* NaN}. <br>
* Infinite values in real or imaginary parts of the input may result in infinite or NaN values
* returned in parts of the result.
*
* <pre>
* Examples:
* <code>
* sinh(1 ± INFINITY i) = NaN + NaN i
* sinh(±INFINITY + i) = ± INFINITY + INFINITY i
* sinh(±INFINITY ± INFINITY i) = NaN + NaN i
* </code>
* </pre>
*
* @return the hyperbolic sine of {@code this}.
* @since 1.2
*/
public Complex sinh() {
if (isNaN) {
return NaN;
}
return createComplex(
FastMath.sinh(real) * FastMath.cos(imaginary),
FastMath.cosh(real) * FastMath.sin(imaginary));
}
/**
* Compute the <a href="http://mathworld.wolfram.com/HyperbolicTangent.html" TARGET="_top">
* hyperbolic tangent</a> of this complex number. Implements the formula:
*
* <pre>
* <code>
* tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) + [sin(2b)/(cosh(2a)+cos(2b))]i
* </code>
* </pre>
*
* where the (real) functions on the right-hand side are {@link FastMath#sin}, {@link
* FastMath#cos}, {@link FastMath#cosh} and {@link FastMath#sinh}. <br>
* Returns {@link Complex#NaN} if either real or imaginary part of the input argument is {@code
* NaN}. <br>
* Infinite values in real or imaginary parts of the input may result in infinite or NaN values
* returned in parts of the result.
*
* <pre>
* Examples:
* <code>
* tanh(a ± INFINITY i) = NaN + NaN i
* tanh(±INFINITY + bi) = ±1 + 0 i
* tanh(±INFINITY ± INFINITY i) = NaN + NaN i
* tanh(0 + (π/2)i) = NaN + INFINITY i
* </code>
* </pre>
*
* @return the hyperbolic tangent of {@code this}.
* @since 1.2
*/
public Complex tanh() {
if (isNaN || Double.isInfinite(imaginary)) {
return NaN;
}
if (real > 20.0) {
return createComplex(1.0, 0.0);
}
if (real < -20.0) {
return createComplex(-1.0, 0.0);
}
double real2 = 2.0 * real;
double imaginary2 = 2.0 * imaginary;
double d = FastMath.cosh(real2) + FastMath.cos(imaginary2);
return createComplex(FastMath.sinh(real2) / d, FastMath.sin(imaginary2) / d);
}