Simplify sinh, cosh and tanh
diff --git a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
index bc91838..a126040 100644
--- a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
+++ b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
@@ -1932,56 +1932,22 @@
* @return the hyperbolic cosine of the complex number
*/
private static Complex cosh(double real, double imaginary, ComplexConstructor constructor) {
- if (Double.isFinite(real)) {
- if (Double.isFinite(imaginary)) {
- return constructor.create(Math.cosh(real) * Math.cos(imaginary),
- Math.sinh(real) * Math.sin(imaginary));
- }
- // ISO C99: Preserve the even function by mapping to positive
- // f(z) = f(-z)
- double re;
- double im;
- if (negative(real)) {
- re = -real;
- im = -imaginary;
- } else {
- re = real;
- im = imaginary;
- }
- // Special case for real == 0
- return constructor.create(Double.NaN,
- re == 0 ? Math.copySign(0, im) : Double.NaN);
+ // ISO C99: Preserve the even function by mapping to positive
+ // f(z) = f(-z)
+ if (Double.isInfinite(real) && !Double.isFinite(imaginary)) {
+ return constructor.create(Math.abs(real), Double.NaN);
}
- if (Double.isInfinite(real)) {
- if (Double.isFinite(imaginary)) {
- if (imaginary == 0) {
- // Determine sign
- final double im = real > 0 ? imaginary : -imaginary;
- return constructor.create(Double.POSITIVE_INFINITY, im);
- }
- // inf * cis(y)
- // ISO C99: Preserve the even function
- // f(z) = f(-z)
- double re;
- double im;
- if (real < 0) {
- re = -real;
- im = -imaginary;
- } else {
- re = real;
- im = imaginary;
- }
- return constructor.create(re * Math.cos(im), re * Math.sin(im));
- }
- // imaginary is infinite or NaN
- return constructor.create(Double.POSITIVE_INFINITY, Double.NaN);
+ if (real == 0 && !Double.isFinite(imaginary)) {
+ return constructor.create(Double.NaN, changeSign(real, imaginary));
}
- // real is NaN
- if (imaginary == 0) {
- return constructor.create(Double.NaN, imaginary);
+ if (real == 0 && imaginary == 0) {
+ return constructor.create(1, changeSign(real, imaginary));
}
- // optionally raises the ‘‘invalid’’ floating-point exception, for nonzero y.
- return NAN;
+ if (imaginary == 0 && !Double.isFinite(real)) {
+ return constructor.create(Math.abs(real), changeSign(imaginary, real));
+ }
+ return constructor.create(Math.cosh(real) * Math.cos(imaginary),
+ Math.sinh(real) * Math.sin(imaginary));
}
/**
@@ -2008,7 +1974,7 @@
im = Math.copySign(1, im);
}
} else {
- if (im == 0 || !Double.isFinite(im)){
+ if (im == 0 || !Double.isFinite(im)) {
return Double.isInfinite(im) ?
new Complex(real, Double.NaN) :
this;
@@ -2236,41 +2202,15 @@
* @return the hyperbolic sine of the complex number
*/
private static Complex sinh(double real, double imaginary, ComplexConstructor constructor) {
- if (Double.isFinite(real)) {
- if (Double.isFinite(imaginary)) {
- return constructor.create(Math.sinh(real) * Math.cos(imaginary),
- Math.cosh(real) * Math.sin(imaginary));
- }
- // Special case for real == 0
- final double re = real == 0 ? real : Double.NaN;
- return constructor.create(re, Double.NaN);
+ if ((Double.isInfinite(real) && !Double.isFinite(imaginary)) ||
+ (real == 0 && !Double.isFinite(imaginary))) {
+ return constructor.create(real, Double.NaN);
}
- if (Double.isInfinite(real)) {
- if (Double.isFinite(imaginary)) {
- if (imaginary == 0) {
- return constructor.create(real, imaginary);
- }
- // inf * cis(y)
- // ISO C99: Preserve the equality
- // sinh(conj(z)) = conj(sinh(z))
- // and the odd function: f(z) = -f(-z)
- // by always computing on a positive valued Complex number.
- // Math.cos(-x) == Math.cos(x) so ignore sign transform.
- final double signIm = imaginary < 0 ? -1 : 1;
- final double re = Double.POSITIVE_INFINITY * Math.cos(imaginary);
- final double im = Double.POSITIVE_INFINITY * Math.sin(imaginary * signIm);
- // Transform back
- return constructor.create(real < 0 ? -re : re, im * signIm);
- }
- // imaginary is infinite or NaN
- return constructor.create(Double.POSITIVE_INFINITY, Double.NaN);
+ if (imaginary == 0 && !Double.isFinite(real)) {
+ return constructor.create(real, imaginary);
}
- // real is NaN
- if (imaginary == 0) {
- return constructor.create(Double.NaN, Math.copySign(0, imaginary));
- }
- // optionally raises the ‘‘invalid’’ floating-point exception, for nonzero y.
- return NAN;
+ return constructor.create(Math.sinh(real) * Math.cos(imaginary),
+ Math.cosh(real) * Math.sin(imaginary));
}
/**
@@ -2438,42 +2378,6 @@
* @return the hyperbolic tangent of the complex number
*/
private static Complex tanh(double real, double imaginary, ComplexConstructor constructor) {
- // Math.cos and Math.sin return NaN for infinity.
- // Perform edge-condition checks on twice the imaginary value.
- // This handles very big imaginary numbers as infinite.
-
- if (Double.isFinite(real)) {
- if (Double.isFinite(imaginary)) {
- if (real == 0) {
- // Identity: sin x / (1 + cos x) = tan(x/2)
- return constructor.create(real, Math.tan(imaginary));
- }
- if (imaginary == 0) {
- // Identity: sinh x / (1 + cosh x) = tanh(x/2)
- return constructor.create(Math.tanh(real), imaginary);
- }
-
- final double real2 = 2 * real;
-
- // Math.cosh returns positive infinity for infinity.
- // cosh -> inf
- final double divisor = Math.cosh(real2) + cos2(imaginary);
-
- // Math.sinh returns the input infinity for infinity.
- // sinh -> inf for positive x; else -inf
- final double sinhRe2 = Math.sinh(real2);
-
- // Avoid inf / inf
- if (Double.isInfinite(sinhRe2) && Double.isInfinite(divisor)) {
- // Handle as if real was infinite
- return constructor.create(Math.copySign(1, real), Math.copySign(0, sin2(imaginary)));
- }
- return constructor.create(sinhRe2 / divisor,
- sin2(imaginary) / divisor);
- }
- // imaginary is infinite or NaN
- return NAN;
- }
if (Double.isInfinite(real)) {
if (Double.isFinite(imaginary)) {
return constructor.create(Math.copySign(1, real), Math.copySign(0, sin2(imaginary)));
@@ -2481,12 +2385,39 @@
// imaginary is infinite or NaN
return constructor.create(Math.copySign(1, real), Math.copySign(0, imaginary));
}
- // real is NaN
- if (imaginary == 0) {
- return constructor.create(Double.NaN, Math.copySign(0, imaginary));
+
+ if (real == 0) {
+ if (Double.isFinite(imaginary)) {
+ // Identity: sin x / (1 + cos x) = tan(x/2)
+ return constructor.create(real, Math.tan(imaginary));
+ }
+ return constructor.create(Double.NaN, Double.NaN);
}
- // optionally raises the ‘‘invalid’’ floating-point exception, for nonzero y.
- return NAN;
+ if (imaginary == 0) {
+ if (Double.isNaN(real)) {
+ return constructor.create(Double.NaN, imaginary);
+ }
+ // Identity: sinh x / (1 + cosh x) = tanh(x/2)
+ return constructor.create(Math.tanh(real), imaginary);
+ }
+
+ final double real2 = 2 * real;
+
+ // Math.cosh returns positive infinity for infinity.
+ // cosh -> inf
+ final double divisor = Math.cosh(real2) + cos2(imaginary);
+
+ // Math.sinh returns the input infinity for infinity.
+ // sinh -> inf for positive x; else -inf
+ final double sinhRe2 = Math.sinh(real2);
+
+ // Avoid inf / inf
+ if (Double.isInfinite(sinhRe2) && Double.isInfinite(divisor)) {
+ // Handle as if real was infinite
+ return constructor.create(Math.copySign(1, real), Math.copySign(0, imaginary));
+ }
+ return constructor.create(sinhRe2 / divisor,
+ sin2(imaginary) / divisor);
}
/**
