[commons-numbers] 01/05: Added special cases of trigonomic functions:

[ah...@apache.org]

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aherbert pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/commons-numbers.git

commit 2ed318c04e6f9afdf6269c6230587ea52378acfc
Author: aherbert <ah...@apache.org>
AuthorDate: Tue Dec 10 12:13:10 2019 +0000

    Added special cases of trigonomic functions:
    
    acos(a + 0 i)  when |a| <= 1
    asinh(0 + b i) = i asin(b)  when |b| <= 1
    atanh(0 + b i) = i atan(b)
---
 .../apache/commons/numbers/complex/Complex.java    | 23 ++++++++++------------
 1 file changed, 10 insertions(+), 13 deletions(-)

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 8e57ac0..f6f4681 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
@@ -974,9 +974,10 @@ public final class Complex implements Serializable  {
     private static Complex acos(double real, double imaginary, ComplexConstructor constructor) {
         if (Double.isFinite(real)) {
             if (Double.isFinite(imaginary)) {
-                // Special case for zero
-                if (real == 0 && imaginary == 0) {
-                    return constructor.create(PI_OVER_2, Math.copySign(0, -imaginary));
+                // Special case for real numbers
+                if (imaginary == 0 && Math.abs(real) <= 1) {
+                    return constructor.create(real == 0.0 ? PI_OVER_2 : Math.acos(real),
+                                              Math.copySign(0, -imaginary));
                 }
                 // ISO C99: Preserve the equality
                 // acos(conj(z)) = conj(acos(z))
@@ -1114,11 +1115,9 @@ public final class Complex implements Serializable  {
                     if (imaginary == 0) {
                         return constructor.create(real, imaginary);
                     }
-                    // TODO: Check why this does not work
-//                    // asinh(iy) = i asin(y)
-//                    final double re = -Math.asin(b);
-//                    return constructor.create(changeSign(re, real),
-//                                              imaginary);
+                    // asinh(iy) = i asin(y)
+                    final double im = Math.asin(imaginary);
+                    return constructor.create(real, im);
                 }
                 // square() is implemented using multiply
                 final Complex z2 = multiply(a, b, a, b);
@@ -1210,11 +1209,9 @@ public final class Complex implements Serializable  {
                     if (imaginary == 0) {
                         return constructor.create(real, imaginary);
                     }
-                    // TODO: Check why this does not work
-//                    // atanh(iy) = i atan(y)
-//                    final double re = -Math.atan(b);
-//                    return constructor.create(changeSign(re, real),
-//                                              imaginary);
+                    // atanh(iy) = i atan(y)
+                    final double im = Math.atan(imaginary);
+                    return constructor.create(real, im);
                 }
                 // (1 + (a + b i)) / (1 - (a + b i))
                 final Complex result = divide(1 + a, b, 1 - a, -b);