[commons-numbers] 01/04: Fix acosh() to preserve the conjugate equality.

[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 73743d3c7f69c0c31ee035ebf5bd57edea0a21fd
Author: Alex Herbert <ah...@apache.org>
AuthorDate: Fri Dec 6 21:43:20 2019 +0000

    Fix acosh() to preserve the conjugate equality.
    
    The returned value is chosen to ensure the result is positive in the
    real component.
---
 .../java/org/apache/commons/numbers/complex/Complex.java | 16 +++++++++-------
 1 file changed, 9 insertions(+), 7 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 7111296..42a88e4 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
@@ -1278,15 +1278,17 @@ public final class Complex implements Serializable  {
         if (Double.isNaN(imaginary) && Double.isFinite(real)) {
             return NAN;
         }
-        return acos(real, imaginary, (re, im) -> {
+        // ISO C99: Preserve the equality
+        // acos(conj(z)) = conj(acos(z))
+        // by always computing on a positive imaginary Complex number.
+        return acos(real, Math.abs(imaginary), (re, im) ->
             // Set the sign appropriately for C99 equalities.
-            // TODO: This function currently conflicts with the CReferenceTest
-            return (negative(im)) ?
+            (im > 0) ?
+                // Multiply by -I and map back to the correct sign
+                new Complex(im, changeSign(-re, imaginary)) :
                 // Multiply by I
-                new Complex(-im, re) :
-                // Multiply by -I
-                new Complex(im, -re);
-        });
+                new Complex(-im, changeSign(re, imaginary))
+        );
     }
 
     /**