From 8a754ace199d84959978b78fb1b175595a1d7af3 Mon Sep 17 00:00:00 2001
From: Alexander Nozik <altavir@gmail.com>
Date: Wed, 7 Feb 2024 21:18:47 +0300
Subject: [PATCH] Fixed GitHub #524 (Complex power of real-valued number

---
 CHANGELOG.md                                  |  1 +
 .../space/kscience/kmath/complex/Complex.kt   | 15 +++++++++++-
 .../kmath/complex/ComplexFieldTest.kt         | 23 ++++++++++---------
 3 files changed, 27 insertions(+), 12 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3c6523a0d..0bc556671 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -19,6 +19,7 @@
 
 ### Fixed
 - Median statistics
+- Complex power of negative real numbers
 
 ### Security
 
diff --git a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
index b5f1aabe7..08c44e036 100644
--- a/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
+++ b/kmath-complex/src/commonMain/kotlin/space/kscience/kmath/complex/Complex.kt
@@ -129,13 +129,25 @@ public object ComplexField :
     }
 
     override fun power(arg: Complex, pow: Number): Complex = if (arg.im == 0.0) {
-        arg.re.pow(pow.toDouble()).toComplex()
+        val powDouble = pow.toDouble()
+        when {
+            arg.re > 0 -> arg.re.pow(powDouble).toComplex()
+            arg.re < 0 -> i * (-arg.re).pow(powDouble)
+            else -> if (powDouble == 0.0) {
+                one
+            } else {
+                zero
+            }
+        }
+
     } else {
         exp(pow * ln(arg))
     }
 
     public fun power(arg: Complex, pow: Complex): Complex = exp(pow * ln(arg))
 
+    public fun Complex.pow(power: Complex): Complex = power(this, power)
+
 
     override fun exp(arg: Complex): Complex = exp(arg.re) * (cos(arg.im) + i * sin(arg.im))
 
@@ -189,6 +201,7 @@ public object ComplexField :
     override fun norm(arg: Complex): Complex = sqrt(arg.conjugate * arg)
 }
 
+
 /**
  * Represents `double`-based complex number.
  *
diff --git a/kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/ComplexFieldTest.kt b/kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/ComplexFieldTest.kt
index e11f1c1ea..a545a0792 100644
--- a/kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/ComplexFieldTest.kt
+++ b/kmath-complex/src/commonTest/kotlin/space/kscience/kmath/complex/ComplexFieldTest.kt
@@ -58,24 +58,25 @@ internal class ComplexFieldTest {
     }
 
     @Test
-    fun testInverseHyperbolicSine() {
-        assertEquals(
-            ComplexField { i * PI.toComplex() / 2 },
-            ComplexField { asinh(i) })
+    fun testInverseHyperbolicSine() = ComplexField {
+        assertEquals(i * PI.toComplex() / 2, asinh(i))
     }
 
     @Test
-    fun testPower() {
-        assertEquals(ComplexField.zero, ComplexField { zero pow 2 })
-        assertEquals(ComplexField.zero, ComplexField { zero pow 2 })
+    fun testPower() = ComplexField {
+        assertEquals(zero, zero pow 2)
+        assertEquals(zero, zero pow 2)
 
         assertEquals(
-            ComplexField { i * 8 }.let { it.im.toInt() to it.re.toInt() },
-            ComplexField { Complex(2, 2) pow 2 }.let { it.im.toInt() to it.re.toInt() })
+            (i * 8).let { it.im.toInt() to it.re.toInt() },
+            (Complex(2, 2) pow 2).let { it.im.toInt() to it.re.toInt() })
+
+        assertEquals(2.0, power(Complex(-4.0, 0.0), 0.5 + 0 * i).im, 0.01)
+        assertEquals(2.0, power(Complex(-4.0, 0.0), 0.5).im, 0.01)
     }
 
     @Test
-    fun testNorm() {
-        assertEquals(2.toComplex(), ComplexField { norm(2 * i) })
+    fun testNorm() = ComplexField {
+        assertEquals(2.toComplex(), norm(2 * i))
     }
 }