From 4d9e8c40b83f4a66b854d0b5bef4d5acfbb2696a Mon Sep 17 00:00:00 2001
From: Jacob Young <jacobly0@users.noreply.github.com>
Date: Fri, 8 Sep 2017 22:11:27 -0400
Subject: [PATCH] Fix #102.

---
 liba/include/math.h     |  1 +
 poincare/src/power.cpp  | 28 +++++++++++++++-------------
 poincare/test/power.cpp |  4 ++++
 3 files changed, 20 insertions(+), 13 deletions(-)

diff --git a/liba/include/math.h b/liba/include/math.h
index 1ecbd2249..d0dedff0f 100644
--- a/liba/include/math.h
+++ b/liba/include/math.h
@@ -10,6 +10,7 @@ LIBA_BEGIN_DECLS
 #define INFINITY __builtin_inff()
 #define M_E 2.71828182845904523536028747135266250
 #define M_PI 3.14159265358979323846264338327950288
+#define M_PI_2 1.57079632679489661923132169163975144
 #define M_PI_4 0.78539816339744830961566084581987572
 #define M_SQRT2 1.41421356237309504880168872420969808
 
diff --git a/poincare/src/power.cpp b/poincare/src/power.cpp
index c2a211cbe..1a8002bb1 100644
--- a/poincare/src/power.cpp
+++ b/poincare/src/power.cpp
@@ -34,19 +34,19 @@ ExpressionLayout * Power::privateCreateLayout(FloatDisplayMode floatDisplayMode,
 
 template<typename T>
 Complex<T> Power::compute(const Complex<T> c, const Complex<T> d) {
-  if (d.b() != 0) {
-    /* First case c and d is complex */
-    if (c.b() != 0 || c.a() <= 0) {
-      return Complex<T>::Float(NAN);
-    }
-    /* Second case only d is complex */
-    T radius = std::pow(c.a(), d.a());
-    T theta = d.b()*std::log(c.a());
-    return Complex<T>::Polar(radius, theta);
-  }
-  /* Third case only c is complex */
-  T radius = std::pow(c.r(), d.a());
-  T theta = d.a()*c.th();
+  // c == c.r * e^(c.th*i)
+  // d == d.a + d.b*i
+  // c^d == e^(ln(c^d))
+  //     == e^(ln(c) * d)
+  //     == e^(ln(c.r * e^(c.th*i))  *  (d.a + d.b*i))
+  //     == e^((ln(c.r) + ln(e^(c.th*i)))  *  (d.a + d.b*i))
+  //     == e^((ln(c.r) + c.th*i)  *  (d.a + d.b*i))
+  //     == e^(ln(c.r)*d.a + ln(c.r)*d.b*i + c.th*i*d.a + c.th*i*d.b*i)
+  //     == e^((ln(c.r^d.a) + ln(e^(c.th*d.b*i^2)))  +  (ln(c.r)*d.b + c.th*d.a)*i)
+  //     == e^(ln(c.r^d.a * e^(-c.th*d.b)))  *  e^((ln(c.r)*d.b + c.th*d.a)*i)
+  //     == c.r^d.a*e^(-c.th*d.b) * e^((ln(c.r)*d.b + c.th*d.a)*i)
+  T radius = std::pow(c.r(), d.a()) * std::exp(-c.th() * d.b());
+  T theta = std::log(c.r())*d.b() + c.th()*d.a();
   return Complex<T>::Polar(radius, theta);
 }
 
@@ -86,4 +86,6 @@ template<typename T> Evaluation<T> * Power::templatedComputeOnComplexMatrices(Ev
   return new Complex<T>(Complex<T>::Float(NAN));
 }
 
+template Complex<float> Power::compute<float>(Complex<float>, Complex<float>);
+template Complex<double> Power::compute<double>(Complex<double>, Complex<double>);
 }
diff --git a/poincare/test/power.cpp b/poincare/test/power.cpp
index dda6d8f08..d8d875c8e 100644
--- a/poincare/test/power.cpp
+++ b/poincare/test/power.cpp
@@ -2,6 +2,7 @@
 #include <poincare.h>
 #include <ion.h>
 #include <assert.h>
+#include <cmath>
 #include "helper.h"
 
 using namespace Poincare;
@@ -23,4 +24,7 @@ QUIZ_CASE(poincare_power_evaluate) {
 
   Complex<float> e[1] = {Complex<float>::Float(0.0f)};
   assert_parsed_expression_evaluates_to("0^2", e);
+
+  Complex<double> f[1] = {Complex<double>::Float(std::exp(-M_PI_2))};
+  assert_parsed_expression_evaluates_to("I^I", f);
 }