From 7ae03975ccdc2492d8727f7ef33ad97ca4360a5d Mon Sep 17 00:00:00 2001
From: Gabriel Ozouf <gabriel.ozouf@numworks.com>
Date: Thu, 3 Dec 2020 14:41:00 +0100
Subject: [PATCH] [poincare/derivative] Derivate special numbers

Derivate the numbers Undefined, Unreal, Infinity symbolically :
  Undefined -> Undefined
  Unreal    -> Unreal
  Infinity  -> Undefined
---
 poincare/include/poincare/infinity.h  | 6 ++++++
 poincare/include/poincare/undefined.h | 4 ++--
 poincare/include/poincare/unreal.h    | 2 +-
 poincare/src/infinity.cpp             | 9 +++++++++
 poincare/test/derivative.cpp          | 3 +++
 5 files changed, 21 insertions(+), 3 deletions(-)

diff --git a/poincare/include/poincare/infinity.h b/poincare/include/poincare/infinity.h
index b4d6aa02c..03740eead 100644
--- a/poincare/include/poincare/infinity.h
+++ b/poincare/include/poincare/infinity.h
@@ -37,6 +37,11 @@ public:
   // Layout
   Layout createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
   int serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode = Preferences::PrintFloatMode::Decimal, int numberOfSignificantDigits = 0) const override;
+
+  /* Derivation
+   * Unlike Numbers that derivate to 0, Infinity derivates to Undefined. */
+  bool derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) override;
+
 private:
   // Simplification
   LayoutShape leftLayoutShape() const override { assert(!m_negative); return LayoutShape::MoreLetters; }
@@ -56,6 +61,7 @@ public:
   static int NameSize() {
     return 4;
   }
+  bool derivate(ExpressionNode::ReductionContext reductionContext, Expression symbol, Expression symbolValue);
 private:
   InfinityNode * node() const { return static_cast<InfinityNode *>(Number::node()); }
 };
diff --git a/poincare/include/poincare/undefined.h b/poincare/include/poincare/undefined.h
index 9a09fe95f..7dfb094f3 100644
--- a/poincare/include/poincare/undefined.h
+++ b/poincare/include/poincare/undefined.h
@@ -30,8 +30,8 @@ public:
   }
 
   /* Derivation
-   * Overrides NumberNode's derivate to revert to a non-derivable state */
-  bool derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) override { return false; }
+   * Unlike Numbers that derivate to 0, Undefined derivates to Undefined. */
+  bool derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) override { return true; }
 
   // Layout
   Layout createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
diff --git a/poincare/include/poincare/unreal.h b/poincare/include/poincare/unreal.h
index 7e4290e3e..d74d253b1 100644
--- a/poincare/include/poincare/unreal.h
+++ b/poincare/include/poincare/unreal.h
@@ -28,7 +28,7 @@ public:
   }
 
   /* Derivation
-   * Overrides NumberNode's derivate to revert to a non-derivable state */
+   * Unlike Numbers that derivate to 0, Unreal derivates to Unreal. */
   bool derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) override { return false; }
 
   // Layout
diff --git a/poincare/src/infinity.cpp b/poincare/src/infinity.cpp
index 8a537a68e..312e74334 100644
--- a/poincare/src/infinity.cpp
+++ b/poincare/src/infinity.cpp
@@ -31,6 +31,10 @@ template<typename T> Evaluation<T> InfinityNode::templatedApproximate() const {
   return Complex<T>::Builder(m_negative ? -INFINITY : INFINITY);
 }
 
+bool InfinityNode::derivate(ReductionContext reductionContext, Expression symbol, Expression symbolValue) {
+  return Infinity(this).derivate(reductionContext, symbol, symbolValue);
+}
+
 Infinity Infinity::Builder(bool negative) {
   void * bufferNode = TreePool::sharedPool()->alloc(sizeof(InfinityNode));
   InfinityNode * node = new (bufferNode) InfinityNode(negative);
@@ -45,6 +49,11 @@ Expression Infinity::setSign(ExpressionNode::Sign s) {
   return result;
 }
 
+bool Infinity::derivate(ExpressionNode::ReductionContext reductionContext, Expression symbol, Expression symbolValue) {
+  replaceWithUndefinedInPlace();
+  return true;
+}
+
 template Evaluation<float> InfinityNode::templatedApproximate<float>() const;
 template Evaluation<double> InfinityNode::templatedApproximate() const;
 }
diff --git a/poincare/test/derivative.cpp b/poincare/test/derivative.cpp
index 89e9a1aee..5cde15597 100644
--- a/poincare/test/derivative.cpp
+++ b/poincare/test/derivative.cpp
@@ -8,6 +8,9 @@ void assert_reduces_to_formal_expression(const char * expression, const char * r
 }
 
 QUIZ_CASE(poincare_derivative_formal) {
+  assert_reduces_to_formal_expression("diff(undef,x,x)", Undefined::Name());
+  assert_reduces_to_formal_expression("diff(unreal,x,x)", Unreal::Name());
+  assert_reduces_to_formal_expression("diff(inf,x,x)", Undefined::Name());
   assert_reduces_to_formal_expression("diff(1,x,x)", "0");
   assert_reduces_to_formal_expression("diff(π,x,x)", "0");
   assert_reduces_to_formal_expression("diff(y,x,x)", "0");