[apps] Add a function "sumBetweenBounds()" on Function (sum of terms on

Sequence, Integral on CartesianFunction)

apps/graph/cartesian_function.cpp

@@ -26,6 +26,17 @@ double CartesianFunction::approximateDerivative(double x, Poincare::Context * co
   return derivative.approximateToScalar<double>(*context);
 }
 
+double CartesianFunction::sumBetweenBounds(double start, double end, Poincare::Context * context) const {
+  Poincare::Complex<double> x = Poincare::Complex<double>::Float(start);
+  Poincare::Complex<double> y = Poincare::Complex<double>::Float(end);
+  Poincare::Expression * args[3] = {expression(context), &x, &y};
+  Poincare::Integral integral(args, true);
+  /* TODO: when we will simplify integral, we might want to simplify the
+   * integral here. However, we might want to do it once for all x (to avoid
+   * lagging in the derivative table. */
+  return integral.approximateToScalar<double>(*context);
+}
+
 char CartesianFunction::symbol() const {
   return 'x';
 }

apps/graph/cartesian_function.h

@@ -12,6 +12,7 @@ public:
   bool displayDerivative();
   void setDisplayDerivative(bool display);
   double approximateDerivative(double x, Poincare::Context * context) const;
+  double sumBetweenBounds(double start, double end, Poincare::Context * context) const override;
   char symbol() const override;
 private:
   bool m_displayDerivative;

apps/sequence/graph/term_sum_controller.cpp

@@ -27,11 +27,6 @@ bool TermSumController::moveCursorHorizontallyToPosition(double position) {
   return SumGraphController::moveCursorHorizontallyToPosition(std::round(position));
 }
 
-double TermSumController::computeSum(double start, double end) {
-  App * myApp = static_cast<App *>(app());
-  return static_cast<Sequence *>(m_function)->sumOfTermsBetweenAbscissa(m_startSum, m_endSum, myApp->localContext());
-}
-
 I18n::Message TermSumController::legendMessageAtStep(Step step) {
   switch(step) {
     case Step::FirstParameter:

apps/sequence/graph/term_sum_controller.h

@@ -14,7 +14,6 @@ public:
   const char * title() override;
 private:
   bool moveCursorHorizontallyToPosition(double position) override;
-  double computeSum(double start, double end) override;
   I18n::Message legendMessageAtStep(Step step) override;
   double cursorNextStep(double position, int direction) override;
 };

apps/sequence/sequence.cpp

@@ -357,7 +357,7 @@ T Sequence::approximateToNextRank(int n, SequenceContext * sqctx) const {
   }
 }
 
-double Sequence::sumOfTermsBetweenAbscissa(double start, double end, Context * context) {
+double Sequence::sumBetweenBounds(double start, double end, Context * context) const {
   double result = 0.0;
   if (end-start > k_maxNumberOfTermsInSum || start + 1.0 == start) {
     return NAN;

apps/sequence/sequence.h

@@ -53,7 +53,7 @@ public:
     return templatedApproximateAtAbscissa(x, static_cast<SequenceContext *>(context));
   }
   template<typename T> T approximateToNextRank(int n, SequenceContext * sqctx) const;
-  double sumOfTermsBetweenAbscissa(double start, double end, Poincare::Context * context);
+  double sumBetweenBounds(double start, double end, Poincare::Context * context) const override;
   void tidy() override;
   constexpr static int k_initialRankNumberOfDigits = 3; // m_initialRank is capped by 999
 private:

apps/shared/function.h

@@ -33,6 +33,7 @@ public:
   virtual double evaluateAtAbscissa(double x, Poincare::Context * context) const {
     return templatedApproximateAtAbscissa(x, context);
   }
+  virtual double sumBetweenBounds(double start, double end, Poincare::Context * context) const = 0;
   virtual void tidy();
 private:
   constexpr static size_t k_dataLengthInBytes = (TextField::maxBufferSize()+2)*sizeof(char)+2;

apps/shared/sum_graph_controller.cpp

@@ -192,7 +192,8 @@ bool SumGraphController::handleEnter() {
     return true;
   }
   m_step = (Step)((int)m_step+1);
-  double sum = computeSum(m_startSum, m_endSum);
+  TextFieldDelegateApp * myApp = static_cast<TextFieldDelegateApp *>(app());
+  double sum = m_function->sumBetweenBounds(m_startSum, m_endSum, myApp->localContext());
   m_legendView.setSumSymbol(m_step, m_startSum, m_endSum, sum, m_function->name());
   m_legendView.setLegendMessage(I18n::Message::Default, m_step);
   m_graphView->setAreaHighlightColor(true);

apps/shared/sum_graph_controller.h

@@ -38,7 +38,6 @@ private:
   constexpr static float k_cursorRightMarginRatio = 0.04f; // (cursorWidth/2)/graphViewWidth
   constexpr static float k_cursorBottomMarginRatio = 0.28f; // (cursorHeight/2+bannerHeigh)/graphViewHeight
   constexpr static float k_cursorLeftMarginRatio = 0.04f;  // (cursorWidth/2)/graphViewWidth
-  virtual double computeSum(double start, double end) = 0;
   virtual I18n::Message legendMessageAtStep(Step step) = 0;
   virtual double cursorNextStep(double position, int direction) = 0;
   Shared::InteractiveCurveViewRange * interactiveCurveViewRange() override { return m_graphRange; }