[poincare] Improve Cosine::immediateSimplify

Change-Id: Icc6329625895c9b33cf8342ab4cdea4ee748d5d4

poincare/Makefile

@@ -77,6 +77,7 @@ objs += $(addprefix poincare/src/,\
   sum.o\
   symbol.o\
   tangent.o\
+  trigonometry.o\
   undefined.o\
   variable_context.o\
 )

poincare/include/poincare/trigonometry.h

@@ -0,0 +1,20 @@
+#ifndef POINCARE_TRIGONOMETRY_H
+#define POINCARE_TRIGONOMETRY_H
+
+#include <poincare/expression.h>
+
+namespace Poincare {
+
+class Trigonometry {
+public:
+  enum class Function {
+    Cosine = 0,
+    Sine = 1,
+  };
+  static Expression * table(const Expression * e, Function f, bool inverse); // , Function f, bool inverse
+  constexpr static int k_numberOfEntries = 3;
+};
+
+}
+
+#endif

poincare/src/cosine.cpp

@@ -3,6 +3,7 @@
 #include <poincare/complex.h>
 #include <poincare/symbol.h>
 #include <poincare/rational.h>
+#include <poincare/trigonometry.h>
 #include <ion.h>
 extern "C" {
 #include <assert.h>
@@ -42,6 +43,10 @@ Expression * Cosine::immediateSimplify() {
     }
     assert(r->sign() > 0);
     assert(r->numerator().isLowerThan(r->denominator()));
+    Expression * lookup = Trigonometry::table(operand(0), Trigonometry::Function::Cosine, false);
+    if (lookup != nullptr) {
+      return replaceWith(lookup, true);
+    }
   }
   return this;
 }

poincare/src/dynamic_hierarchy.cpp

@@ -152,8 +152,8 @@ void DynamicHierarchy::sortChildren() {
 }
 
 Expression * DynamicHierarchy::squashUnaryHierarchy() {
-  assert(parent() != nullptr);
   if (numberOfOperands() == 1) {
+    assert(parent() != nullptr);
     Expression * o = const_cast<Expression *>(operand(0));
     replaceWith(o, true);
     return o;

poincare/src/trigonometry.cpp

@@ -0,0 +1,23 @@
+#include <poincare/trigonometry.h>
+#include <ion.h>
+
+namespace Poincare {
+
+static_assert('\x89' == Ion::Charset::SmallPi, "Incorrect");
+constexpr const char * cheatTable[Trigonometry::k_numberOfEntries][3] = {{"\x89*12^(-1)", "\x89*5*12^(-1)", "6^(1/2)*4^(-1)+2^(1/2)*4^(-1)"}, {"\x89*8^(-1)", "\x89*3*8^(-1)", "(2+2^(1/2))^(1/2)*2^(-1)"}, {"\x89*6^(-1)", "\x89*3^(-1)", "3^(1/2)*2^(-1)"}};
+
+Expression * Trigonometry::table(const Expression * e, Function f, bool inverse) {
+  int inputIndex = inverse ? 2 : (int)f;
+  int outputIndex = inverse ? (int)f : 2;
+  for (int i = 0; i < k_numberOfEntries; i++) {
+    Expression * input = Expression::parse(cheatTable[i][inputIndex]);
+    input->simplify(); // input expression does not change, no root needed and we can use entry after
+    if (input->compareTo(e) == 0) {
+      Expression * output = Expression::parse(cheatTable[i][outputIndex]);
+      return output->simplify();
+    }
+  }
+  return nullptr;
+}
+
+}

poincare/test/simplify_easy.cpp

@@ -149,6 +149,7 @@ QUIZ_CASE(poincare_simplify_easy) {
   assert_parsed_expression_simplify_to("cos(-P*35/29)", "cos(P*6/29)");
   assert_parsed_expression_simplify_to("cos(P*340000)", "1");
   assert_parsed_expression_simplify_to("cos(-P*340000)", "1");
+  assert_parsed_expression_simplify_to("cos(P/12)", "(R(6)+R(2))/4");
 
   /* This does not work but should not as it is above k_primorial32 = 1*3*5*7*11*... (product of first 32 primes. */
   //assert_parsed_expression_simplify_to("1881676377434183981909562699940347954480361860897069^(1/3)", "123456789123456789");