[poincare] Power: do no simplify Power whose result is too big (fix bug

1.00666666666667^60 = undef)

poincare/include/poincare/power.h

@@ -25,7 +25,7 @@ public:
   template<typename T> static Complex<T> compute(const Complex<T> c, const Complex<T> d);
 private:
   constexpr static int k_maxNumberOfTermsInExpandedMultinome = 25;
-  constexpr static int k_maxIntegerPower = 100;
+  constexpr static int k_maxExactPowerMatrix = 100;
   /* Property */
   Expression * setSign(Sign s, Context & context, AngleUnit angleUnit) override;
   /* Layout */
@@ -52,10 +52,9 @@ private:
   static bool TermIsARationalSquareRootOrRational(const Expression * e);
   static const Rational * RadicandInExpression(const Expression * e);
   static const Rational * RationalFactorInExpression(const Expression * e);
-  static bool RationalExponentShouldNotBeReduced(const Rational * r);
+  static bool RationalExponentShouldNotBeReduced(const Rational * b, const Rational * r);
   /* Evaluation */
   constexpr static int k_maxApproximatePowerMatrix = 1000;
-  constexpr static int k_maxExactPowerMatrix = 100;
   template<typename T> static Matrix * computeOnComplexAndMatrix(const Complex<T> * c, const Matrix * n) { return nullptr; }
   template<typename T> static Matrix * computeOnMatrixAndComplex(const Matrix * m, const Complex<T> * d);
   template<typename T> static Matrix * computeOnMatrices(const Matrix * m, const Matrix * n) { return nullptr; }

poincare/src/power.cpp

@@ -282,9 +282,7 @@ Expression * Power::shallowReduce(Context& context, AngleUnit angleUnit) {
     // p^q with p, q rationals
     if (!letPowerAtRoot && operand(1)->type() == Type::Rational) {
       Rational * exp = static_cast<Rational *>(editableOperand(1));
-      /* First, we check that the simplification does not involve too complex power
-       * of integers (ie 3^999) that would take too much time to compute. */
-      if (RationalExponentShouldNotBeReduced(exp)) {
+      if (RationalExponentShouldNotBeReduced(a, exp)) {
         return this;
       }
       return simplifyRationalRationalPower(this, a, exp, context, angleUnit);
@@ -368,9 +366,9 @@ Expression * Power::shallowReduce(Context& context, AngleUnit angleUnit) {
     Addition * a = static_cast<Addition *>(editableOperand(1));
     // Check is b is rational
     if (a->operand(0)->type() == Type::Rational) {
-      /* First, we check that the simplification does not involve too complex power
-       * of integers (ie 3^999) that would take too much time to compute. */
-      if (RationalExponentShouldNotBeReduced(static_cast<const Rational *>(a->operand(0)))) {
+      const Rational * rationalBase = static_cast<const Rational *>(operand(0));
+      const Rational * rationalIndex = static_cast<const Rational *>(a->operand(0));
+      if (RationalExponentShouldNotBeReduced(rationalBase, rationalIndex)) {
         return this;
       }
       Power * p1 = static_cast<Power *>(clone());
@@ -810,10 +808,25 @@ bool Power::isNthRootOfUnity() const {
   return false;
 }
 
-bool Power::RationalExponentShouldNotBeReduced(const Rational * r) {
+bool Power::RationalExponentShouldNotBeReduced(const Rational * b, const Rational * r) {
+  /* We check that the simplification does not involve too complex power of
+   * integers (ie 3^999, 120232323232^50) that would take too much time to
+   * compute:
+   *  - we cap the exponent at k_maxExactPowerMatrix
+   *  - we cap the resulting power at DBL_MAX
+   * The complexity of computing a power of rational is mainly due to computing
+   * the GCD of the resulting numerator and denominator. Euclide algorithm's
+   * complexity is apportionned to the number of decimal digits in the smallest
+   * integer. */
   Integer maxIntegerExponent = r->numerator();
   maxIntegerExponent.setNegative(false);
-  if (Integer::NaturalOrder(maxIntegerExponent, Integer(k_maxIntegerPower)) > 0) {
+  if (Integer::NaturalOrder(maxIntegerExponent, Integer(k_maxExactPowerMatrix)) > 0) {
+    return true;
+  }
+  double index = maxIntegerExponent.approximate<double>();
+  double powerNumerator = std::pow(std::fabs(b->numerator().approximate<double>()), index);
+  double powerDenominator = std::pow(std::fabs(b->denominator().approximate<double>()), index);
+  if (std::isnan(powerNumerator) || std::isnan(powerDenominator) || std::isinf(powerNumerator) || std::isinf(powerDenominator)) {
     return true;
   }
   return false;

poincare/src/round.cpp

@@ -35,11 +35,12 @@ Expression * Round::shallowReduce(Context& context, AngleUnit angleUnit) {
     if (!r2->denominator().isOne()) {
       return replaceWith(new Undefined(), true);
     }
-    if (Power::RationalExponentShouldNotBeReduced(r2)) {
+    const Rational ten(10);
+    if (Power::RationalExponentShouldNotBeReduced(&ten, r2)) {
       return this;
     }
-    Rational err = Rational::Power(Rational(10), r2->numerator());
-    Rational mult = Rational::Multiplication(*r1, Rational(err));
+    Rational err = Rational::Power(ten, r2->numerator());
+    Rational mult = Rational::Multiplication(*r1, err);
     IntegerDivision d = Integer::Division(mult.numerator(), mult.denominator());
     Integer rounding = d.quotient;
     if (Rational::NaturalOrder(Rational(d.remainder, mult.denominator()), Rational(1,2)) >= 0) {

poincare/test/power.cpp

@@ -27,6 +27,12 @@ QUIZ_CASE(poincare_power_evaluate) {
 
   Complex<double> f[1] = {Complex<double>::Float(std::exp(-M_PI_2))};
   assert_parsed_expression_evaluates_to("I^I", f);
+
+  Complex<float> g[1] = {Complex<float>::Float(1.489846)};
+  assert_parsed_expression_evaluates_to("1.006666666666667^60", g);
+
+  Complex<double> h[1] = {Complex<double>::Float(1.48984570830164)};
+  assert_parsed_expression_evaluates_to("1.006666666666667^60", h);
 }
 
 QUIZ_CASE(poincare_power_simplify) {
@@ -84,4 +90,5 @@ QUIZ_CASE(poincare_power_simplify) {
   assert_parsed_expression_simplify_to("(5*P+R(2))^(-5)", "1/(4*R(2)+100*P+500*R(2)*P^2+2500*P^3+3125*R(2)*P^4+3125*P^5)");
   assert_parsed_expression_simplify_to("(1+R(2)+R(3))^5", "296+224*R(2)+184*R(3)+120*R(6)");
   assert_parsed_expression_simplify_to("(P+R(2)+R(3)+x)^(-3)", "1/(11*R(2)+9*R(3)+15*x+6*R(6)*x+3*R(2)*x^2+3*R(3)*x^2+x^3+15*P+6*R(6)*P+6*R(2)*x*P+6*R(3)*x*P+3*x^2*P+3*R(2)*P^2+3*R(3)*P^2+3*x*P^2+P^3)");
+  assert_parsed_expression_simplify_to("1.006666666666667^60", "(1006666666666667/1000000000000000)^60");
 }