[poincare] LCM and GCD accept set of numbers

Change-Id: I367ff5e48fa2856e976aa020ac0d172216f3a421

poincare/include/poincare/arithmetic.h

@@ -2,13 +2,20 @@
 #define POINCARE_ARITHMETIC_H
 
 #include <poincare/integer.h>
+#include <poincare/approximation_helper.h>
 
 namespace Poincare {
 
 class Arithmetic final {
 public:
-  static Integer LCM(const Integer & i, const Integer & j);
   static Integer GCD(const Integer & i, const Integer & j);
+  static Integer LCM(const Integer & i, const Integer & j);
+  static Expression GCD(const Expression & expression);
+  static Expression LCM(const Expression & expression);
+  static int GCD(int i, int j);
+  static int LCM(int i, int j);
+  template<typename T> static Evaluation<T> GCD(const ExpressionNode & expressionNode, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit);
+  template<typename T> static Evaluation<T> LCM(const ExpressionNode & expressionNode, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit);
   /* When outputCoefficients[0] is set to -1, that indicates a special case:
    * i could not be factorized.
    * Before calling PrimeFactorization, we initiate two tables of Integers

poincare/include/poincare/expression.h

@@ -317,6 +317,18 @@ protected:
     assert(children.type() == ExpressionNode::Type::Matrix);
     return U::Builder(children.childAtIndex(0), children.childAtIndex(1), children.childAtIndex(2), children.childAtIndex(3));
   }
+  template<typename U>
+  static Expression UntypedBuilderMultipleChildren(Expression children) {
+    // Only with Expression classes implementing addChildAtIndexInPlace
+    assert(children.type() == ExpressionNode::Type::Matrix);
+    int childrenNumber = children.numberOfChildren();
+    assert(childrenNumber > 0);
+    U expression = U::Builder({children.childAtIndex(0)});
+    for (int i = 1; i < childrenNumber; ++i) {
+      expression.addChildAtIndexInPlace(children.childAtIndex(i), i, i);
+    }
+    return std::move(expression);
+  }
 
   template<class T> T convert() const {
     /* This function allows to convert Expression to derived Expressions.

poincare/include/poincare/great_common_divisor.h

@@ -1,16 +1,15 @@
 #ifndef POINCARE_GREAT_COMMON_DIVISOR_H
 #define POINCARE_GREAT_COMMON_DIVISOR_H
 
-#include <poincare/expression.h>
+#include <poincare/n_ary_expression.h>
 
 namespace Poincare {
 
-class GreatCommonDivisorNode final : public ExpressionNode {
+class GreatCommonDivisorNode final : public NAryExpressionNode {
 public:
 
   // TreeNode
   size_t size() const override { return sizeof(GreatCommonDivisorNode); }
-  int numberOfChildren() const override;
 #if POINCARE_TREE_LOG
   void logNodeName(std::ostream & stream) const override {
     stream << "GreatCommonDivisor";
@@ -26,6 +25,7 @@ private:
   int serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
   // Simplification
   Expression shallowReduce(ReductionContext reductionContext) override;
+  Expression shallowBeautify(ReductionContext reductionContext) override;
   LayoutShape leftLayoutShape() const override { return LayoutShape::MoreLetters; };
   LayoutShape rightLayoutShape() const override { return LayoutShape::BoundaryPunctuation; }
   // Evaluation
@@ -34,14 +34,16 @@ private:
   template<typename T> Evaluation<T> templatedApproximate(Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const;
 };
 
-class GreatCommonDivisor final : public Expression {
+class GreatCommonDivisor final : public NAryExpression {
 public:
-  GreatCommonDivisor(const GreatCommonDivisorNode * n) : Expression(n) {}
-  static GreatCommonDivisor Builder(Expression child0, Expression child1) { return TreeHandle::FixedArityBuilder<GreatCommonDivisor, GreatCommonDivisorNode>({child0, child1}); }
-  static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("gcd", 2, &UntypedBuilderTwoChildren<GreatCommonDivisor>);
+  GreatCommonDivisor(const GreatCommonDivisorNode * n) : NAryExpression(n) {}
+  static GreatCommonDivisor Builder(const Tuple & children = {}) { return TreeHandle::NAryBuilder<GreatCommonDivisor, GreatCommonDivisorNode>(convert(children)); }
+  // Using a -2 as numberOfChildren to allow 2 or more children when parsing
+  static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("gcd", -2, &UntypedBuilderMultipleChildren<GreatCommonDivisor>);
 
   // Expression
   Expression shallowReduce(Context * context);
+  Expression shallowBeautify(Context * context);
 };
 
 }

poincare/include/poincare/least_common_multiple.h

@@ -1,47 +1,49 @@
 #ifndef POINCARE_LEAST_COMMON_MULTIPLE_H
 #define POINCARE_LEAST_COMMON_MULTIPLE_H
 
-#include <poincare/expression.h>
+#include <poincare/n_ary_expression.h>
 
 namespace Poincare {
 
-class LeastCommonMultipleNode final : public ExpressionNode  {
+class LeastCommonMultipleNode final : public NAryExpressionNode  {
 public:
 
   // TreeNode
   size_t size() const override { return sizeof(LeastCommonMultipleNode); }
-  int numberOfChildren() const override;
 #if POINCARE_TREE_LOG
   void logNodeName(std::ostream & stream) const override {
     stream << "LeastCommonMultiple";
   }
 #endif
+
   // ExpressionNode
   Type type() const override { return Type::LeastCommonMultiple; }
 
-
 private:
-  /* Layout */
+  // Layout
   Layout createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
   int serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const override;
-  /* Simplification */
+  // Simplification
   Expression shallowReduce(ReductionContext reductionContext) override;
+  Expression shallowBeautify(ReductionContext reductionContext) override;
   LayoutShape leftLayoutShape() const override { return LayoutShape::MoreLetters; };
   LayoutShape rightLayoutShape() const override { return LayoutShape::BoundaryPunctuation; }
-  /* Evaluation */
+  // Evaluation
   Evaluation<float> approximate(SinglePrecision p, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const override { return templatedApproximate<float>(context, complexFormat, angleUnit); }
   Evaluation<double> approximate(DoublePrecision p, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const override { return templatedApproximate<double>(context, complexFormat, angleUnit); }
   template<typename T> Evaluation<T> templatedApproximate(Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const;
 };
 
-class LeastCommonMultiple final : public Expression {
+class LeastCommonMultiple final : public NAryExpression {
 public:
-  LeastCommonMultiple(const LeastCommonMultipleNode * n) : Expression(n) {}
-  static LeastCommonMultiple Builder(Expression child0, Expression child1) { return TreeHandle::FixedArityBuilder<LeastCommonMultiple, LeastCommonMultipleNode>({child0, child1}); }
-  static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("lcm", 2, &UntypedBuilderTwoChildren<LeastCommonMultiple>);
+  LeastCommonMultiple(const LeastCommonMultipleNode * n) : NAryExpression(n) {}
+  static LeastCommonMultiple Builder(const Tuple & children = {}) { return TreeHandle::NAryBuilder<LeastCommonMultiple, LeastCommonMultipleNode>(convert(children)); }
+  // Using a -2 as numberOfChildren to allow 2 or more children when parsing
+  static constexpr Expression::FunctionHelper s_functionHelper = Expression::FunctionHelper("lcm", -2, &UntypedBuilderMultipleChildren<LeastCommonMultiple>);
 
   // Expression
   Expression shallowReduce(Context * context);
+  Expression shallowBeautify(Context * context);
 };
 
 }

poincare/include/poincare/n_ary_expression.h

@@ -63,6 +63,7 @@ protected:
     node()->sortChildrenInPlace(order, context, canSwapMatrices, canBeInterrupted);
   }
   NAryExpressionNode * node() const { return static_cast<NAryExpressionNode *>(Expression::node()); }
+  Expression checkChildrenAreRationalIntegers(Context * context);
 };
 
 }

poincare/src/arithmetic.cpp

@@ -1,20 +1,10 @@
 #include <poincare/arithmetic.h>
 #include <utility>
+#include <poincare/expression.h>
+#include <poincare/rational.h>
 
 namespace Poincare {
 
-Integer Arithmetic::LCM(const Integer & a, const Integer & b) {
-  if (a.isZero() || b.isZero()) {
-    return Integer(0);
-  }
-  if (a.isEqualTo(b)) {
-    return a;
-  }
-  Integer signResult = Integer::Division(Integer::Multiplication(a, b), GCD(a, b)).quotient;
-  signResult.setNegative(false);
-  return signResult;
-}
-
 Integer Arithmetic::GCD(const Integer & a, const Integer & b) {
   if (a.isOverflow() || b.isOverflow()) {
     return Integer::Overflow(false);
@@ -41,6 +31,110 @@ Integer Arithmetic::GCD(const Integer & a, const Integer & b) {
   } while(true);
 }
 
+Integer Arithmetic::LCM(const Integer & a, const Integer & b) {
+  if (a.isZero() || b.isZero()) {
+    return Integer(0);
+  }
+  if (a.isEqualTo(b)) {
+    return a;
+  }
+  /* Using LCM(a,b) = a*(b/GCD(a,b)). Knowing that GCD(a, b) divides b,
+   * division is performed before multiplication to be more efficient. */
+  Integer signResult = Integer::Multiplication(a, Integer::Division(b, GCD(a, b)).quotient);
+  signResult.setNegative(false);
+  return signResult;
+}
+
+int Arithmetic::GCD(int a, int b) {
+  assert(a >= 0 && b >= 0);
+  if (b > a) {
+    int temp = b;
+    b = a;
+    a = temp;
+  }
+  int r = 0;
+  while(b!=0){
+    r = a - (a/b)*b;
+    a = b;
+    b = r;
+  }
+  return a;
+}
+
+int Arithmetic::LCM(int a, int b) {
+  assert(a >= 0 && b >= 0);
+  if (a * b == 0) {
+    return 0;
+  }
+  // Using LCM(a,b) = a * b / GCD(a,b)
+  return a * (b / GCD(a,b));
+}
+
+Integer getIntegerFromRationalExpression(Expression expression) {
+  // Expression must be a Rational with 1 as denominator.
+  assert(expression.type() == ExpressionNode::Type::Rational);
+  Rational r = static_cast<Rational&>(expression);
+  assert(r.isInteger());
+  Integer i = r.signedIntegerNumerator();
+  assert(!i.isOverflow());
+  return i;
+}
+
+Expression applyAssociativeFunctionOnChildren(const Expression & expression, Integer (*f)(const Integer &, const Integer &)) {
+  /* Use function associativity to compute a function of expression's children.
+   * The function can be GCD or LCM. The expression must have at least 1
+   * child, and all its children must be integer Rationals. */
+  // We define f(a) = f(a,a) = a
+  Integer result = getIntegerFromRationalExpression(expression.childAtIndex(0));
+  // f is associative, f(a,b,c,d) = f(f(f(a,b),c),d)
+  for (int i = 1; i < expression.numberOfChildren(); ++i) {
+    result = f(result, getIntegerFromRationalExpression(expression.childAtIndex(i)));
+  }
+  return Rational::Builder(result);
+}
+
+Expression Arithmetic::GCD(const Expression & expression) {
+  /* Compute GCD of expression's children. the expression must have at least 1
+   * child, and all its children must be integer Rationals. */
+  return applyAssociativeFunctionOnChildren(expression, Arithmetic::GCD);
+}
+
+Expression Arithmetic::LCM(const Expression & expression) {
+  /* Compute LCM of expression's children. the expression must have at least 1
+   * child, and all its children must be integer Rationals. */
+  return applyAssociativeFunctionOnChildren(expression, Arithmetic::LCM);
+}
+
+template<typename T>
+Evaluation<T> applyAssociativeFunctionOnChildren(const ExpressionNode & expressionNode, int (*f)(int, int), Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) {
+  /* Use function associativity to compute a function of expression's children.
+   * The function can be GCD or LCM. */
+  bool isUndefined = false;
+  // We define f(a) = f(a,a) = a
+  int a = ApproximationHelper::PositiveIntegerApproximationIfPossible<T>(expressionNode.childAtIndex(0), &isUndefined, context, complexFormat, angleUnit);
+  // f is associative, f(a,b,c,d) = f(f(f(a,b),c),d)
+  for (int i = 1; i < expressionNode.numberOfChildren(); ++i) {
+    int b = ApproximationHelper::PositiveIntegerApproximationIfPossible<T>(expressionNode.childAtIndex(i), &isUndefined, context, complexFormat, angleUnit);
+    if (isUndefined) {
+      return Complex<T>::RealUndefined();
+    }
+    a = f(a,b);
+  }
+  return Complex<T>::Builder((T)a);
+}
+
+template<typename T>
+Evaluation<T> Arithmetic::GCD(const ExpressionNode & expressionNode, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) {
+  // Evaluate GCD of expression's children
+  return applyAssociativeFunctionOnChildren<T>(expressionNode, Arithmetic::GCD, context, complexFormat, angleUnit);
+}
+
+template<typename T>
+Evaluation<T> Arithmetic::LCM(const ExpressionNode & expressionNode, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) {
+  // Evaluate LCM of expression's children
+  return applyAssociativeFunctionOnChildren<T>(expressionNode, Arithmetic::LCM, context, complexFormat, angleUnit);
+}
+
 const short primeFactors[Arithmetic::k_numberOfPrimeFactors] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
   3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919};
 
@@ -103,4 +197,9 @@ int Arithmetic::PrimeFactorization(const Integer & n, Integer outputFactors[], I
   return t+1;
 }
 
+template Evaluation<double> Arithmetic::GCD<double>(const ExpressionNode & expressionNode, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit);
+template Evaluation<float> Arithmetic::GCD<float>(const ExpressionNode & expressionNode, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit);
+template Evaluation<double> Arithmetic::LCM<double>(const ExpressionNode & expressionNode, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit);
+template Evaluation<float> Arithmetic::LCM<float>(const ExpressionNode & expressionNode, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit);
+
 }

poincare/src/great_common_divisor.cpp

@@ -1,19 +1,12 @@
 #include <poincare/great_common_divisor.h>
-
-#include <poincare/approximation_helper.h>
 #include <poincare/arithmetic.h>
 #include <poincare/layout_helper.h>
-#include <poincare/rational.h>
 #include <poincare/serialization_helper.h>
-#include <poincare/undefined.h>
-#include <cmath>
 
 namespace Poincare {
 
 constexpr Expression::FunctionHelper GreatCommonDivisor::s_functionHelper;
 
-int GreatCommonDivisorNode::numberOfChildren() const { return GreatCommonDivisor::s_functionHelper.numberOfChildren(); }
-
 Layout GreatCommonDivisorNode::createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const {
   return LayoutHelper::Prefix(GreatCommonDivisor(this), floatDisplayMode, numberOfSignificantDigits, GreatCommonDivisor::s_functionHelper.name());
 }
@@ -26,28 +19,22 @@ Expression GreatCommonDivisorNode::shallowReduce(ReductionContext reductionConte
   return GreatCommonDivisor(this).shallowReduce(reductionContext.context());
 }
 
-template<typename T>
-Evaluation<T> GreatCommonDivisorNode::templatedApproximate(Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const {
-  bool isUndefined = false;
-  int a = ApproximationHelper::PositiveIntegerApproximationIfPossible<T>(childAtIndex(0), &isUndefined, context, complexFormat, angleUnit);
-  int b = ApproximationHelper::PositiveIntegerApproximationIfPossible<T>(childAtIndex(1), &isUndefined, context, complexFormat, angleUnit);
-  if (isUndefined) {
-    return Complex<T>::RealUndefined();
-  }
-  if (b > a) {
-    int temp = b;
-    b = a;
-    a = temp;
-  }
-  int r = 0;
-  while((int)b!=0){
-    r = a - (a/b)*b;
-    a = b;
-    b = r;
-  }
-  return Complex<T>::Builder(std::round((T)a));
+Expression GreatCommonDivisorNode::shallowBeautify(ReductionContext reductionContext) {
+  return GreatCommonDivisor(this).shallowBeautify(reductionContext.context());
 }
 
+template<typename T>
+Evaluation<T> GreatCommonDivisorNode::templatedApproximate(Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const {
+  return Arithmetic::GCD<T>(*this, context, complexFormat, angleUnit);
+}
+
+Expression GreatCommonDivisor::shallowBeautify(Context * context) {
+  /* Sort children in decreasing order:
+   * gcd(1,x,x^2) --> gcd(x^2,x,1)
+   * gcd(1,R(2)) --> gcd(R(2),1) */
+  sortChildrenInPlace([](const ExpressionNode * e1, const ExpressionNode * e2, bool canBeInterrupted) { return ExpressionNode::SimplificationOrder(e1, e2, false, canBeInterrupted); }, context, true, true);
+  return *this;
+}
 
 Expression GreatCommonDivisor::shallowReduce(Context * context) {
   {
@@ -57,34 +44,22 @@ Expression GreatCommonDivisor::shallowReduce(Context * context) {
       return e;
     }
   }
-  Expression c0 = childAtIndex(0);
-  Expression c1 = childAtIndex(1);
-  if (c0.deepIsMatrix(context) || c1.deepIsMatrix(context)) {
-    return replaceWithUndefinedInPlace();
-  }
-  if (c0.type() == ExpressionNode::Type::Rational) {
-    Rational r0 = static_cast<Rational &>(c0);
-    if (!r0.isInteger()) {
-      return replaceWithUndefinedInPlace();
-    }
-  }
-  if (c1.type() == ExpressionNode::Type::Rational) {
-    Rational r1 = static_cast<Rational&>(c1);
-    if (!r1.isInteger()) {
-      return replaceWithUndefinedInPlace();
-    }
-  }
-  if (c0.type() != ExpressionNode::Type::Rational || c1.type() != ExpressionNode::Type::Rational) {
-    return *this;
-  }
-  Rational r0 = static_cast<Rational&>(c0);
-  Rational r1 = static_cast<Rational&>(c1);
+  assert(numberOfChildren() > 0);
+
+  // Step 0: Merge children which are GCD
+  mergeSameTypeChildrenInPlace();
+
+  // Step 1: check that all children are compatible
+  {
+    Expression checkChildren = checkChildrenAreRationalIntegers(context);
+    if (!checkChildren.isUninitialized()) {
+      return checkChildren;
+    }
+  }
+
+  // Step 2: Compute GCD
+  Expression result = Arithmetic::GCD(*this);
 
-  Integer a = r0.signedIntegerNumerator();
-  Integer b = r1.signedIntegerNumerator();
-  Integer gcd = Arithmetic::GCD(a, b);
-  assert(!gcd.isOverflow());
-  Expression result = Rational::Builder(gcd);
   replaceWithInPlace(result);
   return result;
 }

poincare/src/least_common_multiple.cpp

@@ -1,19 +1,12 @@
 #include <poincare/least_common_multiple.h>
-#include <poincare/approximation_helper.h>
-#include <poincare/rational.h>
-#include <poincare/undefined.h>
 #include <poincare/arithmetic.h>
 #include <poincare/layout_helper.h>
 #include <poincare/serialization_helper.h>
-#include <cmath>
-#include <assert.h>
 
 namespace Poincare {
 
 constexpr Expression::FunctionHelper LeastCommonMultiple::s_functionHelper;
 
-int LeastCommonMultipleNode::numberOfChildren() const { return LeastCommonMultiple::s_functionHelper.numberOfChildren(); }
-
 Layout LeastCommonMultipleNode::createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const {
   return LayoutHelper::Prefix(LeastCommonMultiple(this), floatDisplayMode, numberOfSignificantDigits, LeastCommonMultiple::s_functionHelper.name());
 }
@@ -26,32 +19,22 @@ Expression LeastCommonMultipleNode::shallowReduce(ReductionContext reductionCont
   return LeastCommonMultiple(this).shallowReduce(reductionContext.context());
 }
 
-template<typename T>
-Evaluation<T> LeastCommonMultipleNode::templatedApproximate(Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const {
-  bool isUndefined = false;
-  int a = ApproximationHelper::PositiveIntegerApproximationIfPossible<T>(childAtIndex(0), &isUndefined, context, complexFormat, angleUnit);
-  int b = ApproximationHelper::PositiveIntegerApproximationIfPossible<T>(childAtIndex(1), &isUndefined, context, complexFormat, angleUnit);
-  if (isUndefined) {
-    return Complex<T>::RealUndefined();
-  }
-  if (a == 0 || b == 0) {
-    return Complex<T>::Builder(0.0);
-  }
-  if (b > a) {
-    int temp = b;
-    b = a;
-    a = temp;
-  }
-  int product = a*b;
-  int r = 0;
-  while((int)b!=0){
-    r = a - (a/b)*b;
-    a = b;
-    b = r;
-  }
-  return Complex<T>::Builder(product/a);
+Expression LeastCommonMultipleNode::shallowBeautify(ReductionContext reductionContext) {
+  return LeastCommonMultiple(this).shallowBeautify(reductionContext.context());
 }
 
+template<typename T>
+Evaluation<T> LeastCommonMultipleNode::templatedApproximate(Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit) const {
+  return Arithmetic::LCM<T>(*this, context, complexFormat, angleUnit);
+}
+
+Expression LeastCommonMultiple::shallowBeautify(Context * context) {
+  /* Sort children in decreasing order:
+   * lcm(1,x,x^2) --> lcm(x^2,x,1)
+   * lcm(1,R(2)) --> lcm(R(2),1) */
+  sortChildrenInPlace([](const ExpressionNode * e1, const ExpressionNode * e2, bool canBeInterrupted) { return ExpressionNode::SimplificationOrder(e1, e2, false, canBeInterrupted); }, context, true, true);
+  return *this;
+}
 
 Expression LeastCommonMultiple::shallowReduce(Context * context) {
   {
@@ -61,36 +44,22 @@ Expression LeastCommonMultiple::shallowReduce(Context * context) {
       return e;
     }
   }
-  Expression c0 = childAtIndex(0);
-  Expression c1 = childAtIndex(1);
-  if (c0.deepIsMatrix(context) || c1.deepIsMatrix(context)) {
-    return replaceWithUndefinedInPlace();
-  }
-  if (c0.type() == ExpressionNode::Type::Rational) {
-    Rational r0 = static_cast<Rational &>(c0);
-    if (!r0.isInteger()) {
-      return replaceWithUndefinedInPlace();
-    }
-  }
-  if (c1.type() == ExpressionNode::Type::Rational) {
-    Rational r1 = static_cast<Rational &>(c1);
-    if (!r1.isInteger()) {
-      return replaceWithUndefinedInPlace();
-    }
-  }
-  if (c0.type() != ExpressionNode::Type::Rational || c1.type() != ExpressionNode::Type::Rational) {
-    return *this;
-  }
-  Rational r0 = static_cast<Rational &>(c0);
-  Rational r1 = static_cast<Rational &>(c1);
+  assert(numberOfChildren() > 0);
 
-  Integer a = r0.signedIntegerNumerator();
-  Integer b = r1.signedIntegerNumerator();
-  Integer lcm = Arithmetic::LCM(a, b);
-  if (lcm.isOverflow()) {
-    return *this;
+  // Step 0: Merge children which are LCM
+  mergeSameTypeChildrenInPlace();
+
+  // Step 1: check that all children are compatible
+  {
+    Expression checkChildren = checkChildrenAreRationalIntegers(context);
+    if (!checkChildren.isUninitialized()) {
+      return checkChildren;
+    }
   }
-  Expression result = Rational::Builder(lcm);
+
+  // Step 2: Compute LCM
+  Expression result = Arithmetic::LCM(*this);
+
   replaceWithInPlace(result);
   return result;
 }

poincare/src/n_ary_expression.cpp

@@ -1,5 +1,6 @@
 #include <poincare/n_ary_expression.h>
 #include <poincare/number.h>
+#include <poincare/rational.h>
 extern "C" {
 #include <assert.h>
 #include <stdlib.h>
@@ -127,4 +128,20 @@ int NAryExpression::allChildrenAreReal(Context * context) const {
   return result;
 }
 
+Expression NAryExpression::checkChildrenAreRationalIntegers(Context * context) {
+  for (int i = 0; i < numberOfChildren(); ++i) {
+    Expression c = childAtIndex(i);
+    if (c.deepIsMatrix(context)) {
+      return replaceWithUndefinedInPlace();
+    }
+    if (c.type() != ExpressionNode::Type::Rational) {
+      return *this;
+    }
+    if (!static_cast<Rational &>(c).isInteger()) {
+      return replaceWithUndefinedInPlace();
+    }
+  }
+  return Expression();
+}
+
 }

poincare/src/parsing/parser.cpp

@@ -386,14 +386,18 @@ void Parser::parseReservedFunction(Expression & leftHandSide, const Expression::
     return;
   }
   int numberOfParameters = parameters.numberOfChildren();
-  while (numberOfParameters > (**functionHelper).numberOfChildren()) {
-    functionHelper++;
-    if (!(functionHelper < s_reservedFunctionsUpperBound && strcmp(name, (**functionHelper).name()) == 0)) {
-      m_status = Status::Error; // Too many parameters provided.
-      return;
+  /* FunctionHelpers with negative numberOfChildren value expect any number of
+   * children greater than this value (in absolute). */
+  if ((**functionHelper).numberOfChildren() >= 0) {
+    while (numberOfParameters > (**functionHelper).numberOfChildren()) {
+      functionHelper++;
+      if (!(functionHelper < s_reservedFunctionsUpperBound && strcmp(name, (**functionHelper).name()) == 0)) {
+        m_status = Status::Error; // Too many parameters provided.
+        return;
+      }
     }
   }
-  if (numberOfParameters < (**functionHelper).numberOfChildren()) {
+  if (numberOfParameters < abs((**functionHelper).numberOfChildren())) {
     m_status = Status::Error; // Too few parameters provided.
     return;
   }
@@ -484,7 +488,7 @@ void Parser::parseCustomIdentifier(Expression & leftHandSide, const char * name,
   }
   assert(!parameter.isUninitialized());
   if (parameter.numberOfChildren() != 1) {
-    m_status = Status::Error; // Unexpected number of paramters.
+    m_status = Status::Error; // Unexpected number of parameters.
     return;
   }
   parameter = parameter.childAtIndex(0);

poincare/src/tree_handle.cpp

@@ -311,7 +311,7 @@ template FloorLayout TreeHandle::FixedArityBuilder<FloorLayout, FloorLayoutNode>
 template FracPart TreeHandle::FixedArityBuilder<FracPart, FracPartNode>(const Tuple &);
 template FractionLayout TreeHandle::FixedArityBuilder<FractionLayout, FractionLayoutNode>(const Tuple &);
 template Ghost TreeHandle::FixedArityBuilder<Ghost, GhostNode>(const Tuple &);
-template GreatCommonDivisor TreeHandle::FixedArityBuilder<GreatCommonDivisor, GreatCommonDivisorNode>(const Tuple &);
+template GreatCommonDivisor TreeHandle::NAryBuilder<GreatCommonDivisor, GreatCommonDivisorNode>(const Tuple &);
 template HorizontalLayout TreeHandle::NAryBuilder<HorizontalLayout, HorizontalLayoutNode>(const Tuple &);
 template HyperbolicArcCosine TreeHandle::FixedArityBuilder<HyperbolicArcCosine, HyperbolicArcCosineNode>(const Tuple &);
 template HyperbolicArcSine TreeHandle::FixedArityBuilder<HyperbolicArcSine, HyperbolicArcSineNode>(const Tuple &);
@@ -324,7 +324,7 @@ template Integral TreeHandle::FixedArityBuilder<Integral, IntegralNode>(const Tu
 template IntegralLayout TreeHandle::FixedArityBuilder<IntegralLayout, IntegralLayoutNode>(const Tuple &);
 template InvBinom TreeHandle::FixedArityBuilder<InvBinom, InvBinomNode>(const Tuple &);
 template InvNorm TreeHandle::FixedArityBuilder<InvNorm, InvNormNode>(const Tuple &);
-template LeastCommonMultiple TreeHandle::FixedArityBuilder<LeastCommonMultiple, LeastCommonMultipleNode>(const Tuple &);
+template LeastCommonMultiple TreeHandle::NAryBuilder<LeastCommonMultiple, LeastCommonMultipleNode>(const Tuple &);
 template LeftParenthesisLayout TreeHandle::FixedArityBuilder<LeftParenthesisLayout, LeftParenthesisLayoutNode>(const Tuple &);
 template LeftSquareBracketLayout TreeHandle::FixedArityBuilder<LeftSquareBracketLayout, LeftSquareBracketLayoutNode>(const Tuple &);
 template Logarithm TreeHandle::FixedArityBuilder<Logarithm, LogarithmNode<2> >(const Tuple &);

poincare/test/parsing.cpp

@@ -376,13 +376,17 @@ QUIZ_CASE(poincare_parsing_identifiers) {
   assert_parsed_expression_is("factor(1)", Factor::Builder(BasedInteger::Builder(1)));
   assert_parsed_expression_is("floor(1)", Floor::Builder(BasedInteger::Builder(1)));
   assert_parsed_expression_is("frac(1)", FracPart::Builder(BasedInteger::Builder(1)));
-  assert_parsed_expression_is("gcd(1,2)", GreatCommonDivisor::Builder(BasedInteger::Builder(1),BasedInteger::Builder(2)));
+  assert_parsed_expression_is("gcd(1,2,3)", GreatCommonDivisor::Builder({BasedInteger::Builder(1),BasedInteger::Builder(2),BasedInteger::Builder(3)}));
+  assert_text_not_parsable("gcd(1)");
+  assert_text_not_parsable("gcd()");
   assert_parsed_expression_is("im(1)", ImaginaryPart::Builder(BasedInteger::Builder(1)));
   assert_parsed_expression_is("int(1,x,2,3)", Integral::Builder(BasedInteger::Builder(1),Symbol::Builder("x",1),BasedInteger::Builder(2),BasedInteger::Builder(3)));
   assert_text_not_parsable("int(1,2,3,4)");
   assert_text_not_parsable("int(1,_s,3,4)");
   assert_parsed_expression_is("inverse(1)", MatrixInverse::Builder(BasedInteger::Builder(1)));
-  assert_parsed_expression_is("lcm(1,2)", LeastCommonMultiple::Builder(BasedInteger::Builder(1),BasedInteger::Builder(2)));
+  assert_parsed_expression_is("lcm(1,2,3)", LeastCommonMultiple::Builder({BasedInteger::Builder(1),BasedInteger::Builder(2),BasedInteger::Builder(3)}));
+  assert_text_not_parsable("lcm(1)");
+  assert_text_not_parsable("lcm()");
   assert_parsed_expression_is("ln(1)", NaperianLogarithm::Builder(BasedInteger::Builder(1)));
   assert_parsed_expression_is("log(1)", CommonLogarithm::Builder(BasedInteger::Builder(1)));
   assert_parsed_expression_is("log(1,2)", Logarithm::Builder(BasedInteger::Builder(1),BasedInteger::Builder(2)));