Expression * Trigonometry::shallowReduceDirectFunction(Expression * e, Context& context, Expression::AngleUnit angleUnit) {
assert(e->type() == Expression::Type::Sine || e->type() == Expression::Type::Cosine || e->type() == Expression::Type::Tangent);
Expression * lookup = Trigonometry::table(e->operand(0), e->type(), context, angleUnit);
if (lookup != nullptr) {
return e->replaceWith(lookup, true);
}
Expression::Type correspondingType = e->type() == Expression::Type::Cosine ? Expression::Type::ArcCosine : (e->type() == Expression::Type::Sine ? Expression::Type::ArcSine : Expression::Type::ArcTangent);
if (e->operand(0)->type() == correspondingType) {
float trigoOp = e->operand(0)->operand(0)->approximateToScalar<float>(context, angleUnit);
if (e->type() == Expression::Type::Tangent || (trigoOp >= -1.0f && trigoOp <= 1.0f)) {
return e->replaceWith(e->editableOperand(0)->editableOperand(0), true);
}
}
if (e->operand(0)->sign() == Expression::Sign::Negative) {
Expression * op = e->editableOperand(0);
Expression * newOp = op->setSign(Expression::Sign::Positive, context, angleUnit);
newOp->shallowReduce(context, angleUnit);
if (e->type() == Expression::Type::Cosine) {
return e->shallowReduce(context, angleUnit);
} else {
Multiplication * m = new Multiplication(new Rational(-1), e->clone(), false);
m->editableOperand(1)->shallowReduce(context, angleUnit);
return e->replaceWith(m, true)->shallowReduce(context, angleUnit);
}
}
if ((angleUnit == Expression::AngleUnit::Radian && e->operand(0)->type() == Expression::Type::Multiplication && e->operand(0)->numberOfOperands() == 2 && e->operand(0)->operand(1)->type() == Expression::Type::Symbol && static_cast<const Symbol *>(e->operand(0)->operand(1))->name() == Ion::Charset::SmallPi && e->operand(0)->operand(0)->type() == Expression::Type::Rational) || (angleUnit == Expression::AngleUnit::Degree && e->operand(0)->type() == Expression::Type::Rational)) {
Rational * r = angleUnit == Expression::AngleUnit::Radian ? static_cast<Rational *>(e->editableOperand(0)->editableOperand(0)) : static_cast<Rational *>(e->editableOperand(0));
int unaryCoefficient = 1; // store 1 or -1
// Replace argument in [0, Pi/2[ or [0, 90[
Integer divisor = angleUnit == Expression::AngleUnit::Radian ? r->denominator() : Integer::Multiplication(r->denominator(), Integer(90));
Integer dividand = angleUnit == Expression::AngleUnit::Radian ? Integer::Addition(r->numerator(), r->numerator()) : r->numerator();
if (divisor.isLowerThan(dividand)) {
Integer piDivisor = angleUnit == Expression::AngleUnit::Radian ? r->denominator() : Integer::Multiplication(r->denominator(), Integer(180));
IntegerDivision div = Integer::Division(r->numerator(), piDivisor);
dividand = angleUnit == Expression::AngleUnit::Radian ? Integer::Addition(div.remainder, div.remainder) : div.remainder;
if (divisor.isLowerThan(dividand)) {
div.remainder = Integer::Subtraction(piDivisor, div.remainder);
if (e->type() == Expression::Type::Cosine || e->type() == Expression::Type::Tangent) {
unaryCoefficient *= -1;
}
}
Rational * newR = new Rational(div.remainder, r->denominator());
Expression * rationalParent = angleUnit == Expression::AngleUnit::Radian ? e->editableOperand(0) : e;
rationalParent->replaceOperand(r, newR, true);
e->editableOperand(0)->shallowReduce(context, angleUnit);
if (Integer::Division(div.quotient, Integer(2)).remainder.isOne() && e->type() != Expression::Type::Tangent) {
unaryCoefficient *= -1;
}
Expression * simplifiedCosine = e->shallowReduce(context, angleUnit); // recursive
Multiplication * m = new Multiplication(new Rational(unaryCoefficient), simplifiedCosine->clone(), false);
return simplifiedCosine->replaceWith(m, true)->shallowReduce(context, angleUnit);
}
assert(r->sign() == Expression::Sign::Positive);
assert(!divisor.isLowerThan(dividand));
}
return e;
}
Expression * BinomialCoefficient::shallowReduce(Context& context, AngleUnit angleUnit) {
Expression * e = Expression::shallowReduce(context, angleUnit);
if (e != this) {
return e;
}
Expression * op0 = editableOperand(0);
Expression * op1 = editableOperand(1);
#if MATRIX_EXACT_REDUCING
if (op0->type() == Type::Matrix || op1->type() == Type::Matrix) {
return replaceWith(new Undefined(), true);
}
#endif
if (op0->type() == Type::Rational) {
Rational * r0 = static_cast<Rational *>(op0);
if (!r0->denominator().isOne() || r0->numerator().isNegative()) {
return replaceWith(new Undefined(), true);
}
}
if (op1->type() == Type::Rational) {
Rational * r1 = static_cast<Rational *>(op1);
if (!r1->denominator().isOne() || r1->numerator().isNegative()) {
return replaceWith(new Undefined(), true);
}
}
if (op0->type() != Type::Rational || op1->type() != Type::Rational) {
return this;
}
Rational * r0 = static_cast<Rational *>(op0);
Rational * r1 = static_cast<Rational *>(op1);
Integer n = r0->numerator();
Integer k = r1->numerator();
if (n.isLowerThan(k)) {
return replaceWith(new Undefined(), true);
}
/* if n is too big, we do not reduce to avoid too long computation.
* The binomial coefficient will be evaluate approximatively later */
if (Integer(k_maxNValue).isLowerThan(n)) {
return this;
}
Rational result(1);
Integer kBis = Integer::Subtraction(n, k);
k = kBis.isLowerThan(k) ? kBis : k;
int clippedK = k.extractedInt(); // Authorized because k < n < k_maxNValue
for (int i = 0; i < clippedK; i++) {
Rational factor = Rational(Integer::Subtraction(n, Integer(i)), Integer::Subtraction(k, Integer(i)));
result = Rational::Multiplication(result, factor);
}
return replaceWith(new Rational(result), true);
}