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Expand integral powers of complex nos #264

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merged 4 commits into from Jul 26, 2014
Merged

Expand integral powers of complex nos #264

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430c554
Updated pow_expand to expand integral powers of complex nos
sushant-hiray Jul 25, 2014
be2083a
Called pow_number in pow. Updated to handle negative power cases.
sushant-hiray Jul 25, 2014
b6087c4
Removed redundant code blocks and replaced with a function
sushant-hiray Jul 25, 2014
662b51f
Updated function definition for `pow_complex`
sushant-hiray Jul 26, 2014
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11 changes: 9 additions & 2 deletions src/add.cpp
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Expand Up @@ -120,11 +120,18 @@ std::string Add::__str__() const
// TODO: extend this for Rationals as well:
if (is_a<Integer>(*p.second) &&
rcp_static_cast<const Integer>(p.second)->is_negative()) {
if (counter >= 1)
if (counter >= 1) {
o << " - ";
else
} else {
o << "-";
}
o << -(rcp_static_cast<const Integer>(p.second))->i;
} else if (is_a<Complex>(*p.second)) {
if (!(rcp_static_cast<const Complex>(p.second)->is_reim_zero())) {
o << "(" << *(p.second) <<")";
} else {
o << *(p.second);
}
} else {
o << *(p.second);
}
Expand Down
2 changes: 1 addition & 1 deletion src/complex.h
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Expand Up @@ -192,7 +192,7 @@ class Complex : public Number {
if (conjugate.get_num() == 0) {
throw std::runtime_error("Divide by zero.");
} else {
return from_mpq((this->real_ * (-other.i)) / conjugate, (this->imaginary_ * other.i) / conjugate);
return from_mpq((this->real_ * other.i) / conjugate, (this->imaginary_ * (-other.i)) / conjugate);
}
}
//! Converts the param `other` appropriately and then calls `addcomp`
Expand Down
88 changes: 48 additions & 40 deletions src/pow.cpp
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Expand Up @@ -115,6 +115,48 @@ std::string Pow::__str__() const
return o.str();
}

RCP<const Number> pow_number(const RCP<const Number> &x, long n)
{
RCP<const Number> r, p;
long mask = 1;
r = one;
p = x;
while (mask > 0 && n >= mask) {
if (n & mask)
r = mulnum(r, p);
mask = mask << 1;
p = mulnum(p, p);
}
return r;
}

void pow_complex(const Ptr<RCP<const Number>> &self,
const RCP<const Complex> &base_,
const RCP<const Integer> &exp_)
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The base_ is passed into functions that expect RCP, but exp_ isn't, so you should just declare it as
const Integer &exp_. Essentially, the rule of thumb is: don't use RCP, unless you have to (as in general, things are faster if you don't use RCP).

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Oh sure, I'll keep note of that next time onwards.

{
if (base_->is_re_zero()) {
// Imaginary Number raised to an integer power.
RCP<const Number> im = Rational::from_mpq(base_->imaginary_);
RCP<const Number> res;
mod(outArg(res), *exp_, *integer(4));
if (eq(res, zero)) {
res = one;
} else if (eq(res, one)) {
res = I;
} else if (eq(res, integer(2))) {
res = minus_one;
} else {
res = mulnum(I, minus_one);
}
*self = mulnum(im->pow(*exp_), res);
} else if (exp_->is_positive()) {
*self = pow_number(base_, exp_->as_int());
} else {
*self = pow_number(divnum(one, base_), -1 * exp_->as_int());
}

}

RCP<const Basic> pow(const RCP<const Basic> &a, const RCP<const Basic> &b)
{
if (eq(b, zero)) return one;
Expand Down Expand Up @@ -142,26 +184,9 @@ RCP<const Basic> pow(const RCP<const Basic> &a, const RCP<const Basic> &b)
} else if (is_a<Complex>(*a)) {
RCP<const Complex> exp_new = rcp_static_cast<const Complex>(a);
RCP<const Integer> pow_new = rcp_static_cast<const Integer>(b);
if (pow_new->is_minus_one()) {
return exp_new->rdivcomp(*pow_new);
} else if (exp_new->is_re_zero()) {
// Imaginary Number raised to an integer power.
RCP<const Number> im = Rational::from_mpq(exp_new->imaginary_);
RCP<const Number> res;
mod(outArg(res), *pow_new, *integer(4));
if (eq(res, zero)) {
res = one;
} else if (eq(res, one)) {
res = I;
} else if (eq(res, integer(2))) {
res = minus_one;
} else {
res = mulnum(I, minus_one);
}
return mul(im->pow(*pow_new), res);
} else {
return rcp(new Pow(a, b));
}
RCP<const Number> res;
pow_complex(outArg(res), exp_new, pow_new);
return res;
} else {
throw std::runtime_error("Not implemented");
}
Expand Down Expand Up @@ -371,27 +396,10 @@ RCP<const Basic> pow_expand(const RCP<const Pow> &self)
pownum(i2->second,
rcp_static_cast<const Number>(exp)));
} else if (is_a<Complex>(*(i2->second))) {
if (exp->is_one()) {
imulnum(outArg(overall_coeff), i2->second);
} else if (exp->is_minus_one()) {
idivnum(outArg(overall_coeff), i2->second);
} else if (rcp_static_cast<const Complex>(i2->second)->is_re_zero() &&
is_a<Integer>(*exp)) {
// Imaginary Number raised to an integer power.
RCP<const Number> im = Rational::from_mpq(rcp_static_cast<const Complex>(i2->second)->imaginary_);
if (is_a<Integer>(*exp)) {
RCP<const Integer> pow_new = rcp_static_cast<const Integer>(exp);
RCP<const Number> res;
mod(outArg(res), *pow_new, *integer(4));
if (eq(res, zero)) {
res = one;
} else if (eq(res, one)) {
res = I;
} else if (eq(res, integer(2))) {
res = minus_one;
} else {
res = mulnum(I, minus_one);
}
imulnum(outArg(overall_coeff), mulnum(im->pow(*pow_new), res));
RCP<const Complex> base_new = rcp_static_cast<const Complex>(i2->second);
pow_complex(outArg(overall_coeff), base_new, pow_new);
} else {
Mul::dict_add_term_new(outArg(overall_coeff), d, exp, i2->second);
}
Expand Down
29 changes: 29 additions & 0 deletions src/tests/basic/test_arit.cpp
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Expand Up @@ -731,6 +731,35 @@ void test_expand3()
<< "ms" << std::endl;
std::cout << "number of terms: "
<< rcp_dynamic_cast<const Add>(r)->dict_.size() << std::endl;

RCP<const Number> rc1, rc2, c1;
rc1 = Rational::from_two_ints(integer(2), integer(1));
rc2 = Rational::from_two_ints(integer(3), integer(1));

c1 = Complex::from_two_nums(*rc1, *rc2);
e = pow(add(x, c1), integer(40));

t1 = std::chrono::high_resolution_clock::now();
r = expand(e);
t2 = std::chrono::high_resolution_clock::now();

std::cout << *r << std::endl;
std::cout
<< std::chrono::duration_cast<std::chrono::milliseconds>(t2-t1).count()
<< "ms" << std::endl;
std::cout << "number of terms: "
<< rcp_dynamic_cast<const Add>(r)->dict_.size() << std::endl;

e = pow(c1, integer(-40));

t1 = std::chrono::high_resolution_clock::now();
r = expand(e);
t2 = std::chrono::high_resolution_clock::now();

std::cout << *r << std::endl;
std::cout
<< std::chrono::duration_cast<std::chrono::milliseconds>(t2-t1).count()
<< "ms" << std::endl;
}

int main(int argc, char* argv[])
Expand Down