RCP<const Basic> Add::subs(const map_basic_basic &subs_dict) const
{
RCP<const Add> self = rcp_const_cast<Add>(rcp(this));
auto it = subs_dict.find(self);
if (it != subs_dict.end())
return it->second;
CSymPy::umap_basic_num d;
RCP<const Number> coef=coef_, coef2;
RCP<const Basic> t;
for (auto &p: dict_) {
RCP<const Basic> term = p.first->subs(subs_dict);
if (term == p.first) {
Add::dict_add_term(d, p.second, p.first);
} else if (is_a<Integer>(*term) &&
rcp_static_cast<const Integer>(term)->is_zero()) {
continue;
} else if (is_a_Number(*term)) {
iaddnum(outArg(coef),
mulnum(p.second, rcp_static_cast<const Number>(term)));
} else if (is_a<Add>(*term)) {
for (auto &q: (rcp_static_cast<const Add>(term))->dict_)
Add::dict_add_term(d, q.second, q.first);
iaddnum(outArg(coef), rcp_static_cast<const Add>(term)->coef_);
} else {
Add::as_coef_term(mul(p.second, term), outArg(coef2), outArg(t));
Add::dict_add_term(d, coef2, t);
}
}
return Add::from_dict(coef, std::move(d));
}
// Mul (t^exp) to the dict "d"
void Mul::dict_add_term(map_basic_basic &d, const RCP<const Basic> &exp,
const RCP<const Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
insert(d, t, exp);
} else {
// Very common case, needs to be fast:
if (is_a_Number(*it->second) && is_a_Number(*exp)) {
RCP<const Number> tmp = rcp_static_cast<const Number>(it->second);
iaddnum(outArg(tmp), rcp_static_cast<const Number>(exp));
if (tmp->is_zero()) {
d.erase(it);
} else {
it->second = tmp;
}
} else {
// General case:
it->second = add(it->second, exp);
if (is_a<Integer>(*it->second) &&
rcp_static_cast<const Integer>(it->second)->is_zero()) {
d.erase(it);
}
}
}
}
static RCP<const Basic> diff(const Mul &self,
const RCP<const Symbol> &x) {
RCP<const Number> overall_coef = zero;
umap_basic_num add_dict;
for (auto &p: self.dict_) {
RCP<const Number> coef = self.coef_;
RCP<const Basic> factor = pow(p.first, p.second)->diff(x);
if (is_a<Integer>(*factor) &&
rcp_static_cast<const Integer>(factor)->is_zero()) continue;
map_basic_basic d = self.dict_;
d.erase(p.first);
if (is_a_Number(*factor)) {
imulnum(outArg(coef), rcp_static_cast<const Number>(factor));
} else if (is_a<Mul>(*factor)) {
RCP<const Mul> tmp = rcp_static_cast<const Mul>(factor);
imulnum(outArg(coef), tmp->coef_);
for (auto &q: tmp->dict_) {
Mul::dict_add_term_new(outArg(coef), d, q.second, q.first);
}
} else {
RCP<const Basic> exp, t;
Mul::as_base_exp(factor, outArg(exp), outArg(t));
Mul::dict_add_term_new(outArg(coef), d, exp, t);
}
if (d.size() == 0) {
iaddnum(outArg(overall_coef), coef);
} else {
RCP<const Basic> mul = Mul::from_dict(one, std::move(d));
Add::dict_add_term(add_dict, coef, mul);
}
}
return Add::from_dict(overall_coef, std::move(add_dict));
}
RCP<const Basic> add(const RCP<const Basic> &a, const RCP<const Basic> &b)
{
CSymPy::umap_basic_num d;
RCP<const Number> coef;
RCP<const Basic> t;
if (CSymPy::is_a<Add>(*a) && CSymPy::is_a<Add>(*b)) {
coef = (rcp_static_cast<const Add>(a))->coef_;
d = (rcp_static_cast<const Add>(a))->dict_;
for (auto &p: (rcp_static_cast<const Add>(b))->dict_)
Add::dict_add_term(d, p.second, p.first);
iaddnum(outArg(coef), rcp_static_cast<const Add>(b)->coef_);
} else if (CSymPy::is_a<Add>(*a)) {
coef = (rcp_static_cast<const Add>(a))->coef_;
d = (rcp_static_cast<const Add>(a))->dict_;
if (is_a_Number(*b)) {
iaddnum(outArg(coef), rcp_static_cast<const Number>(b));
} else {
RCP<const Number> coef2;
Add::as_coef_term(b, outArg(coef2), outArg(t));
Add::dict_add_term(d, coef2, t);
}
} else if (CSymPy::is_a<Add>(*b)) {
coef = (rcp_static_cast<const Add>(b))->coef_;
d = (rcp_static_cast<const Add>(b))->dict_;
if (is_a_Number(*a)) {
iaddnum(outArg(coef), rcp_static_cast<const Number>(a));
} else {
RCP<const Number> coef2;
Add::as_coef_term(a, outArg(coef2), outArg(t));
Add::dict_add_term(d, coef2, t);
}
} else {
Add::as_coef_term(a, outArg(coef), outArg(t));
Add::dict_add_term(d, coef, t);
Add::as_coef_term(b, outArg(coef), outArg(t));
Add::dict_add_term(d, coef, t);
auto it = d.find(one);
if (it == d.end()) {
coef = zero;
} else {
coef = it->second;
d.erase(it);
}
return Add::from_dict(coef, std::move(d));
}
return Add::from_dict(coef, std::move(d));
}
void Add::coef_dict_add_term(const Ptr<RCP<const Number>> &coef, umap_basic_num &d,
const RCP<const Number> &c, const RCP<const Basic> &term)
{
if (is_a_Number(*term)) {
iaddnum(coef, mulnum(c, rcp_static_cast<const Number>(term)));
} else if (is_a<Add>(*term)) {
if (c->is_one()) {
for (const auto &q: (rcp_static_cast<const Add>(term))->dict_)
Add::dict_add_term(d, q.second, q.first);
iaddnum(coef, rcp_static_cast<const Add>(term)->coef_);
} else {
Add::dict_add_term(d, c, term);
}
} else {
RCP<const Number> coef2;
RCP<const Basic> t;
Add::as_coef_term(term, outArg(coef2), outArg(t));
Add::dict_add_term(d, mulnum(c, coef2), t);
}
}
// Mul (t^exp) to the dict "d"
void Mul::dict_add_term_new(const Ptr<RCP<const Number>> &coef, map_basic_basic &d,
const RCP<const Basic> &exp, const RCP<const Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
// Don't check for `exp = 0` here
// `pow` for Complex is not expanded by default
if (is_a<Integer>(*exp) && (is_a<Integer>(*t) || is_a<Rational>(*t))) {
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(exp)));
} else if (is_a<Integer>(*exp) && is_a<Complex>(*t)) {
if (rcp_static_cast<const Integer>(exp)->is_one()) {
imulnum(outArg(*coef), rcp_static_cast<const Number>(t));
} else if (rcp_static_cast<const Integer>(exp)->is_minus_one()) {
idivnum(outArg(*coef), rcp_static_cast<const Number>(t));
} else {
insert(d, t, exp);
}
} else {
insert(d, t, exp);
}
} else {
// Very common case, needs to be fast:
if (is_a_Number(*exp) && is_a_Number(*it->second)) {
RCP<const Number> tmp = rcp_static_cast<const Number>(it->second);
iaddnum(outArg(tmp),
rcp_static_cast<const Number>(exp));
it->second = tmp;
}
else
it->second = add(it->second, exp);
if (is_a<Integer>(*it->second)) {
// `pow` for Complex is not expanded by default
if (is_a<Integer>(*t) || is_a<Rational>(*t)) {
if (!rcp_static_cast<const Integer>(it->second)->is_zero()) {
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(it->second)));
}
d.erase(it);
} else if (rcp_static_cast<const Integer>(it->second)->is_zero()) {
d.erase(it);
} else if (is_a<Complex>(*t)) {
if (rcp_static_cast<const Integer>(it->second)->is_one()) {
imulnum(outArg(*coef), rcp_static_cast<const Number>(t));
d.erase(it);
} else if (rcp_static_cast<const Integer>(it->second)->is_minus_one()) {
idivnum(outArg(*coef), rcp_static_cast<const Number>(t));
d.erase(it);
}
}
}
}
}
// Adds (coef*t) to the dict "d"
// Assumption: "t" does not have any numerical coefficients, those are in "coef"
void Add::dict_add_term(umap_basic_int &d, const RCP<Number> &coef,
const RCP<Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
// Not found, add it in if it is nonzero:
if (!(coef->is_zero())) insert(d, t, coef);
} else {
iaddnum(outArg(it->second), coef);
if (it->second->is_zero()) d.erase(it);
}
}
RCP<const Basic> Add::diff(const RCP<const Symbol> &x) const
{
CSymPy::umap_basic_num d;
RCP<const Number> coef=zero, coef2;
RCP<const Basic> t;
for (auto &p: dict_) {
RCP<const Basic> term = p.first->diff(x);
if (is_a<Integer>(*term) && rcp_static_cast<const Integer>(term)->is_zero()) {
continue;
} else if (is_a_Number(*term)) {
iaddnum(outArg(coef),
mulnum(p.second, rcp_static_cast<const Number>(term)));
} else if (is_a<Add>(*term)) {
for (auto &q: (rcp_static_cast<const Add>(term))->dict_)
Add::dict_add_term(d, q.second, q.first);
iaddnum(outArg(coef), rcp_static_cast<const Add>(term)->coef_);
} else {
Add::as_coef_term(mul(p.second, term), outArg(coef2), outArg(t));
Add::dict_add_term(d, coef2, t);
}
}
return Add::from_dict(coef, std::move(d));
}
RCP<const Basic> add_expand(const RCP<const Add> &self)
{
umap_basic_num d;
RCP<const Number> coef_overall = self->coef_;
RCP<const Number> coef;
RCP<const Basic> tmp, tmp2;
for (auto &p: self->dict_) {
tmp = expand(p.first);
if (is_a<Add>(*tmp)) {
for (auto &q: (rcp_static_cast<const Add>(tmp))->dict_) {
Add::as_coef_term(q.first, outArg(coef), outArg(tmp2));
Add::dict_add_term(d,
mulnum(mulnum(p.second, q.second), coef), tmp2);
}
iaddnum(outArg(coef_overall), mulnum(p.second,
rcp_static_cast<const Add>(tmp)->coef_));
} else {
Add::as_coef_term(tmp, outArg(coef), outArg(tmp));
Add::dict_add_term(d, mulnum(p.second, coef), tmp);
}
}
return Add::from_dict(coef_overall, std::move(d));
}
// Very quickly (!) creates the appropriate instance (i.e. Add, Symbol,
// Integer, Mul) depending on the size of the dictionary 'd'.
// If d.size() > 1 then it just returns Add. This means that the dictionary
// must be in canonical form already. For d.size == 1, it returns Mul, Pow,
// Symbol or Integer, depending on the expression.
RCP<const Basic> Add::from_dict(const RCP<const Number> &coef, umap_basic_num &&d)
{
if (d.size() == 0) {
return coef;
} else if (d.size() == 1 && coef->is_zero()) {
auto p = d.begin();
if (is_a<Integer>(*(p->second))) {
if (rcp_static_cast<const Integer>(p->second)->is_zero()) {
return zero;
}
if (rcp_static_cast<const Integer>(p->second)->is_one()) {
return p->first;
}
if (is_a<Mul>(*(p->first))) {
#if !defined(WITH_CSYMPY_THREAD_SAFE) && defined(WITH_CSYMPY_RCP)
if (rcp_static_cast<const Mul>(p->first)->refcount_ == 1) {
// We can steal the dictionary:
// Cast away const'ness, so that we can move 'dict_', since
// 'p->first' will be destroyed when 'd' is at the end of
// this function, so we "steal" its dict_ to avoid an
// unnecessary copy. We know the refcount_ is one, so
// nobody else is using the Mul except us.
const map_basic_basic &d2 =
rcp_static_cast<const Mul>(p->first)->dict_;
map_basic_basic &d3 = const_cast<map_basic_basic &>(d2);
return Mul::from_dict(p->second, std::move(d3));
} else {
#else
{
#endif
// We need to copy the dictionary:
map_basic_basic d2 =
rcp_static_cast<const Mul>(p->first)->dict_;
return Mul::from_dict(p->second, std::move(d2));
}
}
map_basic_basic m;
if (is_a<Pow>(*(p->first))) {
insert(m, rcp_static_cast<const Pow>(p->first)->base_,
rcp_static_cast<const Pow>(p->first)->exp_);
} else {
insert(m, p->first, one);
}
return rcp(new Mul(p->second, std::move(m)));
}
map_basic_basic m;
if (is_a_Number(*p->second)) {
if (is_a<Mul>(*(p->first))) {
#if !defined(WITH_CSYMPY_THREAD_SAFE) && defined(WITH_CSYMPY_RCP)
if (rcp_static_cast<const Mul>(p->first)->refcount_ == 1) {
// We can steal the dictionary:
// Cast away const'ness, so that we can move 'dict_', since
// 'p->first' will be destroyed when 'd' is at the end of
// this function, so we "steal" its dict_ to avoid an
// unnecessary copy. We know the refcount_ is one, so
// nobody else is using the Mul except us.
const map_basic_basic &d2 =
rcp_static_cast<const Mul>(p->first)->dict_;
map_basic_basic &d3 = const_cast<map_basic_basic &>(d2);
return Mul::from_dict(p->second, std::move(d3));
} else {
#else
{
#endif
// We need to copy the dictionary:
map_basic_basic d2 =
rcp_static_cast<const Mul>(p->first)->dict_;
return Mul::from_dict(p->second, std::move(d2));
}
}
if (is_a<Pow>(*p->first)) {
insert(m, rcp_static_cast<const Pow>(p->first)->base_,
rcp_static_cast<const Pow>(p->first)->exp_);
} else {
insert(m, p->first, one);
}
return rcp(new Mul(p->second, std::move(m)));
} else {
insert(m, p->first, one);
insert(m, p->second, one);
return rcp(new Mul(one, std::move(m)));
}
} else {
return rcp(new Add(coef, std::move(d)));
}
}
// Adds (coef*t) to the dict "d"
// Assumption: "t" does not have any numerical coefficients, those are in "coef"
void Add::dict_add_term(umap_basic_num &d, const RCP<const Number> &coef,
const RCP<const Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
// Not found, add it in if it is nonzero:
if (!(coef->is_zero())) insert(d, t, coef);
} else {
iaddnum(outArg(it->second), coef);
if (it->second->is_zero()) d.erase(it);
}
}
RCP<const Basic> pow_expand(const RCP<const Pow> &self)
{
RCP<const Basic> _base = expand(self->base_);
bool negative_pow = false;
if (! is_a<Integer>(*self->exp_) || ! is_a<Add>(*_base)) {
if (neq(_base, self->base_)) {
return pow(_base, self->exp_);
} else {
return self;
}
}
map_vec_mpz r;
int n = rcp_static_cast<const Integer>(self->exp_)->as_int();
if (n < 0) {
n = -n;
negative_pow = true;
}
RCP<const Add> base = rcp_static_cast<const Add>(_base);
umap_basic_num base_dict = base->dict_;
if (! (base->coef_->is_zero())) {
// Add the numerical coefficient into the dictionary. This
// allows a little bit easier treatment below.
insert(base_dict, base->coef_, one);
}
int m = base_dict.size();
multinomial_coefficients_mpz(m, n, r);
umap_basic_num rd;
// This speeds up overall expansion. For example for the benchmark
// (y + x + z + w)^60 it improves the timing from 135ms to 124ms.
rd.reserve(2*r.size());
RCP<const Number> add_overall_coeff=zero;
for (auto &p: r) {
auto power = p.first.begin();
auto i2 = base_dict.begin();
map_basic_basic d;
RCP<const Number> overall_coeff=one;
for (; power != p.first.end(); ++power, ++i2) {
if (*power > 0) {
RCP<const Integer> exp = rcp(new Integer(*power));
RCP<const Basic> base = i2->first;
if (is_a<Integer>(*base)) {
imulnum(outArg(overall_coeff),
rcp_static_cast<const Number>(
rcp_static_cast<const Integer>(base)->powint(*exp)));
} else if (is_a<Symbol>(*base)) {
Mul::dict_add_term(d, exp, base);
} else {
RCP<const Basic> exp2, t, tmp;
tmp = pow(base, exp);
if (is_a<Mul>(*tmp)) {
for (auto &p: (rcp_static_cast<const Mul>(tmp))->dict_) {
Mul::dict_add_term_new(outArg(overall_coeff), d,
p.second, p.first);
}
imulnum(outArg(overall_coeff), (rcp_static_cast<const Mul>(tmp))->coef_);
} else {
Mul::as_base_exp(tmp, outArg(exp2), outArg(t));
Mul::dict_add_term_new(outArg(overall_coeff), d, exp2, t);
}
}
if (!(i2->second->is_one())) {
if (is_a<Integer>(*(i2->second)) || is_a<Rational>(*(i2->second))) {
imulnum(outArg(overall_coeff),
pownum(i2->second,
rcp_static_cast<const Number>(exp)));
} else if (is_a<Complex>(*(i2->second))) {
RCP<const Number> tmp = rcp_static_cast<const Complex>(i2->second)->pow(*exp);
imulnum(outArg(overall_coeff), tmp);
}
}
}
}
RCP<const Basic> term = Mul::from_dict(overall_coeff, std::move(d));
RCP<const Number> coef2 = rcp(new Integer(p.second));
if (is_a_Number(*term)) {
iaddnum(outArg(add_overall_coeff),
mulnum(rcp_static_cast<const Number>(term), coef2));
} else {
if (is_a<Mul>(*term) &&
!(rcp_static_cast<const Mul>(term)->coef_->is_one())) {
// Tidy up things like {2x: 3} -> {x: 6}
imulnum(outArg(coef2),
rcp_static_cast<const Mul>(term)->coef_);
// We make a copy of the dict_:
map_basic_basic d2 = rcp_static_cast<const Mul>(term)->dict_;
term = Mul::from_dict(one, std::move(d2));
}
Add::dict_add_term(rd, coef2, term);
}
}
RCP<const Basic> result = Add::from_dict(add_overall_coeff, std::move(rd));
if (negative_pow) result = pow(result, minus_one);
return result;
}
RCP<const Basic> mul_expand_two(const RCP<const Basic> &a, const RCP<const Basic> &b)
{
// Both a and b are assumed to be expanded
if (is_a<Add>(*a) && is_a<Add>(*b)) {
RCP<const Number> coef = mulnum(rcp_static_cast<const Add>(a)->coef_,
rcp_static_cast<const Add>(b)->coef_);
umap_basic_num d;
// Improves (x+1)^3(x+2)^3...(x+350)^3 expansion from 0.97s to 0.93s:
d.reserve((rcp_static_cast<const Add>(a))->dict_.size()*
(rcp_static_cast<const Add>(b))->dict_.size());
// Expand dicts first:
for (auto &p: (rcp_static_cast<const Add>(a))->dict_) {
for (auto &q: (rcp_static_cast<const Add>(b))->dict_) {
// The main bottleneck here is the mul(p.first, q.first) command
RCP<const Basic> term = mul(p.first, q.first);
if (is_a_Number(*term)) {
iaddnum(outArg(coef), rcp_static_cast<const Number>(term));
} else {
Add::dict_add_term(d, mulnum(p.second, q.second), term);
}
}
Add::dict_add_term(d,
mulnum(rcp_static_cast<const Add>(b)->coef_, p.second),
p.first);
}
// Handle the coefficient of "a":
for (auto &q: (rcp_static_cast<const Add>(b))->dict_) {
Add::dict_add_term(d,
mulnum(rcp_static_cast<const Add>(a)->coef_, q.second),
q.first);
}
return Add::from_dict(coef, std::move(d));
} else if (is_a<Add>(*a)) {
return mul_expand_two(b, a);
} else if (is_a<Add>(*b)) {
RCP<const Number> a_coef;
RCP<const Basic> a_term;
Add::as_coef_term(a, outArg(a_coef), outArg(a_term));
RCP<const Number> coef = zero;
umap_basic_num d;
d.reserve((rcp_static_cast<const Add>(b))->dict_.size());
for (auto &q: (rcp_static_cast<const Add>(b))->dict_) {
RCP<const Basic> term = mul(a_term, q.first);
if (is_a_Number(*term)) {
iaddnum(outArg(coef), rcp_static_cast<const Number>(term));
} else {
Add::dict_add_term(d, mulnum(a_coef, q.second), term);
}
}
if (eq(a_term, one)) {
iaddnum(outArg(coef),
mulnum(rcp_static_cast<const Add>(b)->coef_, a_coef));
} else {
Add::dict_add_term(d,
mulnum(rcp_static_cast<const Add>(b)->coef_, a_coef),
a_term);
}
return Add::from_dict(coef, std::move(d));
}
return mul(a, b);
}
RCP<const Basic> mul_expand_two(const RCP<const Basic> &a, const RCP<const Basic> &b)
{
// Both a and b are assumed to be expanded
if (is_a<Add>(*a) && is_a<Add>(*b)) {
RCP<const Number> coef = mulnum(rcp_static_cast<const Add>(a)->coef_,
rcp_static_cast<const Add>(b)->coef_);
umap_basic_num d;
// Improves (x+1)**3*(x+2)**3*...(x+350)**3 expansion from 0.97s to 0.93s:
d.reserve((rcp_static_cast<const Add>(a))->dict_.size()*
(rcp_static_cast<const Add>(b))->dict_.size());
// Expand dicts first:
for (auto &p: (rcp_static_cast<const Add>(a))->dict_) {
for (auto &q: (rcp_static_cast<const Add>(b))->dict_) {
// The main bottleneck here is the mul(p.first, q.first) command
RCP<const Basic> term = mul(p.first, q.first);
if (is_a_Number(*term)) {
iaddnum(outArg(coef),
mulnum(mulnum(p.second, q.second), rcp_static_cast<const Number>(term)));
} else {
if (is_a<Mul>(*term) &&
!(rcp_static_cast<const Mul>(term)->coef_->is_one())) {
// Tidy up things like {2x: 3} -> {x: 6}
RCP<const Number> coef2 =
rcp_static_cast<const Mul>(term)->coef_;
// We make a copy of the dict_:
map_basic_basic d2 = rcp_static_cast<const Mul>(term)->dict_;
term = Mul::from_dict(one, std::move(d2));
Add::dict_add_term(d, mulnum(mulnum(p.second, q.second), coef2), term);
} else {
Add::dict_add_term(d, mulnum(p.second, q.second), term);
}
}
}
Add::dict_add_term(d,
mulnum(rcp_static_cast<const Add>(b)->coef_, p.second),
p.first);
}
// Handle the coefficient of "a":
for (auto &q: (rcp_static_cast<const Add>(b))->dict_) {
Add::dict_add_term(d,
mulnum(rcp_static_cast<const Add>(a)->coef_, q.second),
q.first);
}
return Add::from_dict(coef, std::move(d));
} else if (is_a<Add>(*a)) {
return mul_expand_two(b, a);
} else if (is_a<Add>(*b)) {
RCP<const Number> a_coef;
RCP<const Basic> a_term;
Add::as_coef_term(a, outArg(a_coef), outArg(a_term));
RCP<const Number> coef = zero;
umap_basic_num d;
d.reserve((rcp_static_cast<const Add>(b))->dict_.size());
for (auto &q: (rcp_static_cast<const Add>(b))->dict_) {
RCP<const Basic> term = mul(a_term, q.first);
if (is_a_Number(*term)) {
iaddnum(outArg(coef), mulnum(mulnum(q.second, a_coef),
rcp_static_cast<const Number>(term)));
} else {
if (is_a<Mul>(*term) &&
!(rcp_static_cast<const Mul>(term)->coef_->is_one())) {
// Tidy up things like {2x: 3} -> {x: 6}
RCP<const Number> coef2 =
rcp_static_cast<const Mul>(term)->coef_;
// We make a copy of the dict_:
map_basic_basic d2 = rcp_static_cast<const Mul>(term)->dict_;
term = Mul::from_dict(one, std::move(d2));
Add::dict_add_term(d, mulnum(mulnum(q.second, a_coef), coef2), term);
} else {
Add::dict_add_term(d, mulnum(a_coef, q.second), term);
}
}
}
if (eq(*a_term, *one)) {
iaddnum(outArg(coef),
mulnum(rcp_static_cast<const Add>(b)->coef_, a_coef));
} else {
Add::dict_add_term(d,
mulnum(rcp_static_cast<const Add>(b)->coef_, a_coef),
a_term);
}
return Add::from_dict(coef, std::move(d));
}
return mul(a, b);
}
// Mul (t**exp) to the dict "d"
void Mul::dict_add_term_new(const Ptr<RCP<const Number>> &coef, map_basic_basic &d,
const RCP<const Basic> &exp, const RCP<const Basic> &t)
{
auto it = d.find(t);
if (it == d.end()) {
// Don't check for `exp = 0` here
// `pow` for Complex is not expanded by default
if (is_a<Integer>(*t) || is_a<Rational>(*t)) {
if (is_a<Integer>(*exp)) {
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(exp)));
} else if (is_a<Rational>(*exp)) {
// Here we make the exponent postive and a fraction between
// 0 and 1.
mpz_class q, r, num, den;
num = rcp_static_cast<const Rational>(exp)->i.get_num();
den = rcp_static_cast<const Rational>(exp)->i.get_den();
mpz_fdiv_qr(q.get_mpz_t(), r.get_mpz_t(), num.get_mpz_t(),
den.get_mpz_t());
insert(d, t, Rational::from_mpq(mpq_class(r, den)));
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(integer(q))));
} else {
insert(d, t, exp);
}
} else if (is_a<Integer>(*exp) && is_a<Complex>(*t)) {
if (rcp_static_cast<const Integer>(exp)->is_one()) {
imulnum(outArg(*coef), rcp_static_cast<const Number>(t));
} else if (rcp_static_cast<const Integer>(exp)->is_minus_one()) {
idivnum(outArg(*coef), rcp_static_cast<const Number>(t));
} else {
insert(d, t, exp);
}
} else {
insert(d, t, exp);
}
} else {
// Very common case, needs to be fast:
if (is_a_Number(*exp) && is_a_Number(*it->second)) {
RCP<const Number> tmp = rcp_static_cast<const Number>(it->second);
iaddnum(outArg(tmp),
rcp_static_cast<const Number>(exp));
it->second = tmp;
}
else
it->second = add(it->second, exp);
if (is_a<Integer>(*it->second)) {
// `pow` for Complex is not expanded by default
if (is_a<Integer>(*t) || is_a<Rational>(*t)) {
if (!rcp_static_cast<const Integer>(it->second)->is_zero()) {
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(it->second)));
}
d.erase(it);
} else if (rcp_static_cast<const Integer>(it->second)->is_zero()) {
d.erase(it);
} else if (is_a<Complex>(*t)) {
if (rcp_static_cast<const Integer>(it->second)->is_one()) {
imulnum(outArg(*coef), rcp_static_cast<const Number>(t));
d.erase(it);
} else if (rcp_static_cast<const Integer>(it->second)->is_minus_one()) {
idivnum(outArg(*coef), rcp_static_cast<const Number>(t));
d.erase(it);
}
}
} else if (is_a<Rational>(*it->second)) {
if (is_a_Number(*t)) {
mpz_class q, r, num, den;
num = rcp_static_cast<const Rational>(it->second)->i.get_num();
den = rcp_static_cast<const Rational>(it->second)->i.get_den();
// Here we make the exponent postive and a fraction between
// 0 and 1.
if (num > den || num < 0) {
mpz_fdiv_qr(q.get_mpz_t(), r.get_mpz_t(), num.get_mpz_t(),
den.get_mpz_t());
it->second = Rational::from_mpq(mpq_class(r, den));
imulnum(outArg(*coef), pownum(rcp_static_cast<const Number>(t),
rcp_static_cast<const Number>(integer(q))));
}
}
}
}
}