{
// Optimal output of integer powers of symbols to aid compiler CSE.
// C.f. ISO/IEC 14882:1998, section 1.9 [intro execution], paragraph 15
- // to learn why such a hack is really necessary.
+ // to learn why such a parenthisation is really necessary.
if (exp == 1) {
x.print(c);
} else if (exp == 2) {
c.s << ')';
// <expr>^-1 is printed as "1.0/<expr>" or with the recip() function of CLN
- } else if (exponent.compare(_num_1()) == 0) {
+ } else if (exponent.compare(_num_1) == 0) {
if (is_a<print_csrc_cl_N>(c))
c.s << "recip(";
else
} else {
- if (exponent.is_equal(_ex1_2())) {
+ if (exponent.is_equal(_ex1_2)) {
if (is_a<print_latex>(c))
c.s << "\\sqrt{";
else
int power::degree(const ex & s) const
{
- if (is_exactly_of_type(*exponent.bp,numeric)) {
- if (basis.is_equal(s)) {
- if (ex_to<numeric>(exponent).is_integer())
- return ex_to<numeric>(exponent).to_int();
- else
- return 0;
- } else
+ if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+ if (basis.is_equal(s))
+ return ex_to<numeric>(exponent).to_int();
+ else
return basis.degree(s) * ex_to<numeric>(exponent).to_int();
}
return 0;
int power::ldegree(const ex & s) const
{
- if (is_exactly_of_type(*exponent.bp,numeric)) {
- if (basis.is_equal(s)) {
- if (ex_to<numeric>(exponent).is_integer())
- return ex_to<numeric>(exponent).to_int();
- else
- return 0;
- } else
+ if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
+ if (basis.is_equal(s))
+ return ex_to<numeric>(exponent).to_int();
+ else
return basis.ldegree(s) * ex_to<numeric>(exponent).to_int();
}
return 0;
if (n == 0)
return *this;
else
- return _ex0();
+ return _ex0;
} else {
// basis equal to s
- if (is_exactly_of_type(*exponent.bp, numeric) && ex_to<numeric>(exponent).is_integer()) {
+ if (is_ex_exactly_of_type(exponent, numeric) && ex_to<numeric>(exponent).is_integer()) {
// integer exponent
int int_exp = ex_to<numeric>(exponent).to_int();
if (n == int_exp)
- return _ex1();
+ return _ex1;
else
- return _ex0();
+ return _ex0;
} else {
// non-integer exponents are treated as zero
if (n == 0)
return *this;
else
- return _ex0();
+ return _ex0;
}
}
}
+/** Perform automatic term rewriting rules in this class. In the following
+ * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ * stand for such expressions that contain a plain number.
+ * - ^(x,0) -> 1 (also handles ^(0,0))
+ * - ^(x,1) -> x
+ * - ^(0,c) -> 0 or exception (depending on the real part of c)
+ * - ^(1,x) -> 1
+ * - ^(c1,c2) -> *(c1^n,c1^(c2-n)) (so that 0<(c2-n)<1, try to evaluate roots, possibly in numerator and denominator of c1)
+ * - ^(^(x,c1),c2) -> ^(x,c1*c2) (c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
+ * - ^(*(x,y,z),c) -> *(x^c,y^c,z^c) (if c integer)
+ * - ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1>0)
+ * - ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1<0)
+ *
+ * @param level cut-off in recursive evaluation */
ex power::eval(int level) const
{
- // simplifications: ^(x,0) -> 1 (0^0 handled here)
- // ^(x,1) -> x
- // ^(0,c1) -> 0 or exception (depending on real value of c1)
- // ^(1,x) -> 1
- // ^(c1,c2) -> *(c1^n,c1^(c2-n)) (c1, c2 numeric(), 0<(c2-n)<1 except if c1,c2 are rational, but c1^c2 is not)
- // ^(^(x,c1),c2) -> ^(x,c1*c2) (c1, c2 numeric(), c2 integer or -1 < c1 <= 1, case c1=1 should not happen, see below!)
- // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
- // ^(*(x,c1),c2) -> ^(x,c2)*c1^c2 (c1, c2 numeric(), c1>0)
- // ^(*(x,c1),c2) -> ^(-x,c2)*c1^c2 (c1, c2 numeric(), c1<0)
-
debugmsg("power eval",LOGLEVEL_MEMBER_FUNCTION);
if ((level==1) && (flags & status_flags::evaluated))
const numeric *num_basis;
const numeric *num_exponent;
- if (is_exactly_of_type(*ebasis.bp,numeric)) {
+ if (is_ex_exactly_of_type(ebasis, numeric)) {
basis_is_numerical = true;
- num_basis = static_cast<const numeric *>(ebasis.bp);
+ num_basis = &ex_to<numeric>(ebasis);
}
- if (is_exactly_of_type(*eexponent.bp,numeric)) {
+ if (is_ex_exactly_of_type(eexponent, numeric)) {
exponent_is_numerical = true;
- num_exponent = static_cast<const numeric *>(eexponent.bp);
+ num_exponent = &ex_to<numeric>(eexponent);
}
- // ^(x,0) -> 1 (0^0 also handled here)
+ // ^(x,0) -> 1 (0^0 also handled here)
if (eexponent.is_zero()) {
if (ebasis.is_zero())
throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
else
- return _ex1();
+ return _ex1;
}
// ^(x,1) -> x
- if (eexponent.is_equal(_ex1()))
+ if (eexponent.is_equal(_ex1))
return ebasis;
- // ^(0,c1) -> 0 or exception (depending on real value of c1)
+ // ^(0,c1) -> 0 or exception (depending on real value of c1)
if (ebasis.is_zero() && exponent_is_numerical) {
if ((num_exponent->real()).is_zero())
throw (std::domain_error("power::eval(): pow(0,I) is undefined"));
else if ((num_exponent->real()).is_negative())
throw (pole_error("power::eval(): division by zero",1));
else
- return _ex0();
+ return _ex0;
}
// ^(1,x) -> 1
- if (ebasis.is_equal(_ex1()))
- return _ex1();
+ if (ebasis.is_equal(_ex1))
+ return _ex1;
if (exponent_is_numerical) {
- // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
+ // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
// except if c1,c2 are rational, but c1^c2 is not)
if (basis_is_numerical) {
const bool basis_is_crational = num_basis->is_crational();
if (is_ex_exactly_of_type(sub_exponent,numeric)) {
const numeric & num_sub_exponent = ex_to<numeric>(sub_exponent);
GINAC_ASSERT(num_sub_exponent!=numeric(1));
- if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1()).is_negative())
+ if (num_exponent->is_integer() || (abs(num_sub_exponent) - _num1).is_negative())
return power(sub_basis,num_sub_exponent.mul(*num_exponent));
}
}
return expand_mul(ex_to<mul>(ebasis), *num_exponent);
}
- // ^(*(...,x;c1),c2) -> ^(*(...,x;1),c2)*c1^c2 (c1, c2 numeric(), c1>0)
- // ^(*(...,x,c1),c2) -> ^(*(...,x;-1),c2)*(-c1)^c2 (c1, c2 numeric(), c1<0)
+ // ^(*(...,x;c1),c2) -> *(^(*(...,x;1),c2),c1^c2) (c1, c2 numeric(), c1>0)
+ // ^(*(...,x;c1),c2) -> *(^(*(...,x;-1),c2),(-c1)^c2) (c1, c2 numeric(), c1<0)
if (is_ex_exactly_of_type(ebasis,mul)) {
GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
const mul & mulref = ex_to<mul>(ebasis);
- if (!mulref.overall_coeff.is_equal(_ex1())) {
+ if (!mulref.overall_coeff.is_equal(_ex1)) {
const numeric & num_coeff = ex_to<numeric>(mulref.overall_coeff);
if (num_coeff.is_real()) {
if (num_coeff.is_positive()) {
mul *mulp = new mul(mulref);
- mulp->overall_coeff = _ex1();
+ mulp->overall_coeff = _ex1;
mulp->clearflag(status_flags::evaluated);
mulp->clearflag(status_flags::hash_calculated);
return (new mul(power(*mulp,exponent),
power(num_coeff,*num_exponent)))->setflag(status_flags::dynallocated);
} else {
- GINAC_ASSERT(num_coeff.compare(_num0())<0);
- if (num_coeff.compare(_num_1())!=0) {
+ GINAC_ASSERT(num_coeff.compare(_num0)<0);
+ if (!num_coeff.is_equal(_num_1)) {
mul *mulp = new mul(mulref);
- mulp->overall_coeff = _ex_1();
+ mulp->overall_coeff = _ex_1;
mulp->clearflag(status_flags::evaluated);
mulp->clearflag(status_flags::hash_calculated);
return (new mul(power(*mulp,exponent),
throw(std::runtime_error("max recursion level reached"));
} else {
ebasis = basis.evalf(level-1);
- if (!is_ex_exactly_of_type(eexponent,numeric))
+ if (!is_ex_exactly_of_type(exponent,numeric))
eexponent = exponent.evalf(level-1);
else
eexponent = exponent;
&& are_ex_trivially_equal(exponent, subsed_exponent))
return basic::subs(ls, lr, no_pattern);
else
- return ex(power(subsed_basis, subsed_exponent)).bp->basic::subs(ls, lr, no_pattern);
+ return power(subsed_basis, subsed_exponent).basic::subs(ls, lr, no_pattern);
}
ex power::simplify_ncmul(const exvector & v) const
// D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
epvector newseq;
newseq.reserve(2);
- newseq.push_back(expair(basis, exponent - _ex1()));
- newseq.push_back(expair(basis.diff(s), _ex1()));
+ newseq.push_back(expair(basis, exponent - _ex1));
+ newseq.push_back(expair(basis.diff(s), _ex1));
return mul(newseq, exponent);
} else {
// D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
return mul(*this,
add(mul(exponent.diff(s), log(basis)),
- mul(mul(exponent, basis.diff(s)), power(basis, _ex_1()))));
+ mul(mul(exponent, basis.diff(s)), power(basis, _ex_1))));
}
}
int power::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_exactly_of_type(other, power));
+ GINAC_ASSERT(is_exactly_a<power>(other));
const power &o = static_cast<const power &>(other);
int cmpval = basis.compare(o.basis);
term.reserve(m+1);
for (l=0; l<m-1; l++) {
const ex & b = a.op(l);
- GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
- GINAC_ASSERT(!is_ex_exactly_of_type(b,power) ||
- !is_ex_exactly_of_type(ex_to<power>(b).exponent,numeric) ||
+ GINAC_ASSERT(!is_exactly_a<add>(b));
+ GINAC_ASSERT(!is_exactly_a<power>(b) ||
+ !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
!ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
- !is_ex_exactly_of_type(ex_to<power>(b).basis,add) ||
- !is_ex_exactly_of_type(ex_to<power>(b).basis,mul) ||
- !is_ex_exactly_of_type(ex_to<power>(b).basis,power));
+ !is_exactly_a<add>(ex_to<power>(b).basis) ||
+ !is_exactly_a<mul>(ex_to<power>(b).basis) ||
+ !is_exactly_a<power>(ex_to<power>(b).basis));
if (is_ex_exactly_of_type(b,mul))
term.push_back(expand_mul(ex_to<mul>(b),numeric(k[l])));
else
}
const ex & b = a.op(l);
- GINAC_ASSERT(!is_ex_exactly_of_type(b,add));
- GINAC_ASSERT(!is_ex_exactly_of_type(b,power) ||
- !is_ex_exactly_of_type(ex_to<power>(b).exponent,numeric) ||
+ GINAC_ASSERT(!is_exactly_a<add>(b));
+ GINAC_ASSERT(!is_exactly_a<power>(b) ||
+ !is_exactly_a<numeric>(ex_to<power>(b).exponent) ||
!ex_to<numeric>(ex_to<power>(b).exponent).is_pos_integer() ||
- !is_ex_exactly_of_type(ex_to<power>(b).basis,add) ||
- !is_ex_exactly_of_type(ex_to<power>(b).basis,mul) ||
- !is_ex_exactly_of_type(ex_to<power>(b).basis,power));
+ !is_exactly_a<add>(ex_to<power>(b).basis) ||
+ !is_exactly_a<mul>(ex_to<power>(b).basis) ||
+ !is_exactly_a<power>(ex_to<power>(b).basis));
if (is_ex_exactly_of_type(b,mul))
term.push_back(expand_mul(ex_to<mul>(b),numeric(n-k_cum[m-2])));
else
const ex & r = cit0->rest;
const ex & c = cit0->coeff;
- GINAC_ASSERT(!is_ex_exactly_of_type(r,add));
- GINAC_ASSERT(!is_ex_exactly_of_type(r,power) ||
- !is_ex_exactly_of_type(ex_to<power>(r).exponent,numeric) ||
+ GINAC_ASSERT(!is_exactly_a<add>(r));
+ GINAC_ASSERT(!is_exactly_a<power>(r) ||
+ !is_exactly_a<numeric>(ex_to<power>(r).exponent) ||
!ex_to<numeric>(ex_to<power>(r).exponent).is_pos_integer() ||
- !is_ex_exactly_of_type(ex_to<power>(r).basis,add) ||
- !is_ex_exactly_of_type(ex_to<power>(r).basis,mul) ||
- !is_ex_exactly_of_type(ex_to<power>(r).basis,power));
+ !is_exactly_a<add>(ex_to<power>(r).basis) ||
+ !is_exactly_a<mul>(ex_to<power>(r).basis) ||
+ !is_exactly_a<power>(ex_to<power>(r).basis));
- if (are_ex_trivially_equal(c,_ex1())) {
+ if (are_ex_trivially_equal(c,_ex1)) {
if (is_ex_exactly_of_type(r,mul)) {
- sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2()),
- _ex1()));
+ sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
+ _ex1));
} else {
- sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated),
- _ex1()));
+ sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
+ _ex1));
}
} else {
if (is_ex_exactly_of_type(r,mul)) {
- sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2()),
- ex_to<numeric>(c).power_dyn(_num2())));
+ sum.push_back(expair(expand_mul(ex_to<mul>(r),_num2),
+ ex_to<numeric>(c).power_dyn(_num2)));
} else {
- sum.push_back(expair((new power(r,_ex2()))->setflag(status_flags::dynallocated),
- ex_to<numeric>(c).power_dyn(_num2())));
+ sum.push_back(expair((new power(r,_ex2))->setflag(status_flags::dynallocated),
+ ex_to<numeric>(c).power_dyn(_num2)));
}
}
const ex & r1 = cit1->rest;
const ex & c1 = cit1->coeff;
sum.push_back(a.combine_ex_with_coeff_to_pair((new mul(r,r1))->setflag(status_flags::dynallocated),
- _num2().mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
+ _num2.mul(ex_to<numeric>(c)).mul_dyn(ex_to<numeric>(c1))));
}
}
if (!a.overall_coeff.is_zero()) {
epvector::const_iterator i = a.seq.begin(), end = a.seq.end();
while (i != end) {
- sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2())));
+ sum.push_back(a.combine_pair_with_coeff_to_pair(*i, ex_to<numeric>(a.overall_coeff).mul_dyn(_num2)));
++i;
}
- sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2()),_ex1()));
+ sum.push_back(expair(ex_to<numeric>(a.overall_coeff).power_dyn(_num2),_ex1));
}
GINAC_ASSERT(sum.size()==(a_nops*(a_nops+1))/2);
ex power::expand_mul(const mul & m, const numeric & n) const
{
if (n.is_zero())
- return _ex1();
+ return _ex1;
epvector distrseq;
distrseq.reserve(m.seq.size());
return (new mul(distrseq,ex_to<numeric>(m.overall_coeff).power_dyn(n)))->setflag(status_flags::dynallocated);
}
-// helper function
-
-ex sqrt(const ex & a)
-{
- return power(a,_ex1_2());
-}
-
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff