- // simplifications: ^(x,0) -> 1 (0^0 handled here)
- // ^(x,1) -> x
- // ^(0,x) -> 0 (except if x is real and negative, in which case an exception is thrown)
- // ^(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)) {
- return *this;
- } else if (level == -max_recursion_level) {
- throw(std::runtime_error("max recursion level reached"));
- }
-
- ex const & ebasis = level==1 ? basis : basis.eval(level-1);
- ex const & eexponent = level==1 ? exponent : exponent.eval(level-1);
-
- bool basis_is_numerical=0;
- bool exponent_is_numerical=0;
- numeric * num_basis;
- numeric * num_exponent;
-
- if (is_exactly_of_type(*ebasis.bp,numeric)) {
- basis_is_numerical=1;
- num_basis=static_cast<numeric *>(ebasis.bp);
- }
- if (is_exactly_of_type(*eexponent.bp,numeric)) {
- exponent_is_numerical=1;
- num_exponent=static_cast<numeric *>(eexponent.bp);
- }
-
- // ^(x,0) -> 1 (0^0 also handled here)
- if (eexponent.is_zero())
- return exONE();
-
- // ^(x,1) -> x
- if (eexponent.is_equal(exONE()))
- return ebasis;
-
- // ^(0,x) -> 0 (except if x is real and negative)
- if (ebasis.is_zero()) {
- if (exponent_is_numerical && num_exponent->is_negative()) {
- throw(std::overflow_error("power::eval(): division by zero"));
- } else
- return exZERO();
- }
-
- // ^(1,x) -> 1
- if (ebasis.is_equal(exONE()))
- return exONE();
-
- if (basis_is_numerical && exponent_is_numerical) {
- // ^(c1,c2) -> c1^c2 (c1, c2 numeric(),
- // except if c1,c2 are rational, but c1^c2 is not)
- bool basis_is_rational = num_basis->is_rational();
- bool exponent_is_rational = num_exponent->is_rational();
- numeric res = (*num_basis).power(*num_exponent);
-
- if ((!basis_is_rational || !exponent_is_rational)
- || res.is_rational()) {
- return res;
- }
- GINAC_ASSERT(!num_exponent->is_integer()); // has been handled by now
- // ^(c1,n/m) -> *(c1^q,c1^(n/m-q)), 0<(n/m-h)<1, q integer
- if (basis_is_rational && exponent_is_rational
- && num_exponent->is_real()
- && !num_exponent->is_integer()) {
- numeric r, q, n, m;
- n = num_exponent->numer();
- m = num_exponent->denom();
- q = iquo(n, m, r);
- if (r.is_negative()) {
- r = r.add(m);
- q = q.sub(numONE());
- }
- if (q.is_zero()) // the exponent was in the allowed range 0<(n/m)<1
- return this->hold();
- else {
- epvector res(2);
- res.push_back(expair(ebasis,r.div(m)));
- res.push_back(expair(ex(num_basis->power(q)),exONE()));
- return (new mul(res))->setflag(status_flags::dynallocated | status_flags::evaluated);
- /*return mul(num_basis->power(q),
- power(ex(*num_basis),ex(r.div(m)))).hold();
- */
- /* return (new mul(num_basis->power(q),
- power(*num_basis,r.div(m)).hold()))->setflag(status_flags::dynallocated | status_flags::evaluated);
- */
- }
- }
- }
-
- // ^(^(x,c1),c2) -> ^(x,c1*c2)
- // (c1, c2 numeric(), c2 integer or -1 < c1 <= 1,
- // case c1=1 should not happen, see below!)
- if (exponent_is_numerical && is_ex_exactly_of_type(ebasis,power)) {
- power const & sub_power=ex_to_power(ebasis);
- ex const & sub_basis=sub_power.basis;
- ex const & sub_exponent=sub_power.exponent;
- if (is_ex_exactly_of_type(sub_exponent,numeric)) {
- numeric const & num_sub_exponent=ex_to_numeric(sub_exponent);
- GINAC_ASSERT(num_sub_exponent!=numeric(1));
- if (num_exponent->is_integer() || abs(num_sub_exponent)<1) {
- return power(sub_basis,num_sub_exponent.mul(*num_exponent));
- }
- }
- }
-
- // ^(*(x,y,z),c1) -> *(x^c1,y^c1,z^c1) (c1 integer)
- if (exponent_is_numerical && num_exponent->is_integer() &&
- is_ex_exactly_of_type(ebasis,mul)) {
- 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)
- if (exponent_is_numerical && is_ex_exactly_of_type(ebasis,mul)) {
- GINAC_ASSERT(!num_exponent->is_integer()); // should have been handled above
- mul const & mulref=ex_to_mul(ebasis);
- if (!mulref.overall_coeff.is_equal(exONE())) {
- numeric const & num_coeff=ex_to_numeric(mulref.overall_coeff);
- if (num_coeff.is_real()) {
- if (num_coeff.is_positive()>0) {
- mul * mulp=new mul(mulref);
- mulp->overall_coeff=exONE();
- 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(numZERO())<0);
- if (num_coeff.compare(numMINUSONE())!=0) {
- mul * mulp=new mul(mulref);
- mulp->overall_coeff=exMINUSONE();
- mulp->clearflag(status_flags::evaluated);
- mulp->clearflag(status_flags::hash_calculated);
- return (new mul(power(*mulp,exponent),
- power(abs(num_coeff),*num_exponent)))->
- setflag(status_flags::dynallocated);
- }
- }
- }
- }
- }
-
- if (are_ex_trivially_equal(ebasis,basis) &&
- are_ex_trivially_equal(eexponent,exponent)) {
- return this->hold();
- }
- return (new power(ebasis, eexponent))->setflag(status_flags::dynallocated |
- status_flags::evaluated);