- // 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"));
- }
-
- const ex & ebasis = level==1 ? basis : basis.eval(level-1);
- const ex & 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())
- if (ebasis.is_zero())
- throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
- else
- return _ex1();
-
- // ^(x,1) -> x
- if (eexponent.is_equal(_ex1()))
- 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 _ex0();
- }
-
- // ^(1,x) -> 1
- if (ebasis.is_equal(_ex1()))
- return _ex1();
-
- 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_crational = num_basis->is_crational();
- bool exponent_is_crational = num_exponent->is_crational();
- numeric res = (*num_basis).power(*num_exponent);
-
- if ((!basis_is_crational || !exponent_is_crational)
- || res.is_crational()) {
- 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_crational && exponent_is_crational
- && 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(_num1());
- }
- 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)),_ex1()));
- 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)) {
- const power & sub_power=ex_to_power(ebasis);
- const ex & sub_basis=sub_power.basis;
- const ex & sub_exponent=sub_power.exponent;
- 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)<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
- const mul & mulref=ex_to_mul(ebasis);
- 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()>0) {
- mul * mulp=new mul(mulref);
- 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) {
- mul * mulp=new mul(mulref);
- mulp->overall_coeff=_ex_1();
- 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);
+ // 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))
+ return *this;
+ else if (level == -max_recursion_level)
+ throw(std::runtime_error("max recursion level reached"));
+
+ const ex & ebasis = level==1 ? basis : basis.eval(level-1);
+ const ex & 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())
+ if (ebasis.is_zero())
+ throw (std::domain_error("power::eval(): pow(0,0) is undefined"));
+ else
+ return _ex1();
+
+ // ^(x,1) -> x
+ if (eexponent.is_equal(_ex1()))
+ return ebasis;
+
+ // ^(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();
+ }
+
+ // ^(1,x) -> 1
+ if (ebasis.is_equal(_ex1()))
+ return _ex1();
+
+ 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_crational = num_basis->is_crational();
+ bool exponent_is_crational = num_exponent->is_crational();
+ numeric res = (*num_basis).power(*num_exponent);
+
+ if ((!basis_is_crational || !exponent_is_crational)
+ || res.is_crational()) {
+ 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_crational && exponent_is_crational
+ && num_exponent->is_real()
+ && !num_exponent->is_integer()) {
+ numeric n = num_exponent->numer();
+ numeric m = num_exponent->denom();
+ numeric r;
+ numeric q = iquo(n, m, r);
+ if (r.is_negative()) {
+ r = r.add(m);
+ q = q.sub(_num1());
+ }
+ if (q.is_zero()) // the exponent was in the allowed range 0<(n/m)<1
+ return this->hold();
+ else {
+ epvector res;
+ res.push_back(expair(ebasis,r.div(m)));
+ return (new mul(res,ex(num_basis->power(q))))->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)) {
+ const power & sub_power = ex_to_power(ebasis);
+ const ex & sub_basis = sub_power.basis;
+ const ex & sub_exponent = sub_power.exponent;
+ 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)<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
+ const mul & mulref=ex_to_mul(ebasis);
+ 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()>0) {
+ mul * mulp=new mul(mulref);
+ 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) {
+ mul * mulp=new mul(mulref);
+ mulp->overall_coeff=_ex_1();
+ 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);