X-Git-Url: https://ginac.de/ginac.git//ginac.git?a=blobdiff_plain;ds=inline;f=ginac%2Finifcns_trans.cpp;h=507e18f51639f1c003280064b982f81a7d8f27e9;hb=559c3bfd89b822b16708b23af1b0d9af17ededfe;hp=a37f7163ce9647c48969fdb2434a55c7d5a25d71;hpb=591b85b0697370f2f5f25a29a1e94ff831a02c12;p=ginac.git diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp index a37f7163..507e18f5 100644 --- a/ginac/inifcns_trans.cpp +++ b/ginac/inifcns_trans.cpp @@ -42,11 +42,10 @@ namespace GiNaC { static ex exp_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(exp(x)) + if (is_exactly_a(x)) + return exp(ex_to(x)); - return exp(ex_to(x)); // -> numeric exp(numeric) + return exp(x).hold(); } static ex exp_eval(const ex & x) @@ -56,7 +55,7 @@ static ex exp_eval(const ex & x) return _ex1(); } // exp(n*Pi*I/2) -> {+1|+I|-1|-I} - ex TwoExOverPiI=(_ex2()*x)/(Pi*I); + const ex TwoExOverPiI=(_ex2()*x)/(Pi*I); if (TwoExOverPiI.info(info_flags::integer)) { numeric z=mod(ex_to(TwoExOverPiI),_num4()); if (z.is_equal(_num0())) @@ -74,7 +73,7 @@ static ex exp_eval(const ex & x) // exp(float) if (x.info(info_flags::numeric) && !x.info(info_flags::crational)) - return exp_evalf(x); + return exp(ex_to(x)); return exp(x).hold(); } @@ -98,17 +97,16 @@ REGISTER_FUNCTION(exp, eval_func(exp_eval). static ex log_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(log(x)) + if (is_exactly_a(x)) + return log(ex_to(x)); - return log(ex_to(x)); // -> numeric log(numeric) + return log(x).hold(); } static ex log_eval(const ex & x) { if (x.info(info_flags::numeric)) { - if (x.is_equal(_ex0())) // log(0) -> infinity + if (x.is_zero()) // log(0) -> infinity throw(pole_error("log_eval(): log(0)",0)); if (x.info(info_flags::real) && x.info(info_flags::negative)) return (log(-x)+I*Pi); @@ -120,7 +118,7 @@ static ex log_eval(const ex & x) return (Pi*I*_num_1_2()); // log(float) if (!x.info(info_flags::crational)) - return log_evalf(x); + return log(ex_to(x)); } // log(exp(t)) -> t (if -Pi < t.imag() <= Pi): if (is_ex_the_function(x, exp)) { @@ -148,7 +146,7 @@ static ex log_series(const ex &arg, int order, unsigned options) { - GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol)); + GINAC_ASSERT(is_exactly_a(rel.lhs())); ex arg_pt; bool must_expand_arg = false; // maybe substitution of rel into arg fails because of a pole @@ -166,27 +164,35 @@ static ex log_series(const ex &arg, // This is the branch point: Series expand the argument first, then // trivially factorize it to isolate that part which has constant // leading coefficient in this fashion: - // x^n + Order(x^(n+m)) -> x^n * (1 + Order(x^m)). + // x^n + x^(n+1) +...+ Order(x^(n+m)) -> x^n * (1 + x +...+ Order(x^m)). // Return a plain n*log(x) for the x^n part and series expand the // other part. Add them together and reexpand again in order to have // one unnested pseries object. All this also works for negative n. - const pseries argser = ex_to(arg.series(rel, order, options)); - const symbol *s = static_cast(rel.lhs().bp); + pseries argser; // series expansion of log's argument + unsigned extra_ord = 0; // extra expansion order + do { + // oops, the argument expanded to a pure Order(x^something)... + argser = ex_to(arg.series(rel, order+extra_ord, options)); + ++extra_ord; + } while (!argser.is_terminating() && argser.nops()==1); + + const symbol &s = ex_to(rel.lhs()); const ex point = rel.rhs(); - const int n = argser.ldegree(*s); + const int n = argser.ldegree(s); epvector seq; // construct what we carelessly called the n*log(x) term above - ex coeff = argser.coeff(*s, n); + const ex coeff = argser.coeff(s, n); // expand the log, but only if coeff is real and > 0, since otherwise // it would make the branch cut run into the wrong direction if (coeff.info(info_flags::positive)) - seq.push_back(expair(n*log(*s-point)+log(coeff), _ex0())); + seq.push_back(expair(n*log(s-point)+log(coeff), _ex0())); else - seq.push_back(expair(log(coeff*pow(*s-point, n)), _ex0())); + seq.push_back(expair(log(coeff*pow(s-point, n)), _ex0())); + if (!argser.is_terminating() || argser.nops()!=1) { - // in this case n more terms are needed + // in this case n more (or less) terms are needed // (sadly, to generate them, we have to start from the beginning) - ex newarg = ex_to((arg/coeff).series(rel, order+n, options)).shift_exponents(-n).convert_to_poly(true); + const ex newarg = ex_to((arg/coeff).series(rel, order+n, options)).shift_exponents(-n).convert_to_poly(true); return pseries(rel, seq).add_series(ex_to(log(newarg).series(rel, order, options))); } else // it was a monomial return pseries(rel, seq); @@ -196,10 +202,10 @@ static ex log_series(const ex &arg, // method: // This is the branch cut: assemble the primitive series manually and // then add the corresponding complex step function. - const symbol *s = static_cast(rel.lhs().bp); + const symbol &s = ex_to(rel.lhs()); const ex point = rel.rhs(); const symbol foo; - ex replarg = series(log(arg), *s==foo, order).subs(foo==point); + const ex replarg = series(log(arg), s==foo, order).subs(foo==point); epvector seq; seq.push_back(expair(-I*csgn(arg*I)*Pi, _ex0())); seq.push_back(expair(Order(_ex1()), order)); @@ -220,17 +226,16 @@ REGISTER_FUNCTION(log, eval_func(log_eval). static ex sin_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(sin(x)) + if (is_exactly_a(x)) + return sin(ex_to(x)); - return sin(ex_to(x)); // -> numeric sin(numeric) + return sin(x).hold(); } static ex sin_eval(const ex & x) { // sin(n/d*Pi) -> { all known non-nested radicals } - ex SixtyExOverPi = _ex60()*x/Pi; + const ex SixtyExOverPi = _ex60()*x/Pi; ex sign = _ex1(); if (SixtyExOverPi.info(info_flags::integer)) { numeric z = mod(ex_to(SixtyExOverPi),_num120()); @@ -263,7 +268,7 @@ static ex sin_eval(const ex & x) return sign*_ex1(); } - if (is_ex_exactly_of_type(x, function)) { + if (is_exactly_a(x)) { ex t = x.op(0); // sin(asin(x)) -> x if (is_ex_the_function(x, asin)) @@ -278,7 +283,7 @@ static ex sin_eval(const ex & x) // sin(float) -> float if (x.info(info_flags::numeric) && !x.info(info_flags::crational)) - return sin_evalf(x); + return sin(ex_to(x)); return sin(x).hold(); } @@ -302,17 +307,16 @@ REGISTER_FUNCTION(sin, eval_func(sin_eval). static ex cos_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(cos(x)) + if (is_exactly_a(x)) + return cos(ex_to(x)); - return cos(ex_to(x)); // -> numeric cos(numeric) + return cos(x).hold(); } static ex cos_eval(const ex & x) { // cos(n/d*Pi) -> { all known non-nested radicals } - ex SixtyExOverPi = _ex60()*x/Pi; + const ex SixtyExOverPi = _ex60()*x/Pi; ex sign = _ex1(); if (SixtyExOverPi.info(info_flags::integer)) { numeric z = mod(ex_to(SixtyExOverPi),_num120()); @@ -345,7 +349,7 @@ static ex cos_eval(const ex & x) return sign*_ex0(); } - if (is_ex_exactly_of_type(x, function)) { + if (is_exactly_a(x)) { ex t = x.op(0); // cos(acos(x)) -> x if (is_ex_the_function(x, acos)) @@ -360,7 +364,7 @@ static ex cos_eval(const ex & x) // cos(float) -> float if (x.info(info_flags::numeric) && !x.info(info_flags::crational)) - return cos_evalf(x); + return cos(ex_to(x)); return cos(x).hold(); } @@ -384,17 +388,16 @@ REGISTER_FUNCTION(cos, eval_func(cos_eval). static ex tan_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(tan(x)) // -> numeric tan(numeric) + if (is_exactly_a(x)) + return tan(ex_to(x)); - return tan(ex_to(x)); + return tan(x).hold(); } static ex tan_eval(const ex & x) { // tan(n/d*Pi) -> { all known non-nested radicals } - ex SixtyExOverPi = _ex60()*x/Pi; + const ex SixtyExOverPi = _ex60()*x/Pi; ex sign = _ex1(); if (SixtyExOverPi.info(info_flags::integer)) { numeric z = mod(ex_to(SixtyExOverPi),_num60()); @@ -423,7 +426,7 @@ static ex tan_eval(const ex & x) throw (pole_error("tan_eval(): simple pole",1)); } - if (is_ex_exactly_of_type(x, function)) { + if (is_exactly_a(x)) { ex t = x.op(0); // tan(atan(x)) -> x if (is_ex_the_function(x, atan)) @@ -438,7 +441,7 @@ static ex tan_eval(const ex & x) // tan(float) -> float if (x.info(info_flags::numeric) && !x.info(info_flags::crational)) { - return tan_evalf(x); + return tan(ex_to(x)); } return tan(x).hold(); @@ -457,7 +460,7 @@ static ex tan_series(const ex &x, int order, unsigned options) { - GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol)); + GINAC_ASSERT(is_exactly_a(rel.lhs())); // method: // Taylor series where there is no pole falls back to tan_deriv. // On a pole simply expand sin(x)/cos(x). @@ -480,11 +483,10 @@ REGISTER_FUNCTION(tan, eval_func(tan_eval). static ex asin_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(asin(x)) + if (is_exactly_a(x)) + return asin(ex_to(x)); - return asin(ex_to(x)); // -> numeric asin(numeric) + return asin(x).hold(); } static ex asin_eval(const ex & x) @@ -507,7 +509,7 @@ static ex asin_eval(const ex & x) return _num_1_2()*Pi; // asin(float) -> float if (!x.info(info_flags::crational)) - return asin_evalf(x); + return asin(ex_to(x)); } return asin(x).hold(); @@ -532,11 +534,10 @@ REGISTER_FUNCTION(asin, eval_func(asin_eval). static ex acos_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(acos(x)) + if (is_exactly_a(x)) + return acos(ex_to(x)); - return acos(ex_to(x)); // -> numeric acos(numeric) + return acos(x).hold(); } static ex acos_eval(const ex & x) @@ -559,7 +560,7 @@ static ex acos_eval(const ex & x) return Pi; // acos(float) -> float if (!x.info(info_flags::crational)) - return acos_evalf(x); + return acos(ex_to(x)); } return acos(x).hold(); @@ -584,18 +585,17 @@ REGISTER_FUNCTION(acos, eval_func(acos_eval). static ex atan_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(atan(x)) + if (is_exactly_a(x)) + return atan(ex_to(x)); - return atan(ex_to(x)); // -> numeric atan(numeric) + return atan(x).hold(); } static ex atan_eval(const ex & x) { if (x.info(info_flags::numeric)) { // atan(0) -> 0 - if (x.is_equal(_ex0())) + if (x.is_zero()) return _ex0(); // atan(1) -> Pi/4 if (x.is_equal(_ex1())) @@ -607,7 +607,7 @@ static ex atan_eval(const ex & x) throw (pole_error("atan_eval(): logarithmic pole",0)); // atan(float) -> float if (!x.info(info_flags::crational)) - return atan_evalf(x); + return atan(ex_to(x)); } return atan(x).hold(); @@ -626,7 +626,7 @@ static ex atan_series(const ex &arg, int order, unsigned options) { - GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol)); + GINAC_ASSERT(is_exactly_a(rel.lhs())); // method: // Taylor series where there is no pole or cut falls back to atan_deriv. // There are two branch cuts, one runnig from I up the imaginary axis and @@ -647,10 +647,10 @@ static ex atan_series(const ex &arg, // method: // This is the branch cut: assemble the primitive series manually and // then add the corresponding complex step function. - const symbol *s = static_cast(rel.lhs().bp); + const symbol &s = ex_to(rel.lhs()); const ex point = rel.rhs(); const symbol foo; - ex replarg = series(atan(arg), *s==foo, order).subs(foo==point); + const ex replarg = series(atan(arg), s==foo, order).subs(foo==point); ex Order0correction = replarg.op(0)+csgn(arg)*Pi*_ex_1_2(); if ((I*arg_pt)<_ex0()) Order0correction += log((I*arg_pt+_ex_1())/(I*arg_pt+_ex1()))*I*_ex_1_2(); @@ -674,14 +674,12 @@ REGISTER_FUNCTION(atan, eval_func(atan_eval). // inverse tangent (atan2(y,x)) ////////// -static ex atan2_evalf(const ex & y, const ex & x) +static ex atan2_evalf(const ex &y, const ex &x) { - BEGIN_TYPECHECK - TYPECHECK(y,numeric) - TYPECHECK(x,numeric) - END_TYPECHECK(atan2(y,x)) + if (is_exactly_a(y) && is_exactly_a(x)) + return atan2(ex_to(y), ex_to(x)); - return atan(ex_to(y),ex_to(x)); // -> numeric atan(numeric) + return atan2(y, x).hold(); } static ex atan2_eval(const ex & y, const ex & x) @@ -716,11 +714,10 @@ REGISTER_FUNCTION(atan2, eval_func(atan2_eval). static ex sinh_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(sinh(x)) + if (is_exactly_a(x)) + return sinh(ex_to(x)); - return sinh(ex_to(x)); // -> numeric sinh(numeric) + return sinh(x).hold(); } static ex sinh_eval(const ex & x) @@ -729,14 +726,14 @@ static ex sinh_eval(const ex & x) if (x.is_zero()) // sinh(0) -> 0 return _ex0(); if (!x.info(info_flags::crational)) // sinh(float) -> float - return sinh_evalf(x); + return sinh(ex_to(x)); } if ((x/Pi).info(info_flags::numeric) && ex_to(x/Pi).real().is_zero()) // sinh(I*x) -> I*sin(x) return I*sin(x/I); - if (is_ex_exactly_of_type(x, function)) { + if (is_exactly_a(x)) { ex t = x.op(0); // sinh(asinh(x)) -> x if (is_ex_the_function(x, asinh)) @@ -771,11 +768,10 @@ REGISTER_FUNCTION(sinh, eval_func(sinh_eval). static ex cosh_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(cosh(x)) + if (is_exactly_a(x)) + return cosh(ex_to(x)); - return cosh(ex_to(x)); // -> numeric cosh(numeric) + return cosh(x).hold(); } static ex cosh_eval(const ex & x) @@ -784,14 +780,14 @@ static ex cosh_eval(const ex & x) if (x.is_zero()) // cosh(0) -> 1 return _ex1(); if (!x.info(info_flags::crational)) // cosh(float) -> float - return cosh_evalf(x); + return cosh(ex_to(x)); } if ((x/Pi).info(info_flags::numeric) && ex_to(x/Pi).real().is_zero()) // cosh(I*x) -> cos(x) return cos(x/I); - if (is_ex_exactly_of_type(x, function)) { + if (is_exactly_a(x)) { ex t = x.op(0); // cosh(acosh(x)) -> x if (is_ex_the_function(x, acosh)) @@ -826,11 +822,10 @@ REGISTER_FUNCTION(cosh, eval_func(cosh_eval). static ex tanh_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(tanh(x)) + if (is_exactly_a(x)) + return tanh(ex_to(x)); - return tanh(ex_to(x)); // -> numeric tanh(numeric) + return tanh(x).hold(); } static ex tanh_eval(const ex & x) @@ -839,14 +834,14 @@ static ex tanh_eval(const ex & x) if (x.is_zero()) // tanh(0) -> 0 return _ex0(); if (!x.info(info_flags::crational)) // tanh(float) -> float - return tanh_evalf(x); + return tanh(ex_to(x)); } if ((x/Pi).info(info_flags::numeric) && ex_to(x/Pi).real().is_zero()) // tanh(I*x) -> I*tan(x); return I*tan(x/I); - if (is_ex_exactly_of_type(x, function)) { + if (is_exactly_a(x)) { ex t = x.op(0); // tanh(atanh(x)) -> x if (is_ex_the_function(x, atanh)) @@ -875,7 +870,7 @@ static ex tanh_series(const ex &x, int order, unsigned options) { - GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol)); + GINAC_ASSERT(is_exactly_a(rel.lhs())); // method: // Taylor series where there is no pole falls back to tanh_deriv. // On a pole simply expand sinh(x)/cosh(x). @@ -898,11 +893,10 @@ REGISTER_FUNCTION(tanh, eval_func(tanh_eval). static ex asinh_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(asinh(x)) + if (is_exactly_a(x)) + return asinh(ex_to(x)); - return asinh(ex_to(x)); // -> numeric asinh(numeric) + return asinh(x).hold(); } static ex asinh_eval(const ex & x) @@ -913,7 +907,7 @@ static ex asinh_eval(const ex & x) return _ex0(); // asinh(float) -> float if (!x.info(info_flags::crational)) - return asinh_evalf(x); + return asinh(ex_to(x)); } return asinh(x).hold(); @@ -937,11 +931,10 @@ REGISTER_FUNCTION(asinh, eval_func(asinh_eval). static ex acosh_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(acosh(x)) + if (is_exactly_a(x)) + return acosh(ex_to(x)); - return acosh(ex_to(x)); // -> numeric acosh(numeric) + return acosh(x).hold(); } static ex acosh_eval(const ex & x) @@ -958,7 +951,7 @@ static ex acosh_eval(const ex & x) return Pi*I; // acosh(float) -> float if (!x.info(info_flags::crational)) - return acosh_evalf(x); + return acosh(ex_to(x)); } return acosh(x).hold(); @@ -982,11 +975,10 @@ REGISTER_FUNCTION(acosh, eval_func(acosh_eval). static ex atanh_evalf(const ex & x) { - BEGIN_TYPECHECK - TYPECHECK(x,numeric) - END_TYPECHECK(atanh(x)) + if (is_exactly_a(x)) + return atanh(ex_to(x)); - return atanh(ex_to(x)); // -> numeric atanh(numeric) + return atanh(x).hold(); } static ex atanh_eval(const ex & x) @@ -1000,7 +992,7 @@ static ex atanh_eval(const ex & x) throw (pole_error("atanh_eval(): logarithmic pole",0)); // atanh(float) -> float if (!x.info(info_flags::crational)) - return atanh_evalf(x); + return atanh(ex_to(x)); } return atanh(x).hold(); @@ -1019,7 +1011,7 @@ static ex atanh_series(const ex &arg, int order, unsigned options) { - GINAC_ASSERT(is_ex_exactly_of_type(rel.lhs(),symbol)); + GINAC_ASSERT(is_exactly_a(rel.lhs())); // method: // Taylor series where there is no pole or cut falls back to atanh_deriv. // There are two branch cuts, one runnig from 1 up the real axis and one @@ -1040,10 +1032,10 @@ static ex atanh_series(const ex &arg, // method: // This is the branch cut: assemble the primitive series manually and // then add the corresponding complex step function. - const symbol *s = static_cast(rel.lhs().bp); + const symbol &s = ex_to(rel.lhs()); const ex point = rel.rhs(); const symbol foo; - ex replarg = series(atanh(arg), *s==foo, order).subs(foo==point); + const ex replarg = series(atanh(arg), s==foo, order).subs(foo==point); ex Order0correction = replarg.op(0)+csgn(I*arg)*Pi*I*_ex1_2(); if (arg_pt<_ex0()) Order0correction += log((arg_pt+_ex_1())/(arg_pt+_ex1()))*_ex1_2();