Number *Complex::expt(Number *number2){
Complex *tmp = SCAST_COMPLEX(number2);
Float *f = new Float();
Float *real1 =SCAST_FLOAT(f->convert(real_));
Float *imag1 = SCAST_FLOAT(f->convert(imag_));
Float *real2 = SCAST_FLOAT(f->convert(tmp->real_));
Float *imag2 = SCAST_FLOAT(f->convert(tmp->imag_));
complex<double> a(real1->number_, imag1->number_), b(real2->number_, imag2->number_);
complex<double> res = pow(a, b);
Float *real = new Float(res.real()), *imag = new Float(res.imag());
if (real->number_ == -0) real->number_ = 0;
Complex *result = new Complex(real, imag);
delete f, real1, imag1, real2, imag2, real, imag;
return result;
}
Complex::Complex(string real, string imag) {
type_ = COMPLEX;
const char* real2(real.c_str());
const char* imag2(imag.c_str());
Float *f = new Float();
real_ = Rational::from_string(real2);
imag_ = Rational::from_string(imag2);
if (!real_ || !imag_){
if (!imag_) imag_ = Float::from_string(imag2);
else imag_ = f->convert(imag_);
if (!real_) real_ = Float::from_string(real2);
else real_ = f->convert(real_);
if (!real_ || !imag_) throw 0;
}
}
Number* Rational::acoss()
{
Float* res = new Float;
Float* tmp = SCAST_FLOAT(res->convert(this));
if (fabs(tmp->number_)<=1.0)
{
res->number_=asin(tmp->number_);
delete tmp;
return res;
}
else if (tmp->number_>0)
{
complex<double> c_a(tmp->number_,0.0);
complex<double> c_res = asin(c_a);
Complex* res = new Complex;
res->exact_ = false;
res->real_ = new Float(::real(c_res));
res->imag_ = new Float(::imag(c_res));
delete tmp;
return res;
}
else
{
complex<double> c_a(fabs(tmp->number_),0.0);
complex<double> c_res = asin(c_a);
Complex* res = new Complex;
res->exact_ = false;
res->real_ = new Float(::real(c_res)+PI);
res->imag_ = new Float(0.0-::imag(c_res));
delete tmp;
return res;
}
}
Number* Rational::atann()
{
Float* res = new Float;
Float* tmp2 = SCAST_FLOAT(res->convert(this));
res->number_ = atan(tmp2->number_);
delete tmp2;
return res;
}
Number *Complex::ang(){
Float *f = new Float();
Float *real1 = SCAST_FLOAT(f->convert(real_));
Float *imag1 = SCAST_FLOAT(f->convert(imag_));
complex<double> a(real1->number_, imag1->number_);
Float *result = new Float(arg(a));
delete f, real1, imag1;
return result;
}
Number* Rational::expp(Number* number2)
{
Rational* rtmp2 = SCAST_RATIONAL(number2);
if (num_==ZERO_ && rtmp2->num_==ZERO_) return new Float(1);
else if (num_==ZERO_ && rtmp2->num_!=ZERO_) return new Float(0);
if(num_.sgn_)
{
Complex* c = new Complex;
c = SCAST_COMPLEX(c->convert(this));
Complex* d = SCAST_COMPLEX(c->convert(rtmp2));
return c->expp(d);
}
else
{
Float* tmpf = new Float;
tmpf = SCAST_FLOAT(tmpf->convert(rtmp2));
return new Float(pow(SCAST_FLOAT(tmpf->convert(this))->number_, tmpf->number_));
}
}
Number* Rational::expt(Number* obj){
if(sgn()<0){
Complex* c = new Complex();
c = SCAST_COMPLEX(c->convert(this));
Complex* d = SCAST_COMPLEX(c->convert(obj));
return c->expt(d);
}else{
Float* tmpf = new Float();
tmpf = SCAST_FLOAT(tmpf->convert(obj));
return new Float(pow(double(*this), double(*SCAST_RATIONAL(obj))));
}
}
Number* Rational::sqt()
{
if (!num_.sgn_) return new Float(sqrt((double)num_/(double)den_));
else
{
Complex* resc = new Complex;
Float* real = new Float(0.0);
Float* imag = new Float(sqrt(fabs(SCAST_FLOAT(real->convert(this))->number_)));
resc->real_ = real; resc->imag_ = imag; resc->exact_=false;
return resc;
}
}
Number *Complex::logx(){
Float *f = new Float();
Float *real1 = SCAST_FLOAT(f->convert(real_));
Float *imag1 = SCAST_FLOAT(f->convert(imag_));
complex<double> a(real1->number_, imag1->number_);
complex<double> res = log(a);
Float *real = new Float(res.real()), *imag = new Float(res.imag());
if (real->number_ == -0) real->number_ = 0;
Complex *result = new Complex(real, imag);
delete f, real1, imag1, real, imag;
return result;
}
Number* Rational::logg()
{
assert(num_!=ZERO_ && "undefined log0");
if (!num_.sgn_)
{
Float* tmpf = new Float;
tmpf = SCAST_FLOAT(tmpf->convert(this));
return new Float(log(tmpf->number_));
}
else
{
Float* tmp = new Float;
tmp = SCAST_FLOAT(tmp->convert(this));
complex<double> c_x(tmp->number_,0.0);
complex<double> c_res = log(c_x);
Complex* res = new Complex;
res->exact_ = false;
res->real_ = new Float(::real(c_res));
res->imag_ = new Float(::imag(c_res));
delete tmp;
return res;
}
}
Number *Complex::acosx(){
Float *f = new Float();
Float *real1 = SCAST_FLOAT(f->convert(real_));
Float *imag1 = SCAST_FLOAT(f->convert(imag_));
complex<double> a(real1->number_, imag1->number_);
complex<double> res = acos(a);
Float *real = new Float(res.real()), *imag = new Float(res.imag());
if (real->number_ == -0) real->number_ = 0;
Complex *result = new Complex(real, imag);
delete f, real1, imag1, real, imag;
return result;
// Complex *arcsin = SCAST_COMPLEX(this->asinx());
// Complex *halfpi = new Complex("1.57079632679489661923", "0");
// Complex *result = SCAST_COMPLEX(halfpi->sub(arcsin));
// delete arcsin, halfpi;
// return result;
}
Number *Complex::atanx(){
Float *f = new Float();
Float *real1 = SCAST_FLOAT(f->convert(real_));
Float *imag1 = SCAST_FLOAT(f->convert(imag_));
complex<double> a(real1->number_, imag1->number_);
complex<double> res = atan(a);
Float *real = new Float(res.real()), *imag = new Float(res.imag());
if (real->number_ == -0) real->number_ = 0;
Complex *result = new Complex(real, imag);
delete f, real1, imag1, real, imag;
return result;
// complex<double> i(0,1), one(1,0), two(2,0);
// complex<double> res = (log(one + i*a) - log(one - i*a)) / (two*i);
// Float *real = new Float(res.real()), *imag = new Float(res.imag());
// if (real->number_ == -0) real->number_ = 0;
// Complex *result = new Complex(real, imag);
// delete f, real1, imag1, real, imag;
// return result;
}
Number *Complex::asinx(){
Float *f = new Float();
Float *real1 = SCAST_FLOAT(f->convert(real_));
Float *imag1 = SCAST_FLOAT(f->convert(imag_));
complex<double> a(real1->number_, imag1->number_);
complex<double> res = asin(a);
Float *real = new Float(res.real()), *imag = new Float(res.imag());
if (real->number_ == -0) real->number_ = 0;
Complex *result = new Complex(real, imag);
delete f, real1, imag1, real, imag;
return result;
// complex<double> i(0, 1), one(1, 0);
// complex<double> res = (-i)*log(i*a + sqrt(one - pow(a, 2)));
// Float *real = new Float(res.real()), *imag = new Float(res.imag());
// if (real->number_ == -0) real->number_ = 0;
// Complex *result = new Complex(real, imag);
// delete f, real1, imag1, real, imag;
// return result;
}
Number* Rational::exttoinext()
{
Float* res = new Float;
return res->convert(this);
}
Number* Rational::expe()
{
Float* tmpf = new Float;
tmpf = SCAST_FLOAT(tmpf->convert(this));
return new Float(exp(tmpf->number_));
}
