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Merge pull request #75 from JohnCremona/bigcomplex
Implementation of bigcomplex class
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@@ -7,7 +7,7 @@ AC_PREREQ([2.65]) | |
| # The version is the concatenation of 'v' and the year, month, date: vyyyymmdd | ||
| # To access this as a string or integer triple, see libsrc/eclib/version.h | ||
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| AC_INIT([eclib], [20221012], [[email protected]]) | ||
| AC_INIT([eclib], [20230424], [[email protected]]) | ||
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| AM_INIT_AUTOMAKE([-Wall]) | ||
| AC_MSG_NOTICE([Configuring eclib...]) | ||
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@@ -40,9 +40,10 @@ LT_INIT | |
| # | ||
| # NB The suffix of the library name (libec.so here) is (c-a).a.r | ||
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| LT_CURRENT=11 | ||
| LT_CURRENT=12 | ||
| LT_REVISION=0 | ||
| LT_AGE=1 | ||
| LT_AGE=2 | ||
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| AC_SUBST(LT_CURRENT) | ||
| AC_SUBST(LT_REVISION) | ||
| AC_SUBST(LT_AGE) | ||
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| // bigcomplex.h: complex class built on NTL's RR | ||
| ////////////////////////////////////////////////////////////////////////// | ||
| // | ||
| // Copyright 1990-2023 John Cremona | ||
| // | ||
| // This file is part of the eclib package. | ||
| // | ||
| // eclib is free software; you can redistribute it and/or modify it | ||
| // under the terms of the GNU General Public License as published by the | ||
| // Free Software Foundation; either version 2 of the License, or (at your | ||
| // option) any later version. | ||
| // | ||
| // eclib is distributed in the hope that it will be useful, but WITHOUT | ||
| // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | ||
| // FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | ||
| // for more details. | ||
| // | ||
| // You should have received a copy of the GNU General Public License | ||
| // along with eclib; if not, write to the Free Software Foundation, | ||
| // Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA | ||
| // | ||
| ////////////////////////////////////////////////////////////////////////// | ||
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| #ifndef _ECLIB_BIGCOMPLEX_H_ | ||
| #define _ECLIB_BIGCOMPLEX_H_ | ||
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| class bigcomplex{ | ||
| public: | ||
| explicit bigcomplex() : re(RR()), im(RR()) {;} | ||
| explicit bigcomplex(const RR& r) : re(r), im(RR()) {;} | ||
| explicit bigcomplex(const RR& r, const RR& i) : re(r), im(i) {;} | ||
| bigcomplex(const bigcomplex&) = default; | ||
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| // standard class methods | ||
| RR real() const {return re;}; | ||
| RR imag() const {return im;}; | ||
| RR norm() const {return sqr(re)+sqr(im);}; | ||
| RR arg() const { return atan2(im, re);}; | ||
| RR abs() const {return ::NTL::sqrt(norm());}; | ||
| bigcomplex conj() const {return bigcomplex(re,-im);}; | ||
| bigcomplex timesI() const {return bigcomplex(-im,re);}; | ||
| int IsReal() const {return ::NTL::IsZero(im);} | ||
| int IsImaginary() const {return ::NTL::IsZero(re);} | ||
| int IsZero() const {return ::NTL::IsZero(re) && ::NTL::IsZero(im);} | ||
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| bigcomplex operator= (const RR& r) {re=r; im=RR(); return *this;} | ||
| bigcomplex operator+=(const RR& r) {re+=r; return *this;}; | ||
| bigcomplex operator+(const RR& r) const {bigcomplex z(*this); z.re+=r; return z;}; | ||
| bigcomplex operator-=(const RR& r) {re -= r; return *this;}; | ||
| bigcomplex operator-(const RR& r) const {bigcomplex z(*this); z.re-=r; return z;}; | ||
| bigcomplex operator*=(const RR& r) {re*=r; im*=r; return *this;}; | ||
| bigcomplex operator*(const RR& r) const {bigcomplex z(*this); z.re*=r; z.im*=r; return z;}; | ||
| bigcomplex operator/=(const RR& r) {re/=r; im/=r; return *this;}; | ||
| bigcomplex operator/(const RR& r) const {bigcomplex z(*this); z.re/=r; z.im/=r; return z;}; | ||
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| bigcomplex operator=(const bigcomplex& z) {re=z.re; im=z.im; return *this;}; | ||
| bigcomplex operator+=(const bigcomplex& z) {re+=z.re; im+=z.im; return *this;}; | ||
| bigcomplex operator+(const bigcomplex& z) const {return bigcomplex(re+z.re, im+z.im);}; | ||
| bigcomplex operator+() {return *this;}; | ||
| bigcomplex operator-=(const bigcomplex& z) {re-=z.re; im-=z.im; return *this;}; | ||
| bigcomplex operator-(const bigcomplex& z) const {return bigcomplex(re-z.re, im-z.im);}; | ||
| bigcomplex operator-() const {return bigcomplex(-re,-im);}; | ||
| bigcomplex operator*=(const bigcomplex& z) {RR x = re; re=x*z.re-im*z.im; im = x*z.im+im*z.re; return *this;}; | ||
| bigcomplex operator*(const bigcomplex& z) const {bigcomplex w(*this); w*=z; return w;}; | ||
| bigcomplex operator/=(const bigcomplex& z) {RR r=z.norm(), x = re; re=(x*z.re+im*z.im)/r; im = (-x*z.im+im*z.re)/r; return *this;}; | ||
| bigcomplex operator/(const bigcomplex& z) const {bigcomplex w(*this); w/=z; return w;}; | ||
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| // standard functions as class methods: | ||
| bigcomplex sqrt() const {RR r = abs(); RR u = ::NTL::sqrt((r+re)/2), v=::NTL::sqrt((r-re)/2); if (im<0) v=-v; return bigcomplex(u,v);}; | ||
| bigcomplex cos() const {bigcomplex z(this->timesI()); return (z+z.conj())/to_RR(2);}; | ||
| bigcomplex sin() const {bigcomplex z(this->timesI()); return (z-z.conj())/bigcomplex(RR(),to_RR(2));}; | ||
| bigcomplex exp() const {RR e = ::NTL::exp(re); return bigcomplex(e * ::NTL::cos(im), e * ::NTL::sin(im));}; | ||
| bigcomplex log() const {return bigcomplex(::NTL::log(abs()), arg());} | ||
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| operator string() const | ||
| { | ||
| ostringstream s; | ||
| s << "(" << re << "," << im << ")"; | ||
| return s.str(); | ||
| } | ||
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| string pretty_string() const | ||
| { | ||
| ostringstream s; | ||
| if (IsReal()) | ||
| { | ||
| s<<re; | ||
| return s.str(); | ||
| } | ||
| if (IsImaginary()) | ||
| { | ||
| if (IsOne(im)) | ||
| s << ""; | ||
| else | ||
| if (IsOne(-im)) | ||
| s << "-"; | ||
| else s << im; | ||
| } | ||
| else | ||
| { | ||
| s<<re; | ||
| if(im>0) | ||
| s<<"+"; | ||
| else | ||
| s<<"-"; | ||
| RR abs_im(::NTL::abs(im)); | ||
| if (abs_im>1) | ||
| s<<abs_im; | ||
| } | ||
| s<<"i"; | ||
| return s.str(); | ||
| } | ||
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| friend ostream& operator<<(ostream& s, const bigcomplex& z) | ||
| { | ||
| s << string(z); | ||
| return s; | ||
| } | ||
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| // Implementation | ||
| private: | ||
| RR re, im; | ||
| }; | ||
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| // inline functions | ||
| inline RR real(const bigcomplex& z) {return z.real();}; | ||
| inline RR imag(const bigcomplex& z) {return z.imag();}; | ||
| inline RR norm(const bigcomplex& z) {return z.norm();}; | ||
| inline RR arg(const bigcomplex& z) { return z.arg();}; | ||
| inline RR abs(const bigcomplex& z) {return z.abs();}; | ||
| inline bigcomplex conj(const bigcomplex& z) {return z.conj();}; | ||
| inline int IsReal(const bigcomplex& z) {return z.IsReal();} | ||
| inline int IsImaginary(const bigcomplex& z) {return z.IsImaginary();} | ||
| inline int IsZero(const bigcomplex& z) {return z.IsZero();} | ||
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| // operators with left operand RR | ||
| inline bigcomplex operator+(const RR& r, const bigcomplex& z) {return bigcomplex(r)+z;}; | ||
| inline bigcomplex operator-(const RR& r, const bigcomplex& z) {return bigcomplex(r)-z;}; | ||
| inline bigcomplex operator*(const RR& r, const bigcomplex& z) {return bigcomplex(r)*z;}; | ||
| inline bigcomplex operator/(const RR& r, const bigcomplex& z) {return bigcomplex(r)/z;}; | ||
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| // standard method functions as functions: | ||
| inline bigcomplex sqrt(const bigcomplex& z) {bigcomplex w(z); return w.sqrt();}; | ||
| inline bigcomplex cos(const bigcomplex& z) {bigcomplex w(z); return w.cos();}; | ||
| inline bigcomplex sin(const bigcomplex& z) {bigcomplex w(z); return w.sin();}; | ||
| inline bigcomplex exp(const bigcomplex& z) {bigcomplex w(z); return w.exp();}; | ||
| inline bigcomplex log(const bigcomplex& z) {bigcomplex w(z); return w.log();}; | ||
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| inline void swap(bigcomplex& z1, bigcomplex& z2) {bigcomplex z3(z1); z1=z2; z2=z3;} | ||
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| #endif |
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