cp-algo/math/affine.hpp

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Include: #include "cp-algo/math/affine.hpp"

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#ifndef CP_ALGO_MATH_AFFINE_HPP
#define CP_ALGO_MATH_AFFINE_HPP
#include <optional>
#include <utility>
#include <cassert>
#include <tuple>
namespace cp_algo::math {
    // a * x + b
    template<typename base>
    struct lin {
        base a = 1, b = 0;
        std::optional<base> c;
        lin() {}
        lin(base b): a(0), b(b) {}
        lin(base a, base b): a(a), b(b) {}
        lin(base a, base b, base _c): a(a), b(b), c(_c) {}

        // polynomial product modulo x^2 - c
        lin operator * (const lin& t) {
            assert(c && t.c && *c == *t.c);
            return {a * t.b + b * t.a, b * t.b + a * t.a * (*c), *c};
        }

        // a * (t.a * x + t.b) + b
        lin apply(lin const& t) const {
            return {a * t.a, a * t.b + b};
        }

        void prepend(lin const& t) {
            *this = t.apply(*this);
        }

        base eval(base x) const {
            return a * x + b;
        }
    };

    // (ax+b) / (cx+d)
    template<typename base>
    struct linfrac {
        base a, b, c, d;
        linfrac(): a(1), b(0), c(0), d(1) {} // x, identity for composition
        linfrac(base a): a(a), b(1), c(1), d(0) {} // a + 1/x, for continued fractions
        linfrac(base a, base b, base c, base d): a(a), b(b), c(c), d(d) {}

        // composition of two linfracs
        linfrac operator * (linfrac t) const {
            return t.prepend(linfrac(*this));
        }

        linfrac operator-() const {
            return {-a, -b, -c, -d};
        }

        linfrac adj() const {
            return {d, -b, -c, a};
        }
        
        linfrac& prepend(linfrac const& t) {
            t.apply(a, c);
            t.apply(b, d);
            return *this;
        }

        // apply linfrac to A/B
        void apply(base &A, base &B) const {
            std::tie(A, B) = std::pair{a * A + b * B, c * A + d * B};
        }
    };
}
#endif // CP_ALGO_MATH_AFFINE_HPP

#line 1 "cp-algo/math/affine.hpp"


#include <optional>
#include <utility>
#include <cassert>
#include <tuple>
namespace cp_algo::math {
    // a * x + b
    template<typename base>
    struct lin {
        base a = 1, b = 0;
        std::optional<base> c;
        lin() {}
        lin(base b): a(0), b(b) {}
        lin(base a, base b): a(a), b(b) {}
        lin(base a, base b, base _c): a(a), b(b), c(_c) {}

        // polynomial product modulo x^2 - c
        lin operator * (const lin& t) {
            assert(c && t.c && *c == *t.c);
            return {a * t.b + b * t.a, b * t.b + a * t.a * (*c), *c};
        }

        // a * (t.a * x + t.b) + b
        lin apply(lin const& t) const {
            return {a * t.a, a * t.b + b};
        }

        void prepend(lin const& t) {
            *this = t.apply(*this);
        }

        base eval(base x) const {
            return a * x + b;
        }
    };

    // (ax+b) / (cx+d)
    template<typename base>
    struct linfrac {
        base a, b, c, d;
        linfrac(): a(1), b(0), c(0), d(1) {} // x, identity for composition
        linfrac(base a): a(a), b(1), c(1), d(0) {} // a + 1/x, for continued fractions
        linfrac(base a, base b, base c, base d): a(a), b(b), c(c), d(d) {}

        // composition of two linfracs
        linfrac operator * (linfrac t) const {
            return t.prepend(linfrac(*this));
        }

        linfrac operator-() const {
            return {-a, -b, -c, -d};
        }

        linfrac adj() const {
            return {d, -b, -c, a};
        }
        
        linfrac& prepend(linfrac const& t) {
            t.apply(a, c);
            t.apply(b, d);
            return *this;
        }

        // apply linfrac to A/B
        void apply(base &A, base &B) const {
            std::tie(A, B) = std::pair{a * A + b * B, c * A + d * B};
        }
    };
}

#ifndef CP_ALGO_MATH_AFFINE_HPP
#define CP_ALGO_MATH_AFFINE_HPP
#include <optional>
#include <utility>
#include <cassert>
#include <tuple>
namespace cp_algo::math{ template<typename base> struct lin{ base a=1,b=0; std::optional<base>c; lin(){} lin(base b):a(0),b(b){} lin(base a,base b):a(a),b(b){} lin(base a,base b,base _c):a(a),b(b),c(_c){} lin operator*(const lin&t){ assert(c&&t.c&& *c== *t.c); return{a*t.b+b*t.a,b*t.b+a*t.a*(*c),*c}; } lin apply(lin const&t)const{ return{a*t.a,a*t.b+b}; } void prepend(lin const&t){ *this=t.apply(*this); } base eval(base x)const{ return a*x+b; } }; template<typename base> struct linfrac{ base a,b,c,d; linfrac():a(1),b(0),c(0),d(1){} linfrac(base a):a(a),b(1),c(1),d(0){} linfrac(base a,base b,base c,base d):a(a),b(b),c(c),d(d){} linfrac operator*(linfrac t)const{ return t.prepend(linfrac(*this)); } linfrac operator-()const{ return{-a,-b,-c,-d}; } linfrac adj()const{ return{d,-b,-c,a}; } linfrac&prepend(linfrac const&t){ t.apply(a,c); t.apply(b,d); return*this; } void apply(base&A,base&B)const{ std::tie(A,B)=std::pair{a*A+b*B,c*A+d*B}; } }; }
#endif

#line 1 "cp-algo/math/affine.hpp"
#include <optional>
#include <utility>
#include <cassert>
#include <tuple>
namespace cp_algo::math{ template<typename base> struct lin{ base a=1,b=0; std::optional<base>c; lin(){} lin(base b):a(0),b(b){} lin(base a,base b):a(a),b(b){} lin(base a,base b,base _c):a(a),b(b),c(_c){} lin operator*(const lin&t){ assert(c&&t.c&& *c== *t.c); return{a*t.b+b*t.a,b*t.b+a*t.a*(*c),*c}; } lin apply(lin const&t)const{ return{a*t.a,a*t.b+b}; } void prepend(lin const&t){ *this=t.apply(*this); } base eval(base x)const{ return a*x+b; } }; template<typename base> struct linfrac{ base a,b,c,d; linfrac():a(1),b(0),c(0),d(1){} linfrac(base a):a(a),b(1),c(1),d(0){} linfrac(base a,base b,base c,base d):a(a),b(b),c(c),d(d){} linfrac operator*(linfrac t)const{ return t.prepend(linfrac(*this)); } linfrac operator-()const{ return{-a,-b,-c,-d}; } linfrac adj()const{ return{d,-b,-c,a}; } linfrac&prepend(linfrac const&t){ t.apply(a,c); t.apply(b,d); return*this; } void apply(base&A,base&B)const{ std::tie(A,B)=std::pair{a*A+b*B,c*A+d*B}; } }; }