SimplifyRatio.h

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#ifndef PhysicsTools_Utilities_SimplifyRatio_h
#define PhysicsTools_Utilities_SimplifyRatio_h

#include "PhysicsTools/Utilities/interface/Ratio.h"
#include "PhysicsTools/Utilities/interface/Product.h"
#include "PhysicsTools/Utilities/interface/Power.h"
#include "PhysicsTools/Utilities/interface/Minus.h"
#include "PhysicsTools/Utilities/interface/Fraction.h"
#include "PhysicsTools/Utilities/interface/DecomposePower.h"
#include "PhysicsTools/Utilities/interface/ParametricTrait.h"

#include "PhysicsTools/Utilities/interface/Simplify_begin.h"

#include <type_traits>

namespace funct {

  // 0 / a = 0
  RATIO_RULE(TYPT1, NUM(0), A, NUM(0), num<0>());

  // a / 1 = a
  RATIO_RULE(TYPT1, A, NUM(1), A, _1);

  // ( a * b )/ 1 = a * b
  RATIO_RULE(TYPT2, PROD_S(A, B), NUM(1), PROD(A, B), _1);

  // a / ( -n ) = - ( a / n )
  template <int n, typename A, bool positive = (n >= 0)>
  struct SimplifyNegativeRatio {
    typedef RATIO_S(A, NUM(n)) type;
    COMBINE(A, NUM(n), type(_1, _2));
  };

  TEMPL(N1T1)
  struct SimplifyNegativeRatio<n, A, false> {
    typedef MINUS(RATIO(A, NUM(-n))) type;
    COMBINE(A, NUM(n), -(_1 / num<-n>()));
  };

  TEMPL(N1T1) struct Ratio<A, NUM(n)> : public SimplifyNegativeRatio<n, A> {};

  // ( -a ) / b = - ( a / b )
  RATIO_RULE(TYPT2, MINUS_S(A), B, MINUS(RATIO(A, B)), -(_1._ / _2));

  // ( -a ) / n = - ( a / n )
  RATIO_RULE(TYPN1T1, MINUS_S(A), NUM(n), MINUS(RATIO(A, NUM(n))), -(_1._ / _2));

  //TEMPL( N1T2 struct Ratio<PROD_S( A, B ), NUM( n )> :
  //  public SimplifyNegativeRatio<n, PROD_S( A, B )> { };

  // n / ( m * a ) = (n/m) * a
  /* WRONG!!
  RATIO_RULE(TYPN2T1, NUM(n), PROD_S(NUM(m), A), \
         PROD(FRACT(n, m), A), (fract<n, m>() * _2._2));
  */
  // ( a / b ) / c = a / ( b * c )
  RATIO_RULE(TYPT3, RATIO_S(A, B), C, RATIO(A, PROD(B, C)), _1._1 / (_1._2 * _2));

  // ( a / b ) / n = a / ( n * b )
  RATIO_RULE(TYPN1T2, RATIO_S(A, B), NUM(n), RATIO(A, PROD(NUM(n), B)), _1._1 / (_2 * _1._2));

  // ( a / b ) / ( c * d ) = a / ( b * c * d )
  RATIO_RULE(TYPT4, RATIO_S(A, B), PROD_S(C, D), RATIO(A, PROD(PROD(B, C), D)), _1._1 / (_1._2 * _2));

  // ( a * b ) / ( c / d ) = ( a * b * d ) / c
  RATIO_RULE(TYPT4, PROD_S(A, B), RATIO_S(C, D), RATIO(PROD(PROD(A, B), D), C), (_1 * _2._2) / _2._1);

  // ( n * a ) / ( m * b ) = ( n/m ) ( a / b )
  RATIO_RULE(TYPN2T2,
             PROD_S(NUM(n), A),
             PROD_S(NUM(m), B),
             PROD_S(FRACT(n, m), RATIO(A, B)),
             (PROD_S(FRACT(n, m), RATIO(A, B))((fract<n, m>()), (_1._2 / _2._2))));

  //  a / ( b / c ) = a * c / b
  RATIO_RULE(TYPT3, A, RATIO_S(B, C), RATIO(PROD(A, C), B), (_1 * _2._2) / _2._1);

  //  ( a + b ) / ( c / d ) = ( a + b ) * d / c
  RATIO_RULE(TYPT4, SUM_S(A, B), RATIO_S(C, D), RATIO(PROD(SUM(A, B), D), C), (_1 * _2._2) / _2._1);

  // ( a / b ) / ( c / d )= a * d / ( b * c )
  RATIO_RULE(TYPT4, RATIO_S(A, B), RATIO_S(C, D), RATIO(PROD(A, D), PROD(B, C)), (_1._1 * _2._2) / (_1._2 * _2._1));

  // ( a + b ) / ( b + a ) = 1
  template <TYPT2, bool parametric = (Parametric<A>::value == 1) || (Parametric<B>::value == 1)>
  struct SimplifyRatioSum {
    typedef RATIO_S(SUM(A, B), SUM(B, A)) type;
    COMBINE(SUM(A, B), SUM(B, A), type(_1, _2));
  };

  TEMPL(T2) struct SimplifyRatioSum<A, B, false> {
    typedef NUM(1) type;
    COMBINE(SUM(A, B), SUM(B, A), num<1>());
  };

  TEMPL(T2) struct Ratio<SUM_S(A, B), SUM_S(B, A)> : public SimplifyRatioSum<A, B> {};

  // a^b / a^c => a^( b - c)
  template <TYPT3, bool parametric = (Parametric<A>::value == 1)>
  struct SimplifyPowerRatio {
    typedef POWER(A, B) arg1;
    typedef POWER(A, C) arg2;
    typedef RATIO_S(arg1, arg2) type;
    COMBINE(arg1, arg2, type(_1, _2));
  };

  TEMPL(T3)
  struct SimplifyPowerRatio<A, B, C, false> {
    typedef POWER(A, B) arg1;
    typedef POWER(A, C) arg2;
    typedef POWER(A, DIFF(B, C)) type;
    inline static type combine(const arg1& _1, const arg2& _2) {
      return pow(DecomposePower<A, B>::getBase(_1),
                 (DecomposePower<A, B>::getExp(_1) - DecomposePower<A, C>::getExp(_2)));
    }
  };

  TEMPL(T3) struct Ratio<POWER_S(A, B), POWER_S(A, C)> : public SimplifyPowerRatio<A, B, C> {};

  TEMPL(T2) struct Ratio<POWER_S(A, B), POWER_S(A, B)> : public SimplifyPowerRatio<A, B, B> {};

  TEMPL(T2) struct Ratio<A, POWER_S(A, B)> : public SimplifyPowerRatio<A, NUM(1), B> {};

  TEMPL(N1T1) struct Ratio<A, POWER_S(A, NUM(n))> : public SimplifyPowerRatio<A, NUM(1), NUM(n)> {};

  TEMPL(T2) struct Ratio<POWER_S(A, B), A> : public SimplifyPowerRatio<A, B, NUM(1)> {};

  TEMPL(N1T1) struct Ratio<POWER_S(A, NUM(n)), A> : public SimplifyPowerRatio<A, NUM(n), NUM(1)> {};

  TEMPL(T1) struct Ratio<A, A> : public SimplifyPowerRatio<A, NUM(1), NUM(1)> {};

  TEMPL(T2) struct Ratio<PROD_S(A, B), PROD_S(A, B)> : public SimplifyPowerRatio<PROD_S(A, B), NUM(1), NUM(1)> {};

  TEMPL(N1T1)
  struct Ratio<PROD_S(NUM(n), A), PROD_S(NUM(n), A)> : public SimplifyPowerRatio<PROD_S(NUM(n), A), NUM(1), NUM(1)> {};

  RATIO_RULE(TYPN1, NUM(n), NUM(n), NUM(1), num<1>());

  // simplify ( f * g ) / h
  // try ( f / h ) * g and ( g / h ) * f, otherwise leave ( f * g ) / h

  template <typename Prod, bool simplify = Prod::value>
  struct AuxProductRatio {
    typedef PROD(typename Prod::AB, typename Prod::C) type;
    inline static type combine(const typename Prod::A& a, const typename Prod::B& b, const typename Prod::C& c) {
      return (a / b) * c;
    }
  };

  template <typename Prod>
  struct AuxProductRatio<Prod, false> {
    typedef RATIO_S(typename Prod::AB, typename Prod::C) type;
    inline static type combine(const typename Prod::A& a, const typename Prod::B& b, const typename Prod::C& c) {
      return type(a * b, c);
    }
  };

  template <typename F, typename G, typename H>
  struct RatioP1 {
    struct prod0 {
      typedef F A;
      typedef G B;
      typedef H C;
      typedef PROD_S(A, B) AB;
      inline static const A& a(const F& f, const G& g, const H& h) { return f; }
      inline static const B& b(const F& f, const G& g, const H& h) { return g; }
      inline static const C& c(const F& f, const G& g, const H& h) { return h; }
      enum { value = false };
    };
    struct prod1 {
      typedef F A;
      typedef H B;
      typedef G C;
      typedef RATIO_S(A, B) base;
      typedef RATIO(A, B) AB;
      inline static const A& a(const F& f, const G& g, const H& h) { return f; }
      inline static const B& b(const F& f, const G& g, const H& h) { return h; }
      inline static const C& c(const F& f, const G& g, const H& h) { return g; }
      enum { value = not ::std::is_same<AB, base>::value };
    };
    struct prod2 {
      typedef G A;
      typedef H B;
      typedef F C;
      typedef RATIO_S(A, B) base;
      typedef RATIO(A, B) AB;
      inline static const A& a(const F& f, const G& g, const H& h) { return g; }
      inline static const B& b(const F& f, const G& g, const H& h) { return h; }
      inline static const C& c(const F& f, const G& g, const H& h) { return f; }
      enum { value = not ::std::is_same<AB, base>::value };
    };

    typedef
        typename std::conditional<prod1::value, prod1, typename std::conditional<prod2::value, prod2, prod0>::type>::type
            prod;
    typedef typename AuxProductRatio<prod>::type type;
    inline static type combine(const PROD_S(F, G) & fg, const H& h) {
      const F& f = fg._1;
      const G& g = fg._2;
      const typename prod::A& a = prod::a(f, g, h);
      const typename prod::B& b = prod::b(f, g, h);
      const typename prod::C& c = prod::c(f, g, h);
      return AuxProductRatio<prod>::combine(a, b, c);
    }
  };

  // simplify c / ( a * b )
  // try ( c / a ) / b and ( c / b ) / a, otherwise leave c / ( a * b )

  template <typename Prod, bool simplify = Prod::value>
  struct AuxProductRatio2 {
    typedef RATIO(typename Prod::AB, typename Prod::C) type;
    inline static type combine(const typename Prod::A& a, const typename Prod::B& b, const typename Prod::C& c) {
      return (b / a) / c;
    }
  };

  template <typename Prod>
  struct AuxProductRatio2<Prod, false> {
    typedef RATIO_S(typename Prod::C, typename Prod::AB) type;
    inline static type combine(const typename Prod::A& a, const typename Prod::B& b, const typename Prod::C& c) {
      return type(c, a * b);
    }
  };

  template <typename F, typename G, typename H>
  struct RatioP2 {
    struct prod0 {
      typedef F A;
      typedef G B;
      typedef H C;
      typedef PROD_S(A, B) AB;
      inline static const A& a(const F& f, const G& g, const H& h) { return f; }
      inline static const B& b(const F& f, const G& g, const H& h) { return g; }
      inline static const C& c(const F& f, const G& g, const H& h) { return h; }
      enum { value = false };
    };
    struct prod1 {
      typedef F A;
      typedef H B;
      typedef G C;
      typedef RATIO_S(B, A) base;
      typedef RATIO(B, A) AB;
      inline static const A& a(const F& f, const G& g, const H& h) { return f; }
      inline static const B& b(const F& f, const G& g, const H& h) { return h; }
      inline static const C& c(const F& f, const G& g, const H& h) { return g; }
      enum { value = not ::std::is_same<AB, base>::value };
    };
    struct prod2 {
      typedef G A;
      typedef H B;
      typedef F C;
      typedef RATIO_S(B, A) base;
      typedef RATIO(B, A) AB;
      inline static const A& a(const F& f, const G& g, const H& h) { return g; }
      inline static const B& b(const F& f, const G& g, const H& h) { return h; }
      inline static const C& c(const F& f, const G& g, const H& h) { return f; }
      enum { value = not ::std::is_same<AB, base>::value };
    };

    typedef
        typename std::conditional<prod1::value, prod1, typename std::conditional<prod2::value, prod2, prod0>::type>::type
            prod;
    typedef typename AuxProductRatio2<prod>::type type;
    inline static type combine(const H& h, const PROD_S(F, G) & fg) {
      const F& f = fg._1;
      const G& g = fg._2;
      const typename prod::A& a = prod::a(f, g, h);
      const typename prod::B& b = prod::b(f, g, h);
      const typename prod::C& c = prod::c(f, g, h);
      return AuxProductRatio2<prod>::combine(a, b, c);
    }
  };

  TEMPL(T3) struct Ratio<PROD_S(A, B), C> : public RatioP1<A, B, C> {};

  TEMPL(N1T2) struct Ratio<PROD_S(A, B), NUM(n)> : public RatioP1<A, B, NUM(n)> {};

  TEMPL(T3) struct Ratio<C, PROD_S(A, B)> : public RatioP2<A, B, C> {};

  TEMPL(T4) struct Ratio<PROD_S(C, D), PROD_S(A, B)> : public RatioP2<A, B, PROD_S(C, D)> {};

  // simplify ( a + b ) / c trying to simplify ( a / c ) and ( b / c )
  template <TYPT3, bool simplify = false>
  struct AuxSumRatio {
    typedef RATIO_S(SUM_S(A, B), C) type;
    COMBINE(SUM_S(A, B), C, type(_1, _2));
  };

  TEMPL(T3) struct AuxSumRatio<A, B, C, true> {
    typedef SUM(RATIO(A, C), RATIO(B, C)) type;
    COMBINE(SUM_S(A, B), C, (_1._1 / _2) + (_1._2 / _2));
  };

  TEMPL(T3) struct RatioSimpl {
    struct ratio1 {
      typedef RATIO_S(A, C) base;
      typedef RATIO(A, C) type;
      enum { value = not ::std::is_same<type, base>::value };
    };
    struct ratio2 {
      typedef RATIO_S(B, C) base;
      typedef RATIO(B, C) type;
      enum { value = not ::std::is_same<type, base>::value };
    };
    typedef AuxSumRatio<A, B, C, ratio1::value or ratio2::value> aux;
    typedef typename aux::type type;
    COMBINE(SUM_S(A, B), C, aux::combine(_1, _2));
  };

  TEMPL(T3) struct Ratio<SUM_S(A, B), C> : public RatioSimpl<A, B, C> {};

  TEMPL(T4) struct Ratio<SUM_S(A, B), PROD_S(C, D)> : public RatioSimpl<A, B, PROD_S(C, D)> {};

  TEMPL(N1T2) struct Ratio<SUM_S(A, B), NUM(n)> : public RatioSimpl<A, B, NUM(n)> {};

}  // namespace funct

#include "PhysicsTools/Utilities/interface/Simplify_end.h"

#endif