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SimplifyRatio.h
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1 #ifndef PhysicsTools_Utilities_SimplifyRatio_h
2 #define PhysicsTools_Utilities_SimplifyRatio_h
3 
4 #include "PhysicsTools/Utilities/interface/Ratio.h"
5 #include "PhysicsTools/Utilities/interface/Product.h"
6 #include "PhysicsTools/Utilities/interface/Power.h"
7 #include "PhysicsTools/Utilities/interface/Minus.h"
8 #include "PhysicsTools/Utilities/interface/Fraction.h"
9 #include "PhysicsTools/Utilities/interface/DecomposePower.h"
10 #include "PhysicsTools/Utilities/interface/ParametricTrait.h"
11 
12 #include "PhysicsTools/Utilities/interface/Simplify_begin.h"
13 
14 #include <type_traits>
15 
16 namespace funct {
17 
18  // 0 / a = 0
19  RATIO_RULE(TYPT1, NUM(0), A, NUM(0), num<0>());
20 
21  // a / 1 = a
22  RATIO_RULE(TYPT1, A, NUM(1), A, _1);
23 
24  // ( a * b )/ 1 = a * b
25  RATIO_RULE(TYPT2, PROD_S(A, B), NUM(1), PROD(A, B), _1);
26 
27  // a / ( -n ) = - ( a / n )
28  template <int n, typename A, bool positive = (n >= 0)>
29  struct SimplifyNegativeRatio {
30  typedef RATIO_S(A, NUM(n)) type;
31  COMBINE(A, NUM(n), type(_1, _2));
32  };
33 
34  TEMPL(N1T1)
35  struct SimplifyNegativeRatio<n, A, false> {
36  typedef MINUS(RATIO(A, NUM(-n))) type;
37  COMBINE(A, NUM(n), -(_1 / num<-n>()));
38  };
39 
40  TEMPL(N1T1) struct Ratio<A, NUM(n)> : public SimplifyNegativeRatio<n, A> {};
41 
42  // ( -a ) / b = - ( a / b )
43  RATIO_RULE(TYPT2, MINUS_S(A), B, MINUS(RATIO(A, B)), -(_1._ / _2));
44 
45  // ( -a ) / n = - ( a / n )
46  RATIO_RULE(TYPN1T1, MINUS_S(A), NUM(n), MINUS(RATIO(A, NUM(n))), -(_1._ / _2));
47 
48  //TEMPL( N1T2 struct Ratio<PROD_S( A, B ), NUM( n )> :
49  // public SimplifyNegativeRatio<n, PROD_S( A, B )> { };
50 
51  // n / ( m * a ) = (n/m) * a
52  /* WRONG!!
53  RATIO_RULE(TYPN2T1, NUM(n), PROD_S(NUM(m), A), \
54  PROD(FRACT(n, m), A), (fract<n, m>() * _2._2));
55  */
56  // ( a / b ) / c = a / ( b * c )
57  RATIO_RULE(TYPT3, RATIO_S(A, B), C, RATIO(A, PROD(B, C)), _1._1 / (_1._2 * _2));
58 
59  // ( a / b ) / n = a / ( n * b )
60  RATIO_RULE(TYPN1T2, RATIO_S(A, B), NUM(n), RATIO(A, PROD(NUM(n), B)), _1._1 / (_2 * _1._2));
61 
62  // ( a / b ) / ( c * d ) = a / ( b * c * d )
63  RATIO_RULE(TYPT4, RATIO_S(A, B), PROD_S(C, D), RATIO(A, PROD(PROD(B, C), D)), _1._1 / (_1._2 * _2));
64 
65  // ( a * b ) / ( c / d ) = ( a * b * d ) / c
66  RATIO_RULE(TYPT4, PROD_S(A, B), RATIO_S(C, D), RATIO(PROD(PROD(A, B), D), C), (_1 * _2._2) / _2._1);
67 
68  // ( n * a ) / ( m * b ) = ( n/m ) ( a / b )
69  RATIO_RULE(TYPN2T2,
70  PROD_S(NUM(n), A),
71  PROD_S(NUM(m), B),
72  PROD_S(FRACT(n, m), RATIO(A, B)),
73  (PROD_S(FRACT(n, m), RATIO(A, B))((fract<n, m>()), (_1._2 / _2._2))));
74 
75  // a / ( b / c ) = a * c / b
76  RATIO_RULE(TYPT3, A, RATIO_S(B, C), RATIO(PROD(A, C), B), (_1 * _2._2) / _2._1);
77 
78  // ( a + b ) / ( c / d ) = ( a + b ) * d / c
79  RATIO_RULE(TYPT4, SUM_S(A, B), RATIO_S(C, D), RATIO(PROD(SUM(A, B), D), C), (_1 * _2._2) / _2._1);
80 
81  // ( a / b ) / ( c / d )= a * d / ( b * c )
82  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));
83 
84  // ( a + b ) / ( b + a ) = 1
85  template <TYPT2, bool parametric = (Parametric<A>::value == 1) || (Parametric<B>::value == 1)>
86  struct SimplifyRatioSum {
87  typedef RATIO_S(SUM(A, B), SUM(B, A)) type;
88  COMBINE(SUM(A, B), SUM(B, A), type(_1, _2));
89  };
90 
91  TEMPL(T2) struct SimplifyRatioSum<A, B, false> {
92  typedef NUM(1) type;
93  COMBINE(SUM(A, B), SUM(B, A), num<1>());
94  };
95 
96  TEMPL(T2) struct Ratio<SUM_S(A, B), SUM_S(B, A)> : public SimplifyRatioSum<A, B> {};
97 
98  // a^b / a^c => a^( b - c)
99  template <TYPT3, bool parametric = (Parametric<A>::value == 1)>
100  struct SimplifyPowerRatio {
101  typedef POWER(A, B) arg1;
102  typedef POWER(A, C) arg2;
103  typedef RATIO_S(arg1, arg2) type;
104  COMBINE(arg1, arg2, type(_1, _2));
105  };
106 
107  TEMPL(T3)
108  struct SimplifyPowerRatio<A, B, C, false> {
109  typedef POWER(A, B) arg1;
110  typedef POWER(A, C) arg2;
111  typedef POWER(A, DIFF(B, C)) type;
112  inline static type combine(const arg1& _1, const arg2& _2) {
113  return pow(DecomposePower<A, B>::getBase(_1),
114  (DecomposePower<A, B>::getExp(_1) - DecomposePower<A, C>::getExp(_2)));
115  }
116  };
117 
118  TEMPL(T3) struct Ratio<POWER_S(A, B), POWER_S(A, C)> : public SimplifyPowerRatio<A, B, C> {};
119 
120  TEMPL(T2) struct Ratio<POWER_S(A, B), POWER_S(A, B)> : public SimplifyPowerRatio<A, B, B> {};
121 
122  TEMPL(T2) struct Ratio<A, POWER_S(A, B)> : public SimplifyPowerRatio<A, NUM(1), B> {};
123 
124  TEMPL(N1T1) struct Ratio<A, POWER_S(A, NUM(n))> : public SimplifyPowerRatio<A, NUM(1), NUM(n)> {};
125 
126  TEMPL(T2) struct Ratio<POWER_S(A, B), A> : public SimplifyPowerRatio<A, B, NUM(1)> {};
127 
128  TEMPL(N1T1) struct Ratio<POWER_S(A, NUM(n)), A> : public SimplifyPowerRatio<A, NUM(n), NUM(1)> {};
129 
130  TEMPL(T1) struct Ratio<A, A> : public SimplifyPowerRatio<A, NUM(1), NUM(1)> {};
131 
132  TEMPL(T2) struct Ratio<PROD_S(A, B), PROD_S(A, B)> : public SimplifyPowerRatio<PROD_S(A, B), NUM(1), NUM(1)> {};
133 
134  TEMPL(N1T1)
135  struct Ratio<PROD_S(NUM(n), A), PROD_S(NUM(n), A)> : public SimplifyPowerRatio<PROD_S(NUM(n), A), NUM(1), NUM(1)> {};
136 
137  RATIO_RULE(TYPN1, NUM(n), NUM(n), NUM(1), num<1>());
138 
139  // simplify ( f * g ) / h
140  // try ( f / h ) * g and ( g / h ) * f, otherwise leave ( f * g ) / h
141 
142  template <typename Prod, bool simplify = Prod::value>
143  struct AuxProductRatio {
144  typedef PROD(typename Prod::AB, typename Prod::C) type;
145  inline static type combine(const typename Prod::A& a, const typename Prod::B& b, const typename Prod::C& c) {
146  return (a / b) * c;
147  }
148  };
149 
150  template <typename Prod>
151  struct AuxProductRatio<Prod, false> {
152  typedef RATIO_S(typename Prod::AB, typename Prod::C) type;
153  inline static type combine(const typename Prod::A& a, const typename Prod::B& b, const typename Prod::C& c) {
154  return type(a * b, c);
155  }
156  };
157 
158  template <typename F, typename G, typename H>
159  struct RatioP1 {
160  struct prod0 {
161  typedef F A;
162  typedef G B;
163  typedef H C;
164  typedef PROD_S(A, B) AB;
165  inline static const A& a(const F& f, const G& g, const H& h) { return f; }
166  inline static const B& b(const F& f, const G& g, const H& h) { return g; }
167  inline static const C& c(const F& f, const G& g, const H& h) { return h; }
168  enum { value = false };
169  };
170  struct prod1 {
171  typedef F A;
172  typedef H B;
173  typedef G C;
174  typedef RATIO_S(A, B) base;
175  typedef RATIO(A, B) AB;
176  inline static const A& a(const F& f, const G& g, const H& h) { return f; }
177  inline static const B& b(const F& f, const G& g, const H& h) { return h; }
178  inline static const C& c(const F& f, const G& g, const H& h) { return g; }
179  enum { value = not ::std::is_same<AB, base>::value };
180  };
181  struct prod2 {
182  typedef G A;
183  typedef H B;
184  typedef F C;
185  typedef RATIO_S(A, B) base;
186  typedef RATIO(A, B) AB;
187  inline static const A& a(const F& f, const G& g, const H& h) { return g; }
188  inline static const B& b(const F& f, const G& g, const H& h) { return h; }
189  inline static const C& c(const F& f, const G& g, const H& h) { return f; }
190  enum { value = not ::std::is_same<AB, base>::value };
191  };
192 
193  typedef
194  typename std::conditional<prod1::value, prod1, typename std::conditional<prod2::value, prod2, prod0>::type>::type
195  prod;
196  typedef typename AuxProductRatio<prod>::type type;
197  inline static type combine(const PROD_S(F, G) & fg, const H& h) {
198  const F& f = fg._1;
199  const G& g = fg._2;
200  const typename prod::A& a = prod::a(f, g, h);
201  const typename prod::B& b = prod::b(f, g, h);
202  const typename prod::C& c = prod::c(f, g, h);
203  return AuxProductRatio<prod>::combine(a, b, c);
204  }
205  };
206 
207  // simplify c / ( a * b )
208  // try ( c / a ) / b and ( c / b ) / a, otherwise leave c / ( a * b )
209 
210  template <typename Prod, bool simplify = Prod::value>
211  struct AuxProductRatio2 {
212  typedef RATIO(typename Prod::AB, typename Prod::C) type;
213  inline static type combine(const typename Prod::A& a, const typename Prod::B& b, const typename Prod::C& c) {
214  return (b / a) / c;
215  }
216  };
217 
218  template <typename Prod>
219  struct AuxProductRatio2<Prod, false> {
220  typedef RATIO_S(typename Prod::C, typename Prod::AB) type;
221  inline static type combine(const typename Prod::A& a, const typename Prod::B& b, const typename Prod::C& c) {
222  return type(c, a * b);
223  }
224  };
225 
226  template <typename F, typename G, typename H>
227  struct RatioP2 {
228  struct prod0 {
229  typedef F A;
230  typedef G B;
231  typedef H C;
232  typedef PROD_S(A, B) AB;
233  inline static const A& a(const F& f, const G& g, const H& h) { return f; }
234  inline static const B& b(const F& f, const G& g, const H& h) { return g; }
235  inline static const C& c(const F& f, const G& g, const H& h) { return h; }
236  enum { value = false };
237  };
238  struct prod1 {
239  typedef F A;
240  typedef H B;
241  typedef G C;
242  typedef RATIO_S(B, A) base;
243  typedef RATIO(B, A) AB;
244  inline static const A& a(const F& f, const G& g, const H& h) { return f; }
245  inline static const B& b(const F& f, const G& g, const H& h) { return h; }
246  inline static const C& c(const F& f, const G& g, const H& h) { return g; }
247  enum { value = not ::std::is_same<AB, base>::value };
248  };
249  struct prod2 {
250  typedef G A;
251  typedef H B;
252  typedef F C;
253  typedef RATIO_S(B, A) base;
254  typedef RATIO(B, A) AB;
255  inline static const A& a(const F& f, const G& g, const H& h) { return g; }
256  inline static const B& b(const F& f, const G& g, const H& h) { return h; }
257  inline static const C& c(const F& f, const G& g, const H& h) { return f; }
258  enum { value = not ::std::is_same<AB, base>::value };
259  };
260 
261  typedef
262  typename std::conditional<prod1::value, prod1, typename std::conditional<prod2::value, prod2, prod0>::type>::type
263  prod;
264  typedef typename AuxProductRatio2<prod>::type type;
265  inline static type combine(const H& h, const PROD_S(F, G) & fg) {
266  const F& f = fg._1;
267  const G& g = fg._2;
268  const typename prod::A& a = prod::a(f, g, h);
269  const typename prod::B& b = prod::b(f, g, h);
270  const typename prod::C& c = prod::c(f, g, h);
271  return AuxProductRatio2<prod>::combine(a, b, c);
272  }
273  };
274 
275  TEMPL(T3) struct Ratio<PROD_S(A, B), C> : public RatioP1<A, B, C> {};
276 
277  TEMPL(N1T2) struct Ratio<PROD_S(A, B), NUM(n)> : public RatioP1<A, B, NUM(n)> {};
278 
279  TEMPL(T3) struct Ratio<C, PROD_S(A, B)> : public RatioP2<A, B, C> {};
280 
281  TEMPL(T4) struct Ratio<PROD_S(C, D), PROD_S(A, B)> : public RatioP2<A, B, PROD_S(C, D)> {};
282 
283  // simplify ( a + b ) / c trying to simplify ( a / c ) and ( b / c )
284  template <TYPT3, bool simplify = false>
285  struct AuxSumRatio {
286  typedef RATIO_S(SUM_S(A, B), C) type;
287  COMBINE(SUM_S(A, B), C, type(_1, _2));
288  };
289 
290  TEMPL(T3) struct AuxSumRatio<A, B, C, true> {
291  typedef SUM(RATIO(A, C), RATIO(B, C)) type;
292  COMBINE(SUM_S(A, B), C, (_1._1 / _2) + (_1._2 / _2));
293  };
294 
295  TEMPL(T3) struct RatioSimpl {
296  struct ratio1 {
297  typedef RATIO_S(A, C) base;
298  typedef RATIO(A, C) type;
299  enum { value = not ::std::is_same<type, base>::value };
300  };
301  struct ratio2 {
302  typedef RATIO_S(B, C) base;
303  typedef RATIO(B, C) type;
304  enum { value = not ::std::is_same<type, base>::value };
305  };
306  typedef AuxSumRatio<A, B, C, ratio1::value or ratio2::value> aux;
307  typedef typename aux::type type;
308  COMBINE(SUM_S(A, B), C, aux::combine(_1, _2));
309  };
310 
311  TEMPL(T3) struct Ratio<SUM_S(A, B), C> : public RatioSimpl<A, B, C> {};
312 
313  TEMPL(T4) struct Ratio<SUM_S(A, B), PROD_S(C, D)> : public RatioSimpl<A, B, PROD_S(C, D)> {};
314 
315  TEMPL(N1T2) struct Ratio<SUM_S(A, B), NUM(n)> : public RatioSimpl<A, B, NUM(n)> {};
316 
317 } // namespace funct
318 
319 #include "PhysicsTools/Utilities/interface/Simplify_end.h"
320 
321 #endif
funct::value
static const bool value
Definition: Factorize.h:100
TYPN1
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Definition: Simplify_begin.h:11
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Definition: Simplify_begin.h:7
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Definition: SimplifyRatio.h:88
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Definition: Simplify_begin.h:54
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static const B & b(const F &f, const G &g, const H &h)
Definition: SimplifyRatio.h:245
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Definition: Simplify_begin.h:40
g
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