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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 
11 #include "PhysicsTools/Utilities/interface/Simplify_begin.h"
12 
13 namespace funct {
14 
15  // 0 / a = 0
16  RATIO_RULE(TYPT1, NUM(0), A, NUM(0) , num<0>());
17 
18  // a / 1 = a
19  RATIO_RULE(TYPT1, A, NUM(1), A, _1);
20 
21  // ( a * b )/ 1 = a * b
22  RATIO_RULE(TYPT2, PROD_S(A, B), NUM(1), PROD(A, B), _1);
23 
24  // a / ( -n ) = - ( a / n )
25  template <int n, typename A, bool positive = (n>= 0)>
26  struct SimplifyNegativeRatio {
27  typedef RATIO_S(A, NUM(n)) type;
28  COMBINE(A, NUM(n), type(_1, _2));
29  };
30 
31  TEMPL(N1T1)
32  struct SimplifyNegativeRatio<n, A, false> {
33  typedef MINUS(RATIO(A, NUM(-n))) type;
34  COMBINE(A, NUM(n), - (_1 / num<-n>()));
35  };
36 
37  TEMPL(N1T1) struct Ratio<A, NUM(n)> :
38  public SimplifyNegativeRatio<n, A> { };
39 
40  // ( -a ) / b = - ( a / b )
41  RATIO_RULE(TYPT2, MINUS_S(A), B, MINUS(RATIO(A, B)), -(_1._ / _2));
42 
43  // ( -a ) / n = - ( a / n )
44  RATIO_RULE(TYPN1T1, MINUS_S(A), NUM(n), MINUS(RATIO(A, NUM(n))), -(_1._ / _2));
45 
46  //TEMPL( N1T2 struct Ratio<PROD_S( A, B ), NUM( n )> :
47  // public SimplifyNegativeRatio<n, PROD_S( A, B )> { };
48 
49  // n / ( m * a ) = (n/m) * a
50  /* WRONG!!
51  RATIO_RULE(TYPN2T1, NUM(n), PROD_S(NUM(m), A), \
52  PROD(FRACT(n, m), A), (fract<n, m>() * _2._2));
53  */
54  // ( a / b ) / c = a / ( b * c )
55  RATIO_RULE(TYPT3, RATIO_S(A, B), C, \
56  RATIO(A, PROD(B, C)), _1._1 / (_1._2 * _2));
57 
58  // ( a / b ) / n = a / ( n * b )
59  RATIO_RULE(TYPN1T2, RATIO_S(A, B), NUM(n), \
60  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), \
64  RATIO(A, PROD(PROD(B, C), D)), _1._1 / (_1._2 * _2));
65 
66  // ( a * b ) / ( c / d ) = ( a * b * d ) / c
67  RATIO_RULE(TYPT4, PROD_S(A, B), RATIO_S(C, D), \
68  RATIO(PROD(PROD(A, B), D), C), (_1 * _2._2) / _2._1);
69 
70  // ( n * a ) / ( m * b ) = ( n/m ) ( a / b )
71  RATIO_RULE(TYPN2T2, PROD_S(NUM(n), A), 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), \
77  RATIO(PROD(A, C), B), (_1 * _2._2) / _2._1);
78 
79  // ( a + b ) / ( c / d ) = ( a + b ) * d / c
80  RATIO_RULE(TYPT4, SUM_S(A, B), RATIO_S(C, D), \
81  RATIO(PROD(SUM(A, B), D), C), (_1 * _2._2) / _2._1);
82 
83  // ( a / b ) / ( c / d )= a * d / ( b * c )
84  RATIO_RULE(TYPT4, RATIO_S(A, B), RATIO_S(C, D), \
85  RATIO(PROD(A, D), PROD(B, C)), \
86  (_1._1 * _2._2) / (_1._2 * _2._1));
87 
88  // ( a + b ) / ( b + a ) = 1
89  template<TYPT2,
90  bool parametric = (Parametric<A>::value == 1) ||
91  (Parametric<B>::value == 1)>
92  struct SimplifyRatioSum {
93  typedef RATIO_S(SUM(A, B), SUM(B, A)) type;
94  COMBINE(SUM(A, B), SUM(B, A), type(_1, _2));
95  };
96 
97  TEMPL(T2) struct SimplifyRatioSum<A, B, false> {
98  typedef NUM(1) type;
99  COMBINE(SUM(A, B), SUM(B, A), num<1>());
100  };
101 
102  TEMPL(T2) struct Ratio<SUM_S(A, B), SUM_S(B, A)> :
103  public SimplifyRatioSum<A, B> { };
104 
105  // a^b / a^c => a^( b - c)
106  template<TYPT3, bool parametric = (Parametric<A>::value == 1)>
107  struct SimplifyPowerRatio {
108  typedef POWER(A, B) arg1;
109  typedef POWER(A, C) arg2;
110  typedef RATIO_S(arg1, arg2) type;
111  COMBINE(arg1, arg2, type(_1, _2));
112  };
113 
114  TEMPL(T3)
115  struct SimplifyPowerRatio<A, B, C, false> {
116  typedef POWER(A, B) arg1;
117  typedef POWER(A, C) arg2;
118  typedef POWER(A, DIFF(B, C)) type;
119  inline static type combine(const arg1& _1, const arg2& _2) {
120  return pow(DecomposePower<A, B>::getBase(_1),
121  (DecomposePower<A, B>::getExp(_1) -
122  DecomposePower<A, C>::getExp(_2))); }
123  };
124 
125  TEMPL(T3) struct Ratio<POWER_S(A, B), POWER_S(A, C)> :
126  public SimplifyPowerRatio<A, B, C> { };
127 
128  TEMPL(T2) struct Ratio<POWER_S(A, B), POWER_S(A, B)> :
129  public SimplifyPowerRatio<A, B, B> { };
130 
131  TEMPL(T2) struct Ratio<A, POWER_S(A, B)> :
132  public SimplifyPowerRatio<A, NUM(1), B> { };
133 
134  TEMPL(N1T1) struct Ratio<A, POWER_S(A, NUM(n))> :
135  public SimplifyPowerRatio<A, NUM(1), NUM(n)> { };
136 
137  TEMPL(T2) struct Ratio<POWER_S(A, B), A> :
138  public SimplifyPowerRatio<A, B, NUM(1)>{ };
139 
140  TEMPL(N1T1) struct Ratio<POWER_S(A, NUM(n)), A> :
141  public SimplifyPowerRatio<A, NUM(n), NUM(1)> { };
142 
143  TEMPL(T1) struct Ratio<A, A> :
144  public SimplifyPowerRatio<A, NUM(1), NUM(1)> { };
145 
146  TEMPL(T2) struct Ratio<PROD_S(A, B), PROD_S(A, B)> :
147  public SimplifyPowerRatio<PROD_S(A, B), NUM(1), NUM(1)> { };
148 
149  TEMPL(N1T1) struct Ratio<PROD_S(NUM(n), A), PROD_S(NUM(n), A)> :
150  public SimplifyPowerRatio<PROD_S(NUM(n), A), NUM(1), NUM(1)> { };
151 
152  RATIO_RULE(TYPN1, NUM(n), NUM(n), NUM(1), num<1>());
153 
154  // simplify ( f * g ) / h
155  // try ( f / h ) * g and ( g / h ) * f, otherwise leave ( f * g ) / h
156 
157  template <typename Prod, bool simplify = Prod::value> struct AuxProductRatio {
158  typedef PROD(typename Prod::AB, typename Prod::C) type;
159  inline static type combine(const typename Prod::A& a,
160  const typename Prod::B& b,
161  const typename Prod::C& c) { return (a / b) * c; }
162  };
163 
164  template<typename Prod> struct AuxProductRatio<Prod, false> {
165  typedef RATIO_S(typename Prod::AB, typename Prod::C) type;
166  inline static type combine(const typename Prod::A& a,
167  const typename Prod::B& b,
168  const typename Prod::C& c) { return type(a * b, c); }
169  };
170 
171  template<typename F, typename G, typename H>
172  struct RatioP1 {
173  struct prod0 {
174  typedef F A; typedef G B; typedef H C;
175  typedef PROD_S(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 g; }
178  inline static const C& c(const F& f, const G& g, const H& h) { return h; }
179  enum { value = false };
180  };
181  struct prod1 {
182  typedef F A; typedef H B; typedef G C;
183  typedef RATIO_S(A, B) base;
184  typedef RATIO(A, B) AB;
185  inline static const A& a(const F& f, const G& g, const H& h) { return f; }
186  inline static const B& b(const F& f, const G& g, const H& h) { return h; }
187  inline static const C& c(const F& f, const G& g, const H& h) { return g; }
188  enum { value = ::boost::type_traits::ice_not<
189  ::boost::is_same<AB, base>::value>::value };
190  };
191  struct prod2 {
192  typedef G A; typedef H B; typedef F C;
193  typedef RATIO_S(A, B) base;
194  typedef RATIO(A, B) AB;
195  inline static const A& a(const F& f, const G& g, const H& h) { return g; }
196  inline static const B& b(const F& f, const G& g, const H& h) { return h; }
197  inline static const C& c(const F& f, const G& g, const H& h) { return f; }
198  enum { value = ::boost::type_traits::ice_not<
199  ::boost::is_same<AB, base>::value>::value };
200  };
201 
202  typedef typename
203  ::boost::mpl::if_<prod1,
204  prod1,
205  typename ::boost::mpl::if_<prod2,
206  prod2,
207  prod0
208  >::type
209  >::type prod;
210  typedef typename AuxProductRatio<prod>::type type;
211  inline static type combine(const PROD_S(F, G)& fg, const H& h) {
212  const F& f = fg._1;
213  const G& g = fg._2;
214  const typename prod::A & a = prod::a(f, g, h);
215  const typename prod::B & b = prod::b(f, g, h);
216  const typename prod::C & c = prod::c(f, g, h);
217  return AuxProductRatio<prod>::combine(a, b, c);
218  }
219  };
220 
221  // simplify c / ( a * b )
222  // try ( c / a ) / b and ( c / b ) / a, otherwise leave c / ( a * b )
223 
224  template <typename Prod, bool simplify = Prod::value>
225  struct AuxProductRatio2 {
226  typedef RATIO(typename Prod::AB, typename Prod::C) type;
227  inline static type combine(const typename Prod::A& a,
228  const typename Prod::B& b,
229  const typename Prod::C& c) { return (b / a) / c; }
230  };
231 
232  template<typename Prod>
233  struct AuxProductRatio2<Prod, false> {
234  typedef RATIO_S(typename Prod::C, typename Prod::AB) type;
235  inline static type combine(const typename Prod::A& a,
236  const typename Prod::B& b,
237  const typename Prod::C& c) { return type(c, a * b); }
238  };
239 
240  template<typename F, typename G, typename H>
241  struct RatioP2 {
242  struct prod0 {
243  typedef F A; typedef G B; typedef H C;
244  typedef PROD_S(A, B) AB;
245  inline static const A& a(const F& f, const G& g, const H& h) { return f; }
246  inline static const B& b(const F& f, const G& g, const H& h) { return g; }
247  inline static const C& c(const F& f, const G& g, const H& h) { return h; }
248  enum { value = false };
249  };
250  struct prod1 {
251  typedef F A; typedef H B; typedef G C;
252  typedef RATIO_S(B, A) base;
253  typedef RATIO(B, A) AB;
254  inline static const A& a(const F& f, const G& g, const H& h) { return f; }
255  inline static const B& b(const F& f, const G& g, const H& h) { return h; }
256  inline static const C& c(const F& f, const G& g, const H& h) { return g; }
257  enum { value = ::boost::type_traits::ice_not<
258  ::boost::is_same<AB, base>::value>::value };
259  };
260  struct prod2 {
261  typedef G A; typedef H B; typedef F C;
262  typedef RATIO_S(B, A) base;
263  typedef RATIO(B, A) AB;
264  inline static const A& a(const F& f, const G& g, const H& h) { return g; }
265  inline static const B& b(const F& f, const G& g, const H& h) { return h; }
266  inline static const C& c(const F& f, const G& g, const H& h) { return f; }
267  enum { value = ::boost::type_traits::ice_not<
268  ::boost::is_same<AB, base>::value>::value };
269  };
270 
271  typedef typename
272  ::boost::mpl::if_<prod1,
273  prod1,
274  typename ::boost::mpl::if_<prod2,
275  prod2,
276  prod0
277  >::type
278  >::type prod;
279  typedef typename AuxProductRatio2<prod>::type type;
280  inline static type combine(const H& h, const PROD_S(F, G)& fg) {
281  const F& f = fg._1;
282  const G& g = fg._2;
283  const typename prod::A & a = prod::a(f, g, h);
284  const typename prod::B & b = prod::b(f, g, h);
285  const typename prod::C & c = prod::c(f, g, h);
286  return AuxProductRatio2<prod>::combine(a, b, c);
287  }
288  };
289 
290  TEMPL(T3) struct Ratio<PROD_S(A, B), C> :
291  public RatioP1<A, B, C> { };
292 
293  TEMPL(N1T2) struct Ratio<PROD_S(A, B), NUM(n)> :
294  public RatioP1<A, B, NUM(n)> { };
295 
296  TEMPL(T3) struct Ratio<C, PROD_S(A, B)> :
297  public RatioP2<A, B, C> { };
298 
299  TEMPL(T4) struct Ratio<PROD_S(C, D), PROD_S(A, B)> :
300  public RatioP2<A, B, PROD_S(C, D)> { };
301 
302  // simplify ( a + b ) / c trying to simplify ( a / c ) and ( b / c )
303  template <TYPT3, bool simplify = false> struct AuxSumRatio {
304  typedef RATIO_S(SUM_S(A, B), C) type;
305  COMBINE(SUM_S(A, B), C, type(_1, _2));
306  };
307 
308  TEMPL(T3) struct AuxSumRatio<A, B, C, true> {
309  typedef SUM(RATIO(A, C), RATIO(B, C)) type;
310  COMBINE(SUM_S(A, B), C, (_1._1 / _2) + (_1._2 / _2));
311  };
312 
313  TEMPL(T3) struct RatioSimpl {
314  struct ratio1 {
315  typedef RATIO_S(A, C) base;
316  typedef RATIO(A, C) type;
317  enum { value = ::boost::type_traits::ice_not<
318  ::boost::is_same<type, base>::value>::value };
319  };
320  struct ratio2 {
321  typedef RATIO_S(B, C) base;
322  typedef RATIO(B, C) type;
323  enum { value = ::boost::type_traits::ice_not<
324  ::boost::is_same<type, base>::value>::value };
325  };
326  typedef AuxSumRatio<A, B, C,
327  ::boost::type_traits::ice_or<ratio1::value, ratio2::value>::value> aux;
328  typedef typename aux::type type;
329  COMBINE(SUM_S(A, B), C, aux::combine(_1, _2));
330  };
331 
332  TEMPL(T3) struct Ratio<SUM_S(A, B), C> :
333  public RatioSimpl<A, B, C> { };
334 
335  TEMPL(T4) struct Ratio<SUM_S(A, B), PROD_S(C, D)> :
336  public RatioSimpl<A, B, PROD_S(C, D)> { };
337 
338  TEMPL(N1T2) struct Ratio<SUM_S(A, B), NUM(n)> :
339  public RatioSimpl<A, B, NUM(n)> { };
340 
341 }
342 
343 #include "PhysicsTools/Utilities/interface/Simplify_end.h"
344 
345 #endif
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