/ src / minisketch / src / lintrans.h
lintrans.h
  1  /**********************************************************************
  2   * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
  3   * Distributed under the MIT software license, see the accompanying   *
  4   * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
  5   **********************************************************************/
  6  
  7  #ifndef _MINISKETCH_LINTRANS_H_
  8  #define _MINISKETCH_LINTRANS_H_
  9  
 10  #include "int_utils.h"
 11  
 12  /** A type to represent integers in the type system. */
 13  template<int N> struct Num {};
 14  
 15  /** A Linear N-bit transformation over the field I. */
 16  template<typename I, int N> class LinTrans {
 17  private:
 18      I table[1 << N];
 19  public:
 20      LinTrans() = default;
 21  
 22      /* Construct a transformation over 3 to 8 bits, using the images of each bit. */
 23      constexpr LinTrans(I a, I b) : table{I(0), I(a), I(b), I(a ^ b)} {}
 24      constexpr LinTrans(I a, I b, I c) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c)} {}
 25      constexpr LinTrans(I a, I b, I c, I d) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d)} {}
 26      constexpr LinTrans(I a, I b, I c, I d, I e) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d), I(e), I(a ^ e), I(b ^ e), I(a ^ b ^ e), I(c ^ e), I(a ^ c ^ e), I(b ^ c ^ e), I(a ^ b ^ c ^ e), I(d ^ e), I(a ^ d ^ e), I(b ^ d ^ e), I(a ^ b ^ d ^ e), I(c ^ d ^ e), I(a ^ c ^ d ^ e), I(b ^ c ^ d ^ e), I(a ^ b ^ c ^ d ^ e)} {}
 27      constexpr LinTrans(I a, I b, I c, I d, I e, I f) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d), I(e), I(a ^ e), I(b ^ e), I(a ^ b ^ e), I(c ^ e), I(a ^ c ^ e), I(b ^ c ^ e), I(a ^ b ^ c ^ e), I(d ^ e), I(a ^ d ^ e), I(b ^ d ^ e), I(a ^ b ^ d ^ e), I(c ^ d ^ e), I(a ^ c ^ d ^ e), I(b ^ c ^ d ^ e), I(a ^ b ^ c ^ d ^ e), I(f), I(a ^ f), I(b^ f), I(a ^ b ^ f), I(c^ f), I(a ^ c ^ f), I(b ^ c ^ f), I(a ^ b ^ c ^ f), I(d ^ f), I(a ^ d ^ f), I(b ^ d ^ f), I(a ^ b ^ d ^ f), I(c ^ d ^ f), I(a ^ c ^ d ^ f), I(b ^ c ^ d ^ f), I(a ^ b ^ c ^ d ^ f), I(e ^ f), I(a ^ e ^ f), I(b ^ e ^ f), I(a ^ b ^ e ^ f), I(c ^ e ^ f), I(a ^ c ^ e ^ f), I(b ^ c ^ e ^ f), I(a ^ b ^ c ^ e ^ f), I(d ^ e ^ f), I(a ^ d ^ e ^ f), I(b ^ d ^ e ^ f), I(a ^ b ^ d ^ e ^ f), I(c ^ d ^ e ^ f), I(a ^ c ^ d ^ e ^ f), I(b ^ c ^ d ^ e ^ f), I(a ^ b ^ c ^ d ^ e ^ f)} {}
 28      constexpr LinTrans(I a, I b, I c, I d, I e, I f, I g) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d), I(e), I(a ^ e), I(b ^ e), I(a ^ b ^ e), I(c ^ e), I(a ^ c ^ e), I(b ^ c ^ e), I(a ^ b ^ c ^ e), I(d ^ e), I(a ^ d ^ e), I(b ^ d ^ e), I(a ^ b ^ d ^ e), I(c ^ d ^ e), I(a ^ c ^ d ^ e), I(b ^ c ^ d ^ e), I(a ^ b ^ c ^ d ^ e), I(f), I(a ^ f), I(b^ f), I(a ^ b ^ f), I(c^ f), I(a ^ c ^ f), I(b ^ c ^ f), I(a ^ b ^ c ^ f), I(d ^ f), I(a ^ d ^ f), I(b ^ d ^ f), I(a ^ b ^ d ^ f), I(c ^ d ^ f), I(a ^ c ^ d ^ f), I(b ^ c ^ d ^ f), I(a ^ b ^ c ^ d ^ f), I(e ^ f), I(a ^ e ^ f), I(b ^ e ^ f), I(a ^ b ^ e ^ f), I(c ^ e ^ f), I(a ^ c ^ e ^ f), I(b ^ c ^ e ^ f), I(a ^ b ^ c ^ e ^ f), I(d ^ e ^ f), I(a ^ d ^ e ^ f), I(b ^ d ^ e ^ f), I(a ^ b ^ d ^ e ^ f), I(c ^ d ^ e ^ f), I(a ^ c ^ d ^ e ^ f), I(b ^ c ^ d ^ e ^ f), I(a ^ b ^ c ^ d ^ e ^ f), I(g), I(a ^ g), I(b ^ g), I(a ^ b ^ g), I(c ^ g), I(a ^ c ^ g), I(b ^ c ^ g), I(a ^ b ^ c ^ g), I(d ^ g), I(a ^ d ^ g), I(b ^ d ^ g), I(a ^ b ^ d ^ g), I(c ^ d ^ g), I(a ^ c ^ d ^ g), I(b ^ c ^ d ^ g), I(a ^ b ^ c ^ d ^ g), I(e ^ g), I(a ^ e ^ g), I(b ^ e ^ g), I(a ^ b ^ e ^ g), I(c ^ e ^ g), I(a ^ c ^ e ^ g), I(b ^ c ^ e ^ g), I(a ^ b ^ c ^ e ^ g), I(d ^ e ^ g), I(a ^ d ^ e ^ g), I(b ^ d ^ e ^ g), I(a ^ b ^ d ^ e ^ g), I(c ^ d ^ e ^ g), I(a ^ c ^ d ^ e ^ g), I(b ^ c ^ d ^ e ^ g), I(a ^ b ^ c ^ d ^ e ^ g), I(f ^ g), I(a ^ f ^ g), I(b^ f ^ g), I(a ^ b ^ f ^ g), I(c^ f ^ g), I(a ^ c ^ f ^ g), I(b ^ c ^ f ^ g), I(a ^ b ^ c ^ f ^ g), I(d ^ f ^ g), I(a ^ d ^ f ^ g), I(b ^ d ^ f ^ g), I(a ^ b ^ d ^ f ^ g), I(c ^ d ^ f ^ g), I(a ^ c ^ d ^ f ^ g), I(b ^ c ^ d ^ f ^ g), I(a ^ b ^ c ^ d ^ f ^ g), I(e ^ f ^ g), I(a ^ e ^ f ^ g), I(b ^ e ^ f ^ g), I(a ^ b ^ e ^ f ^ g), I(c ^ e ^ f ^ g), I(a ^ c ^ e ^ f ^ g), I(b ^ c ^ e ^ f ^ g), I(a ^ b ^ c ^ e ^ f ^ g), I(d ^ e ^ f ^ g), I(a ^ d ^ e ^ f ^ g), I(b ^ d ^ e ^ f ^ g), I(a ^ b ^ d ^ e ^ f ^ g), I(c ^ d ^ e ^ f ^ g), I(a ^ c ^ d ^ e ^ f ^ g), I(b ^ c ^ d ^ e ^ f ^ g), I(a ^ b ^ c ^ d ^ e ^ f ^ g)} {}
 29      constexpr LinTrans(I a, I b, I c, I d, I e, I f, I g, I h) : table{I(0), I(a), I(b), I(a ^ b), I(c), I(a ^ c), I(b ^ c), I(a ^ b ^ c), I(d), I(a ^ d), I(b ^ d), I(a ^ b ^ d), I(c ^ d), I(a ^ c ^ d), I(b ^ c ^ d), I(a ^ b ^ c ^ d), I(e), I(a ^ e), I(b ^ e), I(a ^ b ^ e), I(c ^ e), I(a ^ c ^ e), I(b ^ c ^ e), I(a ^ b ^ c ^ e), I(d ^ e), I(a ^ d ^ e), I(b ^ d ^ e), I(a ^ b ^ d ^ e), I(c ^ d ^ e), I(a ^ c ^ d ^ e), I(b ^ c ^ d ^ e), I(a ^ b ^ c ^ d ^ e), I(f), I(a ^ f), I(b^ f), I(a ^ b ^ f), I(c^ f), I(a ^ c ^ f), I(b ^ c ^ f), I(a ^ b ^ c ^ f), I(d ^ f), I(a ^ d ^ f), I(b ^ d ^ f), I(a ^ b ^ d ^ f), I(c ^ d ^ f), I(a ^ c ^ d ^ f), I(b ^ c ^ d ^ f), I(a ^ b ^ c ^ d ^ f), I(e ^ f), I(a ^ e ^ f), I(b ^ e ^ f), I(a ^ b ^ e ^ f), I(c ^ e ^ f), I(a ^ c ^ e ^ f), I(b ^ c ^ e ^ f), I(a ^ b ^ c ^ e ^ f), I(d ^ e ^ f), I(a ^ d ^ e ^ f), I(b ^ d ^ e ^ f), I(a ^ b ^ d ^ e ^ f), I(c ^ d ^ e ^ f), I(a ^ c ^ d ^ e ^ f), I(b ^ c ^ d ^ e ^ f), I(a ^ b ^ c ^ d ^ e ^ f), I(g), I(a ^ g), I(b ^ g), I(a ^ b ^ g), I(c ^ g), I(a ^ c ^ g), I(b ^ c ^ g), I(a ^ b ^ c ^ g), I(d ^ g), I(a ^ d ^ g), I(b ^ d ^ g), I(a ^ b ^ d ^ g), I(c ^ d ^ g), I(a ^ c ^ d ^ g), I(b ^ c ^ d ^ g), I(a ^ b ^ c ^ d ^ g), I(e ^ g), I(a ^ e ^ g), I(b ^ e ^ g), I(a ^ b ^ e ^ g), I(c ^ e ^ g), I(a ^ c ^ e ^ g), I(b ^ c ^ e ^ g), I(a ^ b ^ c ^ e ^ g), I(d ^ e ^ g), I(a ^ d ^ e ^ g), I(b ^ d ^ e ^ g), I(a ^ b ^ d ^ e ^ g), I(c ^ d ^ e ^ g), I(a ^ c ^ d ^ e ^ g), I(b ^ c ^ d ^ e ^ g), I(a ^ b ^ c ^ d ^ e ^ g), I(f ^ g), I(a ^ f ^ g), I(b^ f ^ g), I(a ^ b ^ f ^ g), I(c^ f ^ g), I(a ^ c ^ f ^ g), I(b ^ c ^ f ^ g), I(a ^ b ^ c ^ f ^ g), I(d ^ f ^ g), I(a ^ d ^ f ^ g), I(b ^ d ^ f ^ g), I(a ^ b ^ d ^ f ^ g), I(c ^ d ^ f ^ g), I(a ^ c ^ d ^ f ^ g), I(b ^ c ^ d ^ f ^ g), I(a ^ b ^ c ^ d ^ f ^ g), I(e ^ f ^ g), I(a ^ e ^ f ^ g), I(b ^ e ^ f ^ g), I(a ^ b ^ e ^ f ^ g), I(c ^ e ^ f ^ g), I(a ^ c ^ e ^ f ^ g), I(b ^ c ^ e ^ f ^ g), I(a ^ b ^ c ^ e ^ f ^ g), I(d ^ e ^ f ^ g), I(a ^ d ^ e ^ f ^ g), I(b ^ d ^ e ^ f ^ g), I(a ^ b ^ d ^ e ^ f ^ g), I(c ^ d ^ e ^ f ^ g), I(a ^ c ^ d ^ e ^ f ^ g), I(b ^ c ^ d ^ e ^ f ^ g), I(a ^ b ^ c ^ d ^ e ^ f ^ g), I(h), I(a ^ h), I(b ^ h), I(a ^ b ^ h), I(c ^ h), I(a ^ c ^ h), I(b ^ c ^ h), I(a ^ b ^ c ^ h), I(d ^ h), I(a ^ d ^ h), I(b ^ d ^ h), I(a ^ b ^ d ^ h), I(c ^ d ^ h), I(a ^ c ^ d ^ h), I(b ^ c ^ d ^ h), I(a ^ b ^ c ^ d ^ h), I(e ^ h), I(a ^ e ^ h), I(b ^ e ^ h), I(a ^ b ^ e ^ h), I(c ^ e ^ h), I(a ^ c ^ e ^ h), I(b ^ c ^ e ^ h), I(a ^ b ^ c ^ e ^ h), I(d ^ e ^ h), I(a ^ d ^ e ^ h), I(b ^ d ^ e ^ h), I(a ^ b ^ d ^ e ^ h), I(c ^ d ^ e ^ h), I(a ^ c ^ d ^ e ^ h), I(b ^ c ^ d ^ e ^ h), I(a ^ b ^ c ^ d ^ e ^ h), I(f ^ h), I(a ^ f ^ h), I(b^ f ^ h), I(a ^ b ^ f ^ h), I(c^ f ^ h), I(a ^ c ^ f ^ h), I(b ^ c ^ f ^ h), I(a ^ b ^ c ^ f ^ h), I(d ^ f ^ h), I(a ^ d ^ f ^ h), I(b ^ d ^ f ^ h), I(a ^ b ^ d ^ f ^ h), I(c ^ d ^ f ^ h), I(a ^ c ^ d ^ f ^ h), I(b ^ c ^ d ^ f ^ h), I(a ^ b ^ c ^ d ^ f ^ h), I(e ^ f ^ h), I(a ^ e ^ f ^ h), I(b ^ e ^ f ^ h), I(a ^ b ^ e ^ f ^ h), I(c ^ e ^ f ^ h), I(a ^ c ^ e ^ f ^ h), I(b ^ c ^ e ^ f ^ h), I(a ^ b ^ c ^ e ^ f ^ h), I(d ^ e ^ f ^ h), I(a ^ d ^ e ^ f ^ h), I(b ^ d ^ e ^ f ^ h), I(a ^ b ^ d ^ e ^ f ^ h), I(c ^ d ^ e ^ f ^ h), I(a ^ c ^ d ^ e ^ f ^ h), I(b ^ c ^ d ^ e ^ f ^ h), I(a ^ b ^ c ^ d ^ e ^ f ^ h), I(g ^ h), I(a ^ g ^ h), I(b ^ g ^ h), I(a ^ b ^ g ^ h), I(c ^ g ^ h), I(a ^ c ^ g ^ h), I(b ^ c ^ g ^ h), I(a ^ b ^ c ^ g ^ h), I(d ^ g ^ h), I(a ^ d ^ g ^ h), I(b ^ d ^ g ^ h), I(a ^ b ^ d ^ g ^ h), I(c ^ d ^ g ^ h), I(a ^ c ^ d ^ g ^ h), I(b ^ c ^ d ^ g ^ h), I(a ^ b ^ c ^ d ^ g ^ h), I(e ^ g ^ h), I(a ^ e ^ g ^ h), I(b ^ e ^ g ^ h), I(a ^ b ^ e ^ g ^ h), I(c ^ e ^ g ^ h), I(a ^ c ^ e ^ g ^ h), I(b ^ c ^ e ^ g ^ h), I(a ^ b ^ c ^ e ^ g ^ h), I(d ^ e ^ g ^ h), I(a ^ d ^ e ^ g ^ h), I(b ^ d ^ e ^ g ^ h), I(a ^ b ^ d ^ e ^ g ^ h), I(c ^ d ^ e ^ g ^ h), I(a ^ c ^ d ^ e ^ g ^ h), I(b ^ c ^ d ^ e ^ g ^ h), I(a ^ b ^ c ^ d ^ e ^ g ^ h), I(f ^ g ^ h), I(a ^ f ^ g ^ h), I(b^ f ^ g ^ h), I(a ^ b ^ f ^ g ^ h), I(c^ f ^ g ^ h), I(a ^ c ^ f ^ g ^ h), I(b ^ c ^ f ^ g ^ h), I(a ^ b ^ c ^ f ^ g ^ h), I(d ^ f ^ g ^ h), I(a ^ d ^ f ^ g ^ h), I(b ^ d ^ f ^ g ^ h), I(a ^ b ^ d ^ f ^ g ^ h), I(c ^ d ^ f ^ g ^ h), I(a ^ c ^ d ^ f ^ g ^ h), I(b ^ c ^ d ^ f ^ g ^ h), I(a ^ b ^ c ^ d ^ f ^ g ^ h), I(e ^ f ^ g ^ h), I(a ^ e ^ f ^ g ^ h), I(b ^ e ^ f ^ g ^ h), I(a ^ b ^ e ^ f ^ g ^ h), I(c ^ e ^ f ^ g ^ h), I(a ^ c ^ e ^ f ^ g ^ h), I(b ^ c ^ e ^ f ^ g ^ h), I(a ^ b ^ c ^ e ^ f ^ g ^ h), I(d ^ e ^ f ^ g ^ h), I(a ^ d ^ e ^ f ^ g ^ h), I(b ^ d ^ e ^ f ^ g ^ h), I(a ^ b ^ d ^ e ^ f ^ g ^ h), I(c ^ d ^ e ^ f ^ g ^ h), I(a ^ c ^ d ^ e ^ f ^ g ^ h), I(b ^ c ^ d ^ e ^ f ^ g ^ h), I(a ^ b ^ c ^ d ^ e ^ f ^ g ^ h)} {}
 30  
 31      /* Construct a transformation over 3 to 8 bits, using a pointer to the bit's images. */
 32      constexpr LinTrans(const I* p, Num<2>) : LinTrans(I(p[0]), I(p[1])) {}
 33      constexpr LinTrans(const I* p, Num<3>) : LinTrans(I(p[0]), I(p[1]), I(p[2])) {}
 34      constexpr LinTrans(const I* p, Num<4>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3])) {}
 35      constexpr LinTrans(const I* p, Num<5>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3]), I(p[4])) {}
 36      constexpr LinTrans(const I* p, Num<6>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3]), I(p[4]), I(p[5])) {}
 37      constexpr LinTrans(const I* p, Num<7>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3]), I(p[4]), I(p[5]), I(p[6])) {}
 38      constexpr LinTrans(const I* p, Num<8>) : LinTrans(I(p[0]), I(p[1]), I(p[2]), I(p[3]), I(p[4]), I(p[5]), I(p[6]), I(p[7])) {}
 39  
 40      template<I (*F)(const I&)>
 41      inline I Build(Num<1>, I a)
 42      {
 43          table[0] = I(); table[1] = a;
 44          return a;
 45      }
 46  
 47      template<I (*F)(const I&)>
 48      inline I Build(Num<2>, I a)
 49      {
 50          I b = F(a);
 51          table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b;
 52          return b;
 53      }
 54  
 55      template<I (*F)(const I&)>
 56      inline I Build(Num<3>, I a)
 57      {
 58          I b = F(a), c = F(b);
 59          table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b; table[4] = c; table[5] = a ^ c; table[6] = b ^ c; table[7] = a ^ b ^ c;
 60          return c;
 61      }
 62  
 63      template<I (*F)(const I&)>
 64      inline I Build(Num<4>, I a)
 65      {
 66          I b = F(a), c = F(b), d = F(c);
 67          table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b; table[4] = c; table[5] = a ^ c; table[6] = b ^ c; table[7] = a ^ b ^ c;
 68          table[8] = d; table[9] = a ^ d; table[10] = b ^ d; table[11] = a ^ b ^ d; table[12] = c ^ d; table[13] = a ^ c ^ d; table[14] = b ^ c ^ d; table[15] = a ^ b ^ c ^ d;
 69          return d;
 70      }
 71  
 72      template<I (*F)(const I&)>
 73      inline I Build(Num<5>, I a)
 74      {
 75          I b = F(a), c = F(b), d = F(c), e = F(d);
 76          table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b; table[4] = c; table[5] = a ^ c; table[6] = b ^ c; table[7] = a ^ b ^ c;
 77          table[8] = d; table[9] = a ^ d; table[10] = b ^ d; table[11] = a ^ b ^ d; table[12] = c ^ d; table[13] = a ^ c ^ d; table[14] = b ^ c ^ d; table[15] = a ^ b ^ c ^ d;
 78          table[16] = e; table[17] = a ^ e; table[18] = b ^ e; table[19] = a ^ b ^ e; table[20] = c ^ e; table[21] = a ^ c ^ e; table[22] = b ^ c ^ e; table[23] = a ^ b ^ c ^ e;
 79          table[24] = d ^ e; table[25] = a ^ d ^ e; table[26] = b ^ d ^ e; table[27] = a ^ b ^ d ^ e; table[28] = c ^ d ^ e; table[29] = a ^ c ^ d ^ e; table[30] = b ^ c ^ d ^ e; table[31] = a ^ b ^ c ^ d ^ e;
 80          return e;
 81      }
 82  
 83      template<I (*F)(const I&)>
 84      inline I Build(Num<6>, I a)
 85      {
 86          I b = F(a), c = F(b), d = F(c), e = F(d), f = F(e);
 87          table[0] = I(); table[1] = a; table[2] = b; table[3] = a ^ b; table[4] = c; table[5] = a ^ c; table[6] = b ^ c; table[7] = a ^ b ^ c;
 88          table[8] = d; table[9] = a ^ d; table[10] = b ^ d; table[11] = a ^ b ^ d; table[12] = c ^ d; table[13] = a ^ c ^ d; table[14] = b ^ c ^ d; table[15] = a ^ b ^ c ^ d;
 89          table[16] = e; table[17] = a ^ e; table[18] = b ^ e; table[19] = a ^ b ^ e; table[20] = c ^ e; table[21] = a ^ c ^ e; table[22] = b ^ c ^ e; table[23] = a ^ b ^ c ^ e;
 90          table[24] = d ^ e; table[25] = a ^ d ^ e; table[26] = b ^ d ^ e; table[27] = a ^ b ^ d ^ e; table[28] = c ^ d ^ e; table[29] = a ^ c ^ d ^ e; table[30] = b ^ c ^ d ^ e; table[31] = a ^ b ^ c ^ d ^ e;
 91          table[32] = f; table[33] = a ^ f; table[34] = b ^ f; table[35] = a ^ b ^ f; table[36] = c ^ f; table[37] = a ^ c ^ f; table[38] = b ^ c ^ f; table[39] = a ^ b ^ c ^ f;
 92          table[40] = d ^ f; table[41] = a ^ d ^ f; table[42] = b ^ d ^ f; table[43] = a ^ b ^ d ^ f; table[44] = c ^ d ^ f; table[45] = a ^ c ^ d ^ f; table[46] = b ^ c ^ d ^ f; table[47] = a ^ b ^ c ^ d ^ f;
 93          table[48] = e ^ f; table[49] = a ^ e ^ f; table[50] = b ^ e ^ f; table[51] = a ^ b ^ e ^ f; table[52] = c ^ e ^ f; table[53] = a ^ c ^ e ^ f; table[54] = b ^ c ^ e ^ f; table[55] = a ^ b ^ c ^ e ^ f;
 94          table[56] = d ^ e ^ f; table[57] = a ^ d ^ e ^ f; table[58] = b ^ d ^ e ^ f; table[59] = a ^ b ^ d ^ e ^ f; table[60] = c ^ d ^ e ^ f; table[61] = a ^ c ^ d ^ e ^ f; table[62] = b ^ c ^ d ^ e ^ f; table[63] = a ^ b ^ c ^ d ^ e ^ f;
 95          return f;
 96      }
 97  
 98      template<typename O, int P>
 99      inline I constexpr Map(I a) const { return table[O::template MidBits<P, N>(a)]; }
100  
101      template<typename O, int P>
102      inline I constexpr TopMap(I a) const { static_assert(P + N == O::SIZE, "TopMap inconsistency"); return table[O::template TopBits<N>(a)]; }
103  };
104  
105  
106  /** A linear transformation constructed using LinTrans tables for sections of bits. */
107  template<typename I, int... N> class RecLinTrans;
108  
109  template<typename I, int N> class RecLinTrans<I, N> {
110      LinTrans<I, N> trans;
111  public:
112      static constexpr int BITS = N;
113      constexpr RecLinTrans(const I* p, Num<BITS>) : trans(p, Num<N>()) {}
114      constexpr RecLinTrans() = default;
115      constexpr RecLinTrans(const I (&init)[BITS]) : RecLinTrans(init, Num<BITS>()) {}
116  
117      template<typename O, int P = 0>
118      inline I constexpr Map(I a) const { return trans.template TopMap<O, P>(a); }
119  
120      template<I (*F)(const I&)>
121      inline void Build(I a) { trans.template Build<F>(Num<N>(), a); }
122  };
123  
124  template<typename I, int N, int... X> class RecLinTrans<I, N, X...> {
125      LinTrans<I, N> trans;
126      RecLinTrans<I, X...> rec;
127  public:
128      static constexpr int BITS = RecLinTrans<I, X...>::BITS + N;
129      constexpr RecLinTrans(const I* p, Num<BITS>) : trans(p, Num<N>()), rec(p + N, Num<BITS - N>()) {}
130      constexpr RecLinTrans() = default;
131      constexpr RecLinTrans(const I (&init)[BITS]) : RecLinTrans(init, Num<BITS>()) {}
132  
133      template<typename O, int P = 0>
134      inline I constexpr Map(I a) const { return trans.template Map<O, P>(a) ^ rec.template Map<O, P + N>(a); }
135  
136      template<I (*F)(const I&)>
137      inline void Build(I a) { I n = trans.template Build<F>(Num<N>(), a); rec.template Build<F>(F(n)); }
138  };
139  
140  /** The identity transformation. */
141  class IdTrans {
142  public:
143      template<typename O, typename I>
144      inline I constexpr Map(I a) const { return a; }
145  };
146  
147  /** A singleton for the identity transformation. */
148  constexpr IdTrans ID_TRANS{};
149  
150  #endif