1  // Copyright (c) The Bitcoin Core developers
  2  // Distributed under the MIT software license, see the accompanying
  3  // file COPYING or http://www.opensource.org/licenses/mit-license.php.
  4  
  5  #ifndef BITCOIN_UTIL_FEEFRAC_H
  6  #define BITCOIN_UTIL_FEEFRAC_H
  7  
  8  #include <span.h>
  9  #include <util/check.h>
 10  
 11  #include <compare>
 12  #include <cstdint>
 13  #include <vector>
 14  
 15  /** Data structure storing a fee and size, ordered by increasing fee/size.
 16   *
 17   * The size of a FeeFrac cannot be zero unless the fee is also zero.
 18   *
 19   * FeeFracs have a total ordering, first by increasing feerate (ratio of fee over size), and then
 20   * by decreasing size. The empty FeeFrac (fee and size both 0) sorts last. So for example, the
 21   * following FeeFracs are in sorted order:
 22   *
 23   * - fee=0 size=1 (feerate 0)
 24   * - fee=1 size=2 (feerate 0.5)
 25   * - fee=2 size=3 (feerate 0.667...)
 26   * - fee=2 size=2 (feerate 1)
 27   * - fee=1 size=1 (feerate 1)
 28   * - fee=3 size=2 (feerate 1.5)
 29   * - fee=2 size=1 (feerate 2)
 30   * - fee=0 size=0 (undefined feerate)
 31   *
 32   * A FeeFrac is considered "better" if it sorts after another, by this ordering. All standard
 33   * comparison operators (<=>, ==, !=, >, <, >=, <=) respect this ordering.
 34   *
 35   * The FeeRateCompare, and >> and << operators only compare feerate and treat equal feerate but
 36   * different size as equivalent. The empty FeeFrac is neither lower or higher in feerate than any
 37   * other.
 38   */
 39  struct FeeFrac
 40  {
 41      /** Helper function for 32*64 signed multiplication, returning an unspecified but totally
 42       *  ordered type. This is a fallback version, separate so it can be tested on platforms where
 43       *  it isn't actually needed. */
 44      static inline std::pair<int64_t, uint32_t> MulFallback(int64_t a, int32_t b) noexcept
 45      {
 46          int64_t low = int64_t{static_cast<uint32_t>(a)} * b;
 47          int64_t high = (a >> 32) * b;
 48          return {high + (low >> 32), static_cast<uint32_t>(low)};
 49      }
 50  
 51      /** Helper function for 96/32 signed division, rounding towards negative infinity (if
 52       *  round_down) or positive infinity (if !round_down). This is a fallback version, separate so
 53       *  that it can be tested on platforms where it isn't actually needed.
 54       *
 55       * The exact behavior with negative n does not really matter, but this implementation chooses
 56       * to be consistent for testability reasons.
 57       *
 58       * The result must fit in an int64_t, and d must be strictly positive. */
 59      static inline int64_t DivFallback(std::pair<int64_t, uint32_t> n, int32_t d, bool round_down) noexcept
 60      {
 61          Assume(d > 0);
 62          // Compute quot_high = n.first / d, so the result becomes
 63          // (n.second + (n.first - quot_high * d) * 2**32) / d + (quot_high * 2**32), or
 64          // (n.second + (n.first % d) * 2**32) / d + (quot_high * 2**32).
 65          int64_t quot_high = n.first / d;
 66          // Evaluate the parenthesized expression above, so the result becomes
 67          // n_low / d + (quot_high * 2**32)
 68          int64_t n_low = ((n.first % d) << 32) + n.second;
 69          // Evaluate the division so the result becomes quot_low + quot_high * 2**32. It is possible
 70          // that the / operator here rounds in the wrong direction (if n_low is not a multiple of
 71          // size, and is (if round_down) negative, or (if !round_down) positive). If so, make a
 72          // correction.
 73          int64_t quot_low = n_low / d;
 74          int32_t mod_low = n_low % d;
 75          quot_low += (mod_low > 0) - (mod_low && round_down);
 76          // Combine and return the result
 77          return (quot_high << 32) + quot_low;
 78      }
 79  
 80  #ifdef __SIZEOF_INT128__
 81      /** Helper function for 32*64 signed multiplication, returning an unspecified but totally
 82       *  ordered type. This is a version relying on __int128. */
 83      static inline __int128 Mul(int64_t a, int32_t b) noexcept
 84      {
 85          return __int128{a} * b;
 86      }
 87  
 88      /** Helper function for 96/32 signed division, rounding towards negative infinity (if
 89       *  round_down), or towards positive infinity (if !round_down). This is a
 90       *  version relying on __int128.
 91       *
 92       * The result must fit in an int64_t, and d must be strictly positive. */
 93      static inline int64_t Div(__int128 n, int32_t d, bool round_down) noexcept
 94      {
 95          Assume(d > 0);
 96          // Compute the division.
 97          int64_t quot = n / d;
 98          int32_t mod = n % d;
 99          // Correct result if the / operator above rounded in the wrong direction.
100          return quot + ((mod > 0) - (mod && round_down));
101      }
102  #else
103      static constexpr auto Mul = MulFallback;
104      static constexpr auto Div = DivFallback;
105  #endif
106  
107      int64_t fee;
108      int32_t size;
109  
110      /** Construct an IsEmpty() FeeFrac. */
111      constexpr inline FeeFrac() noexcept : fee{0}, size{0} {}
112  
113      /** Construct a FeeFrac with specified fee and size. */
114      constexpr inline FeeFrac(int64_t f, int32_t s) noexcept : fee{f}, size{s} {}
115  
116      constexpr inline FeeFrac(const FeeFrac&) noexcept = default;
117      constexpr inline FeeFrac& operator=(const FeeFrac&) noexcept = default;
118  
119      /** Check if this is empty (size and fee are 0). */
120      bool inline IsEmpty() const noexcept {
121          return size == 0;
122      }
123  
124      /** Add fee and size of another FeeFrac to this one. */
125      void inline operator+=(const FeeFrac& other) noexcept
126      {
127          fee += other.fee;
128          size += other.size;
129      }
130  
131      /** Subtract fee and size of another FeeFrac from this one. */
132      void inline operator-=(const FeeFrac& other) noexcept
133      {
134          fee -= other.fee;
135          size -= other.size;
136      }
137  
138      /** Sum fee and size. */
139      friend inline FeeFrac operator+(const FeeFrac& a, const FeeFrac& b) noexcept
140      {
141          return {a.fee + b.fee, a.size + b.size};
142      }
143  
144      /** Subtract both fee and size. */
145      friend inline FeeFrac operator-(const FeeFrac& a, const FeeFrac& b) noexcept
146      {
147          return {a.fee - b.fee, a.size - b.size};
148      }
149  
150      /** Check if two FeeFrac objects are equal (both same fee and same size). */
151      friend inline bool operator==(const FeeFrac& a, const FeeFrac& b) noexcept
152      {
153          return a.fee == b.fee && a.size == b.size;
154      }
155  
156      /** Compare two FeeFracs just by feerate. */
157      friend inline std::weak_ordering FeeRateCompare(const FeeFrac& a, const FeeFrac& b) noexcept
158      {
159          auto cross_a = Mul(a.fee, b.size), cross_b = Mul(b.fee, a.size);
160          return cross_a <=> cross_b;
161      }
162  
163      /** Check if a FeeFrac object has strictly lower feerate than another. */
164      friend inline bool operator<<(const FeeFrac& a, const FeeFrac& b) noexcept
165      {
166          auto cross_a = Mul(a.fee, b.size), cross_b = Mul(b.fee, a.size);
167          return cross_a < cross_b;
168      }
169  
170      /** Check if a FeeFrac object has strictly higher feerate than another. */
171      friend inline bool operator>>(const FeeFrac& a, const FeeFrac& b) noexcept
172      {
173          auto cross_a = Mul(a.fee, b.size), cross_b = Mul(b.fee, a.size);
174          return cross_a > cross_b;
175      }
176  
177      /** Compare two FeeFracs. <, >, <=, and >= are auto-generated from this. */
178      friend inline std::strong_ordering operator<=>(const FeeFrac& a, const FeeFrac& b) noexcept
179      {
180          auto cross_a = Mul(a.fee, b.size), cross_b = Mul(b.fee, a.size);
181          if (cross_a == cross_b) return b.size <=> a.size;
182          return cross_a <=> cross_b;
183      }
184  
185      /** Swap two FeeFracs. */
186      friend inline void swap(FeeFrac& a, FeeFrac& b) noexcept
187      {
188          std::swap(a.fee, b.fee);
189          std::swap(a.size, b.size);
190      }
191  
192      /** Compute the fee for a given size `at_size` using this object's feerate.
193       *
194       * This effectively corresponds to evaluating (this->fee * at_size) / this->size, with the
195       * result rounded towards negative infinity (if RoundDown) or towards positive infinity
196       * (if !RoundDown).
197       *
198       * Requires this->size > 0, at_size >= 0, and that the correct result fits in a int64_t. This
199       * is guaranteed to be the case when 0 <= at_size <= this->size.
200       */
201      template<bool RoundDown>
202      int64_t EvaluateFee(int32_t at_size) const noexcept
203      {
204          Assume(size > 0);
205          Assume(at_size >= 0);
206          if (fee >= 0 && fee < 0x200000000) [[likely]] {
207              // Common case where (this->fee * at_size) is guaranteed to fit in a uint64_t.
208              if constexpr (RoundDown) {
209                  return (uint64_t(fee) * at_size) / uint32_t(size);
210              } else {
211                  return (uint64_t(fee) * at_size + size - 1U) / uint32_t(size);
212              }
213          } else {
214              // Otherwise, use Mul and Div.
215              return Div(Mul(fee, at_size), size, RoundDown);
216          }
217      }
218  
219  public:
220      /** Compute the fee for a given size `at_size` using this object's feerate, rounding down. */
221      int64_t EvaluateFeeDown(int32_t at_size) const noexcept { return EvaluateFee<true>(at_size); }
222      /** Compute the fee for a given size `at_size` using this object's feerate, rounding up. */
223      int64_t EvaluateFeeUp(int32_t at_size) const noexcept { return EvaluateFee<false>(at_size); }
224  };
225  
226  /** Compare the feerate diagrams implied by the provided sorted chunks data.
227   *
228   * The implied diagram for each starts at (0, 0), then contains for each chunk the cumulative fee
229   * and size up to that chunk, and then extends infinitely to the right with a horizontal line.
230   *
231   * The caller must guarantee that the sum of the FeeFracs in either of the chunks' data set do not
232   * overflow (so sum fees < 2^63, and sum sizes < 2^31).
233   */
234  std::partial_ordering CompareChunks(std::span<const FeeFrac> chunks0, std::span<const FeeFrac> chunks1);
235  
236  /** Tagged wrapper around FeeFrac to avoid unit confusion. */
237  template<typename Tag>
238  struct FeePerUnit : public FeeFrac
239  {
240      // Inherit FeeFrac constructors.
241      using FeeFrac::FeeFrac;
242  
243      /** Convert a FeeFrac to a FeePerUnit. */
244      static FeePerUnit FromFeeFrac(const FeeFrac& feefrac) noexcept
245      {
246          return {feefrac.fee, feefrac.size};
247      }
248  };
249  
250  // FeePerUnit instance for satoshi / vbyte.
251  struct VSizeTag {};
252  using FeePerVSize = FeePerUnit<VSizeTag>;
253  
254  // FeePerUnit instance for satoshi / WU.
255  struct WeightTag {};
256  using FeePerWeight = FeePerUnit<WeightTag>;
257  
258  #endif // BITCOIN_UTIL_FEEFRAC_H