Add FeeFrac utils

Co-authored-by: Suhas Daftuar <sdaftuar@chaincode.com>
Co-authored-by: Pieter Wuille <pieter.wuille@gmail.com>

src/Makefile.am

@@ -302,6 +302,7 @@ BITCOIN_CORE_H = \
   util/error.h \
   util/exception.h \
   util/fastrange.h \
+  util/feefrac.h \
   util/fees.h \
   util/fs.h \
   util/fs_helpers.h \
@@ -741,6 +742,7 @@ libbitcoin_util_a_SOURCES = \
   util/check.cpp \
   util/error.cpp \
   util/exception.cpp \
+  util/feefrac.cpp \
   util/fees.cpp \
   util/fs.cpp \
   util/fs_helpers.cpp \
@@ -983,6 +985,7 @@ libbitcoinkernel_la_SOURCES = \
   util/batchpriority.cpp \
   util/chaintype.cpp \
   util/check.cpp \
+  util/feefrac.cpp \
   util/fs.cpp \
   util/fs_helpers.cpp \
   util/hasher.cpp \

src/util/feefrac.cpp

@@ -0,0 +1,86 @@
+// Copyright (c) The Bitcoin Core developers
+// Distributed under the MIT software license, see the accompanying
+// file COPYING or http://www.opensource.org/licenses/mit-license.php.
+
+#include <util/feefrac.h>
+#include <algorithm>
+#include <array>
+#include <vector>
+
+std::vector<FeeFrac> BuildDiagramFromChunks(const Span<const FeeFrac> chunks)
+{
+    std::vector<FeeFrac> diagram;
+    diagram.reserve(chunks.size() + 1);
+
+    diagram.emplace_back(0, 0);
+    for (auto& chunk : chunks) {
+        diagram.emplace_back(diagram.back() + chunk);
+    }
+    return diagram;
+}
+
+std::partial_ordering CompareFeerateDiagram(Span<const FeeFrac> dia0, Span<const FeeFrac> dia1)
+{
+    /** Array to allow indexed access to input diagrams. */
+    const std::array<Span<const FeeFrac>, 2> dias = {dia0, dia1};
+    /** How many elements we have processed in each input. */
+    size_t next_index[2] = {1, 1};
+    /** Whether the corresponding input is strictly better than the other at least in one place. */
+    bool better_somewhere[2] = {false, false};
+    /** Get the first unprocessed point in diagram number dia. */
+    const auto next_point = [&](int dia) { return dias[dia][next_index[dia]]; };
+    /** Get the last processed point in diagram number dia. */
+    const auto prev_point = [&](int dia) { return dias[dia][next_index[dia] - 1]; };
+
+    // Diagrams should be non-empty, and first elements zero in size and fee
+    Assert(!dia0.empty() && !dia1.empty());
+    Assert(prev_point(0).IsEmpty());
+    Assert(prev_point(1).IsEmpty());
+
+    do {
+        bool done_0 = next_index[0] == dias[0].size();
+        bool done_1 = next_index[1] == dias[1].size();
+        if (done_0 && done_1) break;
+
+        // Determine which diagram has the first unprocessed point. If a single side is finished, use the
+        // other one. Only up to one can be done due to check above.
+        const int unproc_side = (done_0 || done_1) ? done_0 : next_point(0).size > next_point(1).size;
+
+        // Let `P` be the next point on diagram unproc_side, and `A` and `B` the previous and next points
+        // on the other diagram. We want to know if P lies above or below the line AB. To determine this, we
+        // compute the slopes of line AB and of line AP, and compare them. These slopes are fee per size,
+        // and can thus be expressed as FeeFracs.
+        const FeeFrac& point_p = next_point(unproc_side);
+        const FeeFrac& point_a = prev_point(!unproc_side);
+
+        // Slope of AP can be negative, unlike AB
+        const auto slope_ap = point_p - point_a;
+        Assume(slope_ap.size > 0);
+        std::weak_ordering cmp = std::weak_ordering::equivalent;
+        if (done_0 || done_1) {
+            // If a single side has no points left, act as if AB has slope tail_feerate(of 0).
+            Assume(!(done_0 && done_1));
+            cmp = FeeRateCompare(slope_ap, FeeFrac(0, 1));
+        } else {
+            // If both sides have points left, compute B, and the slope of AB explicitly.
+            const FeeFrac& point_b = next_point(!unproc_side);
+            const auto slope_ab = point_b - point_a;
+            Assume(slope_ab.size >= slope_ap.size);
+            cmp = FeeRateCompare(slope_ap, slope_ab);
+
+            // If B and P have the same size, B can be marked as processed (in addition to P, see
+            // below), as we've already performed a comparison at this size.
+            if (point_b.size == point_p.size) ++next_index[!unproc_side];
+        }
+        // If P lies above AB, unproc_side is better in P. If P lies below AB, then !unproc_side is
+        // better in P.
+        if (std::is_gt(cmp)) better_somewhere[unproc_side] = true;
+        if (std::is_lt(cmp)) better_somewhere[!unproc_side] = true;
+        ++next_index[unproc_side];
+    } while(true);
+
+    // If both diagrams are better somewhere, they are incomparable.
+    if (better_somewhere[0] && better_somewhere[1]) return std::partial_ordering::unordered;
+    // Otherwise compare the better_somewhere values.
+    return better_somewhere[0] <=> better_somewhere[1];
+}

src/util/feefrac.h

@@ -0,0 +1,160 @@
+// Copyright (c) The Bitcoin Core developers
+// Distributed under the MIT software license, see the accompanying
+// file COPYING or http://www.opensource.org/licenses/mit-license.php.
+
+#ifndef BITCOIN_UTIL_FEEFRAC_H
+#define BITCOIN_UTIL_FEEFRAC_H
+
+#include <stdint.h>
+#include <compare>
+#include <vector>
+#include <span.h>
+#include <util/check.h>
+
+/** Data structure storing a fee and size, ordered by increasing fee/size.
+ *
+ * The size of a FeeFrac cannot be zero unless the fee is also zero.
+ *
+ * FeeFracs have a total ordering, first by increasing feerate (ratio of fee over size), and then
+ * by decreasing size. The empty FeeFrac (fee and size both 0) sorts last. So for example, the
+ * following FeeFracs are in sorted order:
+ *
+ * - fee=0 size=1 (feerate 0)
+ * - fee=1 size=2 (feerate 0.5)
+ * - fee=2 size=3 (feerate 0.667...)
+ * - fee=2 size=2 (feerate 1)
+ * - fee=1 size=1 (feerate 1)
+ * - fee=3 size=2 (feerate 1.5)
+ * - fee=2 size=1 (feerate 2)
+ * - fee=0 size=0 (undefined feerate)
+ *
+ * A FeeFrac is considered "better" if it sorts after another, by this ordering. All standard
+ * comparison operators (<=>, ==, !=, >, <, >=, <=) respect this ordering.
+ *
+ * The CompareFeeFrac, and >> and << operators only compare feerate and treat equal feerate but
+ * different size as equivalent. The empty FeeFrac is neither lower or higher in feerate than any
+ * other.
+ */
+struct FeeFrac
+{
+    /** Fallback version for Mul (see below).
+     *
+     * Separate to permit testing on platforms where it isn't actually needed.
+     */
+    static inline std::pair<int64_t, uint32_t> MulFallback(int64_t a, int32_t b) noexcept
+    {
+        // Otherwise, emulate 96-bit multiplication using two 64-bit multiplies.
+        int64_t low = int64_t{static_cast<uint32_t>(a)} * b;
+        int64_t high = (a >> 32) * b;
+        return {high + (low >> 32), static_cast<uint32_t>(low)};
+    }
+
+    // Compute a * b, returning an unspecified but totally ordered type.
+#ifdef __SIZEOF_INT128__
+    static inline __int128 Mul(int64_t a, int32_t b) noexcept
+    {
+        // If __int128 is available, use 128-bit wide multiply.
+        return __int128{a} * b;
+    }
+#else
+    static constexpr auto Mul = MulFallback;
+#endif
+
+    int64_t fee;
+    int32_t size;
+
+    /** Construct an IsEmpty() FeeFrac. */
+    inline FeeFrac() noexcept : fee{0}, size{0} {}
+
+    /** Construct a FeeFrac with specified fee and size. */
+    inline FeeFrac(int64_t f, int32_t s) noexcept : fee{f}, size{s} {}
+
+    inline FeeFrac(const FeeFrac&) noexcept = default;
+    inline FeeFrac& operator=(const FeeFrac&) noexcept = default;
+
+    /** Check if this is empty (size and fee are 0). */
+    bool inline IsEmpty() const noexcept {
+        return size == 0;
+    }
+
+    /** Add fee and size of another FeeFrac to this one. */
+    void inline operator+=(const FeeFrac& other) noexcept
+    {
+        fee += other.fee;
+        size += other.size;
+    }
+
+    /** Subtract fee and size of another FeeFrac from this one. */
+    void inline operator-=(const FeeFrac& other) noexcept
+    {
+        fee -= other.fee;
+        size -= other.size;
+    }
+
+    /** Sum fee and size. */
+    friend inline FeeFrac operator+(const FeeFrac& a, const FeeFrac& b) noexcept
+    {
+        return {a.fee + b.fee, a.size + b.size};
+    }
+
+    /** Subtract both fee and size. */
+    friend inline FeeFrac operator-(const FeeFrac& a, const FeeFrac& b) noexcept
+    {
+        return {a.fee - b.fee, a.size - b.size};
+    }
+
+    /** Check if two FeeFrac objects are equal (both same fee and same size). */
+    friend inline bool operator==(const FeeFrac& a, const FeeFrac& b) noexcept
+    {
+        return a.fee == b.fee && a.size == b.size;
+    }
+
+    /** Compare two FeeFracs just by feerate. */
+    friend inline std::weak_ordering FeeRateCompare(const FeeFrac& a, const FeeFrac& b) noexcept
+    {
+        auto cross_a = Mul(a.fee, b.size), cross_b = Mul(b.fee, a.size);
+        return cross_a <=> cross_b;
+    }
+
+    /** Check if a FeeFrac object has strictly lower feerate than another. */
+    friend inline bool operator<<(const FeeFrac& a, const FeeFrac& b) noexcept
+    {
+        auto cross_a = Mul(a.fee, b.size), cross_b = Mul(b.fee, a.size);
+        return cross_a < cross_b;
+    }
+
+    /** Check if a FeeFrac object has strictly higher feerate than another. */
+    friend inline bool operator>>(const FeeFrac& a, const FeeFrac& b) noexcept
+    {
+        auto cross_a = Mul(a.fee, b.size), cross_b = Mul(b.fee, a.size);
+        return cross_a > cross_b;
+    }
+
+    /** Compare two FeeFracs. <, >, <=, and >= are auto-generated from this. */
+    friend inline std::strong_ordering operator<=>(const FeeFrac& a, const FeeFrac& b) noexcept
+    {
+        auto cross_a = Mul(a.fee, b.size), cross_b = Mul(b.fee, a.size);
+        if (cross_a == cross_b) return b.size <=> a.size;
+        return cross_a <=> cross_b;
+    }
+
+    /** Swap two FeeFracs. */
+    friend inline void swap(FeeFrac& a, FeeFrac& b) noexcept
+    {
+        std::swap(a.fee, b.fee);
+        std::swap(a.size, b.size);
+    }
+};
+
+/** Takes the pre-computed and topologically-valid chunks and generates a fee diagram which starts at FeeFrac of (0, 0) */
+std::vector<FeeFrac> BuildDiagramFromChunks(Span<const FeeFrac> chunks);
+
+/** Compares two feerate diagrams. The shorter one is implicitly
+ * extended with a horizontal straight line.
+ *
+ * A feerate diagram consists of a list of (fee, size) points with the property that size
+ * is strictly increasing and that the first entry is (0, 0).
+ */
+std::partial_ordering CompareFeerateDiagram(Span<const FeeFrac> dia0, Span<const FeeFrac> dia1);
+
+#endif // BITCOIN_UTIL_FEEFRAC_H