scalar_multiplication.hpp

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// === AUDIT STATUS ===
// internal:    { status: Planned, auditors: [Sergei], commit: }
// external_1:  { status: not started, auditors: [], commit: }
// external_2:  { status: not started, auditors: [], commit: }
// =====================
 
#pragma once
#include "barretenberg/ecc/groups/precomputed_generators_bn254_impl.hpp"
#include "barretenberg/ecc/groups/precomputed_generators_grumpkin_impl.hpp"
 
#include "barretenberg/ecc/curves/bn254/bn254.hpp"
#include "barretenberg/ecc/curves/grumpkin/grumpkin.hpp"
#include "barretenberg/polynomials/polynomial.hpp"
 
#include "./bitvector.hpp"
#include "./process_buckets.hpp"
namespace bb::scalar_multiplication {
 
template <typename Curve> class MSM {
  public:
    using Element = typename Curve::Element;
    using ScalarField = typename Curve::ScalarField;
    using BaseField = typename Curve::BaseField;
    using AffineElement = typename Curve::AffineElement;
 
    static constexpr size_t NUM_BITS_IN_FIELD = ScalarField::modulus.get_msb() + 1;
 
    // ======================= Algorithm Tuning Constants =======================
    //
    // These constants control the behavior of the Pippenger MSM algorithm.
    // They are empirically tuned for performance on typical hardware.
 
    // Below this threshold, use naive scalar multiplication instead of Pippenger
    static constexpr size_t PIPPENGER_THRESHOLD = 16;
 
    // Below this threshold, the affine batch inversion trick is not beneficial
    // (cost of inversions exceeds savings from cheaper affine additions)
    static constexpr size_t AFFINE_TRICK_THRESHOLD = 128;
 
    // Maximum bits per scalar slice (2^20 = 1M buckets, far beyond practical use)
    static constexpr size_t MAX_SLICE_BITS = 20;
 
    // Number of points to look ahead for memory prefetching
    static constexpr size_t PREFETCH_LOOKAHEAD = 32;
 
    // Prefetch every N iterations (must be power of 2); mask is N-1 for efficient modulo
    static constexpr size_t PREFETCH_INTERVAL = 16;
    static constexpr size_t PREFETCH_INTERVAL_MASK = PREFETCH_INTERVAL - 1;
 
    // ======================= Cost Model Constants =======================
    //
    // These constants define the relative costs of various operations,
    // used to decide between algorithm variants.
 
    // Cost of bucket accumulation relative to a single point addition
    // (2 Jacobian adds per bucket, each ~2.5x cost of affine add)
    static constexpr size_t BUCKET_ACCUMULATION_COST = 5;
 
    // Field multiplications saved per group operation when using affine trick
    static constexpr size_t AFFINE_TRICK_SAVINGS_PER_OP = 5;
 
    // Extra cost of Jacobian group operation when Z coordinate != 1
    static constexpr size_t JACOBIAN_Z_NOT_ONE_PENALTY = 5;
 
    // Cost of computing 4-bit lookup table for modular exponentiation (14 muls)
    static constexpr size_t INVERSION_TABLE_COST = 14;
    // ===========================================================================
 
    // Offset generator used in bucket reduction to probabilistically avoid incomplete-addition
    // edge cases in the accumulator. Derived from domain-separated precomputed generators.
    static const AffineElement& get_offset_generator() noexcept
    {
        static const AffineElement offset_generator = []() {
            if constexpr (std::same_as<typename Curve::Group, bb::g1>) {
                return get_precomputed_generators<typename Curve::Group, "ECCVM_OFFSET_GENERATOR", 1>()[0];
            } else {
                return get_precomputed_generators<typename Curve::Group, "DEFAULT_DOMAIN_SEPARATOR", 8>()[0];
            }
        }();
        return offset_generator;
    }
 
    struct MSMWorkUnit {
        size_t batch_msm_index = 0;
        size_t start_index = 0;
        size_t size = 0;
    };
    using ThreadWorkUnits = std::vector<MSMWorkUnit>;
 
    struct MSMData {
        std::span<const ScalarField> scalars;     // Scalars (non-Montgomery form)
        std::span<const AffineElement> points;    // Input points
        std::span<const uint32_t> scalar_indices; // Indices of nonzero scalars
        std::span<uint64_t> point_schedule;       // Scratch space for point scheduling
 
        static MSMData from_work_unit(std::span<std::span<ScalarField>> all_scalars,
                                      std::span<std::span<const AffineElement>> all_points,
                                      const std::vector<std::vector<uint32_t>>& all_indices,
                                      std::span<uint64_t> point_schedule_buffer,
                                      const MSMWorkUnit& work_unit) noexcept
        {
            return MSMData{
                .scalars = all_scalars[work_unit.batch_msm_index],
                .points = all_points[work_unit.batch_msm_index],
                .scalar_indices =
                    std::span<const uint32_t>{ &all_indices[work_unit.batch_msm_index][work_unit.start_index],
                                               work_unit.size },
                .point_schedule = point_schedule_buffer,
            };
        }
    };
 
    struct BucketAccumulators {
        std::vector<AffineElement> buckets;
        BitVector bucket_exists;
 
        BucketAccumulators(size_t num_buckets) noexcept
            : buckets(num_buckets)
            , bucket_exists(num_buckets)
        {}
    };
 
    struct JacobianBucketAccumulators {
        std::vector<Element> buckets;
        BitVector bucket_exists;
 
        JacobianBucketAccumulators(size_t num_buckets) noexcept
            : buckets(num_buckets)
            , bucket_exists(num_buckets)
        {}
    };
    struct AffineAdditionData {
        static constexpr size_t BATCH_SIZE = 2048;
        // when adding affine points, we have an edge case where the number of points in the batch can overflow by 2
        static constexpr size_t BATCH_OVERFLOW_SIZE = 2;
        std::vector<AffineElement> points_to_add;
        std::vector<BaseField> inversion_scratch_space; // Used for Montgomery batch inversion denominators
        std::vector<uint32_t> addition_result_bucket_destinations;
        AffineElement null_location{}; // Dummy write target for branchless conditional moves
 
        AffineAdditionData() noexcept
            : points_to_add(BATCH_SIZE + BATCH_OVERFLOW_SIZE)
            , inversion_scratch_space(BATCH_SIZE + BATCH_OVERFLOW_SIZE)
            , addition_result_bucket_destinations(((BATCH_SIZE + BATCH_OVERFLOW_SIZE) / 2))
        {}
    };
 
    struct PointScheduleEntry {
        uint64_t data;
 
        [[nodiscard]] static constexpr PointScheduleEntry create(uint32_t point_index, uint32_t bucket_index) noexcept
        {
            return { (static_cast<uint64_t>(point_index) << 32) | bucket_index };
        }
        [[nodiscard]] constexpr uint32_t point_index() const noexcept { return static_cast<uint32_t>(data >> 32); }
        [[nodiscard]] constexpr uint32_t bucket_index() const noexcept { return static_cast<uint32_t>(data); }
    };
 
    // ======================= Public Methods =======================
    // See README.md for algorithm details and mathematical derivations.
 
    static AffineElement msm(std::span<const AffineElement> points,
                             PolynomialSpan<const ScalarField> scalars,
                             bool handle_edge_cases = false) noexcept;
 
    static std::vector<AffineElement> batch_multi_scalar_mul(std::span<std::span<const AffineElement>> points,
                                                             std::span<std::span<ScalarField>> scalars,
                                                             bool handle_edge_cases = true) noexcept;
 
    // ======================= Test-Visible Methods =======================
    // Exposed for unit testing; not part of the public API.
 
    static uint32_t get_num_rounds(size_t num_points) noexcept
    {
        const uint32_t bits_per_slice = get_optimal_log_num_buckets(num_points);
        return static_cast<uint32_t>((NUM_BITS_IN_FIELD + bits_per_slice - 1) / bits_per_slice);
    }
 
    static void add_affine_points(AffineElement* points,
                                  const size_t num_points,
                                  typename Curve::BaseField* scratch_space) noexcept;
 
    static uint32_t get_scalar_slice(const ScalarField& scalar, size_t round, size_t slice_size) noexcept;
 
    static uint32_t get_optimal_log_num_buckets(size_t num_points) noexcept;
 
    static void batch_accumulate_points_into_buckets(std::span<const uint64_t> point_schedule,
                                                     std::span<const AffineElement> points,
                                                     AffineAdditionData& affine_data,
                                                     BucketAccumulators& bucket_data) noexcept;
 
    template <typename BucketType> static Element accumulate_buckets(BucketType& bucket_accumulators) noexcept
    {
        auto& buckets = bucket_accumulators.buckets;
        BB_ASSERT_DEBUG(buckets.size() > static_cast<size_t>(0));
        int starting_index = static_cast<int>(buckets.size() - 1);
        Element running_sum;
        bool found_start = false;
        while (!found_start && starting_index > 0) {
            const size_t idx = static_cast<size_t>(starting_index);
            if (bucket_accumulators.bucket_exists.get(idx)) {
 
                running_sum = buckets[idx];
                found_start = true;
            } else {
                starting_index -= 1;
            }
        }
        if (!found_start) {
            return Curve::Group::point_at_infinity;
        }
        BB_ASSERT_DEBUG(starting_index > 0);
        const auto& offset_generator = get_offset_generator();
        Element sum = running_sum + offset_generator;
        for (int i = starting_index - 1; i > 0; --i) {
            size_t idx = static_cast<size_t>(i);
            BB_ASSERT_DEBUG(idx < bucket_accumulators.bucket_exists.size());
            if (bucket_accumulators.bucket_exists.get(idx)) {
                running_sum += buckets[idx];
            }
            sum += running_sum;
        }
        return sum - offset_generator;
    }
 
  private:
    // ======================= Private Implementation =======================
 
    static void transform_scalar_and_get_nonzero_scalar_indices(std::span<ScalarField> scalars,
                                                                std::vector<uint32_t>& nonzero_scalar_indices) noexcept;
 
    static std::vector<ThreadWorkUnits> get_work_units(std::span<std::span<ScalarField>> scalars,
                                                       std::vector<std::vector<uint32_t>>& msm_scalar_indices) noexcept;
 
    static bool use_affine_trick(size_t num_points, size_t num_buckets) noexcept;
 
    static Element jacobian_pippenger_with_transformed_scalars(MSMData& msm_data) noexcept;
 
    static Element affine_pippenger_with_transformed_scalars(MSMData& msm_data) noexcept;
 
    // Helpers for batch_accumulate_points_into_buckets. Inlined for performance.
 
    // Process single point: if bucket has accumulator, pair them for addition; else cache in bucket.
    __attribute__((always_inline)) static void process_single_point(size_t bucket,
                                                                    const AffineElement* point_source,
                                                                    AffineAdditionData& affine_data,
                                                                    BucketAccumulators& bucket_data,
                                                                    size_t& scratch_it,
                                                                    size_t& point_it) noexcept
    {
        bool has_accumulator = bucket_data.bucket_exists.get(bucket);
        if (has_accumulator) {
            affine_data.points_to_add[scratch_it] = *point_source;
            affine_data.points_to_add[scratch_it + 1] = bucket_data.buckets[bucket];
            bucket_data.bucket_exists.set(bucket, false);
            affine_data.addition_result_bucket_destinations[scratch_it >> 1] = static_cast<uint32_t>(bucket);
            scratch_it += 2;
        } else {
            bucket_data.buckets[bucket] = *point_source;
            bucket_data.bucket_exists.set(bucket, true);
        }
        point_it += 1;
    }
 
    // Branchless bucket pair processing. Updates point_it (by 2 if same bucket, else 1) and scratch_it.
    // See README.md "batch_accumulate_points_into_buckets Algorithm" for case analysis.
    __attribute__((always_inline)) static void process_bucket_pair(size_t lhs_bucket,
                                                                   size_t rhs_bucket,
                                                                   const AffineElement* lhs_source,
                                                                   const AffineElement* rhs_source_if_match,
                                                                   AffineAdditionData& affine_data,
                                                                   BucketAccumulators& bucket_data,
                                                                   size_t& scratch_it,
                                                                   size_t& point_it) noexcept
    {
        bool has_bucket_accumulator = bucket_data.bucket_exists.get(lhs_bucket);
        bool buckets_match = lhs_bucket == rhs_bucket;
        bool do_affine_add = buckets_match || has_bucket_accumulator;
 
        const AffineElement* rhs_source = buckets_match ? rhs_source_if_match : &bucket_data.buckets[lhs_bucket];
 
        AffineElement* lhs_destination =
            do_affine_add ? &affine_data.points_to_add[scratch_it] : &bucket_data.buckets[lhs_bucket];
        AffineElement* rhs_destination =
            do_affine_add ? &affine_data.points_to_add[scratch_it + 1] : &affine_data.null_location;
 
        uint32_t& dest_bucket = affine_data.addition_result_bucket_destinations[scratch_it >> 1];
        dest_bucket = do_affine_add ? static_cast<uint32_t>(lhs_bucket) : dest_bucket;
 
        *lhs_destination = *lhs_source;
        *rhs_destination = *rhs_source;
 
        bucket_data.bucket_exists.set(lhs_bucket, (has_bucket_accumulator && buckets_match) || !do_affine_add);
        scratch_it += do_affine_add ? 2 : 0;
        point_it += (do_affine_add && buckets_match) ? 2 : 1;
    }
};
 
template <typename Curve>
typename Curve::Element pippenger(PolynomialSpan<const typename Curve::ScalarField> scalars,
                                  std::span<const typename Curve::AffineElement> points,
                                  bool handle_edge_cases = true) noexcept;
 
template <typename Curve>
typename Curve::Element pippenger_unsafe(PolynomialSpan<const typename Curve::ScalarField> scalars,
                                         std::span<const typename Curve::AffineElement> points) noexcept;
 
extern template class MSM<curve::Grumpkin>;
extern template class MSM<curve::BN254>;
 
} // namespace bb::scalar_multiplication