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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 #pragma once
 
 #include "Acts/Seeding/SeedFinder.hpp"
 
 #include <algorithm>
 #include <cmath>
 
 namespace Acts {
 
 template <typename external_space_point_t, typename grid_t, typename platform_t>
 SeedFinder<external_space_point_t, grid_t, platform_t>::SeedFinder(
     const SeedFinderConfig<external_space_point_t>& config,
     std::unique_ptr<const Logger> logger)
     : m_config(config), m_logger(std::move(logger)) {
   if (std::isnan(config.deltaRMaxTopSP)) {
     throw std::runtime_error("Value of deltaRMaxTopSP was not initialised");
   }
   if (std::isnan(config.deltaRMinTopSP)) {
     throw std::runtime_error("Value of deltaRMinTopSP was not initialised");
   }
   if (std::isnan(config.deltaRMaxBottomSP)) {
     throw std::runtime_error("Value of deltaRMaxBottomSP was not initialised");
   }
   if (std::isnan(config.deltaRMinBottomSP)) {
     throw std::runtime_error("Value of deltaRMinBottomSP was not initialised");
   }
 }
 
 template <typename external_space_point_t, typename grid_t, typename platform_t>
 template <typename container_t, GridBinCollection sp_range_t>
   requires CollectionStoresSeedsTo<container_t, external_space_point_t, 3ul>
 void SeedFinder<external_space_point_t, grid_t, platform_t>::
     createSeedsForGroup(const SeedFinderOptions& options, SeedingState& state,
                         const grid_t& grid, container_t& outputCollection,
                         const sp_range_t& bottomSPsIdx,
                         const std::size_t middleSPsIdx,
                         const sp_range_t& topSPsIdx,
                         const Range1D<float>& rMiddleSPRange) const {
   // This is used for seed filtering later
   const std::size_t max_num_seeds_per_spm =
       m_config.seedFilter->getSeedFilterConfig().maxSeedsPerSpMConf;
   const std::size_t max_num_quality_seeds_per_spm =
       m_config.seedFilter->getSeedFilterConfig().maxQualitySeedsPerSpMConf;
 
   state.candidatesCollector.setMaxElements(max_num_seeds_per_spm,
                                            max_num_quality_seeds_per_spm);
 
   // If there are no bottom or top bins, just return and waste no time
   if (bottomSPsIdx.size() == 0 || topSPsIdx.size() == 0) {
     return;
   }
 
   // Get the middle space point candidates
   const std::vector<const external_space_point_t*>& middleSPs =
       grid.at(middleSPsIdx);
   // Return if somehow there are no middle sp candidates
   if (middleSPs.empty()) {
     return;
   }
 
   // neighbours
   // clear previous results
   state.bottomNeighbours.clear();
   state.topNeighbours.clear();
 
   // Fill
   // bottoms
   for (const std::size_t idx : bottomSPsIdx) {
     // Only add an entry if the bin has entries
     if (grid.at(idx).size() == 0) {
       continue;
     }
     state.bottomNeighbours.emplace_back(
         grid, idx, middleSPs.front()->radius() - m_config.deltaRMaxBottomSP);
   }
   // if no bottom candidates, then no need to proceed
   if (state.bottomNeighbours.size() == 0) {
     return;
   }
 
   // tops
   for (const std::size_t idx : topSPsIdx) {
     // Only add an entry if the bin has entries
     if (grid.at(idx).size() == 0) {
       continue;
     }
     state.topNeighbours.emplace_back(
         grid, idx, middleSPs.front()->radius() + m_config.deltaRMinTopSP);
   }
   // if no top candidates, then no need to proceed
   if (state.topNeighbours.size() == 0) {
     return;
   }
 
   // we compute this here since all middle space point candidates belong to the
   // same z-bin
   auto [minRadiusRangeForMiddle, maxRadiusRangeForMiddle] =
       retrieveRadiusRangeForMiddle(*middleSPs.front(), rMiddleSPRange);
   ACTS_VERBOSE("Current global bin: " << middleSPsIdx << ", z value of "
                                       << middleSPs.front()->z());
   ACTS_VERBOSE("Validity range (radius) for the middle space point is ["
                << minRadiusRangeForMiddle << ", " << maxRadiusRangeForMiddle
                << "]");
 
   for (const external_space_point_t* spM : middleSPs) {
     const float rM = spM->radius();
 
     // check if spM is outside our radial region of interest
     if (rM < minRadiusRangeForMiddle) {
       continue;
     }
     if (rM > maxRadiusRangeForMiddle) {
       // break because SPs are sorted in r
       break;
     }
 
     const float zM = spM->z();
     const float uIP = -1 / rM;
     const float cosPhiM = -spM->x() * uIP;
     const float sinPhiM = -spM->y() * uIP;
     const float uIP2 = uIP * uIP;
 
     // Iterate over middle-top dublets
     getCompatibleDoublets<SpacePointCandidateType::eTop>(
         options, grid, state.spacePointMutableData, state.topNeighbours, *spM,
         state.linCircleTop, state.compatTopSP, m_config.deltaRMinTopSP,
         m_config.deltaRMaxTopSP, uIP, uIP2, cosPhiM, sinPhiM);
 
     // no top SP found -> try next spM
     if (state.compatTopSP.empty()) {
       ACTS_VERBOSE("No compatible Tops, moving to next middle candidate");
       continue;
     }
 
     // apply cut on the number of top SP if seedConfirmation is true
     SeedFilterState seedFilterState;
     if (m_config.seedConfirmation) {
       // check if middle SP is in the central or forward region
       SeedConfirmationRangeConfig seedConfRange =
           (zM > m_config.centralSeedConfirmationRange.zMaxSeedConf ||
            zM < m_config.centralSeedConfirmationRange.zMinSeedConf)
               ? m_config.forwardSeedConfirmationRange
               : m_config.centralSeedConfirmationRange;
       // set the minimum number of top SP depending on whether the middle SP is
       // in the central or forward region
       seedFilterState.nTopSeedConf = rM > seedConfRange.rMaxSeedConf
                                          ? seedConfRange.nTopForLargeR
                                          : seedConfRange.nTopForSmallR;
       // set max bottom radius for seed confirmation
       seedFilterState.rMaxSeedConf = seedConfRange.rMaxSeedConf;
       // continue if number of top SPs is smaller than minimum
       if (state.compatTopSP.size() < seedFilterState.nTopSeedConf) {
         ACTS_VERBOSE(
             "Number of top SPs is "
             << state.compatTopSP.size()
             << " and is smaller than minimum, moving to next middle candidate");
         continue;
       }
     }
 
     // Iterate over middle-bottom dublets
     getCompatibleDoublets<SpacePointCandidateType::eBottom>(
         options, grid, state.spacePointMutableData, state.bottomNeighbours,
         *spM, state.linCircleBottom, state.compatBottomSP,
         m_config.deltaRMinBottomSP, m_config.deltaRMaxBottomSP, uIP, uIP2,
         cosPhiM, sinPhiM);
 
     // no bottom SP found -> try next spM
     if (state.compatBottomSP.empty()) {
       ACTS_VERBOSE("No compatible Bottoms, moving to next middle candidate");
       continue;
     }
 
     ACTS_VERBOSE("Candidates: " << state.compatBottomSP.size()
                                 << " bottoms and " << state.compatTopSP.size()
                                 << " tops for middle candidate indexed "
                                 << spM->index());
     // filter candidates
     if (m_config.useDetailedDoubleMeasurementInfo) {
       filterCandidates<DetectorMeasurementInfo::eDetailed>(
           *spM, options, seedFilterState, state);
     } else {
       filterCandidates<DetectorMeasurementInfo::eDefault>(
           *spM, options, seedFilterState, state);
     }
 
     m_config.seedFilter->filterSeeds_1SpFixed(state.spacePointMutableData,
                                               state.candidatesCollector,
                                               outputCollection);
 
   }  // loop on mediums
 }
 
 template <typename external_space_point_t, typename grid_t, typename platform_t>
 template <SpacePointCandidateType candidateType, typename out_range_t>
 inline void
 SeedFinder<external_space_point_t, grid_t, platform_t>::getCompatibleDoublets(
     const SeedFinderOptions& options, const grid_t& grid,
     SpacePointMutableData& mutableData,
     boost::container::small_vector<
         Neighbour<grid_t>, detail::ipow(3, grid_t::DIM)>& otherSPsNeighbours,
     const external_space_point_t& mediumSP,
     std::vector<LinCircle>& linCircleVec, out_range_t& outVec,
     const float deltaRMinSP, const float deltaRMaxSP, const float uIP,
     const float uIP2, const float cosPhiM, const float sinPhiM) const {
   float impactMax = m_config.impactMax;
 
   constexpr bool isBottomCandidate =
       candidateType == SpacePointCandidateType::eBottom;
 
   if constexpr (isBottomCandidate) {
     impactMax = -impactMax;
   }
 
   outVec.clear();
   linCircleVec.clear();
 
   // get number of neighbour SPs
   std::size_t nsp = 0;
   for (const auto& otherSPCol : otherSPsNeighbours) {
     nsp += grid.at(otherSPCol.index).size();
   }
 
   linCircleVec.reserve(nsp);
   outVec.reserve(nsp);
 
   const float rM = mediumSP.radius();
   const float xM = mediumSP.x();
   const float yM = mediumSP.y();
   const float zM = mediumSP.z();
   const float varianceRM = mediumSP.varianceR();
   const float varianceZM = mediumSP.varianceZ();
 
   float vIPAbs = 0;
   if (m_config.interactionPointCut) {
     // equivalent to m_config.impactMax / (rM * rM);
     vIPAbs = impactMax * uIP2;
   }
 
   float deltaR = 0;
   float deltaZ = 0;
 
   const auto outsideRangeCheck = [](const float value, const float min,
                                     const float max) -> bool {
     // intentionally using `|` after profiling. faster due to better branch
     // prediction
     return static_cast<bool>(static_cast<int>(value < min) |
                              static_cast<int>(value > max));
   };
 
   for (auto& otherSPCol : otherSPsNeighbours) {
     const std::vector<const external_space_point_t*>& otherSPs =
         grid.at(otherSPCol.index);
     if (otherSPs.empty()) {
       continue;
     }
 
     // we make a copy of the iterator here since we need it to remain
     // the same in the Neighbour object
     auto min_itr = otherSPCol.itr;
 
     // find the first SP inside the radius region of interest and update
     // the iterator so we don't need to look at the other SPs again
     for (; min_itr != otherSPs.end(); ++min_itr) {
       const external_space_point_t* otherSP = *min_itr;
       if constexpr (candidateType == SpacePointCandidateType::eBottom) {
         // if r-distance is too big, try next SP in bin
         if ((rM - otherSP->radius()) <= deltaRMaxSP) {
           break;
         }
       } else {
         // if r-distance is too small, try next SP in bin
         if ((otherSP->radius() - rM) >= deltaRMinSP) {
           break;
         }
       }
     }
     // We update the iterator in the Neighbour object
     // that mean that we have changed the middle space point
     // and the lower bound has moved accordingly
     otherSPCol.itr = min_itr;
 
     for (; min_itr != otherSPs.end(); ++min_itr) {
       const external_space_point_t* otherSP = *min_itr;
 
       if constexpr (isBottomCandidate) {
         deltaR = (rM - otherSP->radius());
 
         // if r-distance is too small, try next SP in bin
         if (deltaR < deltaRMinSP) {
           break;
         }
       } else {
         deltaR = (otherSP->radius() - rM);
 
         // if r-distance is too big, try next SP in bin
         if (deltaR > deltaRMaxSP) {
           break;
         }
       }
 
       if constexpr (isBottomCandidate) {
         deltaZ = (zM - otherSP->z());
       } else {
         deltaZ = (otherSP->z() - zM);
       }
 
       // the longitudinal impact parameter zOrigin is defined as (zM - rM *
       // cotTheta) where cotTheta is the ratio Z/R (forward angle) of space
       // point duplet but instead we calculate (zOrigin * deltaR) and multiply
       // collisionRegion by deltaR to avoid divisions
       const float zOriginTimesDeltaR = (zM * deltaR - rM * deltaZ);
       // check if duplet origin on z axis within collision region
       if (outsideRangeCheck(zOriginTimesDeltaR,
                             m_config.collisionRegionMin * deltaR,
                             m_config.collisionRegionMax * deltaR)) {
         continue;
       }
 
       // if interactionPointCut is false we apply z cuts before coordinate
       // transformation to avoid unnecessary calculations. If
       // interactionPointCut is true we apply the curvature cut first because it
       // is more frequent but requires the coordinate transformation
       if (!m_config.interactionPointCut) {
         // check if duplet cotTheta is within the region of interest
         // cotTheta is defined as (deltaZ / deltaR) but instead we multiply
         // cotThetaMax by deltaR to avoid division
         if (outsideRangeCheck(deltaZ, -m_config.cotThetaMax * deltaR,
                               m_config.cotThetaMax * deltaR)) {
           continue;
         }
         // if z-distance between SPs is within max and min values
         if (outsideRangeCheck(deltaZ, -m_config.deltaZMax,
                               m_config.deltaZMax)) {
           continue;
         }
 
         // transform SP coordinates to the u-v reference frame
         const float deltaX = otherSP->x() - xM;
         const float deltaY = otherSP->y() - yM;
 
         const float xNewFrame = deltaX * cosPhiM + deltaY * sinPhiM;
         const float yNewFrame = deltaY * cosPhiM - deltaX * sinPhiM;
 
         const float deltaR2 = (deltaX * deltaX + deltaY * deltaY);
         const float iDeltaR2 = 1 / deltaR2;
 
         const float uT = xNewFrame * iDeltaR2;
         const float vT = yNewFrame * iDeltaR2;
 
         const float iDeltaR = std::sqrt(iDeltaR2);
         const float cotTheta = deltaZ * iDeltaR;
 
         const float Er =
             ((varianceZM + otherSP->varianceZ()) +
              (cotTheta * cotTheta) * (varianceRM + otherSP->varianceR())) *
             iDeltaR2;
 
         // fill output vectors
         linCircleVec.emplace_back(cotTheta, iDeltaR, Er, uT, vT, xNewFrame,
                                   yNewFrame);
 
         mutableData.setDeltaR(otherSP->index(),
                               std::sqrt(deltaR2 + (deltaZ * deltaZ)));
         outVec.push_back(otherSP);
         continue;
       }
 
       // transform SP coordinates to the u-v reference frame
       const float deltaX = otherSP->x() - xM;
       const float deltaY = otherSP->y() - yM;
 
       const float xNewFrame = deltaX * cosPhiM + deltaY * sinPhiM;
       const float yNewFrame = deltaY * cosPhiM - deltaX * sinPhiM;
 
       const float deltaR2 = deltaX * deltaX + deltaY * deltaY;
       const float iDeltaR2 = 1 / deltaR2;
 
       const float uT = xNewFrame * iDeltaR2;
       const float vT = yNewFrame * iDeltaR2;
 
       // We check the interaction point by evaluating the minimal distance
       // between the origin and the straight line connecting the two points in
       // the doublets. Using a geometric similarity, the Im is given by
       // yNewFrame * rM / deltaR <= m_config.impactMax
       // However, we make here an approximation of the impact parameter
       // which is valid under the assumption yNewFrame / xNewFrame is small
       // The correct computation would be:
       // yNewFrame * yNewFrame * rM * rM <= m_config.impactMax *
       // m_config.impactMax * deltaR2
       if (std::abs(rM * yNewFrame) <= impactMax * xNewFrame) {
         // check if duplet cotTheta is within the region of interest
         // cotTheta is defined as (deltaZ / deltaR) but instead we multiply
         // cotThetaMax by deltaR to avoid division
         if (outsideRangeCheck(deltaZ, -m_config.cotThetaMax * deltaR,
                               m_config.cotThetaMax * deltaR)) {
           continue;
         }
 
         const float iDeltaR = std::sqrt(iDeltaR2);
         const float cotTheta = deltaZ * iDeltaR;
 
         // discard bottom-middle dublets in a certain (r, eta) region according
         // to detector specific cuts
         if (!m_config.experimentCuts(mediumSP, *otherSP, cotTheta,
                                      isBottomCandidate)) {
           continue;
         }
 
         const float Er =
             ((varianceZM + otherSP->varianceZ()) +
              (cotTheta * cotTheta) * (varianceRM + otherSP->varianceR())) *
             iDeltaR2;
 
         // fill output vectors
         linCircleVec.emplace_back(cotTheta, iDeltaR, Er, uT, vT, xNewFrame,
                                   yNewFrame);
         mutableData.setDeltaR(otherSP->index(),
                               std::sqrt(deltaR2 + (deltaZ * deltaZ)));
         outVec.emplace_back(otherSP);
         continue;
       }
 
       // in the rotated frame the interaction point is positioned at x = -rM
       // and y ~= impactParam
       const float vIP = (yNewFrame > 0) ? -vIPAbs : vIPAbs;
 
       // we can obtain aCoef as the slope dv/du of the linear function,
       // estimated using du and dv between the two SP bCoef is obtained by
       // inserting aCoef into the linear equation
       const float aCoef = (vT - vIP) / (uT - uIP);
       const float bCoef = vIP - aCoef * uIP;
       // the distance of the straight line from the origin (radius of the
       // circle) is related to aCoef and bCoef by d^2 = bCoef^2 / (1 +
       // aCoef^2) = 1 / (radius^2) and we can apply the cut on the curvature
       if ((bCoef * bCoef) * options.minHelixDiameter2 > (1 + aCoef * aCoef)) {
         continue;
       }
 
       // check if duplet cotTheta is within the region of interest
       // cotTheta is defined as (deltaZ / deltaR) but instead we multiply
       // cotThetaMax by deltaR to avoid division
       if (outsideRangeCheck(deltaZ, -m_config.cotThetaMax * deltaR,
                             m_config.cotThetaMax * deltaR)) {
         continue;
       }
 
       const float iDeltaR = std::sqrt(iDeltaR2);
       const float cotTheta = deltaZ * iDeltaR;
 
       // discard bottom-middle dublets in a certain (r, eta) region according
       // to detector specific cuts
       if (!m_config.experimentCuts(mediumSP, *otherSP, cotTheta,
                                    isBottomCandidate)) {
         continue;
       }
 
       const float Er =
           ((varianceZM + otherSP->varianceZ()) +
            (cotTheta * cotTheta) * (varianceRM + otherSP->varianceR())) *
           iDeltaR2;
 
       // fill output vectors
       linCircleVec.emplace_back(cotTheta, iDeltaR, Er, uT, vT, xNewFrame,
                                 yNewFrame);
 
       mutableData.setDeltaR(otherSP->index(),
                             std::sqrt(deltaR2 + (deltaZ * deltaZ)));
       outVec.emplace_back(otherSP);
     }
   }
 }
 
 template <typename external_space_point_t, typename grid_t, typename platform_t>
 template <DetectorMeasurementInfo detailedMeasurement>
 inline void
 SeedFinder<external_space_point_t, grid_t, platform_t>::filterCandidates(
     const external_space_point_t& spM, const SeedFinderOptions& options,
     SeedFilterState& seedFilterState, SeedingState& state) const {
   const float rM = spM.radius();
   const float cosPhiM = spM.x() / rM;
   const float sinPhiM = spM.y() / rM;
   const float varianceRM = spM.varianceR();
   const float varianceZM = spM.varianceZ();
 
   std::size_t numTopSp = state.compatTopSP.size();
 
   // sort: make index vector
   std::vector<std::uint32_t> sortedBottoms(state.compatBottomSP.size());
   for (std::uint32_t i = 0; i < sortedBottoms.size(); ++i) {
     sortedBottoms[i] = i;
   }
   std::vector<std::uint32_t> sortedTops(state.linCircleTop.size());
   for (std::uint32_t i = 0; i < sortedTops.size(); ++i) {
     sortedTops[i] = i;
   }
 
   if constexpr (detailedMeasurement == DetectorMeasurementInfo::eDefault) {
     std::vector<float> cotThetaBottoms(state.compatBottomSP.size());
     for (std::uint32_t i = 0; i < sortedBottoms.size(); ++i) {
       cotThetaBottoms[i] = state.linCircleBottom[i].cotTheta;
     }
     std::ranges::sort(sortedBottoms, {}, [&](const std::uint32_t s) {
       return cotThetaBottoms[s];
     });
 
     std::vector<float> cotThetaTops(state.linCircleTop.size());
     for (std::uint32_t i = 0; i < sortedTops.size(); ++i) {
       cotThetaTops[i] = state.linCircleTop[i].cotTheta;
     }
     std::ranges::sort(sortedTops, {},
                       [&](const std::uint32_t s) { return cotThetaTops[s]; });
   }
 
   // Reserve enough space, in case current capacity is too little
   state.topSpVec.reserve(numTopSp);
   state.curvatures.reserve(numTopSp);
   state.impactParameters.reserve(numTopSp);
 
   std::size_t t0 = 0;
 
   // clear previous results and then loop on bottoms and tops
   state.candidatesCollector.clear();
 
   for (const std::size_t b : sortedBottoms) {
     // break if we reached the last top SP
     if (t0 == numTopSp) {
       break;
     }
 
     auto lb = state.linCircleBottom[b];
     float cotThetaB = lb.cotTheta;
     float Vb = lb.V;
     float Ub = lb.U;
     float ErB = lb.Er;
     float iDeltaRB = lb.iDeltaR;
 
     // 1+(cot^2(theta)) = 1/sin^2(theta)
     float iSinTheta2 = 1 + cotThetaB * cotThetaB;
     float sigmaSquaredPtDependent = iSinTheta2 * options.sigmapT2perRadius;
     // calculate max scattering for min momentum at the seed's theta angle
     // scaling scatteringAngle^2 by sin^2(theta) to convert pT^2 to p^2
     // accurate would be taking 1/atan(thetaBottom)-1/atan(thetaTop) <
     // scattering
     // but to avoid trig functions we approximate cot by scaling by
     // 1/sin^4(theta)
     // resolving with pT to p scaling --> only divide by sin^2(theta)
     // max approximation error for allowed scattering angles of 0.04 rad at
     // eta=infinity: ~8.5%
     float scatteringInRegion2 = options.multipleScattering2 * iSinTheta2;
 
     float sinTheta = 1 / std::sqrt(iSinTheta2);
     float cosTheta = cotThetaB * sinTheta;
 
     // clear all vectors used in each inner for loop
     state.topSpVec.clear();
     state.curvatures.clear();
     state.impactParameters.clear();
 
     // coordinate transformation and checks for middle space point
     // x and y terms for the rotation from UV to XY plane
     float rotationTermsUVtoXY[2] = {0, 0};
     if constexpr (detailedMeasurement == DetectorMeasurementInfo::eDetailed) {
       rotationTermsUVtoXY[0] = cosPhiM * sinTheta;
       rotationTermsUVtoXY[1] = sinPhiM * sinTheta;
     }
 
     // minimum number of compatible top SPs to trigger the filter for a certain
     // middle bottom pair if seedConfirmation is false we always ask for at
     // least one compatible top to trigger the filter
     std::size_t minCompatibleTopSPs = 2;
     if (!m_config.seedConfirmation ||
         state.compatBottomSP[b]->radius() > seedFilterState.rMaxSeedConf) {
       minCompatibleTopSPs = 1;
     }
     if (m_config.seedConfirmation &&
         state.candidatesCollector.nHighQualityCandidates()) {
       minCompatibleTopSPs++;
     }
 
     for (std::size_t index_t = t0; index_t < numTopSp; index_t++) {
       const std::size_t t = sortedTops[index_t];
 
       auto lt = state.linCircleTop[t];
 
       float cotThetaT = lt.cotTheta;
       float rMxy = 0;
       float ub = 0;
       float vb = 0;
       float ut = 0;
       float vt = 0;
       double rMTransf[3];
       float xB = 0;
       float yB = 0;
       float xT = 0;
       float yT = 0;
       float iDeltaRB2 = 0;
       float iDeltaRT2 = 0;
 
       if constexpr (detailedMeasurement == DetectorMeasurementInfo::eDetailed) {
         // protects against division by 0
         float dU = lt.U - Ub;
         if (dU == 0) {
           continue;
         }
         // A and B are evaluated as a function of the circumference parameters
         // x_0 and y_0
         float A0 = (lt.V - Vb) / dU;
 
         float zPositionMiddle = cosTheta * std::sqrt(1 + A0 * A0);
 
         // position of Middle SP converted from UV to XY assuming cotTheta
         // evaluated from the Bottom and Middle SPs double
         double positionMiddle[3] = {
             rotationTermsUVtoXY[0] - rotationTermsUVtoXY[1] * A0,
             rotationTermsUVtoXY[0] * A0 + rotationTermsUVtoXY[1],
             zPositionMiddle};
 
         if (!xyzCoordinateCheck(m_config, spM, positionMiddle, rMTransf)) {
           continue;
         }
 
         // coordinate transformation and checks for bottom space point
         float B0 = 2 * (Vb - A0 * Ub);
         float Cb = 1 - B0 * lb.y;
         float Sb = A0 + B0 * lb.x;
         double positionBottom[3] = {
             rotationTermsUVtoXY[0] * Cb - rotationTermsUVtoXY[1] * Sb,
             rotationTermsUVtoXY[0] * Sb + rotationTermsUVtoXY[1] * Cb,
             zPositionMiddle};
 
         auto spB = state.compatBottomSP[b];
         double rBTransf[3];
         if (!xyzCoordinateCheck(m_config, *spB, positionBottom, rBTransf)) {
           continue;
         }
 
         // coordinate transformation and checks for top space point
         float Ct = 1 - B0 * lt.y;
         float St = A0 + B0 * lt.x;
         double positionTop[3] = {
             rotationTermsUVtoXY[0] * Ct - rotationTermsUVtoXY[1] * St,
             rotationTermsUVtoXY[0] * St + rotationTermsUVtoXY[1] * Ct,
             zPositionMiddle};
 
         auto spT = state.compatTopSP[t];
         double rTTransf[3];
         if (!xyzCoordinateCheck(m_config, *spT, positionTop, rTTransf)) {
           continue;
         }
 
         // bottom and top coordinates in the spM reference frame
         xB = rBTransf[0] - rMTransf[0];
         yB = rBTransf[1] - rMTransf[1];
         float zB = rBTransf[2] - rMTransf[2];
         xT = rTTransf[0] - rMTransf[0];
         yT = rTTransf[1] - rMTransf[1];
         float zT = rTTransf[2] - rMTransf[2];
 
         iDeltaRB2 = 1 / (xB * xB + yB * yB);
         iDeltaRT2 = 1 / (xT * xT + yT * yT);
 
         cotThetaB = -zB * std::sqrt(iDeltaRB2);
         cotThetaT = zT * std::sqrt(iDeltaRT2);
       }
 
       // use geometric average
       float cotThetaAvg2 = cotThetaB * cotThetaT;
       if constexpr (detailedMeasurement == DetectorMeasurementInfo::eDetailed) {
         // use arithmetic average
         float averageCotTheta = 0.5f * (cotThetaB + cotThetaT);
         cotThetaAvg2 = averageCotTheta * averageCotTheta;
       }
 
       // add errors of spB-spM and spM-spT pairs and add the correlation term
       // for errors on spM
       float error2 =
           lt.Er + ErB +
           2 * (cotThetaAvg2 * varianceRM + varianceZM) * iDeltaRB * lt.iDeltaR;
 
       float deltaCotTheta = cotThetaB - cotThetaT;
       float deltaCotTheta2 = deltaCotTheta * deltaCotTheta;
 
       // Apply a cut on the compatibility between the r-z slope of the two
       // seed segments. This is done by comparing the squared difference
       // between slopes, and comparing to the squared uncertainty in this
       // difference - we keep a seed if the difference is compatible within
       // the assumed uncertainties. The uncertainties get contribution from
       // the  space-point-related squared error (error2) and a scattering term
       // calculated assuming the minimum pt we expect to reconstruct
       // (scatteringInRegion2). This assumes gaussian error propagation which
       // allows just adding the two errors if they are uncorrelated (which is
       // fair for scattering and measurement uncertainties)
       if (deltaCotTheta2 > error2 + scatteringInRegion2) {
         // skip top SPs based on cotTheta sorting when producing triplets
         if constexpr (detailedMeasurement ==
                       DetectorMeasurementInfo::eDetailed) {
           continue;
         }
         // break if cotTheta from bottom SP < cotTheta from top SP because
         // the SP are sorted by cotTheta
         if (cotThetaB - cotThetaT < 0) {
           break;
         }
         t0 = index_t + 1;
         continue;
       }
 
       if constexpr (detailedMeasurement == DetectorMeasurementInfo::eDetailed) {
         rMxy = std::sqrt(rMTransf[0] * rMTransf[0] + rMTransf[1] * rMTransf[1]);
         float irMxy = 1 / rMxy;
         float Ax = rMTransf[0] * irMxy;
         float Ay = rMTransf[1] * irMxy;
 
         ub = (xB * Ax + yB * Ay) * iDeltaRB2;
         vb = (yB * Ax - xB * Ay) * iDeltaRB2;
         ut = (xT * Ax + yT * Ay) * iDeltaRT2;
         vt = (yT * Ax - xT * Ay) * iDeltaRT2;
       }
 
       float dU = 0;
       float A = 0;
       float S2 = 0;
       float B = 0;
       float B2 = 0;
 
       if constexpr (detailedMeasurement == DetectorMeasurementInfo::eDetailed) {
         dU = ut - ub;
         // protects against division by 0
         if (dU == 0) {
           continue;
         }
         A = (vt - vb) / dU;
         S2 = 1 + A * A;
         B = vb - A * ub;
         B2 = B * B;
       } else {
         dU = lt.U - Ub;
         // protects against division by 0
         if (dU == 0) {
           continue;
         }
         // A and B are evaluated as a function of the circumference parameters
         // x_0 and y_0
         A = (lt.V - Vb) / dU;
         S2 = 1 + A * A;
         B = Vb - A * Ub;
         B2 = B * B;
       }
 
       // sqrt(S2)/B = 2 * helixradius
       // calculated radius must not be smaller than minimum radius
       if (S2 < B2 * options.minHelixDiameter2) {
         continue;
       }
 
       // refinement of the cut on the compatibility between the r-z slope of
       // the two seed segments using a scattering term scaled by the actual
       // measured pT (p2scatterSigma)
       float iHelixDiameter2 = B2 / S2;
       // convert p(T) to p scaling by sin^2(theta) AND scale by 1/sin^4(theta)
       // from rad to deltaCotTheta
       float p2scatterSigma = iHelixDiameter2 * sigmaSquaredPtDependent;
       // if deltaTheta larger than allowed scattering for calculated pT, skip
       if (deltaCotTheta2 > error2 + p2scatterSigma) {
         if constexpr (detailedMeasurement ==
                       DetectorMeasurementInfo::eDetailed) {
           continue;
         }
         if (cotThetaB - cotThetaT < 0) {
           break;
         }
         t0 = index_t;
         continue;
       }
       // A and B allow calculation of impact params in U/V plane with linear
       // function
       // (in contrast to having to solve a quadratic function in x/y plane)
       float Im = 0;
       if constexpr (detailedMeasurement == DetectorMeasurementInfo::eDetailed) {
         Im = std::abs((A - B * rMxy) * rMxy);
       } else {
         Im = std::abs((A - B * rM) * rM);
       }
 
       if (Im > m_config.impactMax) {
         continue;
       }
 
       state.topSpVec.push_back(state.compatTopSP[t]);
       // inverse diameter is signed depending on if the curvature is
       // positive/negative in phi
       state.curvatures.push_back(B / std::sqrt(S2));
       state.impactParameters.push_back(Im);
     }  // loop on tops
 
     // continue if number of top SPs is smaller than minimum required for filter
     if (state.topSpVec.size() < minCompatibleTopSPs) {
       continue;
     }
 
     seedFilterState.zOrigin = spM.z() - rM * lb.cotTheta;
 
     m_config.seedFilter->filterSeeds_2SpFixed(
         state.spacePointMutableData, *state.compatBottomSP[b], spM,
         state.topSpVec, state.curvatures, state.impactParameters,
         seedFilterState, state.candidatesCollector);
   }  // loop on bottoms
 }
 
 template <typename external_space_point_t, typename grid_t, typename platform_t>
 std::pair<float, float> SeedFinder<external_space_point_t, grid_t, platform_t>::
     retrieveRadiusRangeForMiddle(const external_space_point_t& spM,
                                  const Range1D<float>& rMiddleSPRange) const {
   if (m_config.useVariableMiddleSPRange) {
     return {rMiddleSPRange.min(), rMiddleSPRange.max()};
   }
   if (!m_config.rRangeMiddleSP.empty()) {
     /// get zBin position of the middle SP
     auto pVal = std::lower_bound(m_config.zBinEdges.begin(),
                                  m_config.zBinEdges.end(), spM.z());
     int zBin = std::distance(m_config.zBinEdges.begin(), pVal);
     /// protects against zM at the limit of zBinEdges
     zBin == 0 ? zBin : --zBin;
     return {m_config.rRangeMiddleSP[zBin][0], m_config.rRangeMiddleSP[zBin][1]};
   }
   return {m_config.rMinMiddle, m_config.rMaxMiddle};
 }
 
 }  // namespace Acts

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