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 // // Integer representation of floating point arithmetic suitable for FPGA designs
 //
 // Author: Yuri Gershtein
 // Date:   March 2018
 //
 // Functionality:
 //
 //  *note* all integers are assumed to be signed
 //
 //  all variables have units, stored in a map <string,int>, with string a unit (i.e. "phi") and int the power
 //                   "2" is always present in the map, and it's int pair is referred to as 'shift'
 //                   units are properly combined / propagated through calculations
 //                   adding/subtracting variables with different units throws an exception
 //                   adding/subtracting variables with different shifts is allowed and is handled correctly
 //
 // calculate() method re-calculates the variable double and int values based on its operands
 //                   returns false in case of overflows and/or mismatches between double and int calculations.
 //
 // the maximum and minimum values that the variable assumes are stored and updated each time calculate() is called
 // if IMATH_ROOT is defined, all values are also stored in a histogram
 //
 // VarDef     (string name, string units, double fmax, double K):
 //                   define variable with bit value fval = K*ival, and maximum absolute value fmax.
 //                   calculates nbins on its own
 //                   one can assign value to it using set_ methods
 //
 // VarParam   (string name, string units, double fval, int nbits):
 //                   define a parameter. K is calculated based on the fval and nbits
 //
 //         or (string name, std::string units, double fval, double K):
 //                   define a parameer with bit value fval = K*ival.
 //                   calculates nbins on its own
 //
 // VarAdd     (string name, VarBase *p1, VarBase *p2, double range = -1, int nmax = 18):
 // VarSubtract(string name, VarBase *p1, VarBase *p2, double range = -1, int nmax = 18):
 //                   add/subtract variables. Bit length increases by 1, but capped at nmax
 //                   if range>0 specified, bit length is decreased to drop unnecessary high bits
 //
 // VarMult    (string name, VarBase *p1, VarBase *p2, double range = -1, int nmax = 18):
 //                   multiplication. Bit length is a sum of the lengths of the operads, but capped at nmax
 //                   if range>0 specified, bit length is decreased to drop unnecessary high bits or post-shift is reduced
 //
 // VarTimesC  (string name, VarBase *p1, double cF, int ps = 17):
 //                   multiplication by a constant. Bit length stays the same
 //                   ps defines number of bits used to represent the constant
 //
 // VarDSPPostadd (string name, VarBase *p1, VarBase *p2, VarBase *p3, double range = -1, int nmax = 18):
 //                   explicit instantiation of the 3-clock DSP postaddition: p1*p2+p3
 //                   range and nmax have the same meaning as for the VarMult.
 //
 // VarShift  (string name, VarBase *p1, int shift):
 //                   shifts the variable right by shift (equivalent to multiplication by pow(2, -shift));
 //                   Units stay the same, nbits are adjusted.
 //
 // VarShiftround  (string name, VarBase *p1, int shift):
 //                   shifts the variable right by shift, but doing rounding, i.e.
 //                   (p>>(shift-1)+1)>>1;
 //                   Units stay the same, nbits are adjusted.
 //
 // VarNeg    (string name, VarBase *p1):
 //                   multiplies the variable by -1
 //
 // VarInv     (string name, VarBase *p1, double offset, int nbits, int n, unsigned int shift, mode m, int nbaddr=-1):
 //                   LUT-based inversion, f = 1./(offset + f1) and  i = 2^n / (offsetI + i1)
 //                   nbits is the width of the LUT (signed)
 //                   m is from enum mode {pos, neg, both} and refers to possible sign values of f
 //                            for pos and neg, the most significant bit of p1 (i.e. the sign bit) is ignored
 //                   shift is a shift applied in i1<->address conversions (used to reduce size of LUT)
 //                   nbaddr: if not specified, it is taken to be equal to p1->nbits()
 //
 //
 // VarNounits (string name, VarBase *p1, int ps = 17):
 //                   convert a number with units to a number - needed for trig function expansion (i.e. 1 - 0.5*phi^2)
 //                   ps is a number of bits to represent the unit conversion constant
 //
 // VarAdjustK (string name, VarBase *p1, double Knew, double epsilon = 1e-5, bool do_assert = false, int nbits = -1)
 //                   adjust variable shift so the K is as close to Knew as possible (needed for bit length adjustments)
 //                   if do_assert is true, throw an exeption if Knew/Kold is not a power of two
 //                   epsilon is a comparison precision, nbits forces the bit length (possibly discarding MSBs)
 //
 // VarAdjustKR (string name, VarBase *p1, double Knew, double epsilon = 1e-5, bool do_assert = false, int nbits = -1)
 //                   - same as adjustK(), but with rounding, and therefore latency=1
 //
 // bool calculate(int debug_level) runs through the entire formula tree recalculating both ineteger and floating point values
 //                     returns true if everything is OK, false if obvious problems with the calculation exist, i.e
 //                                  -  integer value does not fit into the alotted number of bins
 //                                  -  integer value is more then 10% or more then 2 away from fval_/K_
 //                     debug_level:  0 - no warnings
 //                                   1 - limited warning
 //                                   2 - as 1, but also include explicit warnings when LUT was used out of its range
 //                                   3 - maximum complaints level
 //
 // VarFlag (string name, VarBase *cut_var, VarBase *...)
 //
 //                    flag to apply cuts defined for any variable. When output as Verilog, the flag
 //                    is true if and only if the following conditions are all true:
 //                       1) the cut defined by each VarCut pointer in the argument list must be passed
 //                       by the associated variable
 //                       2) each VarBase pointer in the argument list that is not also a VarCut
 //                       pointer must pass all of its associated cuts
 //                       3) all children of the variables in the argument list must pass all of their
 //                       associated cuts
 //                    The VarFlag::passes() method replicates the behavior of the output Verilog,
 //                    returning true if and only if the above conditions are all true. The
 //                    VarBase::local_passes() method can be used to query if a given variable passes
 //                    its associated cuts, regardless of whether its children do.
 //
 #ifndef L1Trigger_TrackFindingTracklet_interface_imath_h
 #define L1Trigger_TrackFindingTracklet_interface_imath_h
 
 //use root if uncommented
 //#ifndef CMSSW_GIT_HASH
 //#define IMATH_ROOT
 //#endif
 
 #include <limits>
 #include <iostream>
 #include <fstream>
 #include <vector>
 #include <map>
 #include <cmath>
 #include <sstream>
 #include <string>
 #include <cassert>
 #include <set>
 
 #include "L1Trigger/TrackFindingTracklet/interface/Util.h"
 #include "FWCore/MessageLogger/interface/MessageLogger.h"
 #include "FWCore/Utilities/interface/Exception.h"
 #include "L1Trigger/L1TCommon/interface/BitShift.h"
 
 #ifdef IMATH_ROOT
 #include <TH2F.h>
 #include <TFile.h>
 #include <TCanvas.h>
 #include <TTree.h>
 #endif
 
 //operation latencies for proper HDL pipelining
 #define MULT_LATENCY 1
 #define LUT_LATENCY 2
 #define DSP_LATENCY 3
 
 // Print out information on the pass/fail status of all variables. Warning:
 // this outputs a lot of information for busy events!
 
 namespace trklet {
 
   struct imathGlobals {
     bool printCutInfo_{false};
 #ifdef IMATH_ROOT
     TFile *h_file_ = new TFile("imath.root", "RECREATE");
     bool use_root;
 #endif
   };
 
   class VarCut;
   class VarFlag;
 
   class VarBase {
   public:
     VarBase(imathGlobals *globals, std::string name, VarBase *p1, VarBase *p2, VarBase *p3, int l) {
       globals_ = globals;
       p1_ = p1;
       p2_ = p2;
       p3_ = p3;
       name_ = name;
       latency_ = l;
       int step1 = (p1) ? p1->step() + p1->latency() : 0;
       int step2 = (p2) ? p2->step() + p2->latency() : 0;
       step_ = std::max(step1, step2);
 
       cuts_.clear();
       cut_var_ = nullptr;
 
       pipe_counter_ = 0;
       pipe_delays_.clear();
 
       minval_ = std::numeric_limits<double>::max();
       maxval_ = -std::numeric_limits<double>::max();
       readytoprint_ = true;
       readytoanalyze_ = true;
       usedasinput_ = false;
       Kmap_.clear();
       Kmap_["2"] = 0;  // initially, zero shift
 #ifdef IMATH_ROOT
       h_ = 0;
       h_nbins_ = 1024;
       h_precision_ = 0.02;
 #endif
     }
     virtual ~VarBase() {
 #ifdef IMATH_ROOT
       if (globals_->h_file_) {
         globals_->h_file_->ls();
         globals_->h_file_->Close();
         globals_->h_file_ = 0;
       }
 #endif
     }
 
     static struct Verilog {
     } verilog;
     static struct HLS {
     } hls;
 
     std::string kstring() const;
     std::string name() const { return name_; }
     std::string op() const { return op_; }
     VarBase *p1() const { return p1_; }
     VarBase *p2() const { return p2_; }
     VarBase *p3() const { return p3_; }
     double fval() const { return fval_; }
     long int ival() const { return ival_; }
 
     bool local_passes() const;
     void passes(std::map<const VarBase *, std::vector<bool> > &passes,
                 const std::map<const VarBase *, std::vector<bool> > *const previous_passes = nullptr) const;
     void print_cuts(std::map<const VarBase *, std::set<std::string> > &cut_strings,
                     const int step,
                     Verilog,
                     const std::map<const VarBase *, std::set<std::string> > *const previous_cut_strings = nullptr) const;
     void print_cuts(std::map<const VarBase *, std::set<std::string> > &cut_strings,
                     const int step,
                     HLS,
                     const std::map<const VarBase *, std::set<std::string> > *const previous_cut_strings = nullptr) const;
     void add_cut(VarCut *cut, const bool call_set_cut_var = true);
     VarBase *cut_var();
     // observed range of fval_ (only filled if debug_level > 0)
     double minval() const { return minval_; }
     double maxval() const { return maxval_; }
     void analyze();
 #ifdef IMATH_ROOT
     TH2F *h() { return h_; }
 #endif
     void reset() {
       minval_ = std::numeric_limits<double>::max();
       maxval_ = -std::numeric_limits<double>::max();
 #ifdef IMATH_ROOT
       h_->Clear();
 #endif
     }
 
     int nbits() const { return nbits_; }
     std::map<std::string, int> Kmap() const { return Kmap_; }
     double range() const { return (1 << (nbits_ - 1)) * K_; }  // everything is signed
     double K() const { return K_; };
     int shift() const { return Kmap_.at("2"); }
 
     void makeready();
     int step() const { return step_; }
     int latency() const { return latency_; }
     void add_latency(unsigned int l) { latency_ += l; }  //only call before using the variable in calculation!
     bool calculate(int debug_level = 0);
     virtual void local_calculate() {}
     void calcDebug(int debug_level, long int ival_prev, bool &all_ok);
     virtual void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) {
       fs << "// VarBase here. Soemthing is wrong!! " << l1 << ", " << l2 << ", " << l3 << "\n";
     }
     virtual void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) {
       fs << "// VarBase here. Soemthing is wrong!! " << l1 << ", " << l2 << ", " << l3 << "\n";
     }
     void print_step(int step, std::ofstream &fs, Verilog);
     void print_step(int step, std::ofstream &fs, HLS);
     void print_all(std::ofstream &fs, Verilog);
     void print_all(std::ofstream &fs, HLS);
     void print_truncation(std::string &t, const std::string &o1, const int ps, Verilog) const;
     void print_truncation(std::string &t, const std::string &o1, const int ps, HLS) const;
     void inputs(std::vector<VarBase *> *vd);  //collect all inputs
 
     int pipe_counter() { return pipe_counter_; }
     void pipe_increment() { pipe_counter_++; }
     void add_delay(int i) { pipe_delays_.push_back(i); }
     bool has_delay(int i);  //returns true if already have this variable delayed.
     static void verilog_print(const std::vector<VarBase *> &v, std::ofstream &fs) { design_print(v, fs, verilog); }
     static void hls_print(const std::vector<VarBase *> &v, std::ofstream &fs) { design_print(v, fs, hls); }
     static void design_print(const std::vector<VarBase *> &v, std::ofstream &fs, Verilog);
     static void design_print(const std::vector<VarBase *> &v, std::ofstream &fs, HLS);
     static std::string pipe_delay(VarBase *v, int nbits, int delay);
     std::string pipe_delays(const int step);
     static std::string pipe_delay_wire(VarBase *v, std::string name_delayed, int nbits, int delay);
 
 #ifdef IMATH_ROOT
     static TTree *addToTree(imathGlobals *globals, VarBase *v, char *s = 0);
     static TTree *addToTree(imathGlobals *globals, int *v, char *s);
     static TTree *addToTree(imathGlobals *globals, double *v, char *s);
     static void fillTree(imathGlobals *globals);
     static void writeTree(imathGlobals *globals);
 #endif
 
     void dump_msg();
     std::string dump();
     static std::string itos(int i);
 
   protected:
     imathGlobals *globals_;
     std::string name_;
     VarBase *p1_;
     VarBase *p2_;
     VarBase *p3_;
     std::string op_;  // operation
     int latency_;     // number of clock cycles for the operation (for HDL output)
     int step_;        // step number in the calculation (for HDL output)
 
     double fval_;    // exact calculation
     long int ival_;  // integer calculation
     double val_;     // integer calculation converted to double, ival_*K
 
     std::vector<VarBase *> cuts_;
     VarBase *cut_var_;
 
     int nbits_;
     double K_;
     std::map<std::string, int> Kmap_;
 
     int pipe_counter_;
     std::vector<int> pipe_delays_;
 
     bool readytoanalyze_;
     bool readytoprint_;
     bool usedasinput_;
 
     double minval_;
     double maxval_;
 #ifdef IMATH_ROOT
     void set_hist_pars(int n = 256, double p = 0.05) {
       h_nbins_ = n;
       h_precision_ = p;
     }
     int h_nbins_;
     double h_precision_;
     TH2F *h_;
 #endif
   };
 
   class VarAdjustK : public VarBase {
   public:
     VarAdjustK(imathGlobals *globals,
                std::string name,
                VarBase *p1,
                double Knew,
                double epsilon = 1e-5,
                bool do_assert = false,
                int nbits = -1)
         : VarBase(globals, name, p1, nullptr, nullptr, 0) {
       op_ = "adjustK";
       K_ = p1->K();
       Kmap_ = p1->Kmap();
 
       double r = Knew / K_;
 
       lr_ = (r > 1) ? log2(r) + epsilon : log2(r);
       K_ = K_ * pow(2, lr_);
       if (do_assert)
         assert(std::abs(Knew / K_ - 1) < epsilon);
 
       if (nbits > 0)
         nbits_ = nbits;
       else
         nbits_ = p1->nbits() - lr_;
 
       Kmap_["2"] = Kmap_["2"] + lr_;
     }
 
     ~VarAdjustK() override = default;
 
     void adjust(double Knew, double epsilon = 1e-5, bool do_assert = false, int nbits = -1);
 
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int lr_;
   };
 
   class VarAdjustKR : public VarBase {
   public:
     VarAdjustKR(imathGlobals *globals,
                 std::string name,
                 VarBase *p1,
                 double Knew,
                 double epsilon = 1e-5,
                 bool do_assert = false,
                 int nbits = -1)
         : VarBase(globals, name, p1, nullptr, nullptr, 1) {
       op_ = "adjustKR";
       K_ = p1->K();
       Kmap_ = p1->Kmap();
 
       double r = Knew / K_;
 
       lr_ = (r > 1) ? log2(r) + epsilon : log2(r);
       K_ = K_ * pow(2, lr_);
       if (do_assert)
         assert(std::abs(Knew / K_ - 1) < epsilon);
 
       if (nbits > 0)
         nbits_ = nbits;
       else
         nbits_ = p1->nbits() - lr_;
 
       Kmap_["2"] = Kmap_["2"] + lr_;
     }
 
     ~VarAdjustKR() override = default;
 
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int lr_;
   };
 
   class VarParam : public VarBase {
   public:
     VarParam(imathGlobals *globals, std::string name, double fval, int nbits)
         : VarBase(globals, name, nullptr, nullptr, nullptr, 0) {
       op_ = "const";
       nbits_ = nbits;
       int l = log2(std::abs(fval)) + 1.9999999 - nbits;
       Kmap_["2"] = l;
       K_ = pow(2, l);
       fval_ = fval;
       ival_ = fval / K_;
     }
     VarParam(imathGlobals *globals, std::string name, std::string units, double fval, double K)
         : VarBase(globals, name, nullptr, nullptr, nullptr, 0) {
       op_ = "const";
       K_ = K;
       nbits_ = log2(fval / K) + 1.999999;  //plus one to round up
       if (!units.empty())
         Kmap_[units] = 1;
       else {
         //defining a constant, K should be a power of two
         int l = log2(K);
         if (std::abs(pow(2, l) / K - 1) > 1e-5) {
           char slog[100];
           snprintf(slog, 100, "defining unitless constant, yet K is not a power of 2! %g, %g", K, pow(2, l));
           edm::LogVerbatim("Tracklet") << slog;
         }
         Kmap_["2"] = l;
       }
     }
 
     ~VarParam() override = default;
 
     void set_fval(double fval) {
       fval_ = fval;
       if (fval > 0)
         ival_ = fval / K_ + 0.5;
       else
         ival_ = fval / K_ - 0.5;
       val_ = ival_ * K_;
     }
     void set_ival(int ival) {
       ival_ = ival;
       fval_ = ival * K_;
       val_ = fval_;
     }
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
   };
 
   class VarDef : public VarBase {
   public:
     //construct from scratch
     VarDef(imathGlobals *globals, std::string name, std::string units, double fmax, double K)
         : VarBase(globals, name, nullptr, nullptr, nullptr, 1) {
       op_ = "def";
       K_ = K;
       nbits_ = log2(fmax / K) + 1.999999;  //plus one to round up
       if (!units.empty())
         Kmap_[units] = 1;
       else {
         //defining a constant, K should be a power of two
         int l = log2(K);
         if (std::abs(pow(2, l) / K - 1) > 1e-5) {
           char slog[100];
           snprintf(slog, 100, "defining unitless constant, yet K is not a power of 2! %g, %g", K, pow(2, l));
           edm::LogVerbatim("Tracklet") << slog;
         }
         Kmap_["2"] = l;
       }
     }
     //construct from abother variable (all provenance info is lost!)
     VarDef(imathGlobals *globals, std::string name, VarBase *p) : VarBase(globals, name, nullptr, nullptr, nullptr, 1) {
       op_ = "def";
       K_ = p->K();
       nbits_ = p->nbits();
       Kmap_ = p->Kmap();
     }
     void set_fval(double fval) {
       fval_ = fval;
       if (fval > 0)
         ival_ = fval / K_;
       else
         ival_ = fval / K_ - 1;
       val_ = ival_ * K_;
     }
     void set_ival(int ival) {
       ival_ = ival;
       fval_ = ival * K_;
       val_ = ival_ * K_;
     }
     ~VarDef() override = default;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
   };
 
   class VarAdd : public VarBase {
   public:
     VarAdd(imathGlobals *globals, std::string name, VarBase *p1, VarBase *p2, double range = -1, int nmax = 18)
         : VarBase(globals, name, p1, p2, nullptr, 1) {
       op_ = "add";
 
       std::map<std::string, int> map1 = p1->Kmap();
       std::map<std::string, int> map2 = p2->Kmap();
       int s1 = map1["2"];
       int s2 = map2["2"];
 
       //first check if the constants are all lined up
       //go over the two maps subtracting the units
       for (const auto &it : map2) {
         if (map1.find(it.first) == map1.end())
           map1[it.first] = -it.second;
         else
           map1[it.first] = map1[it.first] - it.second;
       }
 
       char slog[100];
 
       //assert if different
       for (const auto &it : map1) {
         if (it.second != 0) {
           if (it.first != "2") {
             snprintf(
                 slog, 100, "VarAdd: bad units! %s^%i for variable %s", (it.first).c_str(), it.second, name_.c_str());
             edm::LogVerbatim("Tracklet") << slog;
             p1->dump_msg();
             p2->dump_msg();
             throw cms::Exception("BadConfig") << "imath units are different!";
           }
         }
       }
 
       double ki1 = p1->K() / pow(2, s1);
       double ki2 = p2->K() / pow(2, s2);
       //those should be the same
       if (std::abs(ki1 / ki2 - 1.) > 1e-6) {
         snprintf(slog, 100, "VarAdd: bad constants! %f %f for variable %s", ki1, ki2, name_.c_str());
         edm::LogVerbatim("Tracklet") << slog;
         p1->dump_msg();
         p2->dump_msg();
         throw cms::Exception("BadConfig") << "imath constants are different!";
       }
       //everything checks out!
 
       Kmap_ = p1->Kmap();
 
       int s0 = s1 < s2 ? s1 : s2;
       shift1 = s1 - s0;
       shift2 = s2 - s0;
 
       int n1 = p1->nbits() + shift1;
       int n2 = p2->nbits() + shift2;
       int n0 = 1 + (n1 > n2 ? n1 : n2);
 
       //before shifting, check the range
       if (range > 0) {
         n0 = log2(range / ki1 / pow(2, s0)) + 1e-9;
         n0 = n0 + 2;
       }
 
       if (n0 <= nmax) {  //if it fits, we're done
         ps_ = 0;
         Kmap_["2"] = s0;
         nbits_ = n0;
       } else {
         ps_ = n0 - nmax;
         Kmap_["2"] = s0 + ps_;
         nbits_ = nmax;
       }
 
       K_ = ki1 * pow(2, Kmap_["2"]);
     }
     ~VarAdd() override = default;
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int ps_;
     int shift1;
     int shift2;
   };
 
   class VarSubtract : public VarBase {
   public:
     VarSubtract(imathGlobals *globals, std::string name, VarBase *p1, VarBase *p2, double range = -1, int nmax = 18)
         : VarBase(globals, name, p1, p2, nullptr, 1) {
       op_ = "subtract";
 
       std::map<std::string, int> map1 = p1->Kmap();
       std::map<std::string, int> map2 = p2->Kmap();
       int s1 = map1["2"];
       int s2 = map2["2"];
 
       //first check if the constants are all lined up go over the two maps subtracting the units
       for (const auto &it : map2) {
         if (map1.find(it.first) == map1.end())
           map1[it.first] = -it.second;
         else
           map1[it.first] = map1[it.first] - it.second;
       }
 
       char slog[100];
 
       //assert if different
       for (const auto &it : map1) {
         if (it.second != 0) {
           if (it.first != "2") {
             snprintf(
                 slog, 100, "VarAdd: bad units! %s^%i for variable %s", (it.first).c_str(), it.second, name_.c_str());
             edm::LogVerbatim("Tracklet") << slog;
             p1->dump_msg();
             p2->dump_msg();
             throw cms::Exception("BadConfig") << "imath units are different!";
           }
         }
       }
 
       double ki1 = p1->K() / pow(2, s1);
       double ki2 = p2->K() / pow(2, s2);
       //those should be the same
       if (std::abs(ki1 / ki2 - 1.) > 1e-6) {
         snprintf(slog, 100, "VarAdd: bad constants! %f %f for variable %s", ki1, ki2, name_.c_str());
         edm::LogVerbatim("Tracklet") << slog;
         p1->dump_msg();
         p2->dump_msg();
         throw cms::Exception("BadConfig") << "imath constants are different!";
       }
       //everything checks out!
 
       Kmap_ = p1->Kmap();
 
       int s0 = s1 < s2 ? s1 : s2;
       shift1 = s1 - s0;
       shift2 = s2 - s0;
 
       int n1 = p1->nbits() + shift1;
       int n2 = p2->nbits() + shift2;
       int n0 = 1 + (n1 > n2 ? n1 : n2);
 
       //before shifting, check the range
       if (range > 0) {
         n0 = log2(range / ki1 / pow(2, s0)) + 1e-9;
         n0 = n0 + 2;
       }
 
       if (n0 <= nmax) {  //if it fits, we're done
         ps_ = 0;
         Kmap_["2"] = s0;
         nbits_ = n0;
       } else {
         ps_ = n0 - nmax;
         Kmap_["2"] = s0 + ps_;
         nbits_ = nmax;
       }
 
       K_ = ki1 * pow(2, Kmap_["2"]);
     }
 
     ~VarSubtract() override = default;
 
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int ps_;
     int shift1;
     int shift2;
   };
 
   class VarNounits : public VarBase {
   public:
     VarNounits(imathGlobals *globals, std::string name, VarBase *p1, int ps = 17)
         : VarBase(globals, name, p1, nullptr, nullptr, MULT_LATENCY) {
       op_ = "nounits";
       ps_ = ps;
       nbits_ = p1->nbits();
 
       int s1 = p1->shift();
       double ki = p1->K() / pow(2, s1);
       int m = log2(ki);
 
       K_ = pow(2, s1 + m);
       Kmap_["2"] = s1 + m;
       double c = ki * pow(2, -m);
       cI_ = c * pow(2, ps_);
     }
     ~VarNounits() override = default;
 
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int ps_;
     int cI_;
   };
 
   class VarShiftround : public VarBase {
   public:
     VarShiftround(imathGlobals *globals, std::string name, VarBase *p1, int shift)
         : VarBase(globals, name, p1, nullptr, nullptr, 1) {  // latency is one because there is an addition
       op_ = "shiftround";
       shift_ = shift;
 
       nbits_ = p1->nbits() - shift;
       Kmap_ = p1->Kmap();
       K_ = p1->K();
     }
     ~VarShiftround() override = default;
 
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int shift_;
   };
 
   class VarShift : public VarBase {
   public:
     VarShift(imathGlobals *globals, std::string name, VarBase *p1, int shift)
         : VarBase(globals, name, p1, nullptr, nullptr, 0) {
       op_ = "shift";
       shift_ = shift;
 
       nbits_ = p1->nbits() - shift;
       Kmap_ = p1->Kmap();
       K_ = p1->K();
     }
     ~VarShift() override = default;
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int shift_;
   };
 
   class VarNeg : public VarBase {
   public:
     VarNeg(imathGlobals *globals, std::string name, VarBase *p1) : VarBase(globals, name, p1, nullptr, nullptr, 1) {
       op_ = "neg";
       nbits_ = p1->nbits();
       Kmap_ = p1->Kmap();
       K_ = p1->K();
     }
     ~VarNeg() override = default;
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
   };
 
   class VarTimesC : public VarBase {
   public:
     VarTimesC(imathGlobals *globals, std::string name, VarBase *p1, double cF, int ps = 17)
         : VarBase(globals, name, p1, nullptr, nullptr, MULT_LATENCY) {
       op_ = "timesC";
       cF_ = cF;
       ps_ = ps;
 
       nbits_ = p1->nbits();
       Kmap_ = p1->Kmap();
       K_ = p1->K();
 
       int s1 = Kmap_["2"];
       double l = log2(std::abs(cF));
       if (l > 0)
         l += 0.999999;
       int m = l;
 
       cI_ = cF * pow(2, ps - m);
       K_ = K_ * pow(2, m);
       Kmap_["2"] = s1 + m;
     }
     ~VarTimesC() override = default;
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int ps_;
     int cI_;
     double cF_;
   };
 
   class VarMult : public VarBase {
   public:
     VarMult(imathGlobals *globals, std::string name, VarBase *p1, VarBase *p2, double range = -1, int nmax = 18)
         : VarBase(globals, name, p1, p2, nullptr, MULT_LATENCY) {
       op_ = "mult";
 
       const std::map<std::string, int> map1 = p1->Kmap();
       const std::map<std::string, int> map2 = p2->Kmap();
       for (const auto &it : map1) {
         if (Kmap_.find(it.first) == Kmap_.end())
           Kmap_[it.first] = it.second;
         else
           Kmap_[it.first] = Kmap_[it.first] + it.second;
       }
       for (const auto &it : map2) {
         if (Kmap_.find(it.first) == Kmap_.end())
           Kmap_[it.first] = it.second;
         else
           Kmap_[it.first] = Kmap_[it.first] + it.second;
       }
       K_ = p1->K() * p2->K();
       int s0 = Kmap_["2"];
 
       int n0 = p1->nbits() + p2->nbits();
       if (range > 0) {
         n0 = log2(range / K_) + 1e-9;
         n0 = n0 + 2;
       }
       if (n0 < nmax) {
         ps_ = 0;
         nbits_ = n0;
       } else {
         ps_ = n0 - nmax;
         nbits_ = nmax;
         Kmap_["2"] = s0 + ps_;
         K_ = K_ * pow(2, ps_);
       }
     }
     ~VarMult() override = default;
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int ps_;
   };
 
   class VarDSPPostadd : public VarBase {
   public:
     VarDSPPostadd(
         imathGlobals *globals, std::string name, VarBase *p1, VarBase *p2, VarBase *p3, double range = -1, int nmax = 18)
         : VarBase(globals, name, p1, p2, p3, DSP_LATENCY) {
       op_ = "DSP_postadd";
 
       //first, get constants for the p1*p2
       std::map<std::string, int> map1 = p1->Kmap();
       std::map<std::string, int> map2 = p2->Kmap();
       for (const auto &it : map2) {
         if (map1.find(it.first) == map1.end())
           map1[it.first] = it.second;
         else
           map1[it.first] = map1[it.first] + it.second;
       }
       double k0 = p1->K() * p2->K();
       int s0 = map1["2"];
 
       //now addition
       std::map<std::string, int> map3 = p3->Kmap();
       int s3 = map3["2"];
 
       //first check if the constants are all lined up
       //go over the two maps subtracting the units
       for (const auto &it : map3) {
         if (map1.find(it.first) == map1.end())
           map1[it.first] = -it.second;
         else
           map1[it.first] = map1[it.first] - it.second;
       }
 
       char slog[100];
 
       //assert if different
       for (const auto &it : map1) {
         if (it.second != 0) {
           if (it.first != "2") {
             snprintf(slog,
                      100,
                      "VarDSPPostadd: bad units! %s^%i for variable %s",
                      (it.first).c_str(),
                      it.second,
                      name_.c_str());
             edm::LogVerbatim("Tracklet") << slog;
             p1->dump_msg();
             p2->dump_msg();
             p3->dump_msg();
             throw cms::Exception("BadConfig") << "imath units are different!";
           }
         }
       }
 
       double ki1 = k0 / pow(2, s0);
       double ki2 = p3->K() / pow(2, s3);
       //those should be the same
       if (std::abs(ki1 / ki2 - 1.) > 1e-6) {
         snprintf(slog, 100, "VarDSPPostadd: bad constants! %f %f for variable %s", ki1, ki2, name_.c_str());
         edm::LogVerbatim("Tracklet") << slog;
         p1->dump_msg();
         p2->dump_msg();
         p3->dump_msg();
         throw cms::Exception("BadConfig") << "imath constants are different!";
       }
       //everything checks out!
 
       shift3_ = s3 - s0;
       if (shift3_ < 0) {
         throw cms::Exception("BadConfig") << "imath VarDSPPostadd: loosing precision on C in A*B+C: " << shift3_;
       }
 
       Kmap_ = p3->Kmap();
       Kmap_["2"] = Kmap_["2"] - shift3_;
 
       int n12 = p1->nbits() + p2->nbits();
       int n3 = p3->nbits() + shift3_;
       int n0 = 1 + (n12 > n3 ? n12 : n3);
 
       //before shifting, check the range
       if (range > 0) {
         n0 = log2(range / ki2 / pow(2, s3)) + 1e-9;
         n0 = n0 + 2;
       }
 
       if (n0 <= nmax) {  //if it fits, we're done
         ps_ = 0;
         nbits_ = n0;
       } else {
         ps_ = n0 - nmax;
         Kmap_["2"] = Kmap_["2"] + ps_;
         nbits_ = nmax;
       }
 
       K_ = ki2 * pow(2, Kmap_["2"]);
     }
     ~VarDSPPostadd() override = default;
 
     void local_calculate() override;
     using VarBase::print;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
 
   protected:
     int ps_;
     int shift3_;
   };
 
   class VarInv : public VarBase {
   public:
     enum mode { pos, neg, both };
 
     VarInv(imathGlobals *globals,
            std::string name,
            VarBase *p1,
            double offset,
            int nbits,
            int n,
            unsigned int shift,
            mode m,
            int nbaddr = -1)
         : VarBase(globals, name, p1, nullptr, nullptr, LUT_LATENCY) {
       op_ = "inv";
       offset_ = offset;
       nbits_ = nbits;
       n_ = n;
       shift_ = shift;
       m_ = m;
       if (nbaddr < 0)
         nbaddr = p1->nbits();
       nbaddr_ = nbaddr - shift;
       if (m_ != mode::both)
         nbaddr_--;
       Nelements_ = 1 << nbaddr_;
       mask_ = Nelements_ - 1;
       ashift_ = sizeof(int) * 8 - nbaddr_;
 
       const std::map<std::string, int> map1 = p1->Kmap();
       for (const auto &it : map1)
         Kmap_[it.first] = -it.second;
       Kmap_["2"] = Kmap_["2"] - n;
       K_ = pow(2, -n) / p1->K();
 
       LUT = new int[Nelements_];
       double offsetI = lround(offset_ / p1_->K());
       for (int i = 0; i < Nelements_; ++i) {
         int i1 = addr_to_ival(i);
         LUT[i] = gen_inv(offsetI + i1);
       }
     }
     ~VarInv() override { delete[] LUT; }
 
     void set_mode(mode m) { m_ = m; }
     void initLUT(double offset);
     double offset() { return offset_; }
     double Ioffset() { return offset_ / p1_->K(); }
 
     void local_calculate() override;
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void writeLUT(std::ofstream &fs) const { writeLUT(fs, verilog); }
     void writeLUT(std::ofstream &fs, Verilog) const;
     void writeLUT(std::ofstream &fs, HLS) const;
 
     int ival_to_addr(int ival) { return ((ival >> shift_) & mask_); }
     int addr_to_ival(int addr) {
       switch (m_) {
         case mode::pos:
           return l1t::bitShift(addr, shift_);
         case mode::neg:
           return l1t::bitShift((addr - Nelements_), shift_);
         case mode::both:
           return l1t::bitShift(addr, ashift_) >> (ashift_ - shift_);
       }
       assert(0);
     }
     int gen_inv(int i) {
       unsigned int ms = sizeof(int) * 8 - nbits_;
       int lut = 0;
       if (i > 0) {
         int i1 = i + (1 << shift_) - 1;
         int lut1 = (lround((1 << n_) / i) << ms) >> ms;
         int lut2 = (lround((1 << n_) / (i1)) << ms) >> ms;
         lut = 0.5 * (lut1 + lut2);
       } else if (i < -1) {
         int i1 = i + (1 << shift_) - 1;
         int i2 = i;
         int lut1 = (lround((1 << n_) / i1) << ms) >> ms;
         int lut2 = (lround((1 << n_) / i2) << ms) >> ms;
         lut = 0.5 * (lut1 + lut2);
       }
       return lut;
     }
 
   protected:
     double offset_;
     int n_;
     mode m_;
     unsigned int shift_;
     unsigned int mask_;
     unsigned int ashift_;
     int Nelements_;
     int nbaddr_;
 
     int *LUT;
   };
 
   class VarCut : public VarBase {
   public:
     VarCut(imathGlobals *globals, double lower_cut, double upper_cut)
         : VarBase(globals, "", nullptr, nullptr, nullptr, 0),
           lower_cut_(lower_cut),
           upper_cut_(upper_cut),
           parent_flag_(nullptr) {
       op_ = "cut";
     }
 
     VarCut(imathGlobals *globals, VarBase *cut_var, double lower_cut, double upper_cut)
         : VarCut(globals, lower_cut, upper_cut) {
       set_cut_var(cut_var);
     }
     ~VarCut() override = default;
 
     double lower_cut() const { return lower_cut_; }
     double upper_cut() const { return upper_cut_; }
 
     void local_passes(std::map<const VarBase *, std::vector<bool> > &passes,
                       const std::map<const VarBase *, std::vector<bool> > *const previous_passes = nullptr) const;
     using VarBase::print;
     void print(std::map<const VarBase *, std::set<std::string> > &cut_strings,
                const int step,
                Verilog,
                const std::map<const VarBase *, std::set<std::string> > *const previous_cut_strings = nullptr) const;
     void print(std::map<const VarBase *, std::set<std::string> > &cut_strings,
                const int step,
                HLS,
                const std::map<const VarBase *, std::set<std::string> > *const previous_cut_strings = nullptr) const;
 
     void set_parent_flag(VarFlag *parent_flag, const bool call_add_cut);
     VarFlag *parent_flag() { return parent_flag_; }
     void set_cut_var(VarBase *cut_var, const bool call_add_cut = true);
 
   protected:
     double lower_cut_;
     double upper_cut_;
     VarFlag *parent_flag_;
   };
 
   class VarFlag : public VarBase {
   public:
     template <class... Args>
     VarFlag(imathGlobals *globals, std::string name, VarBase *cut, Args... args)
         : VarBase(globals, name, nullptr, nullptr, nullptr, 0) {
       op_ = "flag";
       nbits_ = 1;
       add_cuts(cut, args...);
     }
 
     template <class... Args>
     void add_cuts(VarBase *cut, Args... args) {
       add_cut(cut);
       add_cuts(args...);
     }
 
     void add_cuts(VarBase *cut) { add_cut(cut); }
 
     void add_cut(VarBase *cut, const bool call_set_parent_flag = true);
 
     void calculate_step();
     bool passes();
     void print(std::ofstream &fs, Verilog, int l1 = 0, int l2 = 0, int l3 = 0) override;
     void print(std::ofstream &fs, HLS, int l1 = 0, int l2 = 0, int l3 = 0) override;
   };
 };  // namespace trklet
 #endif

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