OpenSTA/dcalc/ArnoldiReduce.cc

// OpenSTA, Static Timing Analyzer
// Copyright (c) 2025, Parallax Software, Inc.
// 
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// 
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// 
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <https://www.gnu.org/licenses/>.
// 
// The origin of this software must not be misrepresented; you must not
// claim that you wrote the original software.
// 
// Altered source versions must be plainly marked as such, and must not be
// misrepresented as being the original software.
// 
// This notice may not be removed or altered from any source distribution.

// (c) 2018 Nefelus, Inc.
//
// Author: W. Scott

#include "ArnoldiReduce.hh"

#include "Debug.hh"
#include "MinMax.hh"
#include "Sdc.hh"
#include "Network.hh"
#include "Units.hh"
#include "Arnoldi.hh"
#include "parasitics/ConcreteParasiticsPvt.hh"

namespace sta {

rcmodel::rcmodel() :
  pinV(nullptr)
{
}

rcmodel::~rcmodel()
{
  free(pinV);
}

float
rcmodel::capacitance() const
{
  return ctot;
}

PinSet
rcmodel::unannotatedLoads(const Pin *,
                          const Parasitics *) const
{
  // This should never be called because the rcmodel is not saved in the Parasitics.
  return PinSet();
}

struct ts_point
{
  ParasiticNode *node_;
  int eN;
  bool is_term;
  int tindex; // index into termV of corresponding term
  ts_edge **eV;
  bool visited;
  ts_edge *in_edge;
  int ts;
  double c;
  double r;
};

struct ts_edge
{
  ParasiticResistor *resistor_;
  ts_point *from;
  ts_point *to;
};

////////////////////////////////////////////////////////////////


const int ArnoldiReduce::ts_point_count_incr_ = 1024;
const int ArnoldiReduce::ts_edge_count_incr_ = 1024;

ArnoldiReduce::ArnoldiReduce(StaState *sta) :
  StaState(sta),
  ts_pointNmax(1024),
  ts_edgeNmax(1024),
  termNmax(256),
  dNmax(8)
{
  ts_pointV = (ts_point*)malloc(ts_pointNmax*sizeof(ts_point));
  ts_ordV = (int*)malloc(ts_pointNmax*sizeof(int));
  ts_pordV = (ts_point**)malloc(ts_pointNmax*sizeof(ts_point*));
  _u0 = (double*)malloc(ts_pointNmax*sizeof(double));
  _u1 = (double*)malloc(ts_pointNmax*sizeof(double));
  y = (double*)malloc(ts_pointNmax*sizeof(double));
  iv = (double*)malloc(ts_pointNmax*sizeof(double));
  r = (double*)malloc(ts_pointNmax*sizeof(double));
  c = (double*)malloc(ts_pointNmax*sizeof(double));
  par = (int*)malloc(ts_pointNmax*sizeof(int));

  ts_edgeV = (ts_edge*)malloc(ts_edgeNmax*sizeof(ts_edge));
  ts_stackV  = (ts_edge**)malloc(ts_edgeNmax*sizeof(ts_edge*));
  ts_eV      = (ts_edge**)malloc(2*ts_edgeNmax*sizeof(ts_edge*));

  pinV = (const Pin**)malloc(termNmax*sizeof(const Pin*));
  termV = (int*)malloc(termNmax*sizeof(int));
  outV = (int*)malloc(termNmax*sizeof(int));

  d = (double*)malloc(dNmax*sizeof(double));
  e = (double*)malloc(dNmax*sizeof(double));
  U = (double**)malloc(dNmax*sizeof(double*));
  U0 = (double*)malloc(dNmax*termNmax*sizeof(double));
  int h;
  for (h=0;h<dNmax;h++) U[h] = U0 + h*termNmax;
}

ArnoldiReduce::~ArnoldiReduce()
{
  free(U0);
  free(U);
  free(e);
  free(d);
  free(outV);
  free(termV);
  free(pinV);
  free(ts_eV);
  free(ts_edgeV);
  free(ts_stackV);
  free(par);
  free(c);
  free(r);
  free(iv);
  free(y);
  free(_u1);
  free(_u0);
  free(ts_pordV);
  free(ts_ordV);
  free(ts_pointV);
}

rcmodel *
ArnoldiReduce::reduceToArnoldi(Parasitic *parasitic,
			       const Pin *drvr_pin,
			       float coupling_cap_factor,
			       const RiseFall *rf,
			       const Corner *corner,
			       const MinMax *min_max,
			       const ParasiticAnalysisPt *ap)
{
  parasitic_network_ = reinterpret_cast<ConcreteParasiticNetwork*>(parasitic);
  drvr_pin_ = drvr_pin;
  coupling_cap_factor_ = coupling_cap_factor;
  rf_ = rf;
  corner_ = corner;
  min_max_ = min_max;
  ap_ = ap;
  loadWork();
  return makeRcmodelDrv();
}

void
ArnoldiReduce::loadWork()
{
  pt_map_.clear();

  const ParasiticResistorSeq &resistors = parasitics_->resistors(parasitic_network_);
  int resistor_count = resistors.size();

  termN = 0;
  int subnode_count = 0;
  ParasiticNodeSeq nodes = parasitics_->nodes(parasitic_network_);
  for (ParasiticNode *node : nodes) {
    if (!parasitics_->isExternal(node)) {
      const Pin *pin = parasitics_->pin(node);
      if (pin)
        termN++;
      else
        subnode_count++;
    }
  }
  ts_pointN = subnode_count + 1 + termN;
  ts_edgeN = resistor_count;
  allocPoints();
  allocTerms(termN);
  ts_point *p0 = ts_pointV;
  pterm0 = p0 + subnode_count + 1;
  ts_point *pend = p0 + ts_pointN;
  ts_point *p;
  ts_edge *e0 = ts_edgeV;
  ts_edge *eend = e0 + ts_edgeN;

  ts_edge *e;
  int tindex;
  for (p = p0; p!=pend; p++) {
    p->node_ = nullptr;
    p->eN = 0;
    p->is_term = false;
  }
  pend = pterm0;
  e = e0;
  int index = 0;

  for (ParasiticNode *node : nodes) {
    if (!parasitics_->isExternal(node)) {
      const Pin *pin = parasitics_->pin(node);
      if (pin) {
        p = pend++;
        pt_map_[node] = p - p0;
        p->node_ = node;
        p->eN = 0;
        p->is_term = true;
        tindex = p - pterm0;
        p->tindex = tindex;
        pinV[tindex] = pin;
      }
      else {
        pt_map_[node] = index;
        p = p0 + index;
        p->node_ = node;
        p->eN = 0;
        p->is_term = false;
        index++;
      }
    }
  }

  ts_edge **eV = ts_eV;
  for (ParasiticResistor *resistor : resistors) {
    ts_point *pt1 = findPt(parasitics_->node1(resistor));
    ts_point *pt2 = findPt(parasitics_->node2(resistor));
    e->from = pt1;
    e->to = pt2;
    e->resistor_ = resistor;
    pt1->eN++;
    if (e->from != e->to)
      pt2->eN++;
    e++;
  }

  for (p=p0;p!=pend;p++) {
    if (p->node_) {
      p->eV = eV;
      eV += p->eN;
      p->eN = 0;
    }
  }
  for (e=e0;e!=eend;e++) {
    e->from->eV[e->from->eN++] = e;
    if (e->to != e->from)
      e->to->eV[e->to->eN++] = e;
  }
}

void
ArnoldiReduce::allocPoints()
{
  if (ts_pointN > ts_pointNmax) {
    free(par);
    free(c);
    free(r);
    free(iv); free(y); free(_u1); free(_u0);
    free(ts_pordV);
    free(ts_ordV);
    free(ts_pointV);
    ts_pointNmax = ts_pointN + ts_point_count_incr_;
    ts_pointV = (ts_point*)malloc(ts_pointNmax*sizeof(ts_point));
    ts_ordV = (int*)malloc(ts_pointNmax*sizeof(int));
    ts_pordV = (ts_point**)malloc(ts_pointNmax*sizeof(ts_point*));
    _u0 = (double*)malloc(ts_pointNmax*sizeof(double));
    _u1 = (double*)malloc(ts_pointNmax*sizeof(double));
    y = (double*)malloc(ts_pointNmax*sizeof(double));
    iv = (double*)malloc(ts_pointNmax*sizeof(double));
    r = (double*)malloc(ts_pointNmax*sizeof(double));
    c = (double*)malloc(ts_pointNmax*sizeof(double));
    par = (int*)malloc(ts_pointNmax*sizeof(int));
  }
  if (ts_edgeN > ts_edgeNmax) {
    free(ts_edgeV);
    free(ts_eV);
    free(ts_stackV);
    ts_edgeNmax = ts_edgeN + ts_edge_count_incr_;
    ts_edgeV = (ts_edge*)malloc(ts_edgeNmax*sizeof(ts_edge));
    ts_stackV  = (ts_edge**)malloc(ts_edgeNmax*sizeof(ts_edge*));
    ts_eV      = (ts_edge**)malloc(2*ts_edgeNmax*sizeof(ts_edge*));
  }
}

void
ArnoldiReduce::allocTerms(int nterms)
{
  if (nterms > termNmax) {
    free(U0);
    free(outV);
    free(termV);
    free(pinV);
    termNmax = nterms+256;
    pinV = (const Pin**)malloc(termNmax*sizeof(const Pin*));
    termV = (int*)malloc(termNmax*sizeof(int));
    outV = (int*)malloc(termNmax*sizeof(int));

    U0 = (double*)malloc(dNmax*termNmax*sizeof(double));
    int h;
    for (h=0;h<dNmax;h++) U[h] = U0 + h*termNmax;
  }
}

ts_point *
ArnoldiReduce::findPt(ParasiticNode *node)
{
  return &ts_pointV[pt_map_[reinterpret_cast<ConcreteParasiticNode*>(node)]];
}

rcmodel *
ArnoldiReduce::makeRcmodelDrv()
{
  ParasiticNode *drv_node =
    parasitics_->findParasiticNode(parasitic_network_, drvr_pin_);
  ts_point *pdrv = findPt(drv_node);
  makeRcmodelDfs(pdrv);
  getRC();
  if (ctot_ < 1e-22) // 1e-10ps
    return nullptr;
  setTerms(pdrv);
  makeRcmodelFromTs();
  return makeRcmodelFromW();
}

#define ts_orient( pp, ee) \
  if (ee->from!=pp) { ee->to = ee->from; ee->from = pp; }

void
ArnoldiReduce::makeRcmodelDfs(ts_point *pdrv)
{
  bool loop = false;
  int k;
  ts_point *p,*q;
  ts_point *p0 = ts_pointV;
  ts_point *pend = p0 + ts_pointN;
  for (p=p0;p!=pend;p++)
    p->visited = 0;
  ts_edge *e;

  ts_edge **stackV = ts_stackV;
  int stackN = 1;
  stackV[0] = e = pdrv->eV[0];
  ts_orient(pdrv,e);
  pdrv->visited = 1;
  pdrv->in_edge = nullptr;
  pdrv->ts = 0;
  ts_ordV[0] = pdrv-p0;
  ts_pordV[0] = pdrv;
  ts_ordN = 1;
  while (stackN>0) {
    e = stackV[stackN-1];
    q = e->to;

    if (q->visited) {
      // if it is a one-rseg self-loop,
      // ignore, and do not even set *loop
      if (e->to != e->from)
        loop = true;
    } else {
      // try to descend
      q->visited = 1;
      q->ts = ts_ordN++;
      ts_pordV[q->ts] = q;
      ts_ordV[q->ts] = q-p0;
      q->in_edge = e;
      if (q->eN>1) {
        for (k=0;k<q->eN;k++) if (q->eV[k] != e) break;
        e = q->eV[k];
        ts_orient(q,e);
        stackV[stackN++] = e;
        continue; // descent
      }
    }
    // try to ascend
    while (--stackN>=0) {
      e = stackV[stackN];
      p = e->from;
      // find e in p->eV
      for (k=0;k<p->eN;k++) if (p->eV[k]==e) break;
      // if (k==p->eN) notice(0,"ERROR, e not found!\n");
      ++k;
      if (k>=p->eN) continue;
      e = p->eV[k];
      // check that next sibling is not the incoming edge
      if (stackN>0 && e==stackV[stackN-1]) {
          ++k;
          if (k>=p->eN) continue;
          e = p->eV[k];
      }
      ts_orient(p,e);
      stackV[stackN++] = e;
      break;
    }

  } // while (stackN)

  if (loop)
    debugPrint(debug_, "arnoldi", 1, "net %s loop",
               network_->pathName(drvr_pin_));
}

// makeRcmodelGetRC
void
ArnoldiReduce::getRC()
{
  ts_point *p, *p0 = ts_pointV;
  ts_point *pend = p0 + ts_pointN;
  ctot_ = 0.0;
  for (p=p0;p!=pend;p++) {
    p->c = 0.0;
    p->r = 0.0;
    if (p->node_) {
      ParasiticNode *node = p->node_;
      double cap = parasitics_->nodeGndCap(node)
	+ pinCapacitance(node);
      if (cap > 0.0) {
	p->c = cap;
	ctot_ += cap;
      }
      else
	p->c = 0.0;
      if (p->in_edge && p->in_edge->resistor_)
        p->r = parasitics_->value(p->in_edge->resistor_);
      if (!(p->r>=0.0 && p->r<100e+3)) { // 0 < r < 100kohm
	debugPrint(debug_, "arnoldi", 1,
                   "R value %g out of range, drvr pin %s",
                   p->r,
                   network_->pathName(drvr_pin_));
      }
    }
  }
  for (ParasiticCapacitor *capacitor : parasitics_->capacitors(parasitic_network_)) {
    float cap = parasitics_->value(capacitor) * ap_->couplingCapFactor();
    ParasiticNode *node1 = parasitics_->node1(capacitor);
    if (!parasitics_->isExternal(node1)) {
      ts_point *pt = findPt(node1);
      pt->c += cap;
    }
    ParasiticNode *node2 = parasitics_->node2(capacitor);
    if (!parasitics_->isExternal(node2)) {
      ts_point *pt = findPt(node2);
      pt->c += cap;
    }
  }
}

float
ArnoldiReduce::pinCapacitance(ParasiticNode *node)
{
  const Pin *pin = parasitics_->pin(node);
  float pin_cap = 0.0;
  if (pin) {
    Port *port = network_->port(pin);
    LibertyPort *lib_port = network_->libertyPort(port);
    if (lib_port)
      pin_cap = sdc_->pinCapacitance(pin,rf_, corner_, min_max_);
    else if (network_->isTopLevelPort(pin))
      pin_cap = sdc_->portExtCap(port, rf_, corner_, min_max_);
  }
  return pin_cap;
}

void
ArnoldiReduce::setTerms(ts_point *pdrv)
{
  // termV: from drv-ordered to fixed order
  // outV:  from drv-ordered to ts_pordV
  ts_point *p;
  int k,k0;
  termV[0] = k0 = pdrv->tindex;
  for (k=1;k<termN;k++) {
    if (k==k0) termV[k] = 0;
    else termV[k] = k;
  }
  for (k=0;k<termN;k++) {
    p = pterm0 + termV[k];
    outV[k] = p->ts;
  }
}

// The guts of the arnoldi reducer.
void
ArnoldiReduce::makeRcmodelFromTs()
{
  ts_point *p, *p0 = ts_pointV;
  int n = ts_ordN;
  int nterms = termN;
  int i,j,k,h;
  if (debug_->check("arnoldi", 1)) {
    for (k=0;k<ts_ordN;k++) {
      p = ts_pordV[k];
      debugPrint(debug_, "arnoldi", 1, "T%d,P%ld c=%s",
                 p->ts,
                 p-p0,
                 units_->capacitanceUnit()->asString(p->c));
      if (p->is_term)
        debugPrint(debug_, "arnoldi", 1, " term %d", p->tindex);
      if (p->in_edge)
	debugPrint(debug_, "arnoldi", 1, "  from T%d,P%ld r=%s",
                   p->in_edge->from->ts,
                   p->in_edge->from-p0,
                   units_->resistanceUnit()->asString(p->r));
    }
    for (i=0;i<nterms;i++)
      debugPrint(debug_, "arnoldi", 1, "outV[%d] = T%d", i, outV[i]);
  }

  int max_order = 5;

  double *u0, *u1;
  u0 = _u0; u1 = _u1;
  double sum,e1;
  order = max_order;
  if (n < order)
    order = n;

  par[0] = -1; r[0] = 0.0;
  c[0] = ts_pordV[0]->c;
  for (j=1;j<n;j++) {
    p = ts_pordV[j];
    c[j] = p->c;
    r[j] = p->r;
    par[j] = p->in_edge->from->ts;
  }

  sum = 0.0;
  for (j=0;j<n;j++) sum += c[j];
  debugPrint(debug_, "arnoldi", 1, "ctot = %s",
             units_->capacitanceUnit()->asString(sum));
  ctot_ = sum;
  sqc_ = sqrt(sum);
  double sqrt_ctot_inv = 1.0/sqc_;
  for (j=0;j<n;j++) u0[j] = sqrt_ctot_inv;
  for (h=0;h<order;h++) {
    for (i=0;i<nterms;i++) U[h][i] = u0[outV[i]];

    // y = R C u0
    for (j=0;j<n;j++) {
      iv[j] = 0.0;
    }
    for (j=n-1;j>0;j--) {
      iv[j] += c[j]*u0[j];
      iv[par[j]] += iv[j];
    }
    iv[0] += c[0]*u0[0];
    y[0] = 0.0;
    for (j=1;j<n;j++) {
      y[j] = y[par[j]] + r[j]*iv[j];
    }

    // d[h] = u0 C y
    sum = 0.0;
    for (j=1;j<n;j++) {
      sum += u0[j]*c[j]*y[j];
    }
    d[h] = sum;
    if (h==order-1) break;
    if (d[h]<1e-13) { // .1ps
       order = h+1;
       break;
    }

    // y = y - d[h]*u0 - e[h-1]*u1
    if (h==0) {
      for (j=0;j<n;j++) y[j] -= sum*u0[j];
    } else {
      e1 = e[h-1];
      for (j=0;j<n;j++) y[j] -= sum*u0[j] + e1*u1[j];
    }

    // e[h] = sqrt(y C y)
    // u1 = y/e[h]
    sum = 0.0;
    for (j=0;j<n;j++) {
      sum += c[j]*y[j]*y[j];
    }
    if (sum<1e-30) { // (1e-6ns)^2
      order = h+1;
      break;
    }
    e[h] = sqrt(sum);
    sum = 1.0/e[h];
    for (j=0;j<n;j++) u1[j] = sum*y[j];

    // swap u0, u1
    if (h%2) {
      u0 = _u0; u1 = _u1;
    } else {
      u0 = _u1; u1 = _u0;
    }
  }

  if (debug_->check("arnoldi", 1)) {
    report_->reportLine("tridiagonal reduced matrix, drvr pin %s",
                        network_->pathName(drvr_pin_));
    report_->reportLine("order %d n %d",order,n);
    for (h=0;h<order;h++) {
      if (h<order-1)
	report_->reportLine(" d[%d] %s    e[%d] %s",
                            h,
                            units_->timeUnit()->asString(d[h]),
                            h,
                            units_->timeUnit()->asString(e[h]));

      else
	report_->reportLine(" d[%d] %s",
                            h,
                            units_->timeUnit()->asString(d[h]));
      string line = stdstrPrint("U[%d]",h);
      for (i=0;i<nterms;i++)
	line += stdstrPrint(" %6.2e",U[h][i]);
      report_->reportLineString(line);
    }
  }
}

rcmodel *
ArnoldiReduce::makeRcmodelFromW()
{
  int j,h;
  int n = termN;
  rcmodel *mod = new rcmodel();
  mod->order = order;
  mod->n = n;
  if (order>0) {
    int totd = order + order - 1 + order*n;
    mod->d = (double *)malloc(totd*sizeof(double));
    if (order>1) mod->e = mod->d + order;
    else mod->e = nullptr;
    mod->U = (double **)malloc(order*sizeof(double*));
    mod->U[0] = mod->d + order + order - 1;
    for (h=1;h<order;h++) mod->U[h]=mod->U[0] + h*n;
    for (h=0;h<order;h++) {
      mod->d[h] = d[h];
      if (h<order-1) mod->e[h] = e[h];
      for (j=0;j<n;j++)
        mod->U[h][j] = U[h][j];
    }
  }

  mod->pinV = (const Pin **)malloc(n*sizeof(const Pin*));
  for (j=0;j<n;j++) {
    int k = termV[j];
    mod->pinV[j] = pinV[k];
  }

  mod->ctot = ctot_;
  mod->sqc = sqc_;
  return mod;
}

} // namespace