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ArnoldiDelayCalc.cc
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// OpenSTA, Static Timing Analyzer
// Copyright (c) 2023, 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/>.
// (c) 2018 Nefelus, Inc.
//
// Author: W. Scott
#include "ArnoldiDelayCalc.hh"
#include <cstdio>
#include <cmath> // abs
#include "Report.hh"
#include "Debug.hh"
#include "Units.hh"
#include "Liberty.hh"
#include "TimingModel.hh"
#include "TimingArc.hh"
#include "TableModel.hh"
#include "Network.hh"
#include "Graph.hh"
#include "Parasitics.hh"
#include "Sdc.hh"
#include "DcalcAnalysisPt.hh"
#include "DelayCalc.hh"
#include "ArcDelayCalc.hh"
#include "RCDelayCalc.hh"
#include "GraphDelayCalc.hh"
#include "Arnoldi.hh"
#include "ArnoldiReduce.hh"
namespace sta {
// wireload8 is n^2
// do not delete arnoldi parasitics
// handle rspf parasitics?
// mv static functions to ArnoldiDelayCalc
// need slew only lookup for
// ra_delay
// ra_get_r
// ra_get_s
using std::abs;
struct delay_work;
struct delay_c;
////////////////////////////////////////////////////////////////
static delay_work *delay_work_create();
static void
delay_work_destroy(delay_work *D);
static double *
delay_work_get_residues(delay_work *D,
int term_index);
static bool
tridiagEV(int n,double *d,double *e,double *p,double **v);
//////////////////////////////////////////////////////////////
struct delay_c
{
double slew_derate;
double vlo;
double vhi;
double vlg;
double smin;
double x1;
double y1;
double vmid; // falling convention, should be >= 0.5
};
// workspace for pole-residue -> delay calculations
// delay_work
// max order is 32
struct delay_work
{
double slew_derate;
double slew_factor; // (0,1.0] table_slew = slew_factor * full_slew
delay_c cV[2];
delay_c *c;
double lo_thresh;
double hi_thresh;
int nmax;
double poles[32]; // 1/tau
double **resi; // resi[jrec][h] h=0,..order
double *v[32];
double *w[32];
double aa[32];
};
////////////////////////////////////////////////////////////////
class ArnoldiDelayCalc : public RCDelayCalc
{
public:
ArnoldiDelayCalc(StaState *sta);
virtual ~ArnoldiDelayCalc();
ArcDelayCalc *copy() override;
Parasitic *findParasitic(const Pin *drvr_pin,
const RiseFall *rf,
const DcalcAnalysisPt *dcalc_ap) override;
ReducedParasiticType reducedParasiticType() const override;
void inputPortDelay(const Pin *port_pin,
float in_slew,
const RiseFall *rf,
const Parasitic *parasitic,
const DcalcAnalysisPt *dcalc_ap) override;
void gateDelay(const LibertyCell *drvr_cell,
const TimingArc *arc,
const Slew &in_slew,
float load_cap,
const Parasitic *drvr_parasitic,
float related_out_cap,
const Pvt *pvt,
const DcalcAnalysisPt *dcalc_ap,
// Return values.
ArcDelay &gate_delay,
Slew &drvr_slew) override;
void loadDelay(const Pin *load_pin,
// Return values.
ArcDelay &wire_delay,
Slew &load_slew) override;
string reportGateDelay(const LibertyCell *drvr_cell,
const TimingArc *arc,
const Slew &in_slew,
float load_cap,
const Parasitic *drvr_parasitic,
float related_out_cap,
const Pvt *pvt,
const DcalcAnalysisPt *dcalc_ap,
int digits) override;
void delay_work_set_thresholds(delay_work *D,
double lo,
double hi,
bool rising,
double derate);
private:
void gateDelaySlew(const LibertyCell *drvr_cell,
const GateTableModel *table_model,
const Slew &in_slew,
float related_out_cap,
const Pvt *pvt,
// Return values.
ArcDelay &gate_delay,
Slew &drvr_slew);
void ar1_ceff_delay(delay_work *D,
timing_table *tab,
arnoldi1 *mod,
double *delays,
double *slews);
double ra_rdelay_1(timing_table *tab,
double ctot);
double ra_get_r(delay_work *D,
timing_table *tab,
double rdelay,
double ctot);
double ra_get_s(delay_work *D,
timing_table *tab,
double r,
double c);
void ra_solve_for_s(delay_work *D,
double p,
double tlohi,
double &s);
// from poles and residues, solve for t20,t50,t80
void pr_solve1(double s,
int order,
double *p,
double *rr,
double v1,
double *t1);
void pr_solve3(double s,
int order,
double *p,
double *rr,
double vhi,
double *thi,
double vmid,
double *tmid,
double vlo,
double *tlo);
//
// routines for linear drive model and ceff
//
double pr_ceff(double s,
double rdrive,
int order,
double *p,
double *rr,
double ceff_time);
double ra_solve_for_t(double p,
double s,
double v);
void ra_solve_for_pt(double ps,
double v,
double *pt,
double *d);
void ra_calc_c(double lo,
double hi,
double *c_smin,
double *c_x1,
double *c_y1);
rcmodel *rcmodel_;
int _pinNmax;
double *_delayV;
double *_slewV;
int pin_n_;
bool input_port_;
ArnoldiReduce *reduce_;
delay_work *delay_work_;
};
ArcDelayCalc *
makeArnoldiDelayCalc(StaState *sta)
{
return new ArnoldiDelayCalc(sta);
}
ArnoldiDelayCalc::ArnoldiDelayCalc(StaState *sta) :
RCDelayCalc(sta),
reduce_(new ArnoldiReduce(sta)),
delay_work_(delay_work_create())
{
_pinNmax = 1024;
_delayV = (double*)malloc(_pinNmax * sizeof(double));
_slewV = (double*)malloc(_pinNmax * sizeof(double));
}
ArcDelayCalc *
ArnoldiDelayCalc::copy()
{
return new ArnoldiDelayCalc(this);
}
ArnoldiDelayCalc::~ArnoldiDelayCalc()
{
delay_work_destroy(delay_work_);
free(_delayV);
free(_slewV);
delete reduce_;
}
Parasitic *
ArnoldiDelayCalc::findParasitic(const Pin *drvr_pin,
const RiseFall *drvr_rf,
const DcalcAnalysisPt *dcalc_ap)
{
const Corner *corner = dcalc_ap->corner();
// set_load has precidence over parasitics.
if (!sdc_->drvrPinHasWireCap(drvr_pin, corner)) {
const ParasiticAnalysisPt *parasitic_ap = dcalc_ap->parasiticAnalysisPt();
Parasitic *parasitic_network =
parasitics_->findParasiticNetwork(drvr_pin, parasitic_ap);
bool delete_parasitic_network = false;
const MinMax *cnst_min_max = dcalc_ap->constraintMinMax();
const OperatingConditions *op_cond = dcalc_ap->operatingConditions();
if (parasitic_network == nullptr) {
Wireload *wireload = sdc_->wireload(cnst_min_max);
if (wireload) {
float pin_cap, wire_cap, fanout;
bool has_wire_cap;
graph_delay_calc_->netCaps(drvr_pin, drvr_rf, dcalc_ap,
pin_cap, wire_cap, fanout, has_wire_cap);
parasitic_network = parasitics_->makeWireloadNetwork(drvr_pin, wireload,
fanout, op_cond,
parasitic_ap);
delete_parasitic_network = true;
}
}
if (parasitic_network) {
Parasitic *parasitic =
reduce_->reduceToArnoldi(parasitic_network,
drvr_pin,
parasitic_ap->couplingCapFactor(),
drvr_rf, op_cond, corner,
cnst_min_max, parasitic_ap);
if (delete_parasitic_network) {
Net *net = network_->net(drvr_pin);
parasitics_->deleteParasiticNetwork(net, parasitic_ap);
}
// Arnoldi parasitics their own class that are not saved in the parasitic db.
unsaved_parasitics_.push_back(parasitic);
return parasitic;
}
}
return nullptr;
}
ReducedParasiticType
ArnoldiDelayCalc::reducedParasiticType() const
{
return ReducedParasiticType::arnoldi;
}
void
ArnoldiDelayCalc::inputPortDelay(const Pin *drvr_pin,
float in_slew,
const RiseFall *rf,
const Parasitic *parasitic,
const DcalcAnalysisPt *dcalc_ap)
{
RCDelayCalc::inputPortDelay(drvr_pin, in_slew, rf, parasitic, dcalc_ap);
rcmodel_ = nullptr;
_delayV[0] = 0.0;
_slewV[0] = in_slew;
int j;
if (parasitic) {
rcmodel_ = reinterpret_cast<rcmodel*>(const_cast<Parasitic*>(parasitic));
pin_n_ = rcmodel_->n;
if (pin_n_ >= _pinNmax) {
_pinNmax *= 2;
if (pin_n_ >= _pinNmax) _pinNmax += pin_n_;
_pinNmax *= 2;
_delayV = (double*)realloc(_delayV,_pinNmax * sizeof(double));
_slewV = (double*)realloc(_slewV,_pinNmax * sizeof(double));
}
pin_n_ = 1;
pin_n_ = rcmodel_->n;
double slew_derate = drvr_library_->slewDerateFromLibrary();
double lo_thresh = drvr_library_->slewLowerThreshold(drvr_rf_);
double hi_thresh = drvr_library_->slewUpperThreshold(drvr_rf_);
bool rising = (drvr_rf_ == RiseFall::rise());
delay_work_set_thresholds(delay_work_, lo_thresh, hi_thresh, rising,
slew_derate);
delay_c *c = delay_work_->c;
double c_log = c->vlg;
for (j=1;j<pin_n_;j++) {
double elmore = rcmodel_->elmore(j);
_delayV[j] = 0.6931472*elmore;
_slewV[j] = in_slew + c_log*elmore/slew_derate;
}
}
}
void
ArnoldiDelayCalc::gateDelay(const LibertyCell *drvr_cell,
const TimingArc *arc,
const Slew &in_slew,
float load_cap,
const Parasitic *drvr_parasitic,
float related_out_cap,
const Pvt *pvt,
const DcalcAnalysisPt *dcalc_ap,
// Return values.
ArcDelay &gate_delay,
Slew &drvr_slew)
{
input_port_ = false;
drvr_rf_ = arc->toEdge()->asRiseFall();
drvr_library_ = drvr_cell->libertyLibrary();
drvr_parasitic_ = drvr_parasitic;
ConcreteParasitic *drvr_cparasitic =
reinterpret_cast<ConcreteParasitic*>(const_cast<Parasitic*>(drvr_parasitic));
rcmodel_ = dynamic_cast<rcmodel*>(drvr_cparasitic);
GateTimingModel *model = gateModel(arc, dcalc_ap);
GateTableModel *table_model = dynamic_cast<GateTableModel*>(model);
if (table_model && rcmodel_)
gateDelaySlew(drvr_cell, table_model, in_slew,
related_out_cap, pvt,
gate_delay, drvr_slew);
else
LumpedCapDelayCalc::gateDelay(drvr_cell, arc, in_slew, load_cap,
drvr_parasitic, related_out_cap, pvt,
dcalc_ap, gate_delay, drvr_slew);
drvr_slew_ = drvr_slew;
multi_drvr_slew_factor_ = 1.0F;
}
void
ArnoldiDelayCalc::gateDelaySlew(const LibertyCell *drvr_cell,
const GateTableModel *table_model,
const Slew &in_slew,
float related_out_cap,
const Pvt *pvt,
// Return values.
ArcDelay &gate_delay,
Slew &drvr_slew)
{
pin_n_ = rcmodel_->n;
if (pin_n_ >= _pinNmax) {
_pinNmax *= 2;
if (pin_n_ >= _pinNmax) _pinNmax += pin_n_;
_delayV = (double*)realloc(_delayV,_pinNmax * sizeof(double));
_slewV = (double*)realloc(_slewV,_pinNmax * sizeof(double));
}
pin_n_ = rcmodel_->n;
if (table_model) {
double slew_derate = drvr_library_->slewDerateFromLibrary();
double lo_thresh = drvr_library_->slewLowerThreshold(drvr_rf_);
double hi_thresh = drvr_library_->slewUpperThreshold(drvr_rf_);
bool rising = (drvr_rf_ == RiseFall::rise());
delay_work_set_thresholds(delay_work_, lo_thresh, hi_thresh, rising,
slew_derate);
if (rcmodel_->order > 0) {
timing_table tab;
tab.table = table_model;
tab.cell = drvr_cell;
tab.pvt = pvt;
tab.in_slew = delayAsFloat(in_slew);
tab.relcap = related_out_cap;
ar1_ceff_delay(delay_work_, &tab, rcmodel_,
_delayV, _slewV);
}
gate_delay = _delayV[0];
drvr_slew = _slewV[0];
}
}
void
ArnoldiDelayCalc::loadDelay(const Pin *load_pin,
// Return values.
ArcDelay &wire_delay,
Slew &load_slew)
{
// This does not appear to handle input port parasitics correctly.
wire_delay = 0.0;
load_slew = drvr_slew_ * multi_drvr_slew_factor_;
if (rcmodel_) {
// HACK
for (int i = 0; i < rcmodel_->n; i++) {
if (rcmodel_->pinV[i] == load_pin) {
wire_delay = _delayV[i] - _delayV[0];
load_slew = _slewV[i] * multi_drvr_slew_factor_;
break;
}
}
}
thresholdAdjust(load_pin, wire_delay, load_slew);
}
string
ArnoldiDelayCalc::reportGateDelay(const LibertyCell *,
const TimingArc *,
const Slew &,
float,
const Parasitic *,
float,
const Pvt *,
const DcalcAnalysisPt *,
int)
{
return "";
}
////////////////////////////////////////////////////////////////
//
// arnoldi1.cpp
//
arnoldi1::~arnoldi1()
{
free(d);
free(U);
}
double
arnoldi1::elmore(int k)
{
if (order==0) return 0.0;
if (order==1) return d[0];
double sqctot = 1.0/U[0][0];
double tau = d[0] + e[0]*U[1][k]*sqctot;
return tau;
}
delay_work *
delay_work_create()
{
int j;
delay_work *D = (delay_work*)malloc(sizeof(delay_work));
D->nmax = 256;
D->resi = (double**)malloc(D->nmax*sizeof(double*));
D->resi[0] = (double*)malloc(D->nmax*32*sizeof(double));
for (j=1;j<D->nmax;j++) D->resi[j] = D->resi[0] + j*32;
D->v[0] = (double*)malloc(32*32*sizeof(double));
for (j=1;j<32;j++) D->v[j] = D->v[0] + j*32;
D->w[0] = (double*)malloc(32*D->nmax*sizeof(double));
for (j=1;j<32;j++) D->w[j] = D->w[0] + j*D->nmax;
D->lo_thresh = 0.0;
D->hi_thresh = 0.0;
D->slew_derate = 0.0;
D->slew_factor = 0.0;
for (j=0;j<2;j++) {
D->cV[j].slew_derate = 0.0;
D->cV[j].vlo = 0.0;
D->cV[j].vhi = 0.0;
D->cV[j].vlg = 0.0;
D->cV[j].smin = 0.0;
D->cV[j].x1 = 0.0;
D->cV[j].y1 = 0.0;
D->cV[j].vmid = 0.0;
}
D->c = D->cV;
return D;
}
static void
delay_work_destroy(delay_work *D)
{
free(D->resi[0]);
free(D->resi);
free(D->v[0]);
free(D->w[0]);
free(D);
}
static void
delay_work_alloc(delay_work *D,int n)
{
if (n<=D->nmax) return;
free(D->w[0]);
free(D->resi[0]);
free(D->resi);
D->nmax *= 2;
if (n > D->nmax) D->nmax = n;
int j;
D->resi = (double**)malloc(D->nmax*sizeof(double*));
D->resi[0] = (double*)malloc(D->nmax*32*sizeof(double));
for (j=1;j<D->nmax;j++) D->resi[j] = D->resi[0] + j*32;
D->w[0] = (double*)malloc(32*D->nmax*sizeof(double));
for (j=1;j<32;j++) D->w[j] = D->w[0] + j*D->nmax;
}
void
ArnoldiDelayCalc::delay_work_set_thresholds(delay_work *D,
double lo,
double hi,
bool rising,
double derate)
{
double mid = 0.5; // 0.0:1.0
int i = rising?1:0;
D->c = D->cV+ i;
// WRONG
bool changed = (lo != D->c->vlo || hi != D->c->vhi);
if (changed) {
if (!(lo>0.01 && hi<0.99)) {
lo = 0.1;
hi = 0.9;
derate = 0.8;
}
D->c->slew_derate = derate;
D->c->vlo = lo;
D->c->vhi = hi;
D->c->vmid = mid;
D->c->vlg = log(hi/lo);
ra_calc_c(lo,hi,
&(D->c->smin), &(D->c->x1),&(D->c->y1));
}
D->lo_thresh = D->c->vlo;
D->hi_thresh = D->c->vhi;
D->slew_derate = derate;
double measured_swing = D->c->vhi - D->c->vlo;
double reported_swing = measured_swing/D->slew_derate;
D->slew_factor = reported_swing;
}
static double *
delay_work_get_residues(delay_work *D,int term_index)
{
return D->resi[term_index];
}
//////////////////////////////////////////////////////////////
//
// calculate_poles_res
//
void arnoldi1::calculate_poles_res(delay_work *D,double rdrive)
{
if (n > D->nmax) delay_work_alloc(D,n);
double *p = D->poles;
double **v = D->v;
double **w = D->w;
double *aa = D->aa;
double **resi = D->resi;
int h,j,k;
double sum, dsave;
dsave = d[0];
d[0] += rdrive*ctot;
if (!tridiagEV(order,d,e,p,v))
criticalError(204, "arnoldi delay calc failed.");
d[0] = dsave;
for (h=0;h<order;h++) {
if (p[h]<1e-14) // .01ps
p[h]=1e-14;
p[h] = 1.0/p[h];
}
for (h=0;h<order;h++) {
for (k=0;k<n;k++) {
sum = 0.0;
for (j=0;j<order;j++)
sum += v[h][j]*U[j][k];
w[h][k] = sum;
}
aa[h] = sqc*v[h][0];
}
for (j=0;j<n;j++) {
for (h=0;h<order;h++)
resi[j][h] = aa[h]*w[h][j];
}
}
////////////////////////////////////////////////////////////////
//
// tridiag.cpp
//
//
// tridiagonal eigenvalues and eigenvectors
// assuming all eigenvalues are positive
//
// tridiagEV(int n,double *d,double *e,double *p,double **v)
// d[0]..d[n-1] diagonal elements
// e[0]..e[n-2] off-diagonal elements
// p[0],..p[n-1] the eigenvalues
// v[0],..v[n-1] the eigenvectors
// M*v[j] = p[j]*v[j]
//
// (M*v[j])[0] = d[0]*v[j][0]+e[0]*v[j][1]
// (M*v[j])[k] = d[k]*v[j][k]+e[k-1]*v[j][k-1]+e[k]*v[j][k+1] 0<k<n-1
// (M*v[j])[n-1] = d[n-1]*v[j][n-1]+e[n-2]*v[j][n-2]
//
static bool
tridiagEV(int n,double *din,double *ein,double *d,double **v)
{
int j,k;
for (j=0;j<n;j++) for (k=0;k<n;k++) v[j][k]=0.0;
for (j=0;j<n;j++) v[j][j] = 1.0;
int m,h,iter,i;
double s,r,p,g,f,c,b;
double e[32];
if (n>32)
return false;
for (i=0;i<n;i++) d[i] = din[i];
for (i=0;i<n-1;i++) e[i+1] = ein[i];
e[0] = 0.0;
for (h=n-1;h>=1;h--) {
iter = 0;
while (abs(e[h])>1e-18) { // 1e-6ps
m=0;
if (m != h) {
if (iter++ == 20)
return false;
g = (d[h-1]-d[h])/(2.0*e[h]);
r = sqrt(1.0+g*g); // watch overflow
g = d[m]-d[h]+e[h]/(g + (g<0?-r:r));
s = c = 1.0;
p = 0.0;
for (i=m+1;i<=h;i++) {
f = s*e[i];
b = c*e[i];
e[i-1] = r = sqrt(f*f+g*g); // watch
if (r == 0.0) {
d[i-1] -= p;
e[m] = 0.0;
break;
}
s = f/r;
c = g/r;
g = d[i-1]-p;
r = (d[i]-g)*s+2.0*c*b;
d[i-1] = g + (p=s*r);
g = c*r-b;
for (k=0;k<n;k++) {
f = v[i-1][k];
v[i-1][k] = s*v[i][k]+c*f;
v[i][k] = c*v[i][k]-s*f;
}
}
if (r == 0.0 && i <= h) continue;
d[h] -= p;
e[h] = g;
e[m] = 0.0;
}
}
}
for (i=0;i<n-1;i++) {
k = i;
p = d[k];
for (j=i+1;j<n;j++)
if (d[j] > p) { k=j; p=d[k]; }
if (k != i) {
d[k] = d[i];
d[i] = p;
for (j=0;j<n;j++) {
p = v[i][j];
v[i][j] = v[k][j];
v[k][j] = p;
}
}
}
return true;
}
////////////////////////////////////////////////////////////////
// prsolve.cpp
// get a waveform point
static void
pr_get_v(double t, double s, int order, double *p, double *rr, double *va)
{
*va = 0.0;
int h;
for (h=0;h<order;h++) {
double pt = p[h]*t;
double ps = p[h]*s;
double f;
if (t<s) {
f = 1.0-t/s + (1.0-exp(-pt))/ps;
} else {
f = exp(ps-pt)*(1.0-exp(-ps))/ps;
}
*va += rr[h]*f;
}
}
static void
get_dv(double t, double s, int order, double *p, double *rr,
double *va, double *dva)
{
*va = 0.0;
*dva = 0.0;
int h;
for (h=0;h<order;h++) {
double p1 = p[h];
double pt = p1*t;
double ps = p1*s;
double f,df,xtmp;
if (t<s) {
xtmp = (1.0-exp(-pt))/ps;
f = 1.0-t/s + xtmp;
df = -p1*xtmp;
} else {
f = exp(ps-pt)*(1.0-exp(-ps))/ps;
df = -p1*f;
}
*va += rr[h]*f;
*dva += rr[h]*df;
}
}
static double
solve_t_bracketed(double s,int order,double *p,double *rr,
double val,double x1,double x2,double v1,double v2)
{
int j;
double df,dx,dxold,f,f2,f1;
double temp,xh,xl,rts;
double xacc = .001e-12; // .001ps
f1 = v1-val;
f2 = v2-val;
if (f1==0.0) return x1;
if (f2==0.0) return x2;
rts = (f1*x2-f2*x1)/(f1-f2);
if (f1<f2) {
xl = x1;
xh = x2;
if (0.0<f1) return x1;
if (f2<0.0) return x2;
} else {
xl = x2;
xh = x1;
if (0.0<f2) return x2;
if (f1<0.0) return x1;
}
dxold = abs(x2-x1);
dx = dxold;
get_dv(rts,s,order,p,rr,&f,&df);
f -= val;
double flast = 0.0;
for (j=1;j<10;j++) {
if ((((rts-xh)*df-f)*((rts-xl)*df-f) >= 0.0)
|| (abs(2.0*f) > abs(dxold*df))) {
dxold = dx;
dx = 0.5*(xh-xl);
if (flast*f >0.0) {
// 2 successive bisections in same direction,
// accelerate
if (f<0.0) dx = 0.9348*(xh-xl);
else dx = 0.0625*(xh-xl);
}
flast = f;
rts = xl+dx;
if (xl == rts) {
return rts;
}
} else {
dxold = dx;
dx = f/df;
flast = 0.0;
temp = rts;
rts -= dx;
if (temp == rts) {
return rts;
}
}
if (abs(dx) < xacc) {
return rts;
}
get_dv(rts,s,order,p,rr,&f,&df); f -= val;
if (f<0.0)
xl = rts;
else
xh = rts;
}
if (abs(f)<1e-6) // 1uV
return rts;
return 0.5*(xl+xh);
}
void
ArnoldiDelayCalc::pr_solve1(double s,
int order,
double *p,
double *rr,
double v1,
double *t1)
{
double tmin = 0.0,tmax = 0.0,vmin = 0.0,vmax = 0.0;
int h, h0 = 0;
while (order>1
&& rr[order-1]<1e-8 // 1e-8V
&& rr[order-1]>-1e-8)
order--;
if (rr[0]<0.5) {
for (h=1;h<order;h++) if (rr[h]>0.3 && rr[h]>rr[0]) { h0 = h; break; }
}
double p0 = p[h0];
double ps,vs,ta,va;
vs = 0.0;
for (h=0;h<order;h++) {
ps = p[h]*s;
vs += rr[h]*(1-exp(-ps))/ps;
}
if (vs<v1) {
// s dominates
ta = 0.5*(1+v1)*s;
pr_get_v(ta,s,order,p,rr,&va);
if (va<v1) {
tmax = ta; vmax = va;
ta = v1*s;
pr_get_v(ta,s,order,p,rr,&va);
if (va<v1) {
// ignoring a typical error at drive node, that comes
// from slight inaccuracies in rr
if (!(rr[order-1]>1.0 && p[order-1]>500.0 && va>v1-0.002))
debugPrint(debug_, "arnoldi", 1, "err, pr_solve1, va<v1");
}
tmin = ta; vmin = va;
} else {
tmin = ta; vmin = va;
ta = s;
pr_get_v(ta,s,order,p,rr,&va);
while (va>v1) {
tmin = ta; vmin = va;
ta *= 2.0;
pr_get_v(ta,s,order,p,rr,&va);
}
if (va>v1)
debugPrint(debug_, "arnoldi", 1, "err, pr_solve1, va>v1");
tmax = ta; vmax = va;
}
} else {
// s is irrelevant
ta = s; va = vs;
while (va >= v1) {
tmin = ta;
vmin = va;
ta += 1.0/p0;
pr_get_v(ta,s,order,p,rr,&va);
}
tmax = ta; vmax = va;
}
*t1 = solve_t_bracketed(s,order,p,rr,v1,tmin,tmax,vmin,vmax);
}
void
ArnoldiDelayCalc::pr_solve3(double s,
int order,
double *p,
double *rr,
double vhi,
double *thi,
double vmid,
double *tmid,
double vlo,
double *tlo)
{
// falling, thi<tmin<tlo
double tmin2,tmax2,vmin2,vmax2;
double tmin5,tmax5,vmin5,vmax5;
double tmin8,tmax8,vmin8,vmax8;
int h, h0 = 0;
while (order>1
&& rr[order-1]<1e-8 // 1e-8V
&& rr[order-1]>-1e-8)
order--;
if (rr[0]<0.5) {
for (h=1;h<order;h++) if (rr[h]>0.3 && rr[h]>rr[0]) { h0 = h; break; }
}
double p0 = p[h0];
if (p0>10e+9) // 1/10ns
p0=10e+9;
double ps,vs,ta,va;
vs = 0.0;
for (h=0;h<order;h++) {
ps = p[h]*s;
vs += rr[h]*(1-exp(-ps))/ps;
}
if (vs<vlo) {
// s dominates
tmax8 = s; vmax8 = vs;
ta = vhi*s;
pr_get_v(ta,s,order,p,rr,&va);
if (va < vmid) {
tmax2 = tmax5 = tmin8 = ta;
vmax2 = vmax5 = vmin8 = va;
ta = vmid*s;
pr_get_v(ta,s,order,p,rr,&va);
if (va>vhi) {
tmin2 = tmin5 = ta;
vmin2 = vmin5 = va;
tmin8 = ta; vmin8 = va;
if (va<vmid) {
tmax5 = ta; vmax5 = va;
} else {
tmin5 = ta; vmin5 = va;
}
} else {
tmax2 = tmin5 = ta;
vmax2 = vmin5 = va;
ta = vlo*s;
pr_get_v(ta,s,order,p,rr,&va);
tmin2 = ta; vmin2 = va;
}
} else {
// rare, s dominates but t=vhi*s is still above vmid
tmin5 = tmin8 = ta;
vmin5 = vmin8 = va;
tmax5 = tmax8;
vmax5 = vmax8;
if (va > vhi) {
tmin2 = tmin5;
vmin2 = vmin5;
tmax2 = tmax5;
vmax2 = tmax5;
} else {
tmax2 = tmin5;
vmax2 = vmin5;
ta = vlo*s;
pr_get_v(ta,s,order,p,rr,&va);
tmin2 = ta; vmin2 = va;
}
}
} else if (vs<vmid) {
// not far from s
tmax2 = tmax5 = tmin8 = s;
vmax2 = vmax5 = vmin8 = vs;
ta = s + 1.6/p0;
pr_get_v(ta,s,order,p,rr,&va);