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DmpCeff.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/>.
// "Performance Computation for Precharacterized CMOS Gates with RC Loads",
// Florentin Dartu, Noel Menezes and Lawrence Pileggi, IEEE Transactions
// on Computer-Aided Design of Integrated Circuits and Systems, Vol 15, No 5,
// May 1996, pg 544-553.
//
// The only real change from the paper is that Vl, the measured low
// slew voltage is matched instead of y20 in eqn 12.
#include "DmpCeff.hh"
#include <algorithm> // abs, min
#include <cmath> // sqrt, log
#include "Report.hh"
#include "Debug.hh"
#include "Units.hh"
#include "TimingArc.hh"
#include "TableModel.hh"
#include "Liberty.hh"
#include "Network.hh"
#include "Sdc.hh"
#include "Parasitics.hh"
#include "DcalcAnalysisPt.hh"
#include "ArcDelayCalc.hh"
namespace sta {
using std::abs;
using std::min;
using std::max;
using std::sqrt;
using std::log;
using std::isnan;
// Tolerance (as a scale of value) for driver parameters (Ceff, delta t, t0).
static const double driver_param_tol = .01;
// Waveform threshold crossing time tolerance (1.0 = 100%).
static const double vth_time_tol = .01;
// A small number used by luDecomp.
static const double tiny_double = 1.0e-20;
// Max iterations for findRoot.
static const int find_root_max_iter = 20;
// Indices of Newton-Raphson parameter vector.
enum DmpParam { t0, dt, ceff };
static const char *dmp_param_index_strings[] = {"t0", "dt", "Ceff"};
// Indices of Newton-Raphson function value vector.
enum DmpFunc { y20, y50, ipi };
static const char *dmp_func_index_strings[] = {"y20", "y50", "Ipi"};
static double
exp2(double x);
class DmpError : public Exception
{
public:
DmpError(const char *what);
virtual ~DmpError() {}
virtual const char *what() const noexcept { return what_; }
private:
const char *what_;
};
static double
gateModelRd(const LibertyCell *cell,
const GateTableModel *gate_model,
const RiseFall *rf,
double in_slew,
double c2,
double c1,
float related_out_cap,
const Pvt *pvt,
bool pocv_enabled);
static void
evalDmpEqnsState(void *state);
static void
evalVoEqns(void *state,
double x,
double &y,
double &dy);
static void
evalVlEqns(void *state,
double x,
double &y,
double &dy);
static double
findRoot(void (*func)(void *state, double x, double &y, double &dy),
void *state,
double x1,
double x2,
double x_tol,
int max_iter);
static void
newtonRaphson(const int max_iter,
double x[],
const int n,
const double x_tol,
// eval(state) is called to fill fvec and fjac.
// Returns false if fails.
void (*eval)(void *state),
void *state,
// Temporaries supplied by caller.
double *fvec,
double **fjac,
int *index,
double *p,
double *scale);
static void
luSolve(double **a,
const int size,
const int *index,
double b[]);
static void
luDecomp(double **a,
const int size,
int *index,
double *scale);
////////////////////////////////////////////////////////////////
// Base class for Dartu/Menezes/Pileggi algorithm.
// Derived classes handle different cases of zero values in the Pi model.
class DmpAlg : public StaState
{
public:
DmpAlg(int nr_order, StaState *sta);
virtual ~DmpAlg();
virtual const char *name() = 0;
// Set driver model and pi model parameters for delay calculation.
virtual void init(const LibertyLibrary *library,
const LibertyCell *drvr_cell,
const Pvt *pvt,
const GateTableModel *gate_model,
const RiseFall *rf,
double rd,
double in_slew,
float related_out_cap,
double c2,
double rpi,
double c1);
virtual void gateDelaySlew(double &delay,
double &slew) = 0;
virtual void loadDelaySlew(const Pin *load_pin,
double elmore,
ArcDelay &delay,
Slew &slew);
double ceff() { return ceff_; }
// Given x_ as a vector of input parameters, fill fvec_ with the
// equations evaluated at x_ and fjac_ with the jabobian evaluated at x_.
virtual void evalDmpEqns() = 0;
// Output response to vs(t) ramp driving pi model load.
double vo(double t);
double dVoDt(double t);
// Load responce to driver waveform.
double vl(double t);
double dVlDt(double t);
double vCross() { return v_cross_; }
protected:
// Find driver parameters t0, delta_t, Ceff.
void findDriverParams(double ceff);
void gateCapDelaySlew(double cl,
double &delay,
double &slew);
void gateDelays(double ceff,
double &t_vth,
double &t_vl,
double &slew);
virtual double dv0dt(double t) = 0;
// Partial derivatives of y(t) (jacobian).
void dy(double t,
double t0,
double dt,
double cl,
double &dydt0,
double &dyddt,
double &dydcl);
double y0dt(double t,
double cl);
double y0dcl(double t,
double cl);
void showX();
void showFvec();
void showJacobian();
void findDriverDelaySlew(double &delay,
double &slew);
double findVoCrossing(double vth);
void showVo();
double findVlCrossing(double vth);
void showVl();
void fail(const char *reason);
// Output response to vs(t) ramp driving capacitive load.
double y(double t,
double t0,
double dt,
double cl);
// Output response to unit ramp driving capacitive load.
double y0(double t,
double cl);
// Output response to unit ramp driving pi model load.
virtual double v0(double t) = 0;
// Upper bound on time that vo crosses vh.
virtual double voCrossingUpperBound() = 0;
// Load responce to driver unit ramp.
virtual double vl0(double t) = 0;
// Upper bound on time that vl crosses vh.
double vlCrossingUpperBound();
// Inputs to the delay calculator.
const LibertyCell *drvr_cell_;
const LibertyLibrary *drvr_library_;
const Pvt *pvt_;
const GateTableModel *gate_model_;
double in_slew_;
float related_out_cap_;
double c2_;
double rpi_;
double c1_;
double rd_;
// Logic threshold (percentage of supply voltage).
double vth_;
// Slew lower limit (percentage of supply voltage).
double vl_;
// Slew upper limit (percentage of supply voltage).
double vh_;
// Table slews are scaled by slew_derate to get
// measured slews from vl to vh.
double slew_derate_;
// Driver parameters calculated by this algorithm.
double t0_;
double dt_;
double ceff_;
// Driver parameter Newton-Raphson state.
int nr_order_;
double *x_;
double *fvec_;
double **fjac_;
double *scale_;
double *p_;
int *index_;
// Driver slew used to check load delay.
double drvr_slew_;
double vo_delay_;
// True if the driver parameters are valid for finding the load delays.
bool driver_valid_;
// Load rspf elmore delay.
double elmore_;
double p3_;
private:
virtual double dvl0dt(double t) = 0;
// Implicit argument passed to evalVoEqns, evalVlEqns.
double v_cross_;
};
DmpAlg::DmpAlg(int nr_order,
StaState *sta):
StaState(sta),
c2_(0.0),
rpi_(0.0),
c1_(0.0),
nr_order_(nr_order)
{
x_ = new double[nr_order_];
fvec_ = new double[nr_order_];
scale_ = new double[nr_order_];
p_ = new double[nr_order_];
fjac_ = new double*[nr_order_];
for (int i = 0; i < nr_order_; i++)
fjac_[i] = new double[nr_order_];
index_ = new int[nr_order_];
}
DmpAlg::~DmpAlg()
{
delete [] x_;
delete [] fvec_;
delete [] scale_;
delete [] p_;
for (int i = 0; i < nr_order_; i++)
delete [] fjac_[i];
delete [] fjac_;
delete [] index_;
}
void
DmpAlg::init(const LibertyLibrary *drvr_library,
const LibertyCell *drvr_cell,
const Pvt *pvt,
const GateTableModel *gate_model,
const RiseFall *rf,
double rd,
double in_slew,
float related_out_cap,
// Pi model.
double c2,
double rpi,
double c1)
{
drvr_library_ = drvr_library;
drvr_cell_ = drvr_cell;
pvt_ = pvt;
gate_model_ = gate_model;
rd_ = rd;
in_slew_ = in_slew;
related_out_cap_ = related_out_cap;
c2_ = c2;
rpi_ = rpi;
c1_ = c1;
driver_valid_ = false;
vth_ = drvr_library->outputThreshold(rf);
vl_ = drvr_library->slewLowerThreshold(rf);
vh_ = drvr_library->slewUpperThreshold(rf);
slew_derate_ = drvr_library->slewDerateFromLibrary();
}
// Find Ceff, delta_t and t0 for the driver.
void
DmpAlg::findDriverParams(double ceff)
{
if (nr_order_ == 3)
x_[DmpParam::ceff] = ceff;
double t_vth, t_vl, slew;
gateDelays(ceff, t_vth, t_vl, slew);
// Scale slew to 0-100%
double dt = slew / (vh_ - vl_);
double t0 = t_vth + log(1.0 - vth_) * rd_ * ceff - vth_ * dt;
x_[DmpParam::dt] = dt;
x_[DmpParam::t0] = t0;
newtonRaphson(100, x_, nr_order_, driver_param_tol, evalDmpEqnsState,
this, fvec_, fjac_, index_, p_, scale_);
t0_ = x_[DmpParam::t0];
dt_ = x_[DmpParam::dt];
debugPrint(debug_, "dmp_ceff", 3, " t0 = %s dt = %s ceff = %s",
units_->timeUnit()->asString(t0_),
units_->timeUnit()->asString(dt_),
units_->capacitanceUnit()->asString(x_[DmpParam::ceff]));
if (debug_->check("dmp_ceff", 4))
showVo();
}
static void
evalDmpEqnsState(void *state)
{
DmpAlg *alg = reinterpret_cast<DmpAlg *>(state);
alg->evalDmpEqns();
}
void
DmpAlg::gateCapDelaySlew(double ceff,
double &delay,
double &slew)
{
ArcDelay model_delay;
Slew model_slew;
gate_model_->gateDelay(drvr_cell_, pvt_, in_slew_, ceff, related_out_cap_,
pocv_enabled_, model_delay, model_slew);
delay = delayAsFloat(model_delay);
slew = delayAsFloat(model_slew);
}
void
DmpAlg::gateDelays(double ceff,
double &t_vth,
double &t_vl,
double &slew)
{
double table_slew;
gateCapDelaySlew(ceff, t_vth, table_slew);
// Convert reported/table slew to measured slew.
slew = table_slew * slew_derate_;
t_vl = t_vth - slew * (vth_ - vl_) / (vh_ - vl_);
}
double
DmpAlg::y(double t,
double t0,
double dt,
double cl)
{
double t1 = t - t0;
if (t1 <= 0.0)
return 0.0;
else if (t1 <= dt)
return y0(t1, cl) / dt;
else
return (y0(t1, cl) - y0(t1 - dt, cl)) / dt;
}
double
DmpAlg::y0(double t,
double cl)
{
return t - rd_ * cl * (1.0 - exp2(-t / (rd_ * cl)));
}
void
DmpAlg::dy(double t,
double t0,
double dt,
double cl,
// Return values.
double &dydt0,
double &dyddt,
double &dydcl)
{
double t1 = t - t0;
if (t1 <= 0.0)
dydt0 = dyddt = dydcl = 0.0;
else if (t1 <= dt) {
dydt0 = -y0dt(t1, cl) / dt;
dyddt = -y0(t1, cl) / (dt * dt);
dydcl = y0dcl(t1, cl) / dt;
}
else {
dydt0 = -(y0dt(t1, cl) - y0dt(t1 - dt, cl)) / dt;
dyddt = -(y0(t1, cl) + y0(t1 - dt, cl)) / (dt * dt)
+ y0dt(t1 - dt, cl) / dt;
dydcl = (y0dcl(t1, cl) - y0dcl(t1 - dt, cl)) / dt;
}
}
double
DmpAlg::y0dt(double t,
double cl)
{
return 1.0 - exp2(-t / (rd_ * cl));
}
double
DmpAlg::y0dcl(double t,
double cl)
{
return rd_ * ((1.0 + t / (rd_ * cl)) * exp2(-t / (rd_ * cl)) - 1);
}
void
DmpAlg::showX()
{
for (int i = 0; i < nr_order_; i++)
report_->reportLine("%4s %12.3e", dmp_param_index_strings[i], x_[i]);
}
void
DmpAlg::showFvec()
{
for (int i = 0; i < nr_order_; i++)
report_->reportLine("%4s %12.3e", dmp_func_index_strings[i], fvec_[i]);
}
void
DmpAlg::showJacobian()
{
string line = " ";
for (int j = 0; j < nr_order_; j++)
line += stdstrPrint("%12s", dmp_param_index_strings[j]);
report_->reportLineString(line);
line.clear();
for (int i = 0; i < nr_order_; i++) {
line += stdstrPrint("%4s ", dmp_func_index_strings[i]);
for (int j = 0; j < nr_order_; j++)
line += stdstrPrint("%12.3e ", fjac_[i][j]);
report_->reportLineString(line);
}
}
void
DmpAlg::findDriverDelaySlew(double &delay,
double &slew)
{
delay = findVoCrossing(vth_);
double tl = findVoCrossing(vl_);
double th = findVoCrossing(vh_);
// Convert measured slew to table slew.
slew = (th - tl) / slew_derate_;
}
// Find t such that vo(t)=v.
double
DmpAlg::findVoCrossing(double vth)
{
v_cross_ = vth;
double ub = voCrossingUpperBound();
return findRoot(evalVoEqns, this, t0_, ub, vth_time_tol, find_root_max_iter);
}
static void
evalVoEqns(void *state,
double x,
double &y,
double &dy)
{
DmpAlg *pi_ceff = reinterpret_cast<DmpAlg *>(state);
y = pi_ceff->vo(x) - pi_ceff->vCross();
dy = pi_ceff->dVoDt(x);
}
double
DmpAlg::vo(double t)
{
double t1 = t - t0_;
if (t1 <= 0.0)
return 0.0;
else if (t1 <= dt_)
return v0(t1) / dt_;
else
return (v0(t1) - v0(t1 - dt_)) / dt_;
}
double
DmpAlg::dVoDt(double t)
{
double t1 = t - t0_;
if (t1 <= 0)
return 0.0;
else if (t1 <= dt_)
return dv0dt(t1) / dt_;
else
return (dv0dt(t1) - dv0dt(t1 - dt_)) / dt_;
}
void
DmpAlg::showVo()
{
report_->reportLine(" t vo(t)");
double ub = voCrossingUpperBound();
for (double t = t0_; t < t0_ + ub; t += dt_ / 10.0)
report_->reportLine(" %g %g", t, vo(t));
}
void
DmpAlg::loadDelaySlew(const Pin *,
double elmore,
ArcDelay &delay,
Slew &slew)
{
if (!driver_valid_
|| elmore == 0.0
// Elmore delay is small compared to driver slew.
|| elmore < drvr_slew_ * 1e-3) {
delay = elmore;
slew = drvr_slew_;
}
else {
// Use the driver thresholds and rely on thresholdAdjust to
// convert the delay and slew to the load's thresholds.
try {
if (debug_->check("dmp_ceff", 4))
showVl();
elmore_ = elmore;
p3_ = 1.0 / elmore;
double load_delay = findVlCrossing(vth_);
double tl = findVlCrossing(vl_);
double th = findVlCrossing(vh_);
// Measure delay from Vo, the load dependent source excitation.
double delay1 = load_delay - vo_delay_;
// Convert measured slew to reported/table slew.
double slew1 = (th - tl) / slew_derate_;
if (delay1 < 0.0) {
// Only report a problem if the difference is significant.
if (-delay1 > vth_time_tol * vo_delay_)
fail("load delay less than zero");
// Use elmore delay.
delay1 = elmore;
}
if (slew1 < drvr_slew_) {
// Only report a problem if the difference is significant.
if ((drvr_slew_ - slew1) > vth_time_tol * drvr_slew_)
fail("load slew less than driver slew");
slew1 = drvr_slew_;
}
delay = delay1;
slew = slew1;
}
catch (DmpError &error) {
delay = elmore_;
slew = drvr_slew_;
}
}
}
// Find t such that vl(t)=v.
// Return true if successful.
double
DmpAlg::findVlCrossing(double vth)
{
v_cross_ = vth;
double ub = vlCrossingUpperBound();
return findRoot(evalVlEqns, this, t0_, ub, vth_time_tol, find_root_max_iter);
}
double
DmpAlg::vlCrossingUpperBound()
{
return voCrossingUpperBound() + elmore_;
}
static void
evalVlEqns(void *state,
double x,
double &y,
double &dy)
{
DmpAlg *pi_ceff = reinterpret_cast<DmpAlg *>(state);
y = pi_ceff->vl(x) - pi_ceff->vCross();
dy = pi_ceff->dVlDt(x);
}
double
DmpAlg::vl(double t)
{
double t1 = t - t0_;
if (t1 <= 0)
return 0.0;
else if (t1 <= dt_)
return vl0(t1) / dt_;
else
return (vl0(t1) - vl0(t1 - dt_)) / dt_;
}
double
DmpAlg::dVlDt(double t)
{
double t1 = t - t0_;
if (t1 <= 0)
return 0.0;
else if (t1 <= dt_)
return dvl0dt(t1) / dt_;
else
return (dvl0dt(t1) - dvl0dt(t1 - dt_)) / dt_;
}
void
DmpAlg::showVl()
{
report_->reportLine(" t vl(t)");
double ub = vlCrossingUpperBound();
for (double t = t0_; t < t0_ + ub * 2.0; t += ub / 10.0)
report_->reportLine(" %g %g", t, vl(t));
}
void
DmpAlg::fail(const char *reason)
{
// Allow only failures to be reported with a unique debug flag.
if (debug_->check("dmp_ceff", 1) || debug_->check("dmp_ceff_fail", 1))
report_->reportLine("delay_calc: DMP failed - %s c2=%s rpi=%s c1=%s rd=%s",
reason,
units_->capacitanceUnit()->asString(c2_),
units_->resistanceUnit()->asString(rpi_),
units_->capacitanceUnit()->asString(c1_),
units_->resistanceUnit()->asString(rd_));
}
////////////////////////////////////////////////////////////////
// Capacitive load.
class DmpCap : public DmpAlg
{
public:
DmpCap(StaState *sta);
virtual const char *name() { return "cap"; }
virtual void init(const LibertyLibrary *library,
const LibertyCell *drvr_cell,
const Pvt *pvt,
const GateTableModel *gate_model,
const RiseFall *rf,
double rd,
double in_slew,
float related_out_cap,
double c2,
double rpi,
double c1);
virtual void gateDelaySlew(double &delay,
double &slew);
virtual void loadDelaySlew(const Pin *,
double elmore,
ArcDelay &delay,
Slew &slew);
virtual void evalDmpEqns();
virtual double voCrossingUpperBound();
private:
virtual double v0(double t);
virtual double dv0dt(double t);
virtual double vl0(double t);
virtual double dvl0dt(double t);
};
DmpCap::DmpCap(StaState *sta):
DmpAlg(1, sta)
{
}
void
DmpCap::init(const LibertyLibrary *drvr_library,
const LibertyCell *drvr_cell,
const Pvt *pvt,
const GateTableModel *gate_model,
const RiseFall *rf,
double rd,
double in_slew,
float related_out_cap,
double c2,
double rpi,
double c1)
{
debugPrint(debug_, "dmp_ceff", 3, "Using DMP cap");
DmpAlg::init(drvr_library, drvr_cell, pvt, gate_model, rf,
rd, in_slew, related_out_cap, c2, rpi, c1);
ceff_ = c1 + c2;
}
void
DmpCap::gateDelaySlew(double &delay,
double &slew)
{
debugPrint(debug_, "dmp_ceff", 3, " ceff = %s",
units_->capacitanceUnit()->asString(ceff_));
gateCapDelaySlew(ceff_, delay, slew);
drvr_slew_ = slew;
}
void
DmpCap::loadDelaySlew(const Pin *,
double elmore,
ArcDelay &delay,
Slew &slew)
{
delay = elmore;
slew = drvr_slew_;
}
void
DmpCap::evalDmpEqns()
{
}
double
DmpCap::v0(double)
{
return 0.0;
}
double
DmpCap::dv0dt(double)
{
return 0.0;
}
double
DmpCap::voCrossingUpperBound()
{
return 0.0;
}
double
DmpCap::vl0(double)
{
return 0.0;
}
double
DmpCap::dvl0dt(double)
{
return 0.0;
}
////////////////////////////////////////////////////////////////
// No non-zero pi model parameters, two poles, one zero
class DmpPi : public DmpAlg
{
public:
DmpPi(StaState *sta);
virtual const char *name() { return "Pi"; }
virtual void init(const LibertyLibrary *library,
const LibertyCell *drvr_cell,
const Pvt *pvt,
const GateTableModel *gate_model,
const RiseFall *rf,
double rd,
double in_slew,
float related_out_cap,
double c2,
double rpi,
double c1);
virtual void gateDelaySlew(double &delay,
double &slew);
virtual void evalDmpEqns();
virtual double voCrossingUpperBound();
private:
void findDriverParamsPi();
virtual double v0(double t);
virtual double dv0dt(double t);
double ipiIceff(double t0,
double dt,
double ceff_time,
double ceff);
virtual double vl0(double t);
virtual double dvl0dt(double t);
// Poles/zero.
double p1_;
double p2_;
double z1_;
// Residues.
double k0_;
double k1_;
double k2_;
double k3_;
double k4_;
// Ipi coefficients.
double A_;
double B_;
double D_;
};
DmpPi::DmpPi(StaState *sta) :
DmpAlg(3, sta),
p1_(0.0),
p2_(0.0),
z1_(0.0),
k0_(0.0),
k1_(0.0),
k2_(0.0),
k3_(0.0),
k4_(0.0),
A_(0.0),
B_(0.0),
D_(0.0)
{
}
void
DmpPi::init(const LibertyLibrary *drvr_library,
const LibertyCell *drvr_cell,
const Pvt *pvt,
const GateTableModel *gate_model,
const RiseFall *rf,
double rd,
double in_slew,
float related_out_cap,
double c2,
double rpi,
double c1)
{
debugPrint(debug_, "dmp_ceff", 3, "Using DMP Pi");
DmpAlg::init(drvr_library, drvr_cell, pvt, gate_model, rf, rd,
in_slew, related_out_cap, c2, rpi, c1);
// Find poles/zeros.
z1_ = 1.0 / (rpi_ * c1_);
k0_ = 1.0 / (rd_ * c2_);
double a = rpi_ * rd_ * c1_ * c2_;
double b = rd_ * (c1_ + c2_) + rpi_ * c1_;
double sqrt_ = sqrt(b * b - 4 * a);
p1_ = (b + sqrt_) / (2 * a);
p2_ = (b - sqrt_) / (2 * a);
double p1p2 = (p1_ * p2_);
k2_ = z1_ / p1p2;
k1_ = (1.0 - k2_ * (p1_ + p2_)) / p1p2;
k4_ = (k1_ * p1_ + k2_) / (p2_ - p1_);
k3_ = -k1_ - k4_;
double z_ = (c1_ + c2_) / (rpi_ * c1_ * c2_);
A_ = z_ / p1p2;
B_ = (z_ - p1_) / (p1_ * (p1_ - p2_));
D_ = (z_ - p2_) / (p2_ * (p2_ - p1_));
}
void
DmpPi::gateDelaySlew(double &delay,
double &slew)
{
driver_valid_ = false;
try {
findDriverParamsPi();
ceff_ = x_[DmpParam::ceff];
double table_delay, table_slew;
gateCapDelaySlew(ceff_, table_delay, table_slew);
delay = table_delay;
//slew = table_slew;
try {
double vo_delay, vo_slew;
findDriverDelaySlew(vo_delay, vo_slew);
driver_valid_ = true;
// Save Vo delay to measure load wire delay waveform.
vo_delay_ = vo_delay;
//delay = vo_delay;
slew = vo_slew;
}
catch (DmpError &error) {
fail(error.what());
// Fall back to table slew.
slew = table_slew;
}
}
catch (DmpError &error) {
fail(error.what());
// Driver calculation failed - use Ceff=c1+c2.
ceff_ = c1_ + c2_;
gateCapDelaySlew(ceff_, delay, slew);
}
drvr_slew_ = slew;
}
void
DmpPi::findDriverParamsPi()
{
try {
findDriverParams(c2_ + c1_);
}
catch (DmpError &) {
findDriverParams(c2_);
}
}
// Given x_ as a vector of input parameters, fill fvec_ with the
// equations evaluated at x_ and fjac_ with the jacobian evaluated at x_.
void
DmpPi::evalDmpEqns()
{
double t0 = x_[DmpParam::t0];
double dt = x_[DmpParam::dt];
double ceff = x_[DmpParam::ceff];
if (ceff < 0.0)
throw DmpError("eqn eval failed: ceff < 0");
if (ceff > (c1_ + c2_))
throw DmpError("eqn eval failed: ceff > c2 + c1");
double t_vth, t_vl, slew;
gateDelays(ceff, t_vth, t_vl, slew);
if (slew == 0.0)
throw DmpError("eqn eval failed: slew = 0");
double ceff_time = slew / (vh_ - vl_);
if (ceff_time > 1.4 * dt)
ceff_time = 1.4 * dt;
if (dt <= 0.0)
throw DmpError("eqn eval failed: dt < 0");
double exp_p1_dt = exp2(-p1_ * dt);
double exp_p2_dt = exp2(-p2_ * dt);
double exp_dt_rd_ceff = exp2(-dt / (rd_ * ceff));
double y50 = y(t_vth, t0, dt, ceff);
// Match Vl.
double y20 = y(t_vl, t0, dt, ceff);
fvec_[DmpFunc::ipi] = ipiIceff(t0, dt, ceff_time, ceff);
fvec_[DmpFunc::y50] = y50 - vth_;
fvec_[DmpFunc::y20] = y20 - vl_;
fjac_[DmpFunc::ipi][DmpParam::t0] = 0.0;
fjac_[DmpFunc::ipi][DmpParam::dt] =
(-A_ * dt + B_ * dt * exp_p1_dt - (2 * B_ / p1_) * (1.0 - exp_p1_dt)
+ D_ * dt * exp_p2_dt - (2 * D_ / p2_) * (1.0 - exp_p2_dt)
+ rd_ * ceff * (dt + dt * exp_dt_rd_ceff
- 2 * rd_ * ceff * (1.0 - exp_dt_rd_ceff)))
/ (rd_ * dt * dt * dt);
fjac_[DmpFunc::ipi][DmpParam::ceff] =
(2 * rd_ * ceff - dt - (2 * rd_ * ceff + dt) * exp2(-dt / (rd_ * ceff)))
/ (dt * dt);
dy(t_vl, t0, dt, ceff,
fjac_[DmpFunc::y20][DmpParam::t0],
fjac_[DmpFunc::y20][DmpParam::dt],
fjac_[DmpFunc::y20][DmpParam::ceff]);