forked from The-OpenROAD-Project/OpenSTA
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathArnoldiDelayCalc.cc
1492 lines (1385 loc) · 35.7 KB
/
ArnoldiDelayCalc.cc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
// OpenSTA, Static Timing Analyzer
// Copyright (c) 2020, 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 <stdio.h>
#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();
virtual ArcDelayCalc *copy();
virtual Parasitic *findParasitic(const Pin *drvr_pin,
const RiseFall *rf,
const DcalcAnalysisPt *dcalc_ap);
virtual ReducedParasiticType reducedParasiticType() const;
virtual void gateDelay(const LibertyCell *drvr_cell,
TimingArc *arc,
const Slew &in_slew,
// Pass in load_cap or drvr_parasitic.
float load_cap,
Parasitic *drvr_parasitic,
float related_out_cap,
const Pvt *pvt,
const DcalcAnalysisPt *dcalc_ap,
// Return values.
ArcDelay &gate_delay,
Slew &drvr_slew);
virtual void loadDelay(const Pin *load_pin,
// Return values.
ArcDelay &wire_delay,
Slew &load_slew);
virtual void inputPortDelay(const Pin *port_pin,
float in_slew,
const RiseFall *rf,
Parasitic *parasitic,
const DcalcAnalysisPt *dcalc_ap);
virtual void reportGateDelay(const LibertyCell *drvr_cell,
TimingArc *arc,
const Slew &in_slew,
float load_cap,
Parasitic *,
float related_out_cap,
const Pvt *pvt,
const DcalcAnalysisPt *dcalc_ap,
int digits,
string *result);
void delay_work_set_thresholds(delay_work *D,
double lo,
double hi,
bool rising,
double derate);
private:
void gateDelaySlew(const LibertyCell *drvr_cell,
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)
{
// set_load has precidence over parasitics.
if (!sdc_->drvrPinHasWireCap(drvr_pin)) {
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();
const Corner *corner = dcalc_ap->corner();
if (parasitic_network == nullptr) {
Wireload *wireload = sdc_->wireloadDefaulted(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);
}
reduced_parasitic_drvrs_.push_back(drvr_pin);
return parasitic;
}
}
return nullptr;
}
ReducedParasiticType
ArnoldiDelayCalc::reducedParasiticType() const
{
return ReducedParasiticType::arnoldi;
}
void
ArnoldiDelayCalc::inputPortDelay(const Pin *drvr_pin,
float in_slew,
const RiseFall *rf,
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*>(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,
TimingArc *arc,
const Slew &in_slew,
float load_cap,
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->toTrans()->asRiseFall();
drvr_library_ = drvr_cell->libertyLibrary();
drvr_parasitic_ = drvr_parasitic;
ConcreteParasitic *drvr_cparasitic =
reinterpret_cast<ConcreteParasitic*>(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,
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)
{
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);
}
void
ArnoldiDelayCalc::reportGateDelay(const LibertyCell *,
TimingArc *,
const Slew &,
float,
Parasitic *,
float,
const Pvt *,
const DcalcAnalysisPt *,
int,
string *)
{
}
////////////////////////////////////////////////////////////////
//
// 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].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);
while (va>vlo) {
tmin8 = ta; vmin8 = va;
ta += 1.0/p0;
pr_get_v(ta,s,order,p,rr,&va);