Ngspice circuit simulator porting to CUDA - MOS-AK

38 Pages·2012·1.91 MB·English

by  Paolo Nenzi

KLU and PSS Analysis Implementations into NGSPICE
Francesco Lannutti1,2, Stefano Perticaroli1,2

1 University of Roma ”Sapienza”, DIET
2 NGSPICE Project

Dec 12th, 2012 – MOS-AK 2012, San Francisco (CA) – USA
NGSPICE People
Italian Wing German Wing
Francesco Lannutti Dietmar Warning
Stefano Perticaroli Holger Vogt
Paolo Nenzi Robert Larice
KLU and PSS Analysis Implementations into 20/12/2012 Page 2
NGSPICE
Overview
A short SPICE Challenges
introduction to
SPICE
SPICE Algorithm
KLU KLU data structures
integration into
The Binding Table Idea
NGSPICE –
New Version
Performance Analysis and Conclusion
PSS Transient Shooting Algorithm
implementation
Autonomous Case Implementation
into NGSPICE
Examples
Appendix: Properties of the Circuit Sparse Matrices (Davis)
KLU Sparse
Direct Linear
How KLU works
Solver
KLU and PSS Analysis Implementations into 20/12/2012 Page 3
NGSPICE
SPICE Challenge
SPICE3 transient analysis performances
Solve time/transient iteration vs Circuit equations
all netlists
1.0000E+000 9
• The processing power of CPUs scales as N0.96 f(x) = 2.9256E-007 x^1.2013E+000 00
1.0000E-001 R² = 9.2062E-001 2
,s
• The total solve time of spice scale as N1.2 is
1.0000E-002 e
h
T
• New technologies are described increasing models onds 1.0000E-003 s’ro
complexity sec le
h
1.0000E-004 c
a
• As technology improves, SPICE will become B
1.0000E-005 ,V
slower in simulating denser circuits a
la
1.0000E-006 1 10 100 1000 10000 100000 tile
D
equations
Actual performances over number of circuit
equations:
0
1
0
2
Total analysis time 8.75E-7 * N^1.3 ,sis
e
h
Total factor time 4.36E-7 * N^1.4 T
D
h
P
Total solve time 2.93E-7 * N^1.2
,N
e
r
p
a
K
KLU and PSS Analysis Implementations into 20-Dec-12 Page 4
NGSPICE
SPICE Algorithm
SPICE3 transient analysis algorithm
( )
Initial trial Operating Point =
F x,x,t 0
= -
h t t
Discretize differential equations in time n+1 n+1 n
k k
å å
( )
= +
x ax h bf x ,t
Linearize non-linear devices around trial n+1 i n- 1 n+1 i n- i n- i
i=0 (i=- 1 )
Define new trial g xm
Load linear conductances in circuit matrix ( )
Operating Point xm+1 = xm - a xm r ,0 <a £ 1
( )
r r r g¢ xm
Solve Linear Equations
r
( ) ( ) ( )
J xm xm+1 = J xm xm - g xm
Convergence ?

LTE Calculation We will focus Axm+1 = b where
on this part
( )
for KLU A = J xm +G
Increment Time
( ) ( )
b= J xm xm - g xm +C
End of Time Interval
?

KLU and PSS Analysis Implementations into 20-Dec-12 Page 5
NGSPICE
KLU INTEGRATION INTO
NGSPICE – NEW VERSION
KLU and PSS Analysis Implementations into 20/12/2012 Page 6
NGSPICE
How spice loads devices into the matrix
BSIM4
J for each device_type (i.e. BSIM4)
45nmHP_n
for each device_model (i.e N_type)
nmos1
for each instance_of_the_model
nmos2 Evaluate J(V) and RHS(V)
Load J and RHS
nmos3
........
nmosn
45nmHP_p
pmos1
pmos2 RHS SPARSE 1.3:
• The matrix is stored as a linked list (Setup Phase)
pmos3
• The matrix is built iteratively by the instances (Setup Phase)
........
• Each instance knows the memory address of its elements
pmosn • This feature gives to device code an O(1) access to the matrix
elements
• Matrix factorization operations alter the structure of the matrix
RES
by changing pointer relationships between elements
resmod
• We want to keep this, but KLU doesn’t, so we need a
res1 solution!
…….
KLU and PSS Analysis Implementations into 20/12/2012 Page 7
NGSPICE
KLU Data Structures
KLU uses data structures based on array for both A and LU factorization
Ap Ai Ax b q p LU • Sparse Matrix is n-by-n
x
b
)D U • It has «nnz» non-zero elements
M L
A • The RHS vector is dense
LO )D sk
C M c • The «p» and «q» vectors contain row
o
d A l
n L b and column permutations
sretnioP nmuloC secidni woR stnemele onroeNz- srotceV esneD SHR a FTB ,snarT xaM( rotcev no OC dna FTB( rotcev noita rotcev xedni kcolB lanogaid lla fo noitazir • LveU12c ..toFrLedLfasoUviUc:ar et b,goe rxotyrahi,n zc ataaLhhtltU a idhbot io lnaohss gctotrocsksunr tcestahta ulte thrbe eelfso,a pccfkottowo irnro itze earvnsteie ortwony
it tu o
at m tc
u
m re a
r p F Thus KLU sacrifices space to
ep w U
n o L improve time, but this is a good
m R
u feature, because today space costs
lo
C
1 z z s less than time!
+ n n b U
n n n n n n N L
KLU and PSS Analysis Implementations into 20/12/2012 Page 8
NGSPICE
KLU integration into NGSPICE
Binding solution idea to respect both SPICE and KLU requirements
1) Netlist Parsing
2) Devices Setup
3) Matrix Allocation as linked list of nodes – no values written yet, only locations
4) Binding Table Creation
5) Linked List to CSC Data Structure Conversion
Linked list of
nodes
CSC
data
structure
KLU and PSS Analysis Implementations into 20/12/2012 Page 9
NGSPICE
Binding Table (“Associative Cache”) Example
Array Of Structure
Sparse original address KLU new address KLU Complex new address
5233563 5982185 5990465
5238545 5985402 5992089
. . .
. . .
. . .
. . .
5236487 5988432 5995679
The New Binding Table is reordered using Quick Sort Algorithm
Every element now is searched using Binary Search Algorithm
instead of Linear Search Algorithm
KLU and PSS Analysis Implementations into 20/12/2012 Page 10
NGSPICE