Simple Circuit

1
Performance libraries Math Kernel Library
2003?3?
2
Agenda

• ??
• ??
• MKL???
• ????
• ????????
• ??
• ?????
• BLAS??

3
??

• ??,??,??!
• MKL?Intel??????????????
• ??,???BLAS? FFT
• ??
• Solvers (BLAS, LAPACK)
• ????/??? solvers(BLAS, LAPACK)
• ????????? (dgemm)
• PDEs, ????, ??, solid-state physics (FFTs)
• General scientific, financial (vector
  transcendental functions VML)
• ????????Intel???????

4
?? donts

• But dont use MKL on
• Dont use MKL on small counts
• Dont call vector math functions on small n

X Y Z W
X Y Z W
4x4 Transformation matrix

????
????????IPP
5
MKL???

• BLAS (Basic Linear Algebra Subroutines)
• Level 1 BLAS vector-vector operations
• 15 function types
• 48 functions
• Level 2 BLAS matrix-vector operations
• 26 function types
• 66 functions
• Level 3 BLAS matrix-matrix operations
• 9 function types
• 30 functions
• Extended BLAS level 1 BLAS for sparse vectors
• 8 function types
• 24 functions

6
MKL Contents

• LAPACK (linear algebra package)
• Solvers eigensolvers Many hundreds of routines
  total!
• Total user callable support routines gt 1000
• FFTs (fast fourier transforms)
• one two dimensional
• with without frequency ordering (bit reversal)
• VML (vector math library)
• Set of vectorized transcendental functions
• Most of libm functions, but faster

7
MKL???

• ??? MKL????Fortran??
• ???????
• BLAS, LAPACK ????????Fortran??
• Cblas?? ????C/C?????BLAS

8
MKL??? - ??

• ??Intel?CVF Fortran ???
• ?? Linux ? Windows ????
• ????????
• ??????? 32-bit and 64-bit
• ????????
• ????? MKL Index

9
????????

• ?????????????
• ???????????? (??????)
• CPU ???????????
• Cache ?????????Cache?
• ???? ?????????
• Computer ??????????
• System ????????? (??)

10
??

• ??? MKL ???????,??
• level 1, level 2 BLAS ????????( O(n) )
• ???????????
• Level 3 BLAS ( O(n3) )
• LAPACK ( O(n3) )
• FFTs ( O(n log(n) )
• VML? Depends on processor and function
• ??????? OpenMP??
• ??MKL?????????????????

11
??? MKL??

• Assume program calls MKL function then what?
• two approaches
• Static link all library objects linked into
  program binary
• DLL use without static link frequent C approach

12
Static Link

• Scenario 1 ifl, BLAS, Pentium III processor
• ifl o myprog myprog.f static L/opt/intel/mkl/li
  b/32 lmkl_p3 lpthread -lguide (Linux)

13
Dynamic Link

• Scenario 2 C program uses BLAS but want optimal
  code determined at runtime
• ifl o myprog myprog.f L/opt/intel/mkl/lib/32
  lmkl lpthread -lguide (Linux)

14
BLAS ??

• 3 levels of functions sparse
• Level 1 vector-vector operations
• Level 2 vector-matrix operations
• Level 3 matrix-matrix operations
• Sparse level 1 operations on sparse vectors
• Levels ???
• Level 1 in early 70s
• Level 2 in mid-70s followed immediately by level
  3

15
BLAS ????

• General scheme ltprecisiongtltnamegtltmodifiergt
• precision one or two letters
• 1 letter implies input and output are same
  type
• s single, d double, c single complex, z
  double complex
• 2 letters input and output are different
• cs, zd complex in, real out sc, dz real in,
  complex out

16
BLAS????

• ltnamegt
• g general ge general gb band(??)
• s symmetric sy symmetric sp packed sb
  band(??)
• h Hermitian he Hermitian hp packed hb
  band( Hermitian??)
• t triangular tr triangular tp packed tb
  band(??)

17
??band(General Band)
18
??band(symmetric band)
19
????band(Hermitian Band)
20
??band(triangular band)
21
packed
22
BLAS Naming Conventions

• Level 1ltmodifiergt
• c conjugated (cdotc), u unconjugated (cdotu),
  g givens (srotg)
• Level 2 ltmodifiergt
• mv matrix-vector sv solve (vector operations)
  r rank update r2 rank 2 update
• dger double-precision general rank update
• A alpha x y A
• Level 3 ltmodifiergt
• mm matrix-matrix sm solve (matrix operations)
  r rank update r2 rank 2 update
• dsyr2k double-precision symmetric rank-2 update

23
Matrix Multiplication

• ??????
• Roll your own
• DDOT (level 1)
• DGEMV (level 2)
• DGEMM (level 3)
• Because C is used, all is not pretty J

24
Matrix MultiplicationRoll Your Own/Dot Product
Roll Your Own
ddot
for( i 0 i lt n i ) for( j 0 j lt m
j ) temp 0.0 for( k 0 k lt
kk k ) temp aik bkj
cij temp
incx 1 incy ldb for( i 0 i lt n i
) for( j 0 j lt m j ) cij
DDOT( n, ai, incx, b0j, incy )

25
Matrix MultiplicationDGEMV/DGEMM
dgemv
incx 1 incy ldb alpha 1.0 beta 0.0
transa 't' for( i 0 i lt n i )
dgemv( transa, m, n, alpha, a, lda,
b0i, ldb, beta, c0i, ldc
)
dgemm
alpha 1.0 beta 0.0 transa 'n' transb
'n' dgemm( transa, transb, m, n, kk,
alpha, b,
ldb, a, lda, beta,
c, ldc )
26
MKL?????? ????? vs DGEMM
2.2 GHz Intel Pentium 4 processor, 512 MB
memory
27
MKL ?????????DGEMM
800 MHz Itanium processor, 4 MB cache NEC
Express5800