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ATLAS.zip_ATLAS研究_atlas_spc_wwwf_ cintf （2000个子文件）

ATL_smm_3dnow_K.c 375KB

ATL_smm6x1x60_x87.c 277KB

ATL_dmm4x2x128_sse2.c 256KB

ATL_dmm_sse2_K.c 251KB

ATL_dmm14x1x56_sse2pABC_K.c 203KB

l2blastst.c 200KB

ATL_smm4x4x128_av.c 174KB

ATL_dmm2x2x128_sse2.c 168KB

ATL_dmm4x4x80_ppc.c 157KB

l1blastst.c 156KB

emit_mm.c 149KB

ATL_smm4x4xURx_mips.c 139KB

ATL_dmm14x1x56_sse2pABC.c 136KB

l3blastst.c 133KB

ATL_dmm14x1x56_sse2pABC_MN.c 129KB

ATL_dmm_julian_gas_30.c 119KB

ATL_mm6x8x8_1p.c 105KB

ATL_smm2x2x256_sse.c 98KB

ATL_dmm6x1x60pABC.c 90KB

ATL_dmm6x1x72_sse2.c 82KB

ATL_dmm4x4xURx_mips.c 81KB

mmsearch.c 81KB

ATL_dmm6x1x30_x87.c 79KB

ATL_smm_sse1_K.c 79KB

ATL_dmm4x1x90_x87.c 78KB

c_c3chke.c 75KB

c_z3chke.c 75KB

ATL_dmm8x1x120_sse2.c 71KB

ATL_dmm1x14x56_sse2pABC.c 69KB

ATL_dmm4x4xUR2_mips.c 68KB

ATL_smm4x4x72_US.c 66KB

ATL_dmm4x4x32_ppc.c 65KB

ATL_dmm4x4xUR3_mips.c 63KB

ATL_smm14x1x84_sseCU.c 62KB

ATL_smm14x1x84_sse.c 60KB

ATL_dmm2x1x40_5pABC.c 57KB

c_s3chke.c 56KB

c_d3chke.c 56KB

ATL_dmm2x1x24_5pABC.c 56KB

ATL_mm4x4x8_bpfabc.c 47KB

ATL_mm4x4x56_av.c 42KB

ATL_smm6x1x120_sse.c 41KB

ATL_dmm6x1x60_sse2_32.c 38KB

ATL_cNCmmJIK.c 37KB

ummsearch.c 37KB

ATL_dmm4x4x16r8_US.c 36KB

ATL_dmm1x6x72_sse2.c 36KB

ATL_cNCmmIJK.c 35KB

ATL_smm4x4x16_US.c 34KB

axpbysrch.c 33KB

c_z2chke.c 33KB

c_c2chke.c 33KB

ATL_mm4x4x8_bpfab.c 33KB

ATL_dmm4x4x16_hppa.c 31KB

c_s2chke.c 31KB

c_d2chke.c 31KB

rotsrch.c 31KB

probe_comp.c 30KB

ATL_dmm6x1x60_sse2.c 30KB

ATL_smm6x1x80_sse.c 30KB

ATL_smm10x1x120_sse.c 30KB

ATL_smm4x4x16_hppa.c 29KB

ATL_CtrsmK.c 29KB

config.c 29KB

ATL_dmm2x2x2_sse2.c 29KB

atlas_install.c 28KB

mvsearch.c 28KB

ATL_dmm4x4x8_US.c 28KB

cpscsrch.c 28KB

gpmmtst.c 27KB

axpysrch.c 27KB

ATL_smm4x1x256_sse.c 27KB

SpewMakeInc.c 27KB

c_zblas2.c 26KB

c_cblas2.c 26KB

dotsrch.c 26KB

gemmtst.c 24KB

ATL_gpmv.c 24KB

scalsrch.c 24KB

copysrch.c 24KB

swapsrch.c 24KB

ATL_cmmJITcp.c 24KB

setsrch.c 23KB

ATL_cNCmmJIK_c.c 23KB

ATL_smm_sse2_112M.c 22KB

slvtst.c 22KB

ATL_dmm6x1x72_sse2_K.c 21KB

ATL_smm6x1x60_sse.c 21KB

invtst.c 21KB

asumsrch.c 21KB

nrm2srch.c 21KB

ATL_cNCmmIJK_c.c 21KB

iamaxsrch.c 20KB

ATL_mm8x8x2.c 20KB

invtrsm.c 20KB

ATL_mm4x4x2US_MN.c 20KB

ATL_gemvN_16x2_1.c 20KB

ATL_smmMNCU_av.c 19KB

ATL_gemvN_16x4_1.c 19KB

emit_rmvT.c 19KB

共 2000 条

Automated Empirical Optimization of Software and the

ATLAS Project

∗

R. Clint Whaley

†

Antoine Petitet

‡

Jack J. Dongarra,

January 22, 2007

Abstract

This paper describes the ATLAS (Automatically Tuned Linear Algebra Software)

project, as well as the fundamental principles that underly it. ATLAS is an instantiation

of a new paradigm in high performance library production and maintenance, which

we term AEOS (Automated Empirical Optimization of Software); this style of library

management has been created in order to allow software to keep pace with the incredible

rate of hardware advancement inherent in Moore’s Law. ATLAS is the application of

this new paradigm to linear algebra software, with the present emphasis on the Basic

Linear Algebra Subprograms (BLAS), a widely used, performance-critical, linear algebra

kernel library.

∗

This work was supported in part by: U.S. Department of Energy under contract number DE-AC05-

96OR22464; National Science Foundation Science and Technology Center Cooperative Agreement No.

CCR-8809615; University of California, Los Alamos National Laboratory, subcontract # B76680017-3Z;

Department of Defense Raytheon E-Systems, subcontract# AA23, prime contract# DAHC94-96-C-0010;

Department of Defense Nichols Research Corporation, subcontract#s NRC CR-96-0011 (ASC) and prime

contract # DAHC-94-96-C-0005; Department of Defense Nichols Research Corporation, subcontract#s NRC

CR-96-0011 (CEWES); prime contract # DAHC-94-96-C-0002

†

Dept. of Computer Sciences, Univ. of TN, Knoxville, TN 37996, rwhaley@cs.utk.edu

‡

Dept. of Computer Sciences, Univ. of TN, Knoxville, TN 37996, petitet@cs.utk.edu

Dept. of Computer Sciences, Univ. of TN, Knoxville, TN 37996, and Mathematical Sciences Section,

ORNL, Oak Ridge, TN 37831, dongarra@cs.utk.edu

Contents

I Introduction 4

II AEOS 4

1 AEOS in Context 5

2 Basic AEOS Requirements 6

3 Methods of Software Adaptation 6

4 Adapting to Constantly Changing Hardware and Software Layers 8

4.1 AEOS/Compiler Synergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

III ATLAS 9

5 Limits of ATLAS’s Approach 10

6 Level 3 BLAS Support in ATLAS 11

6.1 Building the General Matrix Multiply From the L1 Cache-contained Multiply 11

6.1.1 Choosing the Correct Looping Structure . . . . . . . . . . . . . . . . 16

6.1.2 Blocking for Higher Levels of Cache . . . . . . . . . . . . . . . . . . 16

6.2 L1 Cache-contained Matmul . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

6.2.1 Instruction Cache Reuse . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.2.2 Floating Point Instruction Ordering . . . . . . . . . . . . . . . . . . 19

6.2.3 Reducing Loop Overhead . . . . . . . . . . . . . . . . . . . . . . . . 20

6.2.4 Exposing Parallelism . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6.2.5 Finding the Correct Number of Cache Misses . . . . . . . . . . . . . 20

6.2.6 Code Generator Parameters . . . . . . . . . . . . . . . . . . . . . . . 20

6.2.7 Putting It All Together – Outline of the Search Heuristic . . . . . . 21

6.2.8 Timing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

6.3 GEMM-based Level 3 BLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6.3.1 Timing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

7 Optimizing the Level 2 BLAS 27

7.1 Register and Cache Blocking for the Level 2 BLAS . . . . . . . . . . . . . . 27

7.1.1 Register Blocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

7.1.2 Cache Blocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

7.2 ATLAS’s Level 2 Compute Kernels . . . . . . . . . . . . . . . . . . . . . . . 30

7.3 Building ATLAS’s Level 2 BLAS . . . . . . . . . . . . . . . . . . . . . . . . 30

IV Conclusion and future work 31

List of Tables

List of Figures

1 One step of matrix-matrix multiply . . . . . . . . . . . . . . . . . . . . . . . 14

2 General matrix multiplication with A as innermost matrix . . . . . . . . . . 15

3 General matrix multiplication with B as innermost matrix . . . . . . . . . . 15

4 Performance of 500x500 DGEMM across multiple architectures . . . . . . . 23

5 Performance of double precision BLAS on Sun UltraSparc 2200 . . . . . . 26

6 Performance of double precision BLAS on DEC ev56 . . . . . . . . . . . . 26

Part I

Introduction

The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research

eﬀort focusing on applying empirical techniques in order to provide portable performance.

Linear algebra routines are widely used in the computational sciences in general, and sci-

entiﬁc modeli ng in particular. In many of these applications, the performance of the linear

algebra operations are the main constraint preventing the scientist from modeling more

complex problems, which would then more closely match reality. This then dictates an

ongoing need for highly eﬃcient routines; as more compute power becomes available the

scientist typically increases the complexity/accuracy of the model until the limits of the

computational power are reached. Therefore, since many applications have no practical

limit of “enough” accuracy, it is important that each generation of increasingly powerful

computers have optimized linear algebra routines available.

Linear algebra is rich in operations which are highly optimizable, in the sense that a

highly tuned code may run multiple orders of magnitude faster than a naively coded rou-

tine. However, these optimizations are platform speciﬁc, such that an optimization for a

given computer architecture will actually cause a slow-down on another architecture. The

traditional method of handling this problem has been to produce hand-optimized routines

for a given machine. This is a painstaking process, typically requiring many man-months

of highly trained (both in linear algebra and computational optimization) personnel. The

incredible pace of hardware evolution makes this technique untenable in the long run, par-

ticularly so when considering that there are many software layers (eg., operating systems,

compilers, etc), which also eﬀect these kinds of optimizations, that are changing at a similar,

but independent rates.

Therefore a new paradigm is needed for the production of highly eﬃcient routines in

the modern age of computing, and ATLAS represents an implementation of such a set of

new techniques. We call this paradigm ”Automated Empirical Optimization of Software”,

or AEOS. In an AEOS-enabled package such as ATLAS, the package provides many ways

of doing the required operations, and uses empirical timings in order to choose the best

method for a given architecture. Thus, if written generally enough, an AEOS-aware pack-

age can automatically adapt to a new computer architecture in a matter of hours, rather

than requiring months or even years of highly-trained professionals’ time, as dictated by

traditional methods.

ATLAS typically uses code generators (i.e., programs that write other programs) in

order to provide the many diﬀerent ways of doing a given operation, and has sophisticated

search scripts and robust timing mechanisms in order to ﬁnd the best ways of pe rforming

the operation for a given architecture.

One of the main performance kernels of linear algebra has traditionally been a standard

API known as the BLAS (Basic Linear Algebra Subprograms) [14, 17, 6, 7, 5] This API is

supported by hand-tuned eﬀorts of many hardware vendors, and thus provides a good ﬁrst

target for ATLAS, as there is both a large audience for this API, and on those platforms

where vendor-supplied BLAS exist, an easy way to determine if ATLAS can provide the

required level of performance.

Part II

AEOS

1 AEOS in Context

Historically, the research community has pursued two separate paths towards the goal of

making software run at near peak levels. The ﬁrst and most generally successful of these

builds on research into compilers and their asso ciated technologies. The holy grail of com-

pilation research is to take an arbitrary code as an input and produce completely optimal

code as output for given languages and hardware platforms. Despite the immense amount of

eﬀort that has been poured into this approach, its success has been limited both by practical

time constraints (viz. users will not tolerate compile-times that extend into several days)

and by the amount of detailed information the compiler can obtain about the software to

be compiled and the hardware on which it is supposed to execute [16, 23, 24].

A second, complementary thrust has been to identify kernel routines that constitute the

dominant performance cost of a wide variety of applications. When such kernels can be

identiﬁed and an API can be agreed up on by the members of the community, small groups

of programmers with the required level of technical knowledge can concentrate their eﬀorts

on producing optimized kernel libraries for architectures of interest. A prime example of

this kind of eﬀort is the aforementioned BLAS. As experience with the BLAS has shown,

these libraries can be produced by some combination of hardware vendors (e.g. IBM,

Intel), independent software vendors (e.g. Cooke & Associates), and researchers, depending

in large measure on the level of importance the diﬀerent parties attach to the routines in

question. Developers who write their code to call these well-known APIs can then achieve

high performance across all supported architectures.

But just as there are currently boundaries to what can be done to achieve near peak

performance via compiler optimization, the library-oriented approach has signiﬁcant limi-

tations as well. For instance, it is clear that in order to elicit the kind of attention required

to create an optimized library for a given operation, the operation must be regarded as

widely useful by the members of a programming community, who are usually already over-

burdened. Moreover, once an API has been agreed upon, support for various architectures

becomes the dominant problem, especially since the kind of optimizations necessary to

achieve high performance are by their very nature non-portable. Such performance tuning

relies on a careful exploitation of the speciﬁc details the underlying hardware architecture;

if that hardware is changed, a previous optimization may now cause the program to execute

more slowly on the new platform.

The expensive and hardware-relative nature of kernel optimizations becomes all the

more problematic when processor designs are changing at the remarkable pace dictated

by Moore’s Law. These increases in processor performance are, however, largely wasted

unless the key libraries are updated at the same pace as the hardware. With ever-shrinking

hardware generation cycles, these updates become nearl y impossible to do by hand. It is

a fact of the computing industry that by the time highly optimized code is available for a

given architecture, that architecture is generally well on its way towards obsolescence.

We believe the AEOS methodologies address this problem directly, and have the po-

tential to make a signiﬁcant impact on how high performance libraries are produced and

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