status of the development of the unified solids library

Status of the development of the Unified Solids library

Marek Gayer, CERN PH/SFT2nd AIDA Annual Meeting, Frascati 2013

Marek Gayer - Status of the development of the Unified Solids library

Motivations for a common solids

library• Optimize and guarantee better long-term

maintenance of ROOT and Gean4 solids librarieso A rough estimation indicates that about 70-80% of code investment for

the geometry modeler concerns solids, to guarantee the required precision and efficiency in a huge variety of combinations

• Create a single high quality library to replace solid libraries in Geant4 and ROOTo Starting from what exists today in Geant4 and Rooto Adopt a single type for each shapeo Make fast Tessellated Solid and new Multi-Union o Reach complete conformance to GDML solids schema

• Create extensive testing suite

11/04/2013


Solids implemented so far

• Box• Orb• Trapezoid• Sphere (+ sphere section)• Tube (+ cylindrical section) • Cone (+ conical section) • Generic trapezoid• Tetrahedron• Arbitrary Trapezoid (ongoing)• Multi-Union• Tessellated Solid• Polycone (close to be finished)

0

500

1000

0

500

1000

200

400

600

800

1000

-10-5

05x 10

4 -5

0

5

x 104

-6

-4

-2

0

2

4

6

x 104

-4000-3000

-2000-1000

01000

20003000

4000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000-1000

0

1000

-1000

-500

0

500

1000

-1000

-500

0

500

1000-1000

-500

0

500

1000

-1000

-500

0

500

1000

-1000

-500

0

500

1000-1000

-500

0

500

1000

11/04/2013


Testing Suite• Unified Solid Batch Test• Optical Escape

11/04/2013


Unified Solid Batch Test• New powerful diagnosis tool for testing solids of ROOT,

Geant4 and Unified Solids library designed for transition to Unified Solids o The core part of Unified Solids testingo Testing Unified Solids together with existing Geant4 and ROOT solidso Testing methods with groups of points inside, outside and on surfaceo Compares performance and output values from different codeso Support for batch configuration and execution of testso Contains also tests from the original SBT for points and voxels

• Helps us to make sure we have similar or better performance in each method and different test cases

• Useful to detect, report and fix numerous bugs or suspect return values in Geant4, ROOT and Unified Solids

• Two phaseso Sampling phase (generation of data sets, implemented as C++ app.)o Analysis phase (data post-processing, implemented as MATLAB scripts)

11/04/2013


Visualization of scalar and vector data sets

11/04/2013


3D plots allowing to overview data sets

11/04/2013


3D visualization of investigated shapes

-5000

0

5000

0

50000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x 104

11/04/2013


Support for regions of data, focusing on sub-parts

11/04/2013


Visual analysis of differences

11/04/2013


Visual analysis of differences in 3D

11/04/2013


Inside DistanceToOut DistanceToIn Normal SafetyFromOutside SafetyFromInside0

20

40

60

80

100

120

140

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]

Performance of methods at folder trap-1m-performance

Geant4ROOTUSolids

Graphs with comparison of performance

11/04/2013


Visualization of scalability performance for specific

solids

3 10 100

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Count of solid parts

Tim

e [n

anos

econ

ds p

er o

pera

tion]

Performance of method DistanceToIn at folder log

Geant4ROOTUSolid

-1000

-500

0

500

1000

-1000

-500

0

500

10001000

1500

2000

2500

3000

-5000

0

5000

-5000

0

50000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x 104

-500005000-500005000

2

4

6

8

10

12

x 104

3 10 1000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000


Tim

e [n

anos

econ

ds p

er o

pera

tion]

Performance of method DistanceToOut at folder log

Geant4ROOTUSolid

-1000

-500

0

500

1000

-1000

-500

0

500

10001000

1500

2000

2500

3000

-5000

0

5000

-5000

0

50000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

x 104

11/04/2013


Inspection of values and differences of scalar and vector

data sets

11/04/2013


New Multi-Union solid

11/04/2013


Boolean Union solids• Existing CSG Boolean solids (ROOT and

Geant4) are represented as binary treeso To solve navigation requests, most of the solids composing a

complex one have to be checkedo Scalability is typically linear => low performance for solids

composed of many parts

Boolean Union solid: is binary tree of solids, either primitive or Boolean

[The pictures were produced by users of Wikipedia “Captain Sprite” and “Zottie” and are available under Creative Commons Attribution-Share Alike 3.0 Unported license ]

11/04/2013


Multi-Union solid• We implemented a new

solid as a union of many solids using voxelization technique to optimize speed and scalabilityo 3D space partition for fast

localization of componentso Aiming for a log(n) scalability

• Useful for complex composites made of many solids

-0.8-0.6

-0.4-0.2

00.2

0.40.6

0.8

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

11/04/2013


Scaling of Multi-Union vs. Boolean solid

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 850

2

4

6

8

10

12

14

Number of nodes

Tim

e of

exe

cutio

n [s

]

Scaling of Multi-Union inside method with boxes

Multi-UnionBoolean solid

11/04/2013


Test multi-union solid for scalability measurements

Union of random boxes, orbs and trapezoids(on pictures with 5, 10, 20 solids)

11/04/2013


The most performance critical methods

11/04/2013


Fast Tessellated Solid

11/04/2013


Fast Tessellated Solid• Made from connected triangular and

quadrangular facets forming solid• Old implementation was slow, no

spatial optimization• We use spatial division of facets into

3D grid forming voxels (i.e. we are “voxelizing”)

• Voxelizer is based on bitmasks logical and operations during initialization and on pre-calculated list of facets candidates during runtime

• We are factor thousands faster for LHCb provided foil test case (164k facets)

0510152025303540

0

20

40

60

80

100

120

140

160

180

2000

5

10

15

20

11/04/2013


Fast Tessellated Solid• Voxelization resulted in a significant performance

enhancement in all performance critical methods• Also, old Tesselated Solid had several weak parts of

algorithm, used at initialization which had n2 complexity. o This sometimes caused very huge delays when loading (e.g. in case of foil with

164k faces)o Rewrote to have n ∙ log n complexityo Loading the solid is much faster. What before took minutes, now takes seconds

• Implemented also in Geant4 9.6 as G4TesselatedSolid• By improving design of classes and removing inefficiencies,

total memory save is about ~50%, o Voxelization has overhead vs. original G4TS, which reduces to a total memory save of ~25%

11/04/2013


Inside Normal SafetyFromOutside SafetyFromInside DistanceToIn DistanceToOut0

5

10

15x 10

6

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]

Performance of methods at folder tessellatedsolid-test-t100-100k

G4TessellatedSolidNew G4TessellatedSolid

• Speedup: 894x 10.3x 1000x+ ~8.7x 412x 1183x• Speedup: 2423x 72x 1000x+ ~10.9x 1334x 1976x• Speedup: 2925x 46x 1000x+ ~9.8x 1332x 2968x

Performance – 164k/SCL5 with

10k/100k/1M voxels

11/04/2013


DistanceToIn DistanceToOut Inside Normal SafetyFromInsideSafetyFromOutside0

1

2

3

4

5

6

7

8

9

10x 10

4

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]

Performance of methods at folder key-1.1k

G4TessellatedSolidNew G4TessellatedSolid

• Speedup: 17x 9.53 22.0x 2+ 1.8x 166+• Speedup: 22x 9.33 27.5x 20+ 2x 2000+

Performance – 1.1k/SCL 5 with 10k/1k voxels

11/04/2013


Memory footprint change in comparison with old version

Voxels / Case key-1.1k.gdml foil-2.5k.gdml foil-164k.gdml1 -51% (291kB) -48% (575kB) -50% (32.8M)1000 -34% (391kB) -23% (843kb) -30% (46M)10.000 -22% (462kB) -15% (935kb) -29% (47.2M)100.000 +32% (907kB) +45% (1.6MB) -22% (51MB)1.000.000 +523%

(3.7MB)+500% (6.6MB)

+6% (70M)

11/04/2013


Basic primitives – cone, tube, sphere

11/04/2013


Cone performance


50

100

150

200

250

300

350

400

450

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]

Performance of methods at folder cons-test6-p10k

Geant4ROOTUSolids

11/04/2013

Marek Gayer - Status of the development of the Unified Solids libraryInside DistanceToOut DistanceToIn Normal SafetyFromOutside SafetyFromInside

0

200

400

600

800

1000

1200

1400

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]

Performance of methods at folder cons-test6-p10k

Geant4ROOTUSolids

Cone with small wedge

performance

11/04/2013


0 1 2 3 4 5 6 7 8 9 10

x 104

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

All points

Folder: cons-test6-p10k ; Software: Geant4 - USolids

InsideSafetyFromInsideSafetyFromOutsideDistanceToOutDistanceToInNormal-XNormal-YNormal-Z

Cone values comparison

0 1 2 3 4 5 6 7 8 9 10

x 104

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

All points

Folder: cons-test6-p10k ; Software: USolids - Root

InsideSafetyFromInsideSafetyFromOutsideDistanceToOutDistanceToInNormal-XNormal-YNormal-Z

11/04/2013



50

100

150

200

250

300

350

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]

Performance of methods at folder tubs-test2-p10k

Geant4ROOTUSolids

Tube performance

11/04/2013



500

1000

1500

2000

2500

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]

Performance of methods at folder sphere-test4-10k

Geant4ROOTUSolids

Spherical section performance

0

500

1000

0

500

1000-1000

-500

0

500

1000

11/04/2013


Polycone

11/04/2013


New polycone implementation

• Polycone is an important solid, heavily used in most experimental setups

• Optimization for constructs where coordinate of Z sections can only increase (big majority of real cases)o Careful rewrite of Polycone for these cases

• Based on composition of separate instances of cones, tubes (or their sections)o Providing brief, readable, clean and fast code

• Significant performance improvement over Geant4 & ROOT

• Could bring to visible CPU improvement in full simulation of complex setups like ATLAS

-500005000-500005000

2

4

6

8

10

12

x 104

11/04/2013


Polycone Scalability

3s 10s 100s0

500

1000

1500

2000


Tim

e [n

anos

econ

ds p

er o

pera

tion]

Performance of method Inside at folder log

Geant4ROOTUSolid 3s 10s 100s

0

1000

2000

3000

4000


Tim

e [n

anos

econ

ds p

er o

pera

tion]

Performance of method DistanceToIn at folder log

Geant4ROOTUSolid

3s 10s 100s0

1000

2000

3000

4000

5000

6000


Tim

e [n

anos

econ

ds p

er o

pera

tion]

Performance of method DistanceToOut at folder log

Geant4ROOTUSolid

11/04/2013


Current Polycone performance, 3 z

sections • Speedup factor 3.3x vs. Geant4, 7.6x vs. ROOT

for most performance critical methods, i.e.: Inside, DistanceToOut, DistanceToIn


500

1000

1500

2000

2500

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]

Performance of methods at folder polycone-3s-360-perf

Geant4ROOTUSolid

11/04/2013



sections • Speedup factor 8.3x vs. Geant4, 7.9x vs. ROOT

for most performance critical methods


500

1000

1500

2000

2500

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]


Geant4ROOTUSolid

11/04/2013



sections • Speedup factor 34.3x vs. Geant4, 10.7 vs. ROOT

for most performance critical methods


1000

2000

3000

4000

5000

6000

Method

Tim

e pe

r one

met

hod

call

[nan

osec

onds

]


Geant4ROOTUSolid

11/04/2013


Status of work Types and Unified Solids interface are defined Bridge classes for comparison with Geant4 and

ROOT implemented Testing suite defined and deployed Implemented 9 primitives (Box, Orb, Trapezoid,

Sphere, Tube, Cone, Generic trapezoid, Tetrahedron, Arbitrary trapezoid)

Implemented new composed solids Multi-Union, Tessellated, Polycone (close to be finished)

11/04/2013


Future work plan• Marek Gayer

o Complete and eventually further optimize Polyconeo Implement Polyhedrao Hand over the tasks to Tatiana Nikitina

• Tatiana Nikitinao Give priority to the remaining most critical solids and those

where room for improvement can be easily identifiedo Systematically analyze and implement remaining solids in the

new library

11/04/2013

Thank you for your attention.

???Questions and Answers

Marek Gayer - Status of the development of the Unified Solids library 11/04/2013

status of the development of the unified solids library

Documents

testing solids of root

finishedmarek gayer

common solids libraryoptimize

data setsmarek gayer

subpartsmarek gayer

powerpoint presentation

single high quality

regions of data