Warm-Hot Intergalactic Medium
SIMD Acceleration in
Astrophysical Simulations
Center for Computational Sciences

Kohji Yoshikawa

Warm-Hot Intergalactic Medium
Y. Suto (Univ. of Tokyo)
H. Kawahara (Univ. of Tokyo)
S. Sasaki (Tokyo Metro-Univ.)
T. Ohashi (Tokyo Metro-Univ.)
N. Yamasaki (JAXA/ISAS)
K. Mitsuda (JAXA/ISAS)

WHIM as Cosmic Missing Baryons
galaxies

dark matter

hot gas(T>107K)

WHIM(105K<T<107K)

Warm-Hot Intergalactic Medium
temperature : 105K < T <107K
density : 10-6 cm-3 < nH < 10-4 cm-3

distributed along filaments and aroundgroups and clusters of galaxies

30Mpc/hheated by cosmological shocks during
the structure formation

WHIM

Many difficulties in detecting the WHIM
very low emission measure due to its low density
so many contaminations such as Galactic emission and CXB.

Detection of WHIM throughAbsorption Lines

Chandra LETG spectrum toward PKS 2155-304

OVIII Lyα at z=0.05

Fang et al. (2007)

Detection through Emission Lines
Yoshikawa et al. (2003) PASJ, 55, 879
We explored the possibility to detect
WHIM through its emission.
OVII (561eV, 568eV, 574eV / 665eV)OVIII (653eV)
WHIM can be detected through its metalemission lines by next generation X-raymissions.
Requirements for instruments
large effective area and FOVhigh spectral resolution in soft X-ray bands

Example of Simulated Spectra
mock observations based on cosmological hydrodynamic simulations

0.3x0.3 deg2
Texp=106sec

OVIII at z=0.2

OVIII at z=0.04
OVIII & OVII at z=0.11
WHIM at the outskirts of clusters and groups of galaxies
can be detected with next generation X-ray missions.

Detection of WHIM
Yoshikawa et al. (2004) , PASJ, 56, 939
Detectability of WHIM in the local universe (r<100Mpc) based on
the constrained simulation of the local universe
We found several sweet spots for the detection of WHIM throughemission lines.

Kawahara, KY, et al. (2006), PASJ, 58, 657
Detectability of WHIM through absorption lines using GRB afterglows.
Combined analysis of WHIMobs. using both of emission and absorption lines.

timescales forionization and recombination

Non-equilibrium Ionization Statesin WHIM
hubble timetemperature
Timescales for Ionizations and recombinations are not short enough
Ionization equilibrium is not achieved

Time evolution of ionization states is investigated incosmological hydrodynamic simulations

cosmological N-body + Hydro(SPH) simulation
ΛCDM m=0.3,  =0.7, h=0.7,  8=1.0
UV/X-ray background radiation
radiative cooling
non-equilibrium ionization : H, He, C, N, O, Ne, Mg, Si, FeZ1df j j−1=∑ Sf −∑ Sf − j f j j 1 f j1
dt k=1 j −k , k k i= j1 i− j , j jcolor：f(OVII), f(OVIII)
f(OVII), f(OVIII) in equilibrium

contour： gas density

SIMD Acceleration inAstrophysical Simulations
K. Nitadori (Univ. of Tokyo)
J. Makino (NAOJ)

SIMD Instructions on Modern CPUs
SIMD = Single Instruction Multiple Data
Simultaneous execution of the same operations on multiple data
SIMD units are usually equipped on modern commodity CPUs
Intel / x86, x86-64 : Streaming SIMD Extension (SSE/SSE2/SSE3/SSSE3)
AMD / x86, x86-64: 3DNow! (Enhanced 3DNow!, 3DNow! Professional), SSE
IBM / PowerPC G4/G5: AltiVec/VMX

Originally developed for 3D graphics and media streaming

We explore the possibility to accelerate computations inastrophysical simulations with the aid of SIMD units / instructions
In this work, Streaming SIMD Extension is adopted

Streaming SIMD Extension (SSE)
4 single precision (32bit) data
2 double precision (64bit) data
single precision

f0

f1

f0+g0

f1+g1

f3

f2+f3

d1

f0

f1

g2

g3

g0

g1

f2+g2

f3+g3

f0×g0

f1×g1

×f2

f3

g2

g3

f2×g2

f3×g3

=

g1

f2

=

g0

f1
d0

double precisionf0

can be stored in a dedicated 128bit-length register

available operations
add, sub, mul, div, sqrt , inverse sqrt, cast, shuffle, comp, logical ops, horizontal operations

Computing Gravitational Forces using SSE
Phantom GRAPE

j-particle

computing the forces on 4 particles in parallel

mj

xj

yj

zj

mj

mj

mj

mj

xj

xj

xj

xj

yj

yj

yj

yj

zj

zj

zj

Nj

d vi
 rj−r i
=∑ m j3
dt j =1 ∣rj −
r i∣
4 i-particles

zj
3x j− x0i

x j− xi

1x j− xi

2x j− xiy j− y 0i

y j− y i

1y j− y i

2y j− y 3i

0z j−z i1z j−z i

2z j−z i3z j−z i22∣r j−r 0i∣∣r j−r 1i∣
03

1 3i

22

∣r j−r i2∣∣r j−r 3i∣2333

m j /∣r j −r i∣ m j /∣r j −r ∣ m j /∣r j −r i ∣ m j /∣r j −r i∣

xi

0xi

1xi

2xi

3y0i

yi

1yi

2yiz 0i

zi

1zi

2zi

3

3

Gravitational Forces on 4 i-particles
Fx

0Fx

1Fx

2Fx

F 0y

Fy

1

Fy

2

Fy

0Fz

1Fz

2FzFz

333

Phantom GRAPEAcceleration of gravitational force calculation using SSE.
emulation of a GRAPE chip with 4 pipelines on commodity CPUs
significant speed up achieved with the aid of SSE
480M interaction/sec (18.3Gflops) on a single core of Core 2 Duo (2.4GHz)
30M interaction/sec (1.1Gflops) without SSE
Force shapes of newton's law with cutoff are also supported.
260M interaction/sec on a single core of Core 2 Duo (2.4GHz)
50M interaction/sec without SSE
APIs are compatible with those of GRAPE-5, 6 libraries

SPH Calculations using SSEN −1

i = ∑ m j W r ij , hi
j =0

N −1

i  ∇⋅vi = ∑ m j v ij⋅∇ W  r ij , hi 
j=0

4 interactions are simultaneously computed using SSE.

cycle counts per interaction

1st loop
2nd loopwith SSE
54.9
81.3

w/o SSE
166327gain
3.03
4.02