Benchmarks don't lie (TM)
Richard B. Kreckel
kreckel at thep.physik.uni-mainz.de
Wed Sep 24 00:07:40 CEST 2003
Hi,
AMD released the Opteron processor family today leaving people with the
budget to buy new hardware wondering what exactly to purchase next. Here
are some data to underpin your decision-making and convincing (whomever:
head of department, parents, wife).
I've let the suite of benchmarks from GiNaC-1.1.3 run on various machines,
all clocked at 1.4 GHz, with one exception: the Itanium1 in the list was
clocked at a mere 930MHz. Its timings were adjusted to accomodate for
this difference in clock rates as far as possible. You'll notice anyway
how that early silicon isn't worth being listed, it's just way slower than
all the other machines. This has changed with the Itanium2. But apart
from the two monsters M2 and N (with unconclusive results) it seems like
the AMD chips generally perform faster than the Intel silicon.
Naturally, all functions (except, perhaps, A, B and C) exercise some
fairly jerky code with many branches. This is generally the case with
CAS.
Note that with the machines tested, the P-IV's handicap (its ridiculously
large pipeline) was compensated by it having a comparatively fast DDR333,
as opposed to the P-III which had less memory bandwith.
Well, for such reasons the numbers below should be taken with a grain of
salt. But still, my next personal machine won't be from Intel, and it
won't be 32Bit either.
So, without further ado, here are the numbers:
Opteron Itanium2 Itanium1 P-III P-IV Athlon
------------------------------------------------------------------------------------------------------------
commutative expansion and substitution, size 200. 0.45s 0.55s 1.04s 0.63s 0.56s 0.53s
commutative expansion and substitution, size 500. 3.43s 4.17s 7.78s 4.46s 4.25s 4.22s
Laurent series expansion of Gamma function, order 20. 0.34s 0.43s 0.84s 0.57s 0.5s 0.36s
Laurent series expansion of Gamma function, order 25. 1.37s 1.65s 3.27s 2.29s 2.01s 1.59s
determinant of symbolic 10x10 Vandermonde matrix. 0.32s 0.37s 0.65s 0.45s 0.38s 0.27s
determinant of symbolic 12x12 Vandermonde matrix. 2.99s 3.56s 6.07s 4.14s 3.48s 2.62s
determinant of symbolic 8x8 Toeplitz matrix. 0.31s 0.37s 0.66s 0.43s 0.45s 0.27s
determinant of symbolic 9x9 Toeplitz matrix. 1.25s 0.89s 2.59s 1.64s 1.88s 1.29s
hash map size 500000 insert. 1.02s 1.16s 1.8s 1.01s 1.35s 1.15s
hash map size 500000 find. 0.56s 0.69s 1.15s 0.63s 0.93s 0.62s
hash map size 500000 erase. 0.43s 0.5s 0.85s 0.44s 0.66s 0.5s
Lewis-Wester test A (divide factorials). 0.34s 0.357s 0.61s 0.38s 0.4s 0.43s
Lewis-Wester test B (sum of rational numbers). 0.005s 0.008s 0.01s 0.006s 0.005s 0.004s
Lewis-Wester test C (gcd of big integers). 0.059s 0.129s 0.16s 0.093s 0.116s 0.059s
Lewis-Wester test D (normalized sum of rational fcns). 0.095s 0.136s 0.21s 0.135s 0.13s 0.083s
Lewis-Wester test E (normalized sum of rational fcns). 0.07s 0.093s 0.16s 0.10s 0.098s 0.062s
Lewis-Wester test F (gcd of 2-var polys). 0.009s 0.011s 0.021s 0.015s 0.011s 0.008s
Lewis-Wester test G (gcd of 3-var polys). 0.27s 0.42s 0.65s 0.38s 0.43s 0.27s
Lewis-Wester test H (det of 80x80 Hilbert). 1.37s 1.63s 2.45s 2.32s 2.08s 1.18s
Lewis-Wester test I (invert rank 40 Hilbert). 0.38s 0.47s 0.73s 0.64s 0.56s 0.33s
Lewis-Wester test J (check rank 40 Hilbert). 0.21s 0.28s 0.43s 0.34s 0.33s 0.18s
Lewis-Wester test K (invert rank 70 Hilbert). 2.62s 3.24s 4.93s 4.28s 3.92s 2.31s
Lewis-Wester test L (check rank 70 Hilbert). 1.28s 1.7s 2.69s 1.96s 1.9s 1.14s
Lewis-Wester test M1 (26x26 sparse, det). 0.055s 0.064s 0.105s 0.093s 0.07s 0.049s
Lewis-Wester test M2 (101x101 sparse, det). 264.99s 247.25s ---- 219.45s 304.25s 325.45s
Lewis-Wester test N (poly at rational fcns). 205.08s 219.29s ---- 186.6s 242.13s 236.26s
Lewis-Wester test O1 (three 15x15 dets)... (average) 7.95s 9.32s 16.14s 9.23s 10.0s 9.54s
Lewis-Wester test P (det of sparse rank 101). 0.289s 0.24s 0.35s 0.38s 0.38s 0.3s
Lewis-Wester test P' (det of less sparse rank 101). 0.78s 0.96s 1.46s 1.35s 1.16s 0.68s
Lewis-Wester test Q (charpoly(P)). 16.54s 19.18s 31.04s 25.22s 24.01s 14.29s
Lewis-Wester test Q' (charpoly(P')). 33.75s 41.05s 64.28s 49.95s 51.62s 27.46s
computation of antipodes in Yukawa theory...... (total) 8.27s 10.4s 18.52s 12.54s 11.51s 7.15s
Fateman's polynomial expand benchmark. 28.84s 28.29s 38.86s 31.72s 41.8s 41.17s
Cheers
-richy.
--
Richard B. Kreckel
<Richard.Kreckel at GiNaC.DE>
<http://www.ginac.de/~kreckel/>
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