It's fairly stable (when I'm lazy as sysadmin):
[was@modular was]$ date Fri Aug 10 14:23:08 EDT 2001 [was@modular was]$ uptime 2:23pm up 98 days, 4:54, 3 users, load average: 3.26, 3.32, 3.16
SOME MODULAR SYMBOLS BENCHMARKS
William A. Stein
1 October 2000
It is difficult or impossible to make correct general comparisons
between computers with vastly different architectures. However, it is
very easy to make specific and correct but possibly misleading
comparisons. In this short note, we do just that.
At present, my primary high-powered computer use involves memory and processor
intensive modular symbols computations in Magma. Thus I chose some
representative computations, and ran them on each of four
Magma-equipped computers. I also compare the list prices of the four
computers.
The computers are as follows:
miro Sun Ultra 450E Quad w/ 4GB RAM (miro.maths.usyd.edu.au) Magma V2.7-2
shimura Dual 450Mhz Celeron w/ 512MB RAM (shimura.math.berkeley.edu) Magma V2.7-1
z505 Sony Z505HE Laptop, 1 PIII 450, 192MB RAM Magma V2.7-1
modular Dual PIII 933 w/ 2GB RAM (modular at harvard) Magma V2.7-1
Contents:
0. List price
1. Computing "S_2(Gamma_0(512))"
2. q-expansions
3. Characteristic Polynomial over Q
4. Modular symbols over finite fields
0. List price
miro $77477
shimura $ 2200 (est., some assembly required)
z505 $ 2500
modular $ 5000 (some assembly required)
modular(2) Modular, but with Magma V2.8 instead of V2.7.
V2.8 has lots of changes, which sometimes make
things faster, and sometimes *slower* (but less buggy!).
Note: The list price for a Dual processor SUN Enterprise E450 w/ 2GB RAM is $44,447.00.
See http://store.sun.com/webconfig/BuildConfig.jhtml;$sessionid$4S2XVZYAAB2UBAMTA1ESPJT5AAAACJ1K
1. Computing "S_2(Gamma_0(512))"
> time M:=NewformDecomposition(CuspidalSubspace(ModularSymbols(512,2)));
miro 35.390
shimura 36.000
z505 30.000
modular 14.669
modular(2) 19.730
2. q-expansions
Continuing from (3) above:
> time f:=qEigenform(M[1],997);
miro 40.630
shimura 36.270
z505 36.490
modular 18.789
modular(2) 9.750
3. Characteristic Polynomial over Q
> M:=ModularSymbols(5,50,+1);T:=HeckeOperator(M,11);time f:=CharacteristicPolynomial(T);
miro 43.919
shimura 36.900
z505 39.359
modular 18.249
modular(2) 13.020
4. Modular symbols over finite fields
> NextPrime(20000);
20011
> time M:=ModularSymbols(20011,2,GF(2003),+1);
miro 42.740
shimura 32.210
z505 Segmentation fault (uses 313MB, swaps heavily, dies)
modular 15.779
modular(2) 16.700
> time T2:=HeckeOperator(M,2);
miro 50.860
shimura 51.189
z505 --
modular 24.949
modular(2) 20.370
> time f:=CharacteristicPolynomial(T2);
miro 511.860
shimura 349.040
z505 --
modular 189.200
modular(2) 185.590
5. Bonus: Hard drive access speed
[root@modular was]# /sbin/hdparm -t /dev/hda
/dev/hda:
Timing buffered disk reads: 64 MB in ... seconds = ...
miro N/A (but probably fast, since it's ULTRA SCSI)
shimura 12.36 MB/sec
z505 12.33 MB/sec
modular 35.56 MB/sec (60GB IBM GXP-75 Deskstar)
6. Bonus 2: Timings comparison with a mystery Alpha box.
This is an email from Helena Verrill:
OK, the machine gram.math.ku.dk, which is a 600Mhz DEC alpha,
the machine for running computing stuff like magma, we have:
Anyway, I'll start the same computation, on both gram and
your modular computer...
time M80:=ModularSymbols(80,8);
modular: gram:
Time: 25.980 Time: 46.366
modular(2) 40.350 s
(the following finds space of trasportable symbols
for W_N trick with matrix [1,0;80,1]. Returns the space
and it's dimension)
time V1,d1:=FINDSUBSPACE(M80,[1,0,80,1]);
modular: gram:
Time: 0.509 Time: 0.933
(the following finds union of above subspaces
for all matrices [*,*;*,d]. Returns space and it's dimension)
(37 is the first prime where this function returns the full
space of cuspidal symbols)
time W37,d37:=VVV(M80,37);
modular: gram:
Time: 305.699 Time: 390.850
Well, the above is not so great without the stats of gram to give
it more meaning; but it does seem modular is about 2 times as
fast as gram. That's quite a lot! though not 2 times as fast on
the last function - I wonder why?
another couple of examples:
time V2,d2:=FINDSUBSPACE(M80,mat(80*6,37));
modular: gram:
Time: 1.329 Time: 2.050
time M90:=ModularSymbols(90,6);
modular: gram:
Time: 9.819 Time: 22.233
modular(2): 19.380
time M90c:=CuspidalSubspace(M90);
modular: gram:
Time: 0.149 Time: 0.533
time VVV(M90,29);
modular: gram:
Time: 230.569 Time: 278.033