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MPI Library Timing Tests
Hardware/OS
(A) SGI O2 1 x MIPS R10000 250MHz IRIX 6.5.3
(B) IBM RS/6000 43P-240 1 x PowerPC 603e 223MHz AIX 4.3
(C) Dell GX1/L+ 1 x Pentium III 550MHz Linux 2.2.12-20
(D) PowerBook G3 1 x PowerPC 750 266MHz LinuxPPC 2.2.6-15apmac
(E) PowerBook G3 1 x PowerPC 750 266MHz MacOS 8.5.1
(F) PowerBook G3 1 x PowerPC 750 400MHz MacOS 9.0.2
Compiler
(1) MIPSpro C 7.2.1 -O3 optimizations
(2) GCC 2.95.1 -O3 optimizations
(3) IBM AIX xlc -O3 optimizations (version unknown)
(4) EGCS 2.91.66 -O3 optimizations
(5) Metrowerks CodeWarrior 5.0 C, all optimizations
(6) MIPSpro C 7.30 -O3 optimizations
(7) same as (6), with optimized libmalloc.so
Timings are given in seconds, computed using the C library's clock()
function. The first column gives the hardware and compiler
configuration used for the test. The second column indicates the
number of tests that were aggregated to get the statistics for that
size. These were compiled using 16 bit digits.
Source data were generated randomly using a fixed seed, so they should
be internally consistent, but may vary on different systems depending
on the C library. Also, since the resolution of the timer accessed by
clock() varies, there may be some variance in the precision of these
measurements.
Prime Generation (primegen)
128 bits:
A1 200 min=0.03, avg=0.19, max=0.72, sum=38.46
A2 200 min=0.02, avg=0.16, max=0.62, sum=32.55
B3 200 min=0.01, avg=0.07, max=0.22, sum=13.29
C4 200 min=0.00, avg=0.03, max=0.20, sum=6.14
D4 200 min=0.00, avg=0.05, max=0.33, sum=9.70
A6 200 min=0.01, avg=0.09, max=0.36, sum=17.48
A7 200 min=0.00, avg=0.05, max=0.24, sum=10.07
192 bits:
A1 200 min=0.05, avg=0.45, max=3.13, sum=89.96
A2 200 min=0.04, avg=0.39, max=2.61, sum=77.55
B3 200 min=0.02, avg=0.18, max=1.25, sum=36.97
C4 200 min=0.01, avg=0.09, max=0.33, sum=18.24
D4 200 min=0.02, avg=0.15, max=0.54, sum=29.63
A6 200 min=0.02, avg=0.24, max=1.70, sum=47.84
A7 200 min=0.01, avg=0.15, max=1.05, sum=30.88
256 bits:
A1 200 min=0.08, avg=0.92, max=6.13, sum=184.79
A2 200 min=0.06, avg=0.76, max=5.03, sum=151.11
B3 200 min=0.04, avg=0.41, max=2.68, sum=82.35
C4 200 min=0.02, avg=0.19, max=0.69, sum=37.91
D4 200 min=0.03, avg=0.31, max=1.15, sum=63.00
A6 200 min=0.04, avg=0.48, max=3.13, sum=95.46
A7 200 min=0.03, avg=0.37, max=2.36, sum=73.60
320 bits:
A1 200 min=0.11, avg=1.59, max=6.14, sum=318.81
A2 200 min=0.09, avg=1.27, max=4.93, sum=254.03
B3 200 min=0.07, avg=0.82, max=3.13, sum=163.80
C4 200 min=0.04, avg=0.44, max=1.91, sum=87.59
D4 200 min=0.06, avg=0.73, max=3.22, sum=146.73
A6 200 min=0.07, avg=0.93, max=3.50, sum=185.01
A7 200 min=0.05, avg=0.76, max=2.94, sum=151.78
384 bits:
A1 200 min=0.16, avg=2.69, max=11.41, sum=537.89
A2 200 min=0.13, avg=2.15, max=9.03, sum=429.14
B3 200 min=0.11, avg=1.54, max=6.49, sum=307.78
C4 200 min=0.06, avg=0.81, max=4.84, sum=161.13
D4 200 min=0.10, avg=1.38, max=8.31, sum=276.81
A6 200 min=0.11, avg=1.73, max=7.36, sum=345.55
A7 200 min=0.09, avg=1.46, max=6.12, sum=292.02
448 bits:
A1 200 min=0.23, avg=3.36, max=15.92, sum=672.63
A2 200 min=0.17, avg=2.61, max=12.25, sum=522.86
B3 200 min=0.16, avg=2.10, max=9.83, sum=420.86
C4 200 min=0.09, avg=1.44, max=7.64, sum=288.36
D4 200 min=0.16, avg=2.50, max=13.29, sum=500.17
A6 200 min=0.15, avg=2.31, max=10.81, sum=461.58
A7 200 min=0.14, avg=2.03, max=9.53, sum=405.16
512 bits:
A1 200 min=0.30, avg=6.12, max=22.18, sum=1223.35
A2 200 min=0.25, avg=4.67, max=16.90, sum=933.18
B3 200 min=0.23, avg=4.13, max=14.94, sum=825.45
C4 200 min=0.13, avg=2.08, max=9.75, sum=415.22
D4 200 min=0.24, avg=4.04, max=20.18, sum=808.11
A6 200 min=0.22, avg=4.47, max=16.19, sum=893.83
A7 200 min=0.20, avg=4.03, max=14.65, sum=806.02
Modular Exponentation (metime)
The following results are aggregated from 200 pseudo-randomly
generated tests, based on a fixed seed.
base, exponent, and modulus size (bits)
P/C 128 192 256 320 384 448 512 640 768 896 1024
------- -----------------------------------------------------------------
A1 0.015 0.027 0.047 0.069 0.098 0.133 0.176 0.294 0.458 0.680 1.040
A2 0.013 0.024 0.037 0.053 0.077 0.102 0.133 0.214 0.326 0.476 0.668
B3 0.005 0.011 0.021 0.036 0.056 0.084 0.121 0.222 0.370 0.573 0.840
C4 0.002 0.006 0.011 0.020 0.032 0.048 0.069 0.129 0.223 0.344 0.507
D4 0.004 0.010 0.019 0.034 0.056 0.085 0.123 0.232 0.390 0.609 0.899
E5 0.007 0.015 0.031 0.055 0.088 0.133 0.183 0.342 0.574 0.893 1.317
A6 0.008 0.016 0.038 0.042 0.064 0.093 0.133 0.239 0.393 0.604 0.880
A7 0.005 0.011 0.020 0.036 0.056 0.083 0.121 0.223 0.374 0.583 0.855
Multiplication and Squaring tests, (mulsqr)
The following results are aggregated from 500000 pseudo-randomly
generated tests, based on a per-run wall-clock seed. Times are given
in seconds, except where indicated in microseconds (us).
(A1)
bits multiply square ad percent time/mult time/square
64 9.33 9.15 > 1.9 18.7us 18.3us
128 10.88 10.44 > 4.0 21.8us 20.9us
192 13.30 11.89 > 10.6 26.7us 23.8us
256 14.88 12.64 > 15.1 29.8us 25.3us
320 18.64 15.01 > 19.5 37.3us 30.0us
384 23.11 17.70 > 23.4 46.2us 35.4us
448 28.28 20.88 > 26.2 56.6us 41.8us
512 34.09 24.51 > 28.1 68.2us 49.0us
640 47.86 33.25 > 30.5 95.7us 66.5us
768 64.91 43.54 > 32.9 129.8us 87.1us
896 84.49 55.48 > 34.3 169.0us 111.0us
1024 107.25 69.21 > 35.5 214.5us 138.4us
1536 227.97 141.91 > 37.8 456.0us 283.8us
2048 394.05 242.15 > 38.5 788.1us 484.3us
(A2)
bits multiply square ad percent time/mult time/square
64 7.87 7.95 < 1.0 15.7us 15.9us
128 9.40 9.19 > 2.2 18.8us 18.4us
192 11.15 10.59 > 5.0 22.3us 21.2us
256 12.02 11.16 > 7.2 24.0us 22.3us
320 14.62 13.43 > 8.1 29.2us 26.9us
384 17.72 15.80 > 10.8 35.4us 31.6us
448 21.24 18.51 > 12.9 42.5us 37.0us
512 25.36 21.78 > 14.1 50.7us 43.6us
640 34.57 29.00 > 16.1 69.1us 58.0us
768 46.10 37.60 > 18.4 92.2us 75.2us
896 58.94 47.72 > 19.0 117.9us 95.4us
1024 73.76 59.12 > 19.8 147.5us 118.2us
1536 152.00 118.80 > 21.8 304.0us 237.6us
2048 259.41 199.57 > 23.1 518.8us 399.1us
(B3)
bits multiply square ad percent time/mult time/square
64 2.60 2.47 > 5.0 5.20us 4.94us
128 4.43 4.06 > 8.4 8.86us 8.12us
192 7.03 6.10 > 13.2 14.1us 12.2us
256 10.44 8.59 > 17.7 20.9us 17.2us
320 14.44 11.64 > 19.4 28.9us 23.3us
384 19.12 15.08 > 21.1 38.2us 30.2us
448 24.55 19.09 > 22.2 49.1us 38.2us
512 31.03 23.53 > 24.2 62.1us 47.1us
640 45.05 33.80 > 25.0 90.1us 67.6us
768 63.02 46.05 > 26.9 126.0us 92.1us
896 83.74 60.29 > 28.0 167.5us 120.6us
1024 106.73 76.65 > 28.2 213.5us 153.3us
1536 228.94 160.98 > 29.7 457.9us 322.0us
2048 398.08 275.93 > 30.7 796.2us 551.9us
(C4)
bits multiply square ad percent time/mult time/square
64 1.34 1.28 > 4.5 2.68us 2.56us
128 2.76 2.59 > 6.2 5.52us 5.18us
192 4.52 4.16 > 8.0 9.04us 8.32us
256 6.64 5.99 > 9.8 13.3us 12.0us
320 9.20 8.13 > 11.6 18.4us 16.3us
384 12.01 10.58 > 11.9 24.0us 21.2us
448 15.24 13.33 > 12.5 30.5us 26.7us
512 19.02 16.46 > 13.5 38.0us 32.9us
640 27.56 23.54 > 14.6 55.1us 47.1us
768 37.89 31.78 > 16.1 75.8us 63.6us
896 49.24 41.42 > 15.9 98.5us 82.8us
1024 62.59 52.18 > 16.6 125.2us 104.3us
1536 131.66 107.72 > 18.2 263.3us 215.4us
2048 226.45 182.95 > 19.2 453.0us 365.9us
(A7)
bits multiply square ad percent time/mult time/square
64 1.74 1.71 > 1.7 3.48us 3.42us
128 3.48 2.96 > 14.9 6.96us 5.92us
192 5.74 4.60 > 19.9 11.5us 9.20us
256 8.75 6.61 > 24.5 17.5us 13.2us
320 12.5 8.99 > 28.1 25.0us 18.0us
384 16.9 11.9 > 29.6 33.8us 23.8us
448 22.2 15.2 > 31.7 44.4us 30.4us
512 28.3 19.0 > 32.7 56.6us 38.0us
640 42.4 28.0 > 34.0 84.8us 56.0us
768 59.4 38.5 > 35.2 118.8us 77.0us
896 79.5 51.2 > 35.6 159.0us 102.4us
1024 102.6 65.5 > 36.2 205.2us 131.0us
1536 224.3 140.6 > 37.3 448.6us 281.2us
2048 393.4 244.3 > 37.9 786.8us 488.6us
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