The MPFR Library: Timings for Version 0.4 with GMP 3.0
Updated for GMP 3.0, old timings
with GMP 2.0.2 still available here.
32-bit machine
The following tables give the cpu time in milliseconds spent by
several systems or libraries for different operations, at different
precisions. These timings were obtained on a 400Mhz Xeon
(alexandre.medicis.polytechnique.fr) running Linux (libraries were
compiled with gcc -O2). Thanks to the
Médicis center for
providing a machine with all those systems installed on it.
| 100 digits |
Maple V.5.1 |
MuPAD 1.4.2 |
MPF 3.0 |
MPFR 0.4 |
Mathematica 4.0.1 |
Pari 2.0.14 alpha |
Magma V2.6-2 |
Ar. Explorer 1.00 |
| multiplication |
0.04 | 0.024 | 0.0037 | 0.0044 | 0.020 | 0.003 | 0.018 | 0.017 |
| division |
0.15 | 0.027 | 0.007 | 0.009 | 0.143 | 0.007 | 0.033 | 0.018 |
| square root |
0.29 | 0.072 | 0.017 | 0.017 | 0.18 | 0.032 | 0.14 | 0.10 |
| exponential |
1.4 | 0.47 | n/a | 0.23 | 0.94 | 0.16 | 1.1 | n/a |
| logarithm |
2.3 | 0.82 | n/a | 0.40 | 1.24 | 0.35 | 2.0 | n/a |
| 1000 digits |
Maple V.5.1 |
MuPAD 1.4.2 |
MPF 3.0 |
MPFR 0.4 |
Mathematica 4.0.1 |
Pari 2.0.14 alpha |
Magma V2.6-2 |
Ar. Explorer 1.00 |
| multiplication |
1.1 | 0.48 | 0.14 | 0.14 | 0.37 | 0.18 | 1.1 | 0.51 |
| division |
11.3 | 0.56 | 0.22 | 0.23 | 1.12 | 0.25 | 1.3 | 0.40 |
| square root |
15.0 | 1.5 | 0.34 | 0.18 | 1.6 | 0.70 | 3.3 | 1.3 |
| exponential |
53 | 35 | n/a | 15 | 35 | 14 | 79 | n/a |
| logarithm |
69 | 52 | n/a | 15 | 31 | 23 | 119 | n/a |
| 10000 digits |
Maple V.5.1 |
MuPAD 1.4.2 |
MPF 3.0 |
MPFR 0.4 |
Mathematica 4.0.1 |
Pari 2.0.14 alpha |
Magma V2.6-2 |
Ar. Explorer 1.00 |
| multiplication |
39 | 45 | 4.7 | 4.8 | 15 | 17 | 104 | 50 |
| division |
1130 | 49 | 9.8 | 10.1 | 43 | 22 | 111 | 37 |
| square root |
1390 | 160 | 15.6 | 7.3 | 55 | 72 | 362 | 88 |
| exponential |
5330 | 9690 | n/a | 1600 | 930 | 3680 | 22300 | n/a |
| logarithm |
5660 | 15720 | n/a | 420 | 1240 | 6750 | 35400 | n/a |
The source file of these tests is available for
Maple,
MuPAD,
MPF 3.0,
MPFR,
Mathematica,
Pari,
and Magma.
64-bit machine
The following timings were obtained, with the stimulation and help
of Bruno Salvy, on a 500Mhz Compaq XP/1000 (aka Alpha EV6) under OSF/1
4.0 with 640MB of main memory (leon1.medicis.polytechnique.fr).
| 100 digits |
Maple V.5.1 |
MPF 3.0 |
MPFR 0.4 |
Mathematica 3.0 |
Pari 2.0.14 alpha |
Magma V2.6-2 |
| multiplication |
.0125 |
0.0010 |
0.0012 |
0.0114995 |
0.0012 |
0.0033 |
| division |
.0278 |
0.0021 |
0.0029 |
0.108996 |
0.0065 |
0.0116 |
| square root |
.0847 |
0.0051 |
0.0047 |
0.287655 |
0.028 |
0.0484 |
| exponential |
.583 |
n/a |
0.078 |
0.871632 |
0.17 |
0.4316 |
| logarithm |
1.08 |
n/a |
0.29 |
0.836633 |
0.38 |
0.73 |
| 1000 digits |
Maple V.5.1 |
MPF 3.0 |
MPFR 0.4 |
Mathematica 3.0 |
Pari 2.0.14 alpha |
Magma V2.6-2 |
| multiplication |
.185 |
0.031 |
0.031 |
0.101663 |
0.067 |
0.066 |
| division |
.721 |
0.054 |
0.055 |
0.461648 |
0.116 |
0.117 |
| square root |
1.28 |
0.080 |
0.044 |
0.988294 |
0.37 |
0.5 |
| exponential |
14.2 |
n/a |
3.6 |
9.86627 |
7.44 |
7.17 |
| logarithm |
15.8 |
n/a |
3.8 |
19.3326 |
12.9 |
13.5 |
| 10000 digits |
Maple V.5.1 |
MPF 3.0 |
MPFR 0.4 |
Mathematica 3.0 |
Pari 2.0.14 alpha |
Magma V2.6-2 |
| multiplication |
7.20 |
1.1 |
1.1 |
7.5997 |
6.7 |
6.0 |
| division |
57.0 |
2.4 |
2.4 |
22.9991 |
7.6 |
6.6 |
| square root |
73.9 |
3.4 |
1.7 |
34.7653 |
26.0 |
21.7 |
| exponential |
1590. |
n/a |
370. |
1615.94 |
1600 |
1333 |
| logarithm |
1410. |
n/a |
84. |
7418.54 |
2550 |
2217 |
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![[MPFR]](mpfr100.png){kind=small}