PARI library benchmarks: floating point arithmetic
This page refers to version 2.14.0 of the PARI/GP system
[ bench
source code ], with native kernel and GMP
kernel respectively. PARI and GMP-6.1.2 were linked dynamically to the bench
program. This benchmark was adapted from the
MPFR bench, with a minor change: we precompute log(2) and
π.
The following tables give the cpu time in milliseconds spent by the PARI
kernels for different operations, at different (decimal) digitsizes.
64-bit machine: pari.math.u-bordeaux.fr
Xeon Silver 4110 @ 2.10Ghz, running Linux 4.19.0-18-amd64.
Libraries were compiled with gcc 8.3.0 and native flags.
| 100 digits |
pari-2.14.0-gmp |
pari-2.14.0 |
mpfr-4.1.0 |
| x*y |
0.000062 |
0.000060 |
0.000069 |
| x*x |
0.000050 |
0.000048 |
0.000059 |
| x/y |
0.00016 |
0.00029 |
0.00017 |
| sqrt(x) |
0.00024 |
0.00078 |
0.00024 |
| exp(x) |
0.0055 |
0.0058 |
0.0031 |
| log(x) |
0.0071 |
0.012 |
0.0055 |
| sin(x) |
0.0048 |
0.0057 |
0.0038 |
| cos(x) |
0.0044 |
0.0047 |
0.0029 |
| arccos(x) |
0.013 |
0.024 |
0.021 |
| arctan(x) |
0.013 |
0.023 |
0.017 |
|
| 1000 digits |
pari-2.14.0-gmp |
pari-2.14.0 |
mpfr-4.1.0 |
| x*y |
0.0023 |
0.0021 |
0.0013 |
| x*x |
0.0011 |
0.0021 |
0.00078 |
| x/y |
0.0029 |
0.0041 |
0.0019 |
| sqrt(x) |
0.0021 |
0.0043 |
0.0016 |
| exp(x) |
0.16 |
0.19 |
0.083 |
| log(x) |
0.098 |
0.15 |
0.063 |
| sin(x) |
0.12 |
0.15 |
0.077 |
| cos(x) |
0.12 |
0.15 |
0.073 |
| arccos(x) |
0.34 |
0.55 |
0.16 |
| arctan(x) |
0.33 |
0.54 |
0.16 |
|
| 10000 digits |
pari-2.14.0-gmp |
pari-2.14.0 |
mpfr-4.1.0 |
| x*y |
0.053 |
0.12 |
0.050 |
| x*x |
0.038 |
0.081 |
0.028 |
| x/y |
0.12 |
0.24 |
0.083 |
| sqrt(x) |
0.078 |
0.20 |
0.059 |
| exp(x) |
5.7 |
13 |
4.3 |
| log(x) |
3.7 |
8.9 |
2.9 |
| sin(x) |
9.5 |
20 |
7.5 |
| cos(x) |
9.4 |
19 |
7.5 |
| arccos(x) |
16 |
36 |
7.6 |
| arctan(x) |
16 |
35 |
6.9 |
|
32-bit machine: pari.math.u-bordeaux.fr
Xeon Silver 4110 @ 2.10Ghz, running Linux 4.19.0-18-amd64.
Libraries were compiled with gcc 8.3.0 -m32 and native flags.
| 100 digits |
pari-2.14.0-gmp |
pari-2.14.0 |
mpfr-4.1.0 |
| x*y |
0.00017 |
0.00017 |
0.00024 |
| x*x |
0.00015 |
0.00015 |
0.00018 |
| x/y |
0.00036 |
0.00030 |
0.00040 |
| sqrt(x) |
0.00057 |
0.0011 |
0.00050 |
| exp(x) |
0.0095 |
0.0097 |
0.0090 |
| log(x) |
0.011 |
0.016 |
0.014 |
| sin(x) |
0.0093 |
0.010 |
0.0091 |
| cos(x) |
0.0085 |
0.0086 |
0.0070 |
| arccos(x) |
0.027 |
0.036 |
0.050 |
| arctan(x) |
0.024 |
0.032 |
0.042 |
|
| 1000 digits |
pari-2.14.0-gmp |
pari-2.14.0 |
mpfr-4.1.0 |
| x*y |
0.0072 |
0.0091 |
0.0060 |
| x*x |
0.0048 |
0.0079 |
0.0035 |
| x/y |
0.012 |
0.011 |
0.0085 |
| sqrt(x) |
0.0079 |
0.012 |
0.0050 |
| exp(x) |
0.63 |
0.67 |
0.33 |
| log(x) |
0.34 |
0.50 |
0.24 |
| sin(x) |
0.47 |
0.62 |
0.32 |
| cos(x) |
0.46 |
0.60 |
0.31 |
| arccos(x) |
1.5 |
1.8 |
0.57 |
| arctan(x) |
1.5 |
1.7 |
0.55 |
|
| 10000 digits |
pari-2.14.0-gmp |
pari-2.14.0 |
mpfr-4.1.0 |
| x*y |
0.20 |
0.46 |
0.18 |
| x*x |
0.14 |
0.36 |
0.12 |
| x/y |
0.50 |
0.93 |
0.37 |
| sqrt(x) |
0.34 |
0.77 |
0.24 |
| exp(x) |
23 |
48 |
16 |
| log(x) |
15 |
34 |
11 |
| sin(x) |
34 |
78 |
27 |
| cos(x) |
33 |
77 |
27 |
| arccos(x) |
61 |
137 |
29 |
| arctan(x) |
61 |
136 |
26 |
|
| 