PARI library benchmarks: integer arithmetic
This page refers to version 2.9.5 of the PARI/GP system
[ bench
source code ], with native kernel and GMP
kernel respectively. PARI and GMP-6.0.0 were linked dynamically to the bench
program.
The following tables give the cpu time in milliseconds spent by the PARI
kernels for different operations, at different (decimal) digitsizes. For
everything but divisions, a test for N digits means two operands with
N decimal digits. For divisions, the dividend has 2N decimal
digits, and the divisor has N decimal digits.
64-bit machine: pari.math.u-bordeaux.fr
Xeon E5540 @ 2.53Ghz, running Linux 3.16.0-5-amd64.
Libraries were compiled with gcc 7.3.0 and native flags.
| 100 digits |
pari-2.9.5-gmp |
pari-2.9.5 |
| addii |
0.000032 |
0.000032 |
| sqri |
0.000062 |
0.000094 |
| mulii |
0.000088 |
0.00011 |
| sqrti |
0.00024 |
0.00078 |
| diviiexact |
0.00013 |
0.00018 |
| divii |
0.00023 |
0.00026 |
| dvmdii |
0.00023 |
0.00028 |
| redc |
0.00014 |
0.00015 |
| gcdii |
0.0021 |
0.0096 |
| bezout |
0.0032 |
0.0055 |
| invmod |
0.0029 |
0.0047 |
| ratlift |
0.0025 |
0.0024 |
|
| 1000 digits |
pari-2.9.5-gmp |
pari-2.9.5 |
| addii |
0.00013 |
0.000083 |
| sqri |
0.0022 |
0.0031 |
| mulii |
0.0036 |
0.0052 |
| sqrti |
0.0014 |
0.0035 |
| diviiexact |
0.0032 |
0.0039 |
| divii |
0.0057 |
0.0077 |
| dvmdii |
0.0056 |
0.0078 |
| redc |
0.0065 |
0.0067 |
| gcdii |
0.050 |
0.22 |
| bezout |
0.066 |
0.12 |
| invmod |
0.059 |
0.094 |
| ratlift |
0.053 |
0.049 |
|
| 10000 digits |
pari-2.9.5-gmp |
pari-2.9.5 |
| addii |
0.0011 |
0.00065 |
| sqri |
0.092 |
0.14 |
| mulii |
0.12 |
0.22 |
| sqrti |
0.037 |
0.090 |
| diviiexact |
0.19 |
0.31 |
| divii |
0.28 |
0.64 |
| dvmdii |
0.28 |
0.64 |
| redc |
0.64 |
0.65 |
| gcdii |
1.3 |
13 |
| bezout |
2.3 |
6.1 |
| invmod |
2.0 |
4.2 |
| ratlift |
2.3 |
2.2 |
|
| 100000 digits |
pari-2.9.5-gmp |
pari-2.9.5 |
| addii |
0.010 |
0.0066 |
| sqri |
2.2 |
3.7 |
| mulii |
3.0 |
5.2 |
| sqrti |
1.7 |
6.5 |
| diviiexact |
5.6 |
30 |
| divii |
7.4 |
63 |
| dvmdii |
7.4 |
63 |
| redc |
63 |
65 |
| gcdii |
45 |
1192 |
| bezout |
74 |
569 |
| invmod |
66 |
376 |
| ratlift |
210 |
194 |
|
32-bit machine: pari.math.u-bordeaux.fr
Xeon E5540 @ 2.53Ghz, running Linux 3.16.0-5-amd64.
Libraries were compiled with gcc 7.3.0 -m32 and native flags.
| 100 digits |
pari-2.9.5-gmp |
pari-2.9.5 |
| addii |
0.000034 |
0.000041 |
| sqri |
0.00012 |
0.00025 |
| mulii |
0.00017 |
0.00033 |
| sqrti |
0.00044 |
0.0012 |
| diviiexact |
0.00028 |
0.00041 |
| divii |
0.00052 |
0.00055 |
| dvmdii |
0.00052 |
0.00058 |
| redc |
0.00041 |
0.00040 |
| gcdii |
0.0038 |
0.015 |
| bezout |
0.0054 |
0.013 |
| invmod |
0.0048 |
0.011 |
| ratlift |
0.0051 |
0.0052 |
|
| 1000 digits |
pari-2.9.5-gmp |
pari-2.9.5 |
| addii |
0.00010 |
0.00015 |
| sqri |
0.0049 |
0.012 |
| mulii |
0.0074 |
0.018 |
| sqrti |
0.0034 |
0.0079 |
| diviiexact |
0.0075 |
0.015 |
| divii |
0.019 |
0.030 |
| dvmdii |
0.019 |
0.031 |
| redc |
0.026 |
0.027 |
| gcdii |
0.088 |
0.37 |
| bezout |
0.14 |
0.38 |
| invmod |
0.12 |
0.27 |
| ratlift |
0.11 |
0.14 |
|
| 10000 digits |
pari-2.9.5-gmp |
pari-2.9.5 |
| addii |
0.00078 |
0.0013 |
| sqri |
0.15 |
0.56 |
| mulii |
0.22 |
0.74 |
| sqrti |
0.14 |
0.35 |
| diviiexact |
0.38 |
1.2 |
| divii |
0.64 |
2.8 |
| dvmdii |
0.64 |
2.8 |
| redc |
2.6 |
2.5 |
| gcdii |
3.8 |
25 |
| bezout |
5.1 |
24 |
| invmod |
4.5 |
16 |
| ratlift |
5.6 |
8.5 |
|
| 100000 digits |
pari-2.9.5-gmp |
pari-2.9.5 |
| addii |
0.0083 |
0.013 |
| sqri |
3.1 |
8.7 |
| mulii |
4.7 |
13 |
| sqrti |
3.4 |
26 |
| diviiexact |
9.4 |
119 |
| divii |
12 |
281 |
| dvmdii |
12 |
281 |
| redc |
258 |
253 |
| gcdii |
93 |
2352 |
| bezout |
151 |
2336 |
| invmod |
137 |
1544 |
| ratlift |
516 |
800 |
|
| 