I hadn't written an Euclidean factorizer since high school, and my kids are now in primary school doing GCDs and LCMs all the time, so I decided to do a naive prime factorizer not using the Sieve of Eratosthenes, thus getting a complexity advantage when factoring composites.
Compute the factors to a pre-selected 17-digit number (64bit): 12345678901234567.
Compiler gnu-style CLI:
$ g++ -Ofast -fno-rtti -fno-exceptions -mcpu=<isa> -mtune=<isa> main.cpp -o euclid_all64 -DNUM_64BIT=1
$ g++ -Ofast -fno-rtti -fno-exceptions -mcpu=<isa> -mtune=<isa> main_odd.cpp -o euclid_odd64 -DNUM_64BIT=1Note: at the absence of linux perf, cpu frequency verified via Willy Tarreau's mhz utility.
| CPU | time, ms | CPU cycles, 1e6 |
|---|---|---|
| BCM2712 Cortex-A76 2.4GHz (all) | 215 | 514 |
| BCM2712 Cortex-A76 2.4GHz (odd) | 108 | 258 |
| T234 Cortex-A78AE 2.2GHz (all) | 236 | 514 |
| T234 Cortex-A78AE 2.2GHz (odd) | 120 | 258 |
$ perf stat -e task-clock:u,cycles:u,instructions:u,branches:u,branch-misses:u ./euclid_all64_gcc 12345678901234567
prime: 7, power: 1 (7)
prime: 1763668414462081, power: 1 (1763668414462081)
Performance counter stats for './euclid_all64_gcc 12345678901234567':
214.93 msec task-clock:u # 0.998 CPUs utilized
514,345,644 cycles:u # 2.393 GHz
295,317,919 instructions:u # 0.57 insn per cycle
126,272,544 branches:u # 587.493 M/sec
10,143 branch-misses:u # 0.01% of all branches
0.215285783 seconds time elapsed
0.215341000 seconds user
0.000000000 seconds sys$ perf stat -e task-clock:u,cycles:u,instructions:u,branches:u,branch-misses:u ./euclid_odd64_gcc 12345678901234567
prime: 7, power: 1 (7)
prime: 1763668414462081, power: 1 (1763668414462081)
Performance counter stats for './euclid_odd64_gcc 12345678901234567':
107.96 msec task-clock:u # 0.998 CPUs utilized
257,855,069 cycles:u # 2.388 GHz
148,331,724 instructions:u # 0.58 insn per cycle
63,278,464 branches:u # 586.111 M/sec
9,561 branch-misses:u # 0.02% of all branches
0.108223428 seconds time elapsed
0.108320000 seconds user
0.000000000 seconds sys$ perf stat -e task-clock:u,cycles:u,instructions:u,br_retired:u,br_mis_pred_retired:u ./euclid_all64 12345678901234567
prime: 7, power: 1 (7)
prime: 1763668414462081, power: 1 (1763668414462081)
Performance counter stats for './euclid_all64 12345678901234567':
235.24 msec task-clock:u # 0.996 CPUs utilized
514,341,917 cycles:u # 2.186 GHz
295,564,406 instructions:u # 0.57 insn per cycle
126,320,176 br_retired:u # 536.981 M/sec
11,679 br_mis_pred_retired:u # 0.050 M/sec
0.236098786 seconds time elapsed
0.235930000 seconds user
0.000000000 seconds sys$ perf stat -e task-clock:u,cycles:u,instructions:u,br_retired:u,br_mis_pred_retired:u ./euclid_odd64 12345678901234567
prime: 7, power: 1 (7)
prime: 1763668414462081, power: 1 (1763668414462081)
Performance counter stats for './euclid_odd64 12345678901234567':
118.99 msec task-clock:u # 0.994 CPUs utilized
258,165,755 cycles:u # 2.170 GHz
148,578,230 instructions:u # 0.58 insn per cycle
63,326,100 br_retired:u # 532.206 M/sec
11,599 br_mis_pred_retired:u # 0.097 M/sec
0.119667683 seconds time elapsed
0.119447000 seconds user
0.000000000 seconds sys