Computes parallel curves of the ECM (Elliptic Curve Method) factoring algorithm using AVX-512 vector arithmetic. On CPUs where AVX512 is supported, AVX-ECM has been observed to have about 1.5 to 2.5 times the throughput (curves/sec) of GMP-ECM, for numbers up to a thousand bits or so. Large numbers will be more efficient with GMP-ECM because AVX-ECM so far does not use sub-quadratic multiplier algorithms.
Both stage 1 and stage 2 are computed in parallel, but stage 2 is just the standard continuation with pairing (by default, B2=100xB1).
The program is also multi-threaded using the pthreads library.
It will output a savefile after stage 1 that will work with GMP-ECM stage 2, if desired. e.g.: ecm -resume save_b1.txt 1000000 < input.txt
Compile on linux using either icc or gcc-7.3.0 or above (I've only tested icc and gcc-7.3.0).
e.g.: make COMPILER=gcc730 SKYLAKEX=1
COMPILER options currently are gcc730 (which invokes gcc-7.3.0), gcc (which invokes gcc), mingw (using MSYS2 and mingw64 on windows) and icc (icc). Edit the makefile if you have some other compiler name (ymmv).
Use SKYLAKEX=1 to build for skylakex CPUs. Alternatively use KNL=1 to build for Knight's Landing Xeon Phi systems.
The program will run constant-time curves in steps of 208 bits (meaning, e.g., that 417 bit curves take the same amount of time as 623-bit curves) and 8 curves are performed in parallel per thread.
You can optionally specify DIGITBITS=32 during make. Doing so results in constant-time curves in steps of 128 bits and 16 curves performed in parallel per thread.
The 52-bit version is generally faster (and the default) but for some sizes a 32-bit version can have higher throughput (because of the 208-bit jumps between sizes).
Command line: avx-ecm input curves B1 threads B2
The input number can be specified using these operators if desired: +,-,*,/,^,%,# (primorial), ! (factorial), fib(), and luc()
Example: ./avx-ecm "fib(791)/13/677/216416017" 8 1000000 1
See https://www.mersenneforum.org/showthread.php?t=25056 for more info.
Happy factoring!