ECM montgomery and edwards, torsion 8 and 16

Author: cherubrock-seb

README.md

@@ -211,29 +211,34 @@ ECM on Mersenne numbers
 ------------------------
 ECM is a probabilistic generalization of P−1/P+1: it succeeds when the group order on a random curve has a cofactor that’s B1,B2-smooth, so B1/B2 should be chosen for the target factor size.
 
-ECM on Mersenne numbers N = 2^p - 1. Stage 1 multiplies by all prime powers <= B1; Stage 2 scans primes in (B1, B2]. Without flags you get the plain prime-by-prime Stage 2. "-brent d" enables a simplified Brent-Suyama extension by using q^d (a bit more extra reach beyond B2). "-bsgs" batches several multipliers into one ladder call to reduce overhead. Both flags are complementary and can be combined. You can pass pre-known factors via "-factors <list>" (decimal or 0x hex); they are divided out (with multiplicities) before ECM. For p=701, 796337 is a known factor. Runs are checkpointed periodically; re-running the same command resumes safely.
-```
-# Plain ECM on M_p (here p=701)
-./prmers 701 -ecm -b1 6000 -b2 33333 -K 8
-
-# ECM + batching only (same primes, fewer ladder calls)
-./prmers 701 -ecm -b1 6000 -b2 33333 -K 8 -bsgs
-
-# ECM + simplified Brent-Suyama only (q -> q^3 here)
-./prmers 701 -ecm -b1 6000 -b2 33333 -K 8 -brent 3
-
-# ECM + both (complementary: q -> q^3 and batched multipliers)
-./prmers 701 -ecm -b1 6000 -b2 33333 -K 8 -brent 3 -bsgs
-
-# Provide known factors (e.g., for p=701, factor 796337)
-./prmers 701 -ecm -b1 6000 -b2 33333 -K 8 -factors 796337
-
-# Combine known factors with brent+bsgs
-./prmers 701 -ecm -b1 6000 -b2 33333 -K 8 -brent 3 -bsgs -factors 796337
-
-# Resume after interrupt (same command; auto-checkpointed)
-./prmers 701 -ecm -b1 6000 -b2 33333 -K 8 -brent 3 -bsgs -factors 796337
-```
+ECM on Mersenne numbers
+-----------------------
+ECM on N = 2^p - 1.
+
+Curve model and torsion:
+- default: Edwards, torsion 8
+- -montgomery: use Montgomery model
+- -torsion16: force torsion 16
+- -notorsion: no torsion
+
+Outputs:
+- results append to ecm_result.json
+- last curve saved to lastcurve.gp (PARI/GP)
+- checkpoints auto-resume on re-run
+
+Examples:
+  # Stage-1 only
+  ./prmers 701 -ecm -b1 6000 -K 8
+
+  # Enable Stage-2
+  ./prmers 701 -ecm -b1 6000 -b2 33333 -K 8
+
+  # Model / torsion variants
+  ./prmers 701 -ecm -b1 6000 -K 8 -montgomery
+  ./prmers 701 -ecm -b1 6000 -K 8 -torsion16
+  ./prmers 701 -ecm -b1 6000 -K 8 -notorsion
+  ./prmers 701 -ecm -b1 6000 -K 8 -montgomery -torsion16
+  ./prmers 701 -ecm -b1 6000 -K 8 -montgomery -notorsion
 
 
 ## GPU Memory Test (`-memtest`)

src/io/CliParser.cpp

@@ -85,8 +85,8 @@ void printUsage(const char* progName) {
     std::cout << "  -montgomery          : (Optional) use Montgomery instead of twisted Edwards curve" << std::endl;
     std::cout << "  -torsion16           : (Optional) use torsion-16 instead of default torsion-8" << std::endl;
     std::cout << "  -notorsion           : (Optional) use no torsion instead of default torsion-8" << std::endl;
-    std::cout << "  -brent [<d>]         : (Optional) use Brent-Suyama variant with default or specified degree d (e.g., -brent 6)" << std::endl;
-    std::cout << "  -bsgs                : (Optional) enable batching of multipliers in ECM stage 2 to reduce ladder calls" << std::endl;
+    //std::cout << "  -brent [<d>]         : (Optional) use Brent-Suyama variant with default or specified degree d (e.g., -brent 6)" << std::endl;
+    //std::cout << "  -bsgs                : (Optional) enable batching of multipliers in ECM stage 2 to reduce ladder calls" << std::endl;
     std::cout << "  -marin               : (Optional) deactivate use of marin backend" << std::endl;
     std::cout << "  -resume              : (Optional) write GMP-ECM and Prime 95 resume file after P-1 stage 1" << std::endl;
     //std::cout << "  -p95                 : (Optional) write Prime 95 resume file after P-1 stage 1" << std::endl;