Elara (GPT) suggests: Markov replacement relaxation is O(k log k)

vm6502q · Jan 16, 2025 · c530ba4 · c530ba4
1 parent 86da1ed
commit c530ba4
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Showing 5 changed files with 10 additions and 8 deletions.
diff --git a/FindAFactor/_find_a_factor.cpp b/FindAFactor/_find_a_factor.cpp
@@ -756,7 +756,6 @@ struct Factorizer {
   BigInteger wheelRadius;
   size_t wheelEntryCount;
   size_t smoothBatchLimit;
-  size_t rowOffset;
   bool isIncomplete;
   std::vector<size_t> primes;
   std::vector<size_t> sqrPrimes;
@@ -765,7 +764,7 @@ struct Factorizer {
   Factorizer(const BigInteger &tfsqr, const BigInteger &tf, const BigInteger &tfsqrt, const BigInteger &range, size_t nodeCount, size_t nodeId, size_t w, size_t spl,
              const std::vector<size_t> &p, ForwardFn fn)
     : dis(0U, p.size() - 1U), wordDis(0ULL, -1ULL), toFactorSqr(tfsqr), toFactor(tf), toFactorSqrt(tfsqrt), batchRange(range), batchNumber(0U), batchOffset(nodeId * range),
-    batchTotal(nodeCount * range), wheelRadius(1U), wheelEntryCount(w), smoothBatchLimit(spl), rowOffset(p.size()), isIncomplete(true), primes(p), forwardFn(fn)
+    batchTotal(nodeCount * range), wheelRadius(1U), wheelEntryCount(w), smoothBatchLimit(spl), isIncomplete(true), primes(p), forwardFn(fn)
   {
     for (size_t i = 0U; i < primes.size(); ++i) {
       const size_t& p = primes[i];
@@ -829,6 +828,7 @@ struct Factorizer {
         // The number is now a smooth perfect square larger than toFactor.
         // Keep going until we exceed the square of toFactor.
         // We are given a smooth perfect square as input.
+        size_t batchPart = 0U;
         while (perfectSquare < toFactorSqr) {
           // Compute x and y
           const BigInteger x = perfectSquare % toFactor;
@@ -859,6 +859,7 @@ struct Factorizer {
           // (The factorization vector assumes that each increment is a square prime factor,
           // not a single prime factor.)
           ++(fv[pi]);
+          ++batchPart;
         }
 
         if (!isIncomplete) {
@@ -904,14 +905,15 @@ struct Factorizer {
           // (The factorization vector assumes that each increment is a square prime factor,
           // not a single prime factor.)
           --(fv[pi]);
+          ++batchPart;
         }
 
         if (!isIncomplete) {
           return 1U;
         }
 
         // Repeat indefinitely until reseeding.
-        ++batchId;
+        batchId += batchPart >> 1U;
         if (batchId >= smoothBatchLimit) {
           break;
         }
@@ -1098,7 +1100,7 @@ std::string find_a_factor(std::string toFactorStr, size_t method, size_t nodeCou
   // This manages the work of all threads.
   Factorizer worker(toFactor * toFactor, toFactor, fullMaxBase,
                     nodeRange, nodeCount, nodeId,
-                    wheelEntryCount, batchSizeMultiplier * (isFactorFinder ? smoothPrimes.size() * smoothPrimes.size() : (wheelEntryCount << 1U)),
+                    wheelEntryCount, (size_t)(batchSizeMultiplier * smoothPrimes.size() * log(smoothPrimes.size())),
                     smoothPrimes, forward(SMALLEST_WHEEL));
   // Square of count of smooth primes, for FACTOR_FINDER batch multiplier base unit, was suggested by Lyra (OpenAI GPT)
 

diff --git a/FindAFactor/find_a_factor.py b/FindAFactor/find_a_factor.py
@@ -17,7 +17,7 @@ def find_a_factor(n,
                   gear_factorization_level=int(os.environ.get('FINDAFACTOR_GEAR_FACTORIZATION_LEVEL')) if os.environ.get('FINDAFACTOR_GEAR_FACTORIZATION_LEVEL') else 11,
                   wheel_factorization_level=int(os.environ.get('FINDAFACTOR_WHEEL_FACTORIZATION_LEVEL')) if os.environ.get('FINDAFACTOR_WHEEL_FACTORIZATION_LEVEL') else 11,
                   smoothness_bound_multiplier=float(os.environ.get('FINDAFACTOR_SMOOTHNESS_BOUND_MULTIPLIER')) if os.environ.get('FINDAFACTOR_SMOOTHNESS_BOUND_MULTIPLIER') else 1.0,
-                  batch_size_multiplier=float(os.environ.get('FINDAFACTOR_BATCH_SIZE_MULTIPLIER')) if os.environ.get('FINDAFACTOR_BATCH_SIZE_MULTIPLIER') else 4.0):
+                  batch_size_multiplier=float(os.environ.get('FINDAFACTOR_BATCH_SIZE_MULTIPLIER')) if os.environ.get('FINDAFACTOR_BATCH_SIZE_MULTIPLIER') else 192.0):
     return int(_find_a_factor._find_a_factor(str(n),
                                              int(method),
                                              node_count, node_id,

diff --git a/find_a_factor b/find_a_factor
@@ -21,7 +21,7 @@ def main():
     gear_factorization_level = int(os.environ.get('FINDAFACTOR_GEAR_FACTORIZATION_LEVEL')) if os.environ.get('FINDAFACTOR_GEAR_FACTORIZATION_LEVEL') else 11
     wheel_factorization_level = int(os.environ.get('FINDAFACTOR_WHEEL_FACTORIZATION_LEVEL')) if os.environ.get('FINDAFACTOR_WHEEL_FACTORIZATION_LEVEL') else 11
     smoothness_bound_multiplier = float(os.environ.get('FINDAFACTOR_SMOOTHNESS_BOUND_MULTIPLIER')) if os.environ.get('FINDAFACTOR_SMOOTHNESS_BOUND_MULTIPLIER') else 1.0
-    batch_size_multiplier=float(os.environ.get('FINDAFACTOR_BATCH_SIZE_MULTIPLIER')) if os.environ.get('FINDAFACTOR_BATCH_SIZE_MULTIPLIER') else 4.0
+    batch_size_multiplier=float(os.environ.get('FINDAFACTOR_BATCH_SIZE_MULTIPLIER')) if os.environ.get('FINDAFACTOR_BATCH_SIZE_MULTIPLIER') else 192.0
 
     if argv_len > 2:
         method = FactoringMethod(int(sys.argv[2]))

diff --git a/pyproject.toml b/pyproject.toml
@@ -8,7 +8,7 @@ build-backend = "setuptools.build_meta"
 
 [project]
 name = "FindAFactor"
-version = "4.5.0"
+version = "4.5.1"
 requires-python = ">=3.8"
 description = "Find any nontrivial factor of a number"
 readme = {file = "README.txt", content-type = "text/markdown"}

diff --git a/setup.py b/setup.py
@@ -40,7 +40,7 @@ def build_extension(self, ext):
 
 setup(
     name='FindAFactor',
-    version='4.5.0',
+    version='4.5.1',
     author='Dan Strano',
     author_email='[email protected]',
     description='Find any nontrivial factor of a number',