Increase random uniformity

Author: WrathfulSpatula

FindAFactor/_find_a_factor.cpp

@@ -849,10 +849,11 @@ struct Factorizer {
         while (perfectSquare < toFactorSqr) {
           // Pick a random prime ordinal.
           const size_t pi = dis(gen) % primes.size();
+          const size_t lm = (dis(gen) % ladderMultiple) + 1U;
           // Retrieve the square prime for the ordinal.
           const size_t& rsp = sqrPrimes[pi];
           size_t& fvc = fv[pi];
-          for (size_t i = 0U; i < ladderMultiple; ++i) {
+          for (size_t i = 0U; i < lm; ++i) {
             // Compute x and y
             const BigInteger x = perfectSquare % toFactor;
             const BigInteger y = modExp(x, toFactor >> 1U, toFactor);

FindAFactor/find_a_factor.py

@@ -18,8 +18,8 @@ def find_a_factor(n,
                   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 256.0,
-                  batch_size_variance=int(os.environ.get('FINDAFACTOR_BATCH_SIZE_VARIANCE')) if os.environ.get('FINDAFACTOR_BATCH_SIZE_VARIANCE') else 2,
-                  ladder_multiple=int(os.environ.get('FINDAFACTOR_LADDER_MULTIPLE')) if os.environ.get('FINDAFACTOR_LADDER_MULTIPLE') else 5):
+                  batch_size_variance=int(os.environ.get('FINDAFACTOR_BATCH_SIZE_VARIANCE')) if os.environ.get('FINDAFACTOR_BATCH_SIZE_VARIANCE') else 3,
+                  ladder_multiple=int(os.environ.get('FINDAFACTOR_LADDER_MULTIPLE')) if os.environ.get('FINDAFACTOR_LADDER_MULTIPLE') else 6):
     return int(_find_a_factor._find_a_factor(str(n),
                                              int(method),
                                              node_count, node_id,

README.md

@@ -50,7 +50,7 @@ The `find_a_factor()` function should return any nontrivial factor of `to_factor
 - `smoothness_bound_multiplier` (default value: `1.0`): starting with the first prime number after wheel factorization, the congruence of squares approach (with Quadratic Sieve) has a "smoothness bound" unit with as many distinct prime numbers as bits in the number to factor (for argument of `1.0` multiplier). To increase or decrease this number, consider it multiplied by the value of `smoothness_bound_multiplier`.
 - `batch_size_multiplier` (default value: `256.0`): For `FACTOR_FINDER`/`1` method, each `1.0` increment of the multiplier adds `k ln k` Markov mixing replacement steps for `k` count of smooth primes, before reseeding Monte Carlo.
 - `batch_size_variance` (default value: `2`): For `FACTOR_FINDER`/`1` method, `k ln k` is the right proportionality for a Markov mixing process, but a linear factor in front is hard to predict. As such, it can be useful to dynamically vary the batch size, as if to cover and amortize the cost of several different batch sizes at once. In sequence, each batch size will be multiplied by `2 ** i` for `i` in `range(batch_size_variance)`, repeating from `0`.
-- `ladder_multiple` (default value: `5`): Controls how many times randomly-selected square prime multiplication is repeated with the same square prime per random selection, in ascending a "ladder" of smooth perfect squares, while division still occurs 1 square prime multiple at a time. (Any smooth perfect square can be multiplied by any square prime in the factor base, or any other smooth perfect square, and produce a different smooth perfect square.)
+- `ladder_multiple` (default value: `6`): Controls how many times randomly-selected square prime multiplication is repeated with the same square prime per random selection, in ascending a "ladder" of smooth perfect squares. A random number between `1` and `ladder_multiple` is selected for how many times the current smooth perfect square is multiplied each randomly selected square prime, while division still occurs 1 square prime multiple at a time. (Any smooth perfect square can be multiplied by any square prime in the factor base, or any other smooth perfect square, and produce a different smooth perfect square.)
 
 All variables defaults can also be controlled by environment variables:
 - `FINDAFACTOR_METHOD` (integer value)

find_a_factor

@@ -23,7 +23,7 @@ def main():
     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 256.0
     batch_size_variance=int(os.environ.get('FINDAFACTOR_BATCH_SIZE_VARIANCE')) if os.environ.get('FINDAFACTOR_BATCH_SIZE_VARIANCE') else 2
-    ladder_multiple=int(os.environ.get('FINDAFACTOR_LADDER_MULTIPLE')) if os.environ.get('FINDAFACTOR_LADDER_MULTIPLE') else 5
+    ladder_multiple=int(os.environ.get('FINDAFACTOR_LADDER_MULTIPLE')) if os.environ.get('FINDAFACTOR_LADDER_MULTIPLE') else 6
 
     if argv_len > 2:
         method = FactoringMethod(int(sys.argv[2]))

pyproject.toml

@@ -8,7 +8,7 @@ build-backend = "setuptools.build_meta"
 
 [project]
 name = "FindAFactor"
-version = "4.7.7"
+version = "4.7.8"
 requires-python = ">=3.8"
 description = "Find any nontrivial factor of a number"
 readme = {file = "README.txt", content-type = "text/markdown"}

setup.py

@@ -40,7 +40,7 @@ def build_extension(self, ext):
 
 setup(
     name='FindAFactor',
-    version='4.7.7',
+    version='4.7.8',
     author='Dan Strano',
     author_email='stranoj@gmail.com',
     description='Find any nontrivial factor of a number',