Clean up polynomial LUTs

tests/polys/luts/irreducible_polys.py

@@ -0,0 +1,68 @@
+"""
+A module containing LUTs for irreducible polynomials.
+"""
+
+from .irreducible_polys_2 import (
+ IRREDUCIBLE_POLYS_2_1,
+ IRREDUCIBLE_POLYS_2_2,
+ IRREDUCIBLE_POLYS_2_3,
+ IRREDUCIBLE_POLYS_2_4,
+ IRREDUCIBLE_POLYS_2_5,
+ IRREDUCIBLE_POLYS_2_6,
+ IRREDUCIBLE_POLYS_2_7,
+ IRREDUCIBLE_POLYS_2_8,
+)
+from .irreducible_polys_3 import (
+ IRREDUCIBLE_POLYS_3_1,
+ IRREDUCIBLE_POLYS_3_2,
+ IRREDUCIBLE_POLYS_3_3,
+ IRREDUCIBLE_POLYS_3_4,
+ IRREDUCIBLE_POLYS_3_5,
+ IRREDUCIBLE_POLYS_3_6,
+)
+from .irreducible_polys_4 import (
+ IRREDUCIBLE_POLYS_4_1,
+ IRREDUCIBLE_POLYS_4_2,
+ IRREDUCIBLE_POLYS_4_3,
+)
+from .irreducible_polys_5 import (
+ IRREDUCIBLE_POLYS_5_1,
+ IRREDUCIBLE_POLYS_5_2,
+ IRREDUCIBLE_POLYS_5_3,
+ IRREDUCIBLE_POLYS_5_4,
+)
+from .irreducible_polys_9 import (
+ IRREDUCIBLE_POLYS_9_1,
+ IRREDUCIBLE_POLYS_9_2,
+ IRREDUCIBLE_POLYS_9_3,
+)
+from .irreducible_polys_25 import IRREDUCIBLE_POLYS_25_1, IRREDUCIBLE_POLYS_25_2
+
+IRREDUCIBLE_POLYS = [
+ (2, 1, IRREDUCIBLE_POLYS_2_1),
+ (2, 2, IRREDUCIBLE_POLYS_2_2),
+ (2, 3, IRREDUCIBLE_POLYS_2_3),
+ (2, 4, IRREDUCIBLE_POLYS_2_4),
+ (2, 5, IRREDUCIBLE_POLYS_2_5),
+ (2, 6, IRREDUCIBLE_POLYS_2_6),
+ (2, 7, IRREDUCIBLE_POLYS_2_7),
+ (2, 8, IRREDUCIBLE_POLYS_2_8),
+ (2**2, 1, IRREDUCIBLE_POLYS_4_1),
+ (2**2, 2, IRREDUCIBLE_POLYS_4_2),
+ (2**2, 3, IRREDUCIBLE_POLYS_4_3),
+ (3, 1, IRREDUCIBLE_POLYS_3_1),
+ (3, 2, IRREDUCIBLE_POLYS_3_2),
+ (3, 3, IRREDUCIBLE_POLYS_3_3),
+ (3, 4, IRREDUCIBLE_POLYS_3_4),
+ (3, 5, IRREDUCIBLE_POLYS_3_5),
+ (3, 6, IRREDUCIBLE_POLYS_3_6),
+ (3**2, 1, IRREDUCIBLE_POLYS_9_1),
+ (3**2, 2, IRREDUCIBLE_POLYS_9_2),
+ (3**2, 3, IRREDUCIBLE_POLYS_9_3),
+ (5, 1, IRREDUCIBLE_POLYS_5_1),
+ (5, 2, IRREDUCIBLE_POLYS_5_2),
+ (5, 3, IRREDUCIBLE_POLYS_5_3),
+ (5, 4, IRREDUCIBLE_POLYS_5_4),
+ (5**2, 1, IRREDUCIBLE_POLYS_25_1),
+ (5**2, 2, IRREDUCIBLE_POLYS_25_2),
+]

tests/polys/luts/irreducible_polys_min.py

@@ -0,0 +1,19 @@
+"""
+A module containing LUTs for lexicographically-first irreducible polynomials with minimal terms.
+
+LUT items obtained by randomly picking degrees and checking the PDF,
+
+References:
+ - Gadiel Seroussi's table (1998). https://www.hpl.hp.com/techreports/98/HPL-98-135.pdf.
+"""
+
+# LUT items are (order, degree, nonzero_degrees, nonzero_coeffs) in degree-descending order.
+# sorted(numpy.random.default_rng(1337).integers(size=5, low=500, high=10_000, endpoint=True))
+
+IRREDUCIBLE_POLYS_MIN = [
+ (2, 2262, [[2262, 57, 0], [1, 1, 1]]),
+ (2, 5632, [[5632, 17, 15, 5, 0], [1, 1, 1, 1, 1]]),
+ (2, 5690, [[5690, 1623, 0], [1, 1, 1]]),
+ (2, 7407, [[7407, 27, 21, 17, 0], [1, 1, 1, 1, 1]]),
+ (2, 8842, [[8842, 4143, 0], [1, 1, 1]]),
+]

tests/polys/luts/poly_factors.py

@@ -640,3 +640,13 @@
  [1, 1, 1, 1],
  ),
 ]
+
+
+POLY_FACTORS = [
+ (2, 1, POLY_FACTORS_2_1),
+ (3, 1, POLY_FACTORS_3_1),
+ (5, 1, POLY_FACTORS_5_1),
+ (2, 2, POLY_FACTORS_2_2),
+ (3, 2, POLY_FACTORS_3_2),
+ (5, 2, POLY_FACTORS_5_2),
+]

tests/polys/luts/primitive_elements.py

@@ -0,0 +1,35 @@
+"""
+A module containing LUTs for primitive elements.
+"""
+
+from .primitive_elements_2 import (
+ PRIMITIVE_ELEMENTS_2_2,
+ PRIMITIVE_ELEMENTS_2_3,
+ PRIMITIVE_ELEMENTS_2_4,
+ PRIMITIVE_ELEMENTS_2_5,
+ PRIMITIVE_ELEMENTS_2_6,
+)
+from .primitive_elements_3 import (
+ PRIMITIVE_ELEMENTS_3_2,
+ PRIMITIVE_ELEMENTS_3_3,
+ PRIMITIVE_ELEMENTS_3_4,
+)
+from .primitive_elements_5 import (
+ PRIMITIVE_ELEMENTS_5_2,
+ PRIMITIVE_ELEMENTS_5_3,
+ PRIMITIVE_ELEMENTS_5_4,
+)
+
+PRIMITIVE_ELEMENTS = [
+ (2, 2, PRIMITIVE_ELEMENTS_2_2),
+ (2, 3, PRIMITIVE_ELEMENTS_2_3),
+ (2, 4, PRIMITIVE_ELEMENTS_2_4),
+ (2, 5, PRIMITIVE_ELEMENTS_2_5),
+ (2, 6, PRIMITIVE_ELEMENTS_2_6),
+ (3, 2, PRIMITIVE_ELEMENTS_3_2),
+ (3, 3, PRIMITIVE_ELEMENTS_3_3),
+ (3, 4, PRIMITIVE_ELEMENTS_3_4),
+ (5, 2, PRIMITIVE_ELEMENTS_5_2),
+ (5, 3, PRIMITIVE_ELEMENTS_5_3),
+ (5, 4, PRIMITIVE_ELEMENTS_5_4),
+]

tests/polys/luts/primitive_polys.py

@@ -0,0 +1,68 @@
+"""
+A module containing LUTs for primitive polynomials.
+"""
+
+from .primitive_polys_2 import (
+ PRIMITIVE_POLYS_2_1,
+ PRIMITIVE_POLYS_2_2,
+ PRIMITIVE_POLYS_2_3,
+ PRIMITIVE_POLYS_2_4,
+ PRIMITIVE_POLYS_2_5,
+ PRIMITIVE_POLYS_2_6,
+ PRIMITIVE_POLYS_2_7,
+ PRIMITIVE_POLYS_2_8,
+)
+from .primitive_polys_3 import (
+ PRIMITIVE_POLYS_3_1,
+ PRIMITIVE_POLYS_3_2,
+ PRIMITIVE_POLYS_3_3,
+ PRIMITIVE_POLYS_3_4,
+ PRIMITIVE_POLYS_3_5,
+ PRIMITIVE_POLYS_3_6,
+)
+from .primitive_polys_4 import (
+ PRIMITIVE_POLYS_4_1,
+ PRIMITIVE_POLYS_4_2,
+ PRIMITIVE_POLYS_4_3,
+)
+from .primitive_polys_5 import (
+ PRIMITIVE_POLYS_5_1,
+ PRIMITIVE_POLYS_5_2,
+ PRIMITIVE_POLYS_5_3,
+ PRIMITIVE_POLYS_5_4,
+)
+from .primitive_polys_9 import (
+ PRIMITIVE_POLYS_9_1,
+ PRIMITIVE_POLYS_9_2,
+ PRIMITIVE_POLYS_9_3,
+)
+from .primitive_polys_25 import PRIMITIVE_POLYS_25_1, PRIMITIVE_POLYS_25_2
+
+PRIMITIVE_POLYS = [
+ (2, 1, PRIMITIVE_POLYS_2_1),
+ (2, 2, PRIMITIVE_POLYS_2_2),
+ (2, 3, PRIMITIVE_POLYS_2_3),
+ (2, 4, PRIMITIVE_POLYS_2_4),
+ (2, 5, PRIMITIVE_POLYS_2_5),
+ (2, 6, PRIMITIVE_POLYS_2_6),
+ (2, 7, PRIMITIVE_POLYS_2_7),
+ (2, 8, PRIMITIVE_POLYS_2_8),
+ (2**2, 1, PRIMITIVE_POLYS_4_1),
+ (2**2, 2, PRIMITIVE_POLYS_4_2),
+ (2**2, 3, PRIMITIVE_POLYS_4_3),
+ (3, 1, PRIMITIVE_POLYS_3_1),
+ (3, 2, PRIMITIVE_POLYS_3_2),
+ (3, 3, PRIMITIVE_POLYS_3_3),
+ (3, 4, PRIMITIVE_POLYS_3_4),
+ (3, 5, PRIMITIVE_POLYS_3_5),
+ (3, 6, PRIMITIVE_POLYS_3_6),
+ (3**2, 1, PRIMITIVE_POLYS_9_1),
+ (3**2, 2, PRIMITIVE_POLYS_9_2),
+ (3**2, 3, PRIMITIVE_POLYS_9_3),
+ (5, 1, PRIMITIVE_POLYS_5_1),
+ (5, 2, PRIMITIVE_POLYS_5_2),
+ (5, 3, PRIMITIVE_POLYS_5_3),
+ (5, 4, PRIMITIVE_POLYS_5_4),
+ (5**2, 1, PRIMITIVE_POLYS_25_1),
+ (5**2, 2, PRIMITIVE_POLYS_25_2),
+]

tests/polys/test_factors.py

@@ -7,23 +7,7 @@
 
 import galois
 
-from .luts.poly_factors import (
- POLY_FACTORS_2_1,
- POLY_FACTORS_2_2,
- POLY_FACTORS_3_1,
- POLY_FACTORS_3_2,
- POLY_FACTORS_5_1,
- POLY_FACTORS_5_2,
-)
-
-PARAMS = [
- (2, 1, POLY_FACTORS_2_1),
- (3, 1, POLY_FACTORS_3_1),
- (5, 1, POLY_FACTORS_5_1),
- (2, 2, POLY_FACTORS_2_2),
- (3, 2, POLY_FACTORS_3_2),
- (5, 2, POLY_FACTORS_5_2),
-]
+from .luts.poly_factors import POLY_FACTORS
 
 
 def test_factors_exceptions():
@@ -71,7 +55,7 @@ def test_factors_random():
  assert f == multiply_factors(factors, multiplicities)
 
 
-@pytest.mark.parametrize("characteristic,degree,lut", PARAMS)
+@pytest.mark.parametrize("characteristic,degree,lut", POLY_FACTORS)
 def test_factors(characteristic, degree, lut):
  GF = galois.GF(characteristic**degree)