chore: use mpmath for non-integer n

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---

Author: officiallyanee

lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/decimals.json

@@ -21,6 +21,7 @@
 import os
 import json
 import numpy as np
+from mpmath import mp, legendre as mp_legendre
 from scipy.special import eval_legendre
 
 # Get the file path:
@@ -64,6 +65,33 @@ def gen(n, x, name):
         outfile.write("\n")
 
 
+def gen_mp(n, x, name):
+    """Generate fixture data using mpmath and write to file.
+
+    # Arguments
+
+    * `n`: degree
+    * `x`: evaluation point
+    * `name::str`: output filename
+    """
+    mp.dps = 35
+    y = [float(mp_legendre(ni, xi)) for ni, xi in zip(n, x)]
+    y = ["PINF" if np.isposinf(val) else "NINF" if np.isneginf(val) else val for val in y]
+    data = {
+        "n": n.tolist(),
+        "x": x.tolist(),
+        "expected": y,
+    }
+
+    # Based on the script directory, create an output filepath:
+    filepath = os.path.join(DIR, name)
+
+    # Write the data to the output filepath as JSON:
+    with open(filepath, "w", encoding="utf-8") as outfile:
+        json.dump(data, outfile)
+        outfile.write("\n")
+
+
 def main():
     """Generate fixture data."""
     # Integer degrees, x in [-1, 1]:
@@ -76,7 +104,7 @@ def main():
     n = 1000
     n_vals = np.linspace(-20.0, 20.0, n)
     x = np.linspace(-1.0, 1.0, n)
-    gen(n_vals, x, "decimals.json")
+    gen_mp(n_vals, x, "decimals.json")
 
     # Large integer degrees, x in [-1, 1]:
     n = 500

lib/node_modules/@stdlib/math/base/special/legendre-polynomial/test/fixtures/python/runner.py

@@ -156,7 +156,7 @@ tape( 'the function correctly evaluates the Legendre polynomial', function test(
 			t.strictEqual( v, NINF, 'returns expected value' );
 			continue;
 		}
-		t.strictEqual( isAlmostSameValue( v, expected[ i ], 2.1e12 ), true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( v, expected[ i ], 5e9 ), true, 'returns expected value' );
 	}
 	t.end();
 });