beam: add extended Euclidean gcd/lcm module with tests

wizard-work/beam/egcd.py

@@ -0,0 +1,24 @@
+"""Extended Euclidean algorithm.
+
+egcd(a, b) returns (g, x, y) such that a*x + b*y == g == gcd(a, b).
+Works for negative inputs and zero.
+"""
+
+def egcd(a, b):
+    if b == 0:
+        if a < 0:
+            return (-a, -1, 0)
+        return (a, 1, 0)
+    g, x1, y1 = egcd(b, a % b)
+    q = a // b
+    return (g, y1, x1 - q * y1)
+
+
+def gcd(a, b):
+    return egcd(a, b)[0]
+
+
+def lcm(a, b):
+    if a == 0 or b == 0:
+        return 0
+    return abs(a // gcd(a, b) * b)

wizard-work/beam/test_egcd.py

@@ -0,0 +1,25 @@
+import sys, os
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from egcd import egcd, gcd, lcm
+
+def test_basic():
+    assert egcd(30, 12) == (6, -1, 3) or egcd(30,12)[0]==6
+    assert gcd(30,12)==6
+    assert lcm(4,6)==12
+
+def test_negatives():
+    g,x,y = egcd(-30,12)
+    assert g==6 and -30*x + 12*y == g
+
+def test_zero():
+    assert gcd(0,5)==5
+    assert gcd(5,0)==5
+    assert lcm(0,5)==0
+
+def test_identity():
+    g,x,y = egcd(17,31)
+    assert g==1 and 17*x+31*y==1
+if __name__=="__main__":
+    for f in [test_basic,test_negatives,test_zero,test_identity]:
+        f()
+    print("ALL PASS")