Derive an industrial-strength conjoin() via cross-recursion loop unrolling,

and fiddle the conjoin tests to exercise all the new possible paths.

Lib/test/test_generators.py

@@ -776,6 +776,62 @@ def conjoin(gs):
     for x in gen(0):
         yield x
 
+# That works fine, but recursing a level and checking i against len(gs) for
+# each item produced is inefficient.  By doing manual loop unrolling across
+# generator boundaries, it's possible to eliminate most of that overhead.
+# This isn't worth the bother *in general* for generators, but conjoin() is
+# a core building block for some CPU-intensive generator applications.
+
+def conjoin(gs):
+
+    n = len(gs)
+    values = [None] * n
+
+    # Do one loop nest at time recursively, until the # of loop nests
+    # remaining is divisible by 3.
+
+    def gen(i, values=values):
+        if i >= n:
+            yield values
+
+        elif (n-i) % 3:
+            ip1 = i+1
+            for values[i] in gs[i]():
+                for x in gen(ip1):
+                    yield x
+
+        else:
+            for x in _gen3(i):
+                yield x
+
+    # Do three loop nests at a time, recursing only if at least three more
+    # remain.  Don't call directly:  this is an internal optimization for
+    # gen's use.
+
+    def _gen3(i, values=values):
+        assert i < n and (n-i) % 3 == 0
+        ip1, ip2, ip3 = i+1, i+2, i+3
+        g, g1, g2 = gs[i : ip3]
+
+        if ip3 >= n:
+            # These are the last three, so we can yield values directly.
+            for values[i] in g():
+                for values[ip1] in g1():
+                    for values[ip2] in g2():
+                        yield values
+
+        else:
+            # At least 6 loop nests remain; peel off 3 and recurse for the
+            # rest.
+            for values[i] in g():
+                for values[ip1] in g1():
+                    for values[ip2] in g2():
+                        for x in _gen3(ip3):
+                            yield x
+
+    for x in gen(0):
+        yield x
+
 # A conjoin-based N-Queens solver.
 
 class Queens:
@@ -804,8 +860,7 @@ class Queens:
             def rowgen(rowuses=rowuses):
                 for j in rangen:
                     uses = rowuses[j]
-                    if uses & self.used:
-                        continue
+                    if uses & self.used == 0:
                         self.used |= uses
                         yield j
                         self.used &= ~uses
@@ -834,10 +889,7 @@ conjoin_tests = """
 Generate the 3-bit binary numbers in order.  This illustrates dumbest-
 possible use of conjoin, just to generate the full cross-product.
 
->>> def g():
-...    return [0, 1]
-
->>> for c in conjoin([g] * 3):
+>>> for c in conjoin([lambda: (0, 1)] * 3):
 ...     print c
 [0, 0, 0]
 [0, 0, 1]
@@ -848,6 +900,28 @@ possible use of conjoin, just to generate the full cross-product.
 [1, 1, 0]
 [1, 1, 1]
 
+For efficiency in typical backtracking apps, conjoin() yields the same list
+object each time.  So if you want to save away a full account of its
+generated sequence, you need to copy its results.
+
+>>> def gencopy(iterator):
+...     for x in iterator:
+...         yield x[:]
+
+>>> for n in range(10):
+...     all = list(gencopy(conjoin([lambda: (0, 1)] * n)))
+...     print n, len(all), all[0] == [0] * n, all[-1] == [1] * n
+0 1 1 1
+1 2 1 1
+2 4 1 1
+3 8 1 1
+4 16 1 1
+5 32 1 1
+6 64 1 1
+7 128 1 1
+8 256 1 1
+9 512 1 1
+
 And run an 8-queens solver.
 
 >>> q = Queens(8)