poly_int: Handle more can_div_trunc_p cases

can_div_trunc_p (a, b, &Q, &r) tries to compute a Q and r that
satisfy the usual conditions for truncating division:

     (1) a = b * Q + r
     (2) |b * Q| <= |a|
     (3) |r| < |b|

We can compute Q using the constant component (the case when
all indeterminates are zero).  Since |r| < |b| for the constant
case, the requirements for indeterminate xi with coefficients
ai (for a) and bi (for b) are:

     (2') |bi * Q| <= |ai|
     (3') |ai - bi * Q| <= |bi|

(See the big comment for more details, restrictions, and reasoning).

However, the function works on abstract arithmetic types, and so
it has to be careful not to introduce new overflow.  The code
therefore only handled the extreme for (3'), that is:

     |ai - bi * Q| = |bi|

for the case where Q is zero.

Looking at it again, the overflow issue is a bit easier to handle than
I'd originally thought (or so I hope).  This patch therefore extends the
code to handle |ai - bi * Q| = |bi| for all Q, with Q = 0 no longer
being a separate case.

The net effect is to allow the function to succeed for things like:

     (a0 + b1 (Q+1) x) / (b0 + b1 x)

where Q = a0 / b0, with various sign conditions.  E.g. we now handle:

     (7 + 8x) / (4 + 4x)

with Q = 1 and r = 3 + 4x,

gcc/
	* poly-int.h (can_div_trunc_p): Succeed for more boundary conditions.

gcc/testsuite/
	* gcc.dg/plugin/poly-int-tests.h (test_can_div_trunc_p_const)
	(test_can_div_trunc_p_const): Add more tests.

2 files changed, 98 insertions, 32 deletions

diff --git a/gcc/poly-int.h b/gcc/poly-int.h
index 1257145..7bff5e5 100644
--- a/gcc/poly-int.h
+++ b/gcc/poly-int.h
@@ -2355,28 +2355,31 @@ can_div_trunc_p (const poly_int_pod<N, Ca> &a,
 	}
       else
 	{
-	  if (q == 0)
-	    {
-	      /* For Q == 0 we simply need: (3') |ai| <= |bi|.  */
-	      if (a.coeffs[i] != ICa (0))
-		{
-		  /* Use negative absolute to avoid overflow, i.e.
-		     -|ai| >= -|bi|.  */
-		  C neg_abs_a = (a.coeffs[i] < 0 ? a.coeffs[i] : -a.coeffs[i]);
-		  C neg_abs_b = (b.coeffs[i] < 0 ? b.coeffs[i] : -b.coeffs[i]);
-		  if (neg_abs_a < neg_abs_b)
-		    return false;
-		  rem_p = true;
-		}
-	    }
+	  /* The only unconditional arithmetic that we can do on ai,
+	     bi and Q is ai / bi and ai % bi.  (ai == minimum int and
+	     bi == -1 would be UB in the caller.)  Anything else runs
+	     the risk of overflow.  */
+	  auto qi = NCa (a.coeffs[i]) / NCb (b.coeffs[i]);
+	  auto ri = NCa (a.coeffs[i]) % NCb (b.coeffs[i]);
+	  /* (2') and (3') are satisfied when ai /[trunc] bi == q.
+	     So is the stricter condition |ai - bi * Q| < |bi|.  */
+	  if (qi == q)
+	    rem_p |= (ri != 0);
+	  /* The only other case is when:
+
+		 |bi * Q| + |bi| = |ai| (for (2'))
+	     and |ai - bi * Q|   = |bi| (for (3'))
+
+	     The first is equivalent to |bi|(|Q| + 1) == |ai|.
+	     The second requires ai == bi * (Q + 1) or ai == bi * (Q - 1).  */
+	  else if (ri != 0)
+	    return false;
+	  else if (q <= 0 && qi < q && qi + 1 == q)
+	    ;
+	  else if (q >= 0 && qi > q && qi - 1 == q)
+	    ;
 	  else
-	    {
-	      /* Otherwise just check for the case in which ai / bi == Q.  */
-	      if (NCa (a.coeffs[i]) / NCb (b.coeffs[i]) != q)
-		return false;
-	      if (NCa (a.coeffs[i]) % NCb (b.coeffs[i]) != 0)
-		rem_p = true;
-	    }
+	    return false;
 	}
     }
 
diff --git a/gcc/testsuite/gcc.dg/plugin/poly-int-tests.h b/gcc/testsuite/gcc.dg/plugin/poly-int-tests.h
index 0b89acd..7af9859 100644
--- a/gcc/testsuite/gcc.dg/plugin/poly-int-tests.h
+++ b/gcc/testsuite/gcc.dg/plugin/poly-int-tests.h
@@ -1899,14 +1899,19 @@ test_can_div_trunc_p_const ()
 				ph::make (4, 8, 12),
 				&const_quot));
   ASSERT_EQ (const_quot, C (2));
-  ASSERT_EQ (can_div_trunc_p (ph::make (15, 25, 40),
+  ASSERT_TRUE (can_div_trunc_p (ph::make (15, 25, 40),
+				ph::make (4, 8, 10),
+				&const_quot));
+  ASSERT_EQ (const_quot, C (3));
+  const_quot = 0;
+  ASSERT_EQ (can_div_trunc_p (ph::make (15, 25, 41),
 			      ph::make (4, 8, 10),
 			      &const_quot), N <= 2);
-  ASSERT_EQ (const_quot, C (N <= 2 ? 3 : 2));
+  ASSERT_EQ (const_quot, C (N <= 2 ? 3 : 0));
   ASSERT_EQ (can_div_trunc_p (ph::make (43, 79, 80),
 			      ph::make (4, 8, 10),
 			      &const_quot), N == 1);
-  ASSERT_EQ (const_quot, C (N == 1 ? 10 : N == 2 ? 3 : 2));
+  ASSERT_EQ (const_quot, C (N == 1 ? 10 : N == 2 ? 3 : 0));
   ASSERT_TRUE (can_div_trunc_p (ph::make (3, 4, 5),
 				ph::make (4, 5, 6),
 				&const_quot));
@@ -1964,16 +1969,22 @@ test_can_div_trunc_p_const ()
 				&const_quot, &rem));
   ASSERT_EQ (const_quot, C (2));
   ASSERT_KNOWN_EQ (rem, ph::make (1, 7, 6));
-  ASSERT_EQ (can_div_trunc_p (ph::make (15, 25, 40),
+  ASSERT_TRUE (can_div_trunc_p (ph::make (15, 25, 40),
+				ph::make (4, 8, 10),
+				&const_quot, &rem));
+  ASSERT_EQ (const_quot, C (3));
+  ASSERT_KNOWN_EQ (rem, ph::make (3, 1, 10));
+  const_quot = 0, rem = 0;
+  ASSERT_EQ (can_div_trunc_p (ph::make (15, 25, 41),
 			      ph::make (4, 8, 10),
 			      &const_quot, &rem), N <= 2);
-  ASSERT_EQ (const_quot, C (N <= 2 ? 3 : 2));
+  ASSERT_EQ (const_quot, C (N <= 2 ? 3 : 0));
   if (N <= 2)
     ASSERT_KNOWN_EQ (rem, ph::make (3, 1, 0));
   ASSERT_EQ (can_div_trunc_p (ph::make (43, 79, 80),
 			      ph::make (4, 8, 10),
 			      &const_quot, &rem), N == 1);
-  ASSERT_EQ (const_quot, C (N == 1 ? 10 : N == 2 ? 3 : 2));
+  ASSERT_EQ (const_quot, C (N == 1 ? 10 : N == 2 ? 3 : 0));
   if (N == 1)
     ASSERT_KNOWN_EQ (rem, ch::make (3));
   ASSERT_TRUE (can_div_trunc_p (ph::make (3, 4, 5),
@@ -2024,6 +2035,19 @@ test_can_div_trunc_p_const ()
 				&const_quot, &rem));
   ASSERT_EQ (const_quot, C (0));
   ASSERT_KNOWN_EQ (rem, ch::make (0));
+  ASSERT_TRUE (can_div_trunc_p (ph::make (9, 10, 20),
+				ph::make (5, 5, 20),
+				&const_quot, &rem));
+  ASSERT_EQ (const_quot, C (1));
+  ASSERT_KNOWN_EQ (rem, ph::make (4, 5, 0));
+  ASSERT_EQ (can_div_trunc_p (ph::make (9, 11, 20),
+			      ph::make (5, 5, 20),
+			      &const_quot, &rem), N == 1);
+  if (N == 1)
+    {
+      ASSERT_EQ (const_quot, C (1));
+      ASSERT_KNOWN_EQ (rem, C (4));
+    }
 }
 
 /* Test the form of can_div_trunc_p that returns a polynomail quotient,
@@ -2093,14 +2117,14 @@ test_can_div_away_from_zero_p ()
 					 ph::make (4, 8, 12),
 					 &const_quot));
   ASSERT_EQ (const_quot, C (3));
-  ASSERT_EQ (can_div_away_from_zero_p (ph::make (15, 25, 40),
-				       ph::make (4, 8, 10),
-				       &const_quot), N <= 2);
-  ASSERT_EQ (const_quot, C (N <= 2 ? 4 : 3));
+  ASSERT_TRUE (can_div_away_from_zero_p (ph::make (15, 25, 40),
+					 ph::make (4, 8, 10),
+					 &const_quot));
+  ASSERT_EQ (const_quot, C (4));
   ASSERT_EQ (can_div_away_from_zero_p (ph::make (43, 79, 80),
 				       ph::make (4, 8, 10),
 				       &const_quot), N == 1);
-  ASSERT_EQ (const_quot, C (N == 1 ? 11 : N == 2 ? 4 : 3));
+  ASSERT_EQ (const_quot, C (N == 1 ? 11 : 4));
   ASSERT_TRUE (can_div_away_from_zero_p (ph::make (3, 4, 5),
 					 ph::make (4, 5, 6),
 					 &const_quot));
@@ -3232,6 +3256,45 @@ test_signed_can_div_trunc_p_const ()
 				&const_quot, &rem));
   ASSERT_EQ (const_quot, -2);
   ASSERT_KNOWN_EQ (rem, ph::make (2, 1, 3));
+  ASSERT_TRUE (can_div_trunc_p (ph::make (-9, -10, -20),
+				ph::make (-5, -5, -20),
+				&const_quot, &rem));
+  ASSERT_EQ (const_quot, C (1));
+  ASSERT_KNOWN_EQ (rem, ph::make (-4, -5, 0));
+  ASSERT_EQ (can_div_trunc_p (ph::make (-9, -11, -20),
+			      ph::make (-5, -5, -20),
+			      &const_quot, &rem), N == 1);
+  if (N == 1)
+    {
+      ASSERT_EQ (const_quot, C (1));
+      ASSERT_KNOWN_EQ (rem, C (-4));
+    }
+  ASSERT_TRUE (can_div_trunc_p (ph::make (9, 10, 20),
+				ph::make (-5, -5, -20),
+				&const_quot, &rem));
+  ASSERT_EQ (const_quot, C (-1));
+  ASSERT_KNOWN_EQ (rem, ph::make (4, 5, 0));
+  ASSERT_EQ (can_div_trunc_p (ph::make (9, 11, 20),
+			      ph::make (-5, -5, -20),
+			      &const_quot, &rem), N == 1);
+  if (N == 1)
+    {
+      ASSERT_EQ (const_quot, C (-1));
+      ASSERT_KNOWN_EQ (rem, C (4));
+    }
+  ASSERT_TRUE (can_div_trunc_p (ph::make (-9, -10, -20),
+				ph::make (5, 5, 20),
+				&const_quot, &rem));
+  ASSERT_EQ (const_quot, C (-1));
+  ASSERT_KNOWN_EQ (rem, ph::make (-4, -5, 0));
+  ASSERT_EQ (can_div_trunc_p (ph::make (-9, -11, -20),
+			      ph::make (5, 5, 20),
+			      &const_quot, &rem), N == 1);
+  if (N == 1)
+    {
+      ASSERT_EQ (const_quot, C (-1));
+      ASSERT_KNOWN_EQ (rem, C (-4));
+    }
 }
 
 /* Test the form of can_div_trunc_p that returns a poly_int, for signed C.  */