Index: lib/Support/APInt.cpp
===================================================================
--- lib/Support/APInt.cpp
+++ lib/Support/APInt.cpp
@@ -1503,21 +1503,18 @@
   assert(u && "Must provide dividend");
   assert(v && "Must provide divisor");
   assert(q && "Must provide quotient");
-  assert(u != v && u != q && v != q && "Must us different memory");
+  assert(u != v && u != q && v != q && "Must use different memory");
   assert(n>1 && "n must be > 1");
 
-  // Knuth uses the value b as the base of the number system. In our case b
-  // is 2^31 so we just set it to -1u.
-  uint64_t b = uint64_t(1) << 32;
+  // b denotes the base of the number system. In our case b is 2^32.
+  LLVM_CONSTEXPR uint64_t b = uint64_t(1) << 32;
 
-#if 0
   DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
   DEBUG(dbgs() << "KnuthDiv: original:");
   DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
   DEBUG(dbgs() << " by");
   DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
   DEBUG(dbgs() << '\n');
-#endif
   // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
   // u and v by d. Note that we have taken Knuth's advice here to use a power
   // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
@@ -1542,13 +1539,12 @@
     }
   }
   u[m+n] = u_carry;
-#if 0
+
   DEBUG(dbgs() << "KnuthDiv:   normal:");
   DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
   DEBUG(dbgs() << " by");
   DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
   DEBUG(dbgs() << '\n');
-#endif
 
   // D2. [Initialize j.]  Set j to m. This is the loop counter over the places.
   int j = m;
@@ -1578,46 +1574,35 @@
     // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
     // consists of a simple multiplication by a one-place number, combined with
     // a subtraction.
+    // The digits (u[j+n]...u[j]) should be kept positive; if the result of
+    // this step is actually negative, (u[j+n]...u[j]) should be left as the
+    // true value plus b**(n+1), namely as the b's complement of
+    // the true value, and a "borrow" to the left should be remembered.
     bool isNeg = false;
     for (unsigned i = 0; i < n; ++i) {
-      uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
+      uint64_t u_tmp = (uint64_t(u[j+i+1]) << 32) | uint64_t(u[j+i]);
       uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
       bool borrow = subtrahend > u_tmp;
-      DEBUG(dbgs() << "KnuthDiv: u_tmp == " << u_tmp
-                   << ", subtrahend == " << subtrahend
+      DEBUG(dbgs() << "KnuthDiv: u_tmp = " << u_tmp
+                   << ", subtrahend = " << subtrahend
                    << ", borrow = " << borrow << '\n');
 
       uint64_t result = u_tmp - subtrahend;
       unsigned k = j + i;
-      u[k++] = (unsigned)(result & (b-1)); // subtract low word
-      u[k++] = (unsigned)(result >> 32);   // subtract high word
-      while (borrow && k <= m+n) { // deal with borrow to the left
+      u[k++] = (unsigned)result;         // subtraction low word
+      u[k++] = (unsigned)(result >> 32); // subtraction high word
+      while (borrow && k <= m+n) {       // deal with borrow to the left
         borrow = u[k] == 0;
         u[k]--;
         k++;
       }
       isNeg |= borrow;
-      DEBUG(dbgs() << "KnuthDiv: u[j+i] == " << u[j+i] << ",  u[j+i+1] == " <<
-                    u[j+i+1] << '\n');
+      DEBUG(dbgs() << "KnuthDiv: u[j+i] = " << u[j+i] 
+                   << ", u[j+i+1] = " << u[j+i+1] << '\n');
     }
     DEBUG(dbgs() << "KnuthDiv: after subtraction:");
     DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
     DEBUG(dbgs() << '\n');
-    // The digits (u[j+n]...u[j]) should be kept positive; if the result of
-    // this step is actually negative, (u[j+n]...u[j]) should be left as the
-    // true value plus b**(n+1), namely as the b's complement of
-    // the true value, and a "borrow" to the left should be remembered.
-    //
-    if (isNeg) {
-      bool carry = true;  // true because b's complement is "complement + 1"
-      for (unsigned i = 0; i <= m+n; ++i) {
-        u[i] = ~u[i] + carry; // b's complement
-        carry = carry && u[i] == 0;
-      }
-    }
-    DEBUG(dbgs() << "KnuthDiv: after complement:");
-    DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
-    DEBUG(dbgs() << '\n');
 
     // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
     // negative, go to step D6; otherwise go on to step D7.
@@ -1639,7 +1624,7 @@
       u[j+n] += carry;
     }
     DEBUG(dbgs() << "KnuthDiv: after correction:");
-    DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]);
+    DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
     DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
 
   // D7. [Loop on j.]  Decrease j by one. Now if j >= 0, go back to D3.
@@ -1672,9 +1657,7 @@
     }
     DEBUG(dbgs() << '\n');
   }
-#if 0
   DEBUG(dbgs() << '\n');
-#endif
 }
 
 void APInt::divide(const APInt LHS, unsigned lhsWords,
@@ -1798,6 +1781,8 @@
 
     // The quotient is in Q. Reconstitute the quotient into Quotient's low
     // order words.
+    // This case is currently dead as all users of divide() handle trivial cases
+    // earlier.
     if (lhsWords == 1) {
       uint64_t tmp =
         uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));
Index: unittests/ADT/APIntTest.cpp
===================================================================
--- unittests/ADT/APIntTest.cpp
+++ unittests/ADT/APIntTest.cpp
@@ -209,6 +209,206 @@
   }
 }
 
+TEST(APIntTest, divrem_big1) {
+  // Tests KnuthDiv rare step D6
+  APInt a{256, "1ffffffffffffffff", 16};
+  APInt b{256, "1ffffffffffffffff", 16};
+  APInt c{256, 0};
+
+  auto p = a * b + c;
+  auto q = p.udiv(a);
+  auto r = p.urem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  APInt::udivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.udiv(b);
+  r = p.urem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  APInt::udivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(a);
+  r = p.srem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  APInt::sdivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(b);
+  r = p.srem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  APInt::sdivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+}
+
+TEST(APIntTest, divrem_big2) {
+  // Tests KnuthDiv rare step D6
+  APInt a{1024,           "111111ffffffffffffffff"
+                "ffffffffffffffffffffffffffffffff"
+                "fffffffffffffffffffffffffffffccf"
+                "ffffffffffffffffffffffffffffff00", 16};
+  APInt b{1024,                       "112233ceff"
+                "cecece000000ffffffffffffffffffff"
+                "ffffffffffffffffffffffffffffffff"
+                "ffffffffffffffffffffffffffffffff"
+                "ffffffffffffffffffffffffffffff33", 16};
+  APInt c{1024, 7919};
+
+  auto p = a * b + c;
+  auto q = p.udiv(a);
+  auto r = p.urem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  APInt::udivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.udiv(b);
+  r = p.urem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  APInt::udivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(a);
+  r = p.srem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  APInt::sdivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(b);
+  r = p.srem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  APInt::sdivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+}
+
+TEST(APIntTest, divrem_big3) {
+  // Tests KnuthDiv case without shift
+  APInt a{256, "ffffffffffffff0000000", 16};
+  APInt b{256, "80000001ffffffffffffffff", 16};
+  APInt c{256, 4219};
+
+  auto p = a * b + c;
+  auto q = p.udiv(a);
+  auto r = p.urem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  APInt::udivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.udiv(b);
+  r = p.urem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  APInt::udivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(a);
+  r = p.srem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  APInt::sdivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(b);
+  r = p.srem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  APInt::sdivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+}
+
+TEST(APIntTest, divrem_big4) {
+  // Tests heap allocation in divide() enfoced by huge numbers
+  auto a = APInt{4096, 1}.shl(2000);
+  auto b = APInt{4096, 5}.shl(2001);
+  auto c = APInt{4096, 4219*13};
+
+  auto p = a * b + c;
+  auto q = p.udiv(a);
+  auto r = p.urem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = APInt{1024, 0}; // test non-single word APInt conversion in divide()
+  r = APInt{1024, 0};
+  APInt::udivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.udiv(b);
+  r = p.urem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  q = APInt{1024, 0};
+  r = APInt{1024, 0};
+  APInt::udivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(a);
+  r = p.srem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = APInt{1024, 0};
+  r = APInt{1024, 0};
+  APInt::sdivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(b);
+  r = p.srem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  q = APInt{1024, 0};
+  r = APInt{1024, 0};
+  APInt::sdivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+}
+
+TEST(APIntTest, divrem_big5) {
+  // Tests one word divisor case of divide()
+  auto a = APInt{1024, 19}.shl(811);
+  auto b = APInt{1024, 4356013}; // one word
+  auto c = APInt{1024, 1};
+
+  auto p = a * b + c;
+  auto q = p.udiv(a);
+  auto r = p.urem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  APInt::udivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.udiv(b);
+  r = p.urem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  APInt::udivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(a);
+  r = p.srem(a);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  APInt::sdivrem(p, a, q, r);
+  EXPECT_EQ(q, b);
+  EXPECT_EQ(r, c);
+  q = p.sdiv(b);
+  r = p.srem(b);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+  APInt::sdivrem(p, b, q, r);
+  EXPECT_EQ(q, a);
+  EXPECT_EQ(r, c);
+}
+
 TEST(APIntTest, fromString) {
   EXPECT_EQ(APInt(32, 0), APInt(32,   "0", 2));
   EXPECT_EQ(APInt(32, 1), APInt(32,   "1", 2));