Support: Add BranchProbability::scale() and ::scaleByInverse()

Add API to `BranchProbability` for scaling big integers.  Next job is to
rip the logic out of `BlockMass` and `BlockFrequency`.

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@207544 91177308-0d34-0410-b5e6-96231b3b80d8

include/llvm/Support/BranchProbability.h

@@ -50,6 +50,30 @@ public:
 
   void dump() const;
 
+  /// \brief Scale a large integer.
+  ///
+  /// Scales \c Num.  Guarantees full precision.  Returns the floor of the
+  /// result.
+  ///
+  /// \return \c Num times \c this.
+  ///
+  /// \note This code should be shared with (or replaced by) the implementation
+  /// of \a BlockFrequency::scale(), which seems to be calculating something
+  /// similar.
+  uint64_t scale(uint64_t Num) const;
+
+  /// \brief Scale a large integer by the inverse.
+  ///
+  /// Scales \c Num by the inverse of \c this.  Guarantees full precision.
+  /// Returns the floor of the result.
+  ///
+  /// \return \c Num divided by \c this.
+  ///
+  /// \note This code should be shared with (or replaced by) the implementation
+  /// of \a BlockFrequency::scale(), which seems to be calculating something
+  /// similar.
+  uint64_t scaleByInverse(uint64_t Num) const;
+
   bool operator==(BranchProbability RHS) const {
     return (uint64_t)N * RHS.D == (uint64_t)D * RHS.N;
   }

lib/Support/BranchProbability.cpp

@@ -26,6 +26,53 @@ void BranchProbability::dump() const {
   dbgs() << *this << '\n';
 }
 
+static uint64_t scale(uint64_t Num, uint32_t N, uint32_t D) {
+  assert(D && "divide by 0");
+
+  // Fast path for multiplying by 1.0.
+  if (!Num || D == N)
+    return Num;
+
+  // Split Num into upper and lower parts to multiply, then recombine.
+  uint64_t ProductHigh = (Num >> 32) * N;
+  uint64_t ProductLow = (Num & UINT32_MAX) * N;
+
+  // Split into 32-bit digits.
+  uint32_t Upper32 = ProductHigh >> 32;
+  uint32_t Lower32 = ProductLow & UINT32_MAX;
+  uint32_t Mid32Partial = ProductHigh & UINT32_MAX;
+  uint32_t Mid32 = Mid32Partial + (ProductLow >> 32);
+
+  // Carry.
+  Upper32 += Mid32 < Mid32Partial;
+
+  // Check for overflow.
+  if (Upper32 >= D)
+    return UINT64_MAX;
+
+  uint64_t Rem = (uint64_t(Upper32) << 32) | Mid32;
+  uint64_t UpperQ = Rem / D;
+
+  // Check for overflow.
+  if (UpperQ > UINT32_MAX)
+    return UINT64_MAX;
+
+  Rem = ((Rem % D) << 32) | Lower32;
+  uint64_t LowerQ = Rem / D;
+  uint64_t Q = (UpperQ << 32) + LowerQ;
+
+  // Check for overflow.
+  return Q < LowerQ ? UINT64_MAX : Q;
+}
+
+uint64_t BranchProbability::scale(uint64_t Num) const {
+  return ::scale(Num, N, D);
+}
+
+uint64_t BranchProbability::scaleByInverse(uint64_t Num) const {
+  return ::scale(Num, D, N);
+}
+
 namespace llvm {
 
 raw_ostream &operator<<(raw_ostream &OS, const BranchProbability &Prob) {

unittests/Support/BranchProbabilityTest.cpp

@@ -87,4 +87,72 @@ TEST(BranchProbabilityTest, getCompl) {
   EXPECT_EQ(BP::getOne(), BP(0, 7).getCompl());
 }
 
+TEST(BranchProbabilityTest, scale) {
+  // Multiply by 1.0.
+  EXPECT_EQ(UINT64_MAX, BP(1, 1).scale(UINT64_MAX));
+  EXPECT_EQ(UINT64_MAX, BP(7, 7).scale(UINT64_MAX));
+  EXPECT_EQ(UINT32_MAX, BP(1, 1).scale(UINT32_MAX));
+  EXPECT_EQ(UINT32_MAX, BP(7, 7).scale(UINT32_MAX));
+  EXPECT_EQ(0u, BP(1, 1).scale(0));
+  EXPECT_EQ(0u, BP(7, 7).scale(0));
+
+  // Multiply by 0.0.
+  EXPECT_EQ(0u, BP(0, 1).scale(UINT64_MAX));
+  EXPECT_EQ(0u, BP(0, 1).scale(UINT64_MAX));
+  EXPECT_EQ(0u, BP(0, 1).scale(0));
+
+  auto Two63 = UINT64_C(1) << 63;
+  auto Two31 = UINT64_C(1) << 31;
+
+  // Multiply by 0.5.
+  EXPECT_EQ(Two63 - 1, BP(1, 2).scale(UINT64_MAX));
+
+  // Big fractions.
+  EXPECT_EQ(1u, BP(Two31, UINT32_MAX).scale(2));
+  EXPECT_EQ(Two31, BP(Two31, UINT32_MAX).scale(Two31 * 2));
+  EXPECT_EQ(Two63 + Two31, BP(Two31, UINT32_MAX).scale(UINT64_MAX));
+
+  // High precision.
+  EXPECT_EQ(UINT64_C(9223372047592194055),
+            BP(Two31 + 1, UINT32_MAX - 2).scale(UINT64_MAX));
+}
+
+TEST(BranchProbabilityTest, scaleByInverse) {
+  // Divide by 1.0.
+  EXPECT_EQ(UINT64_MAX, BP(1, 1).scaleByInverse(UINT64_MAX));
+  EXPECT_EQ(UINT64_MAX, BP(7, 7).scaleByInverse(UINT64_MAX));
+  EXPECT_EQ(UINT32_MAX, BP(1, 1).scaleByInverse(UINT32_MAX));
+  EXPECT_EQ(UINT32_MAX, BP(7, 7).scaleByInverse(UINT32_MAX));
+  EXPECT_EQ(0u, BP(1, 1).scaleByInverse(0));
+  EXPECT_EQ(0u, BP(7, 7).scaleByInverse(0));
+
+  // Divide by something very small.
+  EXPECT_EQ(UINT64_MAX, BP(1, UINT32_MAX).scaleByInverse(UINT64_MAX));
+  EXPECT_EQ(uint64_t(UINT32_MAX) * UINT32_MAX,
+            BP(1, UINT32_MAX).scaleByInverse(UINT32_MAX));
+  EXPECT_EQ(UINT32_MAX, BP(1, UINT32_MAX).scaleByInverse(1));
+
+  auto Two63 = UINT64_C(1) << 63;
+  auto Two31 = UINT64_C(1) << 31;
+
+  // Divide by 0.5.
+  EXPECT_EQ(UINT64_MAX - 1, BP(1, 2).scaleByInverse(Two63 - 1));
+  EXPECT_EQ(UINT64_MAX, BP(1, 2).scaleByInverse(Two63));
+
+  // Big fractions.
+  EXPECT_EQ(1u, BP(Two31, UINT32_MAX).scaleByInverse(1));
+  EXPECT_EQ(2u, BP(Two31 - 1, UINT32_MAX).scaleByInverse(1));
+  EXPECT_EQ(Two31 * 2 - 1, BP(Two31, UINT32_MAX).scaleByInverse(Two31));
+  EXPECT_EQ(Two31 * 2 + 1, BP(Two31 - 1, UINT32_MAX).scaleByInverse(Two31));
+  EXPECT_EQ(UINT64_MAX, BP(Two31, UINT32_MAX).scaleByInverse(Two63 + Two31));
+
+  // High precision.  The exact answers to these are close to the successors of
+  // the floor.  If we were rounding, these would round up.
+  EXPECT_EQ(UINT64_C(18446744065119617030),
+            BP(Two31 + 2, UINT32_MAX - 2)
+                .scaleByInverse(UINT64_C(9223372047592194055)));
+  EXPECT_EQ(UINT64_C(18446744065119617026),
+            BP(Two31 + 1, UINT32_MAX).scaleByInverse(Two63 + Two31));
+}
+
 }