[complex] Teach Clang to preserve different-type operands to arithmetic

operators where one type is a C complex type, and to emit both the
efficient and correct implementation for complex arithmetic according to
C11 Annex G using this extra information.

For both multiply and divide the old code was writing a long-hand
reduced version of the math without any of the special handling of inf
and NaN recommended by the standard here. Instead of putting more
complexity here, this change does what GCC does which is to emit
a libcall for the fully general case.

However, the old code also failed to do the proper minimization of the
set of operations when there was a mixed complex and real operation. In
those cases, C provides a spec for much more minimal operations that are
valid. Clang now emits the exact suggested operations. This change isn't
*just* about performance though, without minimizing these operations, we
again lose the correct handling of infinities and NaNs. It is critical
that this happen in the frontend based on assymetric type operands to
complex math operations.

The performance implications of this change aren't trivial either. I've
run a set of benchmarks in Eigen, an open source mathematics library
that makes heavy use of complex. While a few have slowed down due to the
libcall being introduce, most sped up and some by a huge amount: up to
100% and 140%.

In order to make all of this work, also match the algorithm in the
constant evaluator to the one in the runtime library. Currently it is
a broken port of the simplifications from C's Annex G to the long-hand
formulation of the algorithm.

Splitting this patch up is very hard because none of this works without
the AST change to preserve non-complex operands. Sorry for the enormous
change.

Follow-up changes will include support for sinking the libcalls onto
cold paths in common cases and fastmath improvements to allow more
aggressive backend folding.

Differential Revision: http://reviews.llvm.org/D5698

llvm-svn: 219557

1 files changed, 156 insertions, 52 deletions

diff --git a/clang/lib/AST/ExprConstant.cpp b/clang/lib/AST/ExprConstant.cpp
index f7eef828063..db300c4fec4 100644
--- a/clang/lib/AST/ExprConstant.cpp
+++ b/clang/lib/AST/ExprConstant.cpp
@@ -7874,24 +7874,49 @@ bool ComplexExprEvaluator::VisitBinaryOperator(const BinaryOperator *E) {
   if (E->isPtrMemOp() || E->isAssignmentOp() || E->getOpcode() == BO_Comma)
     return ExprEvaluatorBaseTy::VisitBinaryOperator(E);
 
-  bool LHSOK = Visit(E->getLHS());
+  // Track whether the LHS or RHS is real at the type system level. When this is
+  // the case we can simplify our evaluation strategy.
+  bool LHSReal = false, RHSReal = false;
+
+  bool LHSOK;
+  if (E->getLHS()->getType()->isRealFloatingType()) {
+    LHSReal = true;
+    APFloat &Real = Result.FloatReal;
+    LHSOK = EvaluateFloat(E->getLHS(), Real, Info);
+    if (LHSOK) {
+      Result.makeComplexFloat();
+      Result.FloatImag = APFloat(Real.getSemantics());
+    }
+  } else {
+    LHSOK = Visit(E->getLHS());
+  }
   if (!LHSOK && !Info.keepEvaluatingAfterFailure())
     return false;
 
   ComplexValue RHS;
-  if (!EvaluateComplex(E->getRHS(), RHS, Info) || !LHSOK)
+  if (E->getRHS()->getType()->isRealFloatingType()) {
+    RHSReal = true;
+    APFloat &Real = RHS.FloatReal;
+    if (!EvaluateFloat(E->getRHS(), Real, Info) || !LHSOK)
+      return false;
+    RHS.makeComplexFloat();
+    RHS.FloatImag = APFloat(Real.getSemantics());
+  } else if (!EvaluateComplex(E->getRHS(), RHS, Info) || !LHSOK)
     return false;
 
-  assert(Result.isComplexFloat() == RHS.isComplexFloat() &&
-         "Invalid operands to binary operator.");
+  assert(!(LHSReal && RHSReal) &&
+         "Cannot have both operands of a complex operation be real.");
   switch (E->getOpcode()) {
   default: return Error(E);
   case BO_Add:
     if (Result.isComplexFloat()) {
       Result.getComplexFloatReal().add(RHS.getComplexFloatReal(),
                                        APFloat::rmNearestTiesToEven);
-      Result.getComplexFloatImag().add(RHS.getComplexFloatImag(),
-                                       APFloat::rmNearestTiesToEven);
+      if (LHSReal)
+        Result.getComplexFloatImag() = RHS.getComplexFloatImag();
+      else if (!RHSReal)
+        Result.getComplexFloatImag().add(RHS.getComplexFloatImag(),
+                                         APFloat::rmNearestTiesToEven);
     } else {
       Result.getComplexIntReal() += RHS.getComplexIntReal();
       Result.getComplexIntImag() += RHS.getComplexIntImag();
@@ -7901,8 +7926,13 @@ bool ComplexExprEvaluator::VisitBinaryOperator(const BinaryOperator *E) {
     if (Result.isComplexFloat()) {
       Result.getComplexFloatReal().subtract(RHS.getComplexFloatReal(),
                                             APFloat::rmNearestTiesToEven);
-      Result.getComplexFloatImag().subtract(RHS.getComplexFloatImag(),
-                                            APFloat::rmNearestTiesToEven);
+      if (LHSReal) {
+        Result.getComplexFloatImag() = RHS.getComplexFloatImag();
+        Result.getComplexFloatImag().changeSign();
+      } else if (!RHSReal) {
+        Result.getComplexFloatImag().subtract(RHS.getComplexFloatImag(),
+                                              APFloat::rmNearestTiesToEven);
+      }
     } else {
       Result.getComplexIntReal() -= RHS.getComplexIntReal();
       Result.getComplexIntImag() -= RHS.getComplexIntImag();
@@ -7910,25 +7940,75 @@ bool ComplexExprEvaluator::VisitBinaryOperator(const BinaryOperator *E) {
     break;
   case BO_Mul:
     if (Result.isComplexFloat()) {
+      // This is an implementation of complex multiplication according to the
+      // constraints laid out in C11 Annex G. The implemantion uses the
+      // following naming scheme:
+      //   (a + ib) * (c + id)
       ComplexValue LHS = Result;
-      APFloat &LHS_r = LHS.getComplexFloatReal();
-      APFloat &LHS_i = LHS.getComplexFloatImag();
-      APFloat &RHS_r = RHS.getComplexFloatReal();
-      APFloat &RHS_i = RHS.getComplexFloatImag();
-
-      APFloat Tmp = LHS_r;
-      Tmp.multiply(RHS_r, APFloat::rmNearestTiesToEven);
-      Result.getComplexFloatReal() = Tmp;
-      Tmp = LHS_i;
-      Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
-      Result.getComplexFloatReal().subtract(Tmp, APFloat::rmNearestTiesToEven);
-
-      Tmp = LHS_r;
-      Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
-      Result.getComplexFloatImag() = Tmp;
-      Tmp = LHS_i;
-      Tmp.multiply(RHS_r, APFloat::rmNearestTiesToEven);
-      Result.getComplexFloatImag().add(Tmp, APFloat::rmNearestTiesToEven);
+      APFloat &A = LHS.getComplexFloatReal();
+      APFloat &B = LHS.getComplexFloatImag();
+      APFloat &C = RHS.getComplexFloatReal();
+      APFloat &D = RHS.getComplexFloatImag();
+      APFloat &ResR = Result.getComplexFloatReal();
+      APFloat &ResI = Result.getComplexFloatImag();
+      if (LHSReal) {
+        assert(!RHSReal && "Cannot have two real operands for a complex op!");
+        ResR = A * C;
+        ResI = A * D;
+      } else if (RHSReal) {
+        ResR = C * A;
+        ResI = C * B;
+      } else {
+        // In the fully general case, we need to handle NaNs and infinities
+        // robustly.
+        APFloat AC = A * C;
+        APFloat BD = B * D;
+        APFloat AD = A * D;
+        APFloat BC = B * C;
+        ResR = AC - BD;
+        ResI = AD + BC;
+        if (ResR.isNaN() && ResI.isNaN()) {
+          bool Recalc = false;
+          if (A.isInfinity() || B.isInfinity()) {
+            A = APFloat::copySign(
+                APFloat(A.getSemantics(), A.isInfinity() ? 1 : 0), A);
+            B = APFloat::copySign(
+                APFloat(B.getSemantics(), B.isInfinity() ? 1 : 0), B);
+            if (C.isNaN())
+              C = APFloat::copySign(APFloat(C.getSemantics()), C);
+            if (D.isNaN())
+              D = APFloat::copySign(APFloat(D.getSemantics()), D);
+            Recalc = true;
+          }
+          if (C.isInfinity() || D.isInfinity()) {
+            C = APFloat::copySign(
+                APFloat(C.getSemantics(), C.isInfinity() ? 1 : 0), C);
+            D = APFloat::copySign(
+                APFloat(D.getSemantics(), D.isInfinity() ? 1 : 0), D);
+            if (A.isNaN())
+              A = APFloat::copySign(APFloat(A.getSemantics()), A);
+            if (B.isNaN())
+              B = APFloat::copySign(APFloat(B.getSemantics()), B);
+            Recalc = true;
+          }
+          if (!Recalc && (AC.isInfinity() || BD.isInfinity() ||
+                          AD.isInfinity() || BC.isInfinity())) {
+            if (A.isNaN())
+              A = APFloat::copySign(APFloat(A.getSemantics()), A);
+            if (B.isNaN())
+              B = APFloat::copySign(APFloat(B.getSemantics()), B);
+            if (C.isNaN())
+              C = APFloat::copySign(APFloat(C.getSemantics()), C);
+            if (D.isNaN())
+              D = APFloat::copySign(APFloat(D.getSemantics()), D);
+            Recalc = true;
+          }
+          if (Recalc) {
+            ResR = APFloat::getInf(A.getSemantics()) * (A * C - B * D);
+            ResI = APFloat::getInf(A.getSemantics()) * (A * D + B * C);
+          }
+        }
+      }
     } else {
       ComplexValue LHS = Result;
       Result.getComplexIntReal() =
@@ -7941,33 +8021,57 @@ bool ComplexExprEvaluator::VisitBinaryOperator(const BinaryOperator *E) {
     break;
   case BO_Div:
     if (Result.isComplexFloat()) {
+      // This is an implementation of complex division according to the
+      // constraints laid out in C11 Annex G. The implemantion uses the
+      // following naming scheme:
+      //   (a + ib) / (c + id)
       ComplexValue LHS = Result;
-      APFloat &LHS_r = LHS.getComplexFloatReal();
-      APFloat &LHS_i = LHS.getComplexFloatImag();
-      APFloat &RHS_r = RHS.getComplexFloatReal();
-      APFloat &RHS_i = RHS.getComplexFloatImag();
-      APFloat &Res_r = Result.getComplexFloatReal();
-      APFloat &Res_i = Result.getComplexFloatImag();
-
-      APFloat Den = RHS_r;
-      Den.multiply(RHS_r, APFloat::rmNearestTiesToEven);
-      APFloat Tmp = RHS_i;
-      Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
-      Den.add(Tmp, APFloat::rmNearestTiesToEven);
-
-      Res_r = LHS_r;
-      Res_r.multiply(RHS_r, APFloat::rmNearestTiesToEven);
-      Tmp = LHS_i;
-      Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
-      Res_r.add(Tmp, APFloat::rmNearestTiesToEven);
-      Res_r.divide(Den, APFloat::rmNearestTiesToEven);
-
-      Res_i = LHS_i;
-      Res_i.multiply(RHS_r, APFloat::rmNearestTiesToEven);
-      Tmp = LHS_r;
-      Tmp.multiply(RHS_i, APFloat::rmNearestTiesToEven);
-      Res_i.subtract(Tmp, APFloat::rmNearestTiesToEven);
-      Res_i.divide(Den, APFloat::rmNearestTiesToEven);
+      APFloat &A = LHS.getComplexFloatReal();
+      APFloat &B = LHS.getComplexFloatImag();
+      APFloat &C = RHS.getComplexFloatReal();
+      APFloat &D = RHS.getComplexFloatImag();
+      APFloat &ResR = Result.getComplexFloatReal();
+      APFloat &ResI = Result.getComplexFloatImag();
+      if (RHSReal) {
+        ResR = A / C;
+        ResI = B / C;
+      } else {
+        if (LHSReal) {
+          // No real optimizations we can do here, stub out with zero.
+          B = APFloat::getZero(A.getSemantics());
+        }
+        int DenomLogB = 0;
+        APFloat MaxCD = maxnum(abs(C), abs(D));
+        if (MaxCD.isFinite()) {
+          DenomLogB = ilogb(MaxCD);
+          C = scalbn(C, -DenomLogB);
+          D = scalbn(D, -DenomLogB);
+        }
+        APFloat Denom = C * C + D * D;
+        ResR = scalbn((A * C + B * D) / Denom, -DenomLogB);
+        ResI = scalbn((B * C - A * D) / Denom, -DenomLogB);
+        if (ResR.isNaN() && ResI.isNaN()) {
+          if (Denom.isPosZero() && (!A.isNaN() || !B.isNaN())) {
+            ResR = APFloat::getInf(ResR.getSemantics(), C.isNegative()) * A;
+            ResI = APFloat::getInf(ResR.getSemantics(), C.isNegative()) * B;
+          } else if ((A.isInfinity() || B.isInfinity()) && C.isFinite() &&
+                     D.isFinite()) {
+            A = APFloat::copySign(
+                APFloat(A.getSemantics(), A.isInfinity() ? 1 : 0), A);
+            B = APFloat::copySign(
+                APFloat(B.getSemantics(), B.isInfinity() ? 1 : 0), B);
+            ResR = APFloat::getInf(ResR.getSemantics()) * (A * C + B * D);
+            ResI = APFloat::getInf(ResI.getSemantics()) * (B * C - A * D);
+          } else if (MaxCD.isInfinity() && A.isFinite() && B.isFinite()) {
+            C = APFloat::copySign(
+                APFloat(C.getSemantics(), C.isInfinity() ? 1 : 0), C);
+            D = APFloat::copySign(
+                APFloat(D.getSemantics(), D.isInfinity() ? 1 : 0), D);
+            ResR = APFloat::getZero(ResR.getSemantics()) * (A * C + B * D);
+            ResI = APFloat::getZero(ResI.getSemantics()) * (B * C - A * D);
+          }
+        }
+      }
     } else {
       if (RHS.getComplexIntReal() == 0 && RHS.getComplexIntImag() == 0)
         return Error(E, diag::note_expr_divide_by_zero);