Index: include/llvm/Analysis/ValueTracking.h
===================================================================
--- include/llvm/Analysis/ValueTracking.h
+++ include/llvm/Analysis/ValueTracking.h
@@ -116,6 +116,11 @@
   ///
   bool CannotBeNegativeZero(const Value *V, unsigned Depth = 0);
 
+  /// CannotBeOrderedLessThanZero - Return true if we can prove that the 
+  /// specified FP value is either a NaN or never less than 0.0.
+  ///
+  bool CannotBeOrderedLessThanZero(const Value *V, unsigned Depth = 0);
+
   /// isBytewiseValue - If the specified value can be set by repeating the same
   /// byte in memory, return the i8 value that it is represented with.  This is
   /// true for all i8 values obviously, but is also true for i32 0, i32 -1,
Index: lib/Analysis/InstructionSimplify.cpp
===================================================================
--- lib/Analysis/InstructionSimplify.cpp
+++ lib/Analysis/InstructionSimplify.cpp
@@ -3087,6 +3087,20 @@
           }
         }
       }
+      if (CFP->getValueAPF().isZero()) {
+        switch (Pred) {
+        case FCmpInst::FCMP_UGE:
+          if (CannotBeOrderedLessThanZero(LHS)) 
+            return ConstantInt::getTrue(CFP->getContext());
+          break;
+        case FCmpInst::FCMP_OLT:
+          if (CannotBeOrderedLessThanZero(LHS)) 
+            return ConstantInt::getFalse(CFP->getContext());
+          break;
+        default:
+          break;
+        }
+     }
     }
   }
 
Index: lib/Analysis/ValueTracking.cpp
===================================================================
--- lib/Analysis/ValueTracking.cpp
+++ lib/Analysis/ValueTracking.cpp
@@ -2044,6 +2044,59 @@
   return false;
 }
 
+bool llvm::CannotBeOrderedLessThanZero(const Value *V, unsigned Depth) {
+  if (const ConstantFP *CFP = dyn_cast<ConstantFP>(V))
+    return !CFP->getValueAPF().isNegative() || CFP->getValueAPF().isZero();
+
+  if (Depth == 6)
+    return false;  // Limit search depth.
+
+  const Operator *I = dyn_cast<Operator>(V);
+  if (!I) return false;
+
+  switch (I->getOpcode()) {
+  default: break;
+  case Instruction::FMul:
+    // x*x is always non-negative or a NaN.
+    if (I->getOperand(0) == I->getOperand(1)) 
+      return true;
+    // Fall through
+  case Instruction::FAdd:
+  case Instruction::FDiv:
+  case Instruction::FRem:
+    return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1) &&
+           CannotBeOrderedLessThanZero(I->getOperand(1), Depth+1);
+  case Instruction::FPExt:
+  case Instruction::FPTrunc:
+    // Widening/narrowing never change sign.
+    return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1);
+  case Instruction::Call: 
+    if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(I)) 
+      switch (II->getIntrinsicID()) {
+      default: break;
+      case Intrinsic::exp:
+      case Intrinsic::exp2:
+      case Intrinsic::fabs:
+      case Intrinsic::sqrt:
+        return true;
+      case Intrinsic::powi: 
+        if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
+          // powi(x,n) is non-negative if n is even.
+          if (CI->getBitWidth() <= 64 && CI->getSExtValue() % 2u == 0)
+            return true;
+        }
+        return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1);
+      case Intrinsic::fma:
+      case Intrinsic::fmuladd:
+        // x*x+y is non-negative if y is non-negative.
+        return I->getOperand(0) == I->getOperand(1) && 
+               CannotBeOrderedLessThanZero(I->getOperand(2), Depth+1);
+      }
+    break;
+  }
+  return false; 
+}
+
 /// If the specified value can be set by repeating the same byte in memory,
 /// return the i8 value that it is represented with.  This is
 /// true for all i8 values obviously, but is also true for i32 0, i32 -1,
Index: test/Transforms/InstSimplify/floating-point-compare.ll
===================================================================
--- test/Transforms/InstSimplify/floating-point-compare.ll
+++ test/Transforms/InstSimplify/floating-point-compare.ll
@@ -0,0 +1,60 @@
+; RUN: opt < %s -instsimplify -S | FileCheck %s
+
+; These tests choose arbitrarily between float and double,
+; and between uge and olt, to give reasonble coverage 
+; without combinatorial explosion.
+
+declare float @llvm.fabs.f32(float)
+declare float @llvm.sqrt.f32(float)
+declare double @llvm.powi.f64(double,i32)
+declare float @llvm.exp.f32(float)
+declare double @llvm.exp2.f64(double)
+declare float @llvm.fma.f32(float,float,float)
+
+declare void @expect_equal(i1,i1)
+
+; CHECK-LABEL: @orderedLessZeroTree(
+define i1 @orderedLessZeroTree(float,float,float,float) {
+  %square = fmul float %0, %0
+  %abs = call float @llvm.fabs.f32(float %1)
+  %sqrt = call float @llvm.sqrt.f32(float %2)
+  %fma = call float @llvm.fma.f32(float %3, float %3, float %sqrt)
+  %div = fdiv float %square, %abs
+  %rem = frem float %sqrt, %fma
+  %add = fadd float %div, %rem
+  %uge = fcmp uge float %add, 0.000000e+00
+; CHECK: ret i1 true
+  ret i1 %uge
+}
+
+; CHECK-LABEL: @orderedLessZeroExpExt(
+define i1 @orderedLessZeroExpExt(float) {
+  %a = call float @llvm.exp.f32(float %0)
+  %b = fpext float %a to double
+  %uge = fcmp uge double %b, 0.000000e+00
+; CHECK: ret i1 true
+  ret i1 %uge
+}
+
+; CHECK-LABEL: @orderedLessZeroExp2Trunc(
+define i1 @orderedLessZeroExp2Trunc(double) {
+  %a = call double @llvm.exp2.f64(double %0)
+  %b = fptrunc double %a to float
+  %olt = fcmp olt float %b, 0.000000e+00
+; CHECK: ret i1 false
+  ret i1 %olt
+}
+
+; CHECK-LABEL: @orderedLessZeroPowi(
+define i1 @orderedLessZeroPowi(double,double) {
+  ; Even constant exponent
+  %a = call double @llvm.powi.f64(double %0, i32 2)
+  %square = fmul double %1, %1
+  ; Odd constant exponent with provably non-negative base
+  %b = call double @llvm.powi.f64(double %square, i32 3)
+  %c = fadd double %a, %b
+  %olt = fcmp olt double %b, 0.000000e+00
+; CHECK: ret i1 false
+  ret i1 %olt
+}
+