Index: llvm/lib/Analysis/ValueTracking.cpp
===================================================================
--- llvm/lib/Analysis/ValueTracking.cpp
+++ llvm/lib/Analysis/ValueTracking.cpp
@@ -2645,7 +2645,8 @@
     return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
                                            Depth + 1);
   case Instruction::Call:
-    Intrinsic::ID IID = getIntrinsicForCallSite(cast<CallInst>(I), TLI);
+    const auto *CI = cast<CallInst>(I);
+    Intrinsic::ID IID = getIntrinsicForCallSite(CI, TLI);
     switch (IID) {
     default:
       break;
@@ -2662,12 +2663,19 @@
     case Intrinsic::exp:
     case Intrinsic::exp2:
     case Intrinsic::fabs:
-    case Intrinsic::sqrt:
       return true;
+
+    case Intrinsic::sqrt:
+      // sqrt(x) is always >= -0 or NaN.  Moreover, sqrt(x) == -0 iff x == -0.
+      if (!SignBitOnly)
+        return true;
+      return CI->hasNoNaNs() && (CI->hasNoSignedZeros() ||
+                                 CannotBeNegativeZero(CI->getOperand(0), TLI));
+
     case Intrinsic::powi:
-      if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
+      if (ConstantInt *Exponent = dyn_cast<ConstantInt>(I->getOperand(1))) {
         // powi(x,n) is non-negative if n is even.
-        if (CI->getBitWidth() <= 64 && CI->getSExtValue() % 2u == 0)
+        if (Exponent->getBitWidth() <= 64 && Exponent->getSExtValue() % 2u == 0)
           return true;
       }
       return cannotBeOrderedLessThanZeroImpl(I->getOperand(0), TLI, SignBitOnly,
Index: llvm/test/Transforms/InstSimplify/floating-point-arithmetic.ll
===================================================================
--- llvm/test/Transforms/InstSimplify/floating-point-arithmetic.ll
+++ llvm/test/Transforms/InstSimplify/floating-point-arithmetic.ll
@@ -104,6 +104,7 @@
 }
 
 declare float @llvm.fabs.f32(float)
+declare float @llvm.sqrt.f32(float)
 
 ; CHECK-LABEL: @fabs_select_positive_constants(
 ; CHECK: %select = select i1 %cmp, float 1.000000e+00, float 2.000000e+00
@@ -195,3 +196,56 @@
   %fabs = call float @llvm.fabs.f32(float %select)
   ret float %fabs
 }
+
+; CHECK-LABEL: @fabs_sqrt
+; CHECK: call float @llvm.sqrt.f32
+; CHECK: call float @llvm.fabs.f32
+define float @fabs_sqrt(float %a) {
+; The fabs can't be eliminated because llvm.sqrt.f32 may return -0 or NaN with
+; an arbitrary sign bit.
+  %sqrt = call float @llvm.sqrt.f32(float %a)
+  %fabs = call float @llvm.fabs.f32(float %sqrt)
+  ret float %fabs
+}
+
+; CHECK-LABEL: @fabs_sqrt_nnan
+; CHECK: call nnan float @llvm.sqrt.f32
+; CHECK: call float @llvm.fabs.f32
+define float @fabs_sqrt_nnan(float %a) {
+; The fabs can't be eliminated because the nnan sqrt may still return -0.
+  %sqrt = call nnan float @llvm.sqrt.f32(float %a)
+  %fabs = call float @llvm.fabs.f32(float %sqrt)
+  ret float %fabs
+}
+
+; CHECK-LABEL: @fabs_sqrt_nsz
+; CHECK: call nsz float @llvm.sqrt.f32
+; CHECK: call float @llvm.fabs.f32
+define float @fabs_sqrt_nsz(float %a) {
+; The fabs can't be eliminated because the nsz sqrt may still return NaN.
+  %sqrt = call nsz float @llvm.sqrt.f32(float %a)
+  %fabs = call float @llvm.fabs.f32(float %sqrt)
+  ret float %fabs
+}
+
+; CHECK-LABEL: @fabs_sqrt_nnan_nsz
+; CHECK: call nnan nsz float @llvm.sqrt.f32
+; CHECK-NOT: call float @llvm.fabs.f32
+define float @fabs_sqrt_nnan_nsz(float %a) {
+; The fabs can be eliminated because we're nsz and nnan.
+  %sqrt = call nnan nsz float @llvm.sqrt.f32(float %a)
+  %fabs = call float @llvm.fabs.f32(float %sqrt)
+  ret float %fabs
+}
+
+; CHECK-LABEL: @fabs_sqrt_nnan_fabs
+; CHECK: call float @llvm.fabs.f32
+; CHECK: call nnan float @llvm.sqrt.f32
+; CHECK-NOT: call float @llvm.fabs.f32
+define float @fabs_sqrt_nnan_fabs(float %a) {
+; The second fabs can be eliminated because the operand to sqrt cannot be -0.
+  %b = call float @llvm.fabs.f32(float %a)
+  %sqrt = call nnan float @llvm.sqrt.f32(float %b)
+  %fabs = call float @llvm.fabs.f32(float %sqrt)
+  ret float %fabs
+}