Index: lib/Analysis/InstructionSimplify.cpp
===================================================================
--- lib/Analysis/InstructionSimplify.cpp
+++ lib/Analysis/InstructionSimplify.cpp
@@ -4239,10 +4239,13 @@
   if (FMF.noNaNs() && FMF.noSignedZeros() && match(Op1, m_AnyZero()))
     return Op1;
 
-  // sqrt(X) * sqrt(X) --> X
+  // sqrt(X) * sqrt(X) --> X, if we can:
+  // 1. Remove the intermediate rounding (reassociate).
+  // 2. Ignore non-zero negative numbers because sqrt would produce NAN.
+  // 3. Ignore -0.0 because sqrt(-0.0) == -0.0, but -0.0 * -0.0 == 0.0.
   Value *X;
-  if (FMF.isFast() && Op0 == Op1 &&
-      match(Op0, m_Intrinsic<Intrinsic::sqrt>(m_Value(X))))
+  if (Op0 == Op1 && match(Op0, m_Intrinsic<Intrinsic::sqrt>(m_Value(X))) &&
+      FMF.allowReassoc() && FMF.noNaNs() && FMF.noSignedZeros())
     return X;
 
   return nullptr;
Index: test/Transforms/InstSimplify/fast-math.ll
===================================================================
--- test/Transforms/InstSimplify/fast-math.ll
+++ test/Transforms/InstSimplify/fast-math.ll
@@ -205,7 +205,7 @@
 }
 
 ; PR21126: http://llvm.org/bugs/show_bug.cgi?id=21126
-; With unsafe/fast math, sqrt(X) * sqrt(X) is just X.
+; With loose math, sqrt(X) * sqrt(X) is just X.
 
 declare double @llvm.sqrt.f64(double)
 
@@ -214,7 +214,42 @@
 ; CHECK-NEXT:    ret double [[F:%.*]]
 ;
   %sqrt = call double @llvm.sqrt.f64(double %f)
-  %mul = fmul fast double %sqrt, %sqrt
+  %mul = fmul reassoc nnan nsz double %sqrt, %sqrt
+  ret double %mul
+}
+
+; Negative tests for the above transform: we need all 3 of those flags.
+
+define double @sqrt_squared_not_fast_enough1(double %f) {
+; CHECK-LABEL: @sqrt_squared_not_fast_enough1(
+; CHECK-NEXT:    [[SQRT:%.*]] = call double @llvm.sqrt.f64(double [[F:%.*]])
+; CHECK-NEXT:    [[MUL:%.*]] = fmul nnan nsz double [[SQRT]], [[SQRT]]
+; CHECK-NEXT:    ret double [[MUL]]
+;
+  %sqrt = call double @llvm.sqrt.f64(double %f)
+  %mul = fmul nnan nsz double %sqrt, %sqrt
+  ret double %mul
+}
+
+define double @sqrt_squared_not_fast_enough2(double %f) {
+; CHECK-LABEL: @sqrt_squared_not_fast_enough2(
+; CHECK-NEXT:    [[SQRT:%.*]] = call double @llvm.sqrt.f64(double [[F:%.*]])
+; CHECK-NEXT:    [[MUL:%.*]] = fmul reassoc nnan double [[SQRT]], [[SQRT]]
+; CHECK-NEXT:    ret double [[MUL]]
+;
+  %sqrt = call double @llvm.sqrt.f64(double %f)
+  %mul = fmul reassoc nnan double %sqrt, %sqrt
+  ret double %mul
+}
+
+define double @sqrt_squared_not_fast_enough3(double %f) {
+; CHECK-LABEL: @sqrt_squared_not_fast_enough3(
+; CHECK-NEXT:    [[SQRT:%.*]] = call double @llvm.sqrt.f64(double [[F:%.*]])
+; CHECK-NEXT:    [[MUL:%.*]] = fmul reassoc nsz double [[SQRT]], [[SQRT]]
+; CHECK-NEXT:    ret double [[MUL]]
+;
+  %sqrt = call double @llvm.sqrt.f64(double %f)
+  %mul = fmul reassoc nsz double %sqrt, %sqrt
   ret double %mul
 }