Index: lib/Transforms/InstCombine/InstCombineCompares.cpp
===================================================================
--- lib/Transforms/InstCombine/InstCombineCompares.cpp
+++ lib/Transforms/InstCombine/InstCombineCompares.cpp
@@ -4997,6 +4997,24 @@
                               ConstantExpr::getFNeg(RHSC));
         break;
       }
+      case Instruction::FDiv: {
+        if (I.getFastMathFlags().noInfs() &&
+            LHSI->getFastMathFlags().noInfs() && RHSC->isZeroValue()) {
+          Value *Op;
+          const APFloat *C;
+          if (match(LHSI, m_FDiv(m_APFloat(C), m_Value(Op)))) {
+            // fcmp ninf pred (fdiv ninf 1.0, x), 0   ->   fcmp pred x, 0
+            if (C->isExactlyValue(1.0))
+              return new FCmpInst(I.getPredicate(), Op,
+                                  ConstantFP::getNullValue(LHSI->getType()));
+            // fcmp ninf pred (fdiv ninf -1.0, x), 0  ->   fcmp swap(pred) x, 0
+            if (C->isExactlyValue(-1.0))
+              return new FCmpInst(I.getSwappedPredicate(), Op,
+                                  ConstantFP::getNullValue(LHSI->getType()));
+          }
+        }
+        break;
+      }
       case Instruction::Load:
         if (GetElementPtrInst *GEP =
             dyn_cast<GetElementPtrInst>(LHSI->getOperand(0))) {
Index: test/Transforms/InstCombine/fcmp_reciproc.ll
===================================================================
--- /dev/null
+++ test/Transforms/InstCombine/fcmp_reciproc.ll
@@ -0,0 +1,212 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt < %s -instcombine -S | FileCheck %s
+
+define i1 @cmp_olt_recip(double %x) {
+; CHECK-LABEL: @cmp_olt_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp olt double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf olt double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_ole_recip(double %x) {
+; CHECK-LABEL: @cmp_ole_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ole double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf ole double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_ogt_recip(double %x) {
+; CHECK-LABEL: @cmp_ogt_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ogt double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf ogt double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_oge_recip(double %x) {
+; CHECK-LABEL: @cmp_oge_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp oge double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf oge double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_oeq_recip(double %x) {
+; CHECK-LABEL: @cmp_oeq_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp oeq double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf oeq double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_une_recip(double %x) {
+; CHECK-LABEL: @cmp_une_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp une double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf une double %div, 0.0
+  ret i1 %cmp
+}
+
+; Could test all 16 fcmp variants, but they're really all the same...
+
+define i1 @cmp_olt_neg_recip(double %x) {
+; CHECK-LABEL: @cmp_olt_neg_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ogt double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double -1.0, %x
+  %cmp = fcmp ninf olt double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_ole_neg_recip(double %x) {
+; CHECK-LABEL: @cmp_ole_neg_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp oge double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double -1.0, %x
+  %cmp = fcmp ninf ole double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_ogt_neg_recip(double %x) {
+; CHECK-LABEL: @cmp_ogt_neg_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp olt double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double -1.0, %x
+  %cmp = fcmp ninf ogt double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_oge_neg_recip(double %x) {
+; CHECK-LABEL: @cmp_oge_neg_recip(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ole double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double -1.0, %x
+  %cmp = fcmp ninf oge double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_olt_recip_sz(double %x) {
+; CHECK-LABEL: @cmp_olt_recip_sz(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp olt double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf olt double %div, -0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_ole_recip_sz(double %x) {
+; CHECK-LABEL: @cmp_ole_recip_sz(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ole double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf ole double %div, -0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_ogt_recip_sz(double %x) {
+; CHECK-LABEL: @cmp_ogt_recip_sz(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ogt double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf ogt double %div, -0.0
+  ret i1 %cmp
+}
+
+define i1 @cmp_oge_recip_sz(double %x) {
+; CHECK-LABEL: @cmp_oge_recip_sz(
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp oge double [[X:%.*]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf oge double %div, -0.0
+  ret i1 %cmp
+}
+
+
+
+define i1 @noopt0(double %x) {
+; CHECK-LABEL: @noopt0(
+; CHECK-NEXT:    [[DIV:%.*]] = fdiv ninf double 1.100000e+00, [[X:%.*]]
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ninf oeq double [[DIV]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.1, %x
+  %cmp = fcmp ninf oeq double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @noopt1(double %x) {
+; CHECK-LABEL: @noopt1(
+; CHECK-NEXT:    [[DIV:%.*]] = fdiv ninf double 1.000000e+00, [[X:%.*]]
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ninf oeq double [[DIV]], 1.000000e-01
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp ninf oeq double %div, 0.1
+  ret i1 %cmp
+}
+
+define i1 @noopt2(double %x) {
+; CHECK-LABEL: @noopt2(
+; CHECK-NEXT:    [[DIV:%.*]] = fdiv double 1.000000e+00, [[X:%.*]]
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ninf oeq double [[DIV]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv double 1.0, %x
+  %cmp = fcmp ninf oeq double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @noopt3(double %x) {
+; CHECK-LABEL: @noopt3(
+; CHECK-NEXT:    [[DIV:%.*]] = fdiv ninf double 1.000000e+00, [[X:%.*]]
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp oeq double [[DIV]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp oeq double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @noopt4(double %x) {
+; CHECK-LABEL: @noopt4(
+; CHECK-NEXT:    [[DIV:%.*]] = fdiv ninf double 1.000000e+00, [[X:%.*]]
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp nnan oeq double [[DIV]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv ninf double 1.0, %x
+  %cmp = fcmp nnan oeq double %div, 0.0
+  ret i1 %cmp
+}
+
+define i1 @noopt5(double %x) {
+; CHECK-LABEL: @noopt5(
+; CHECK-NEXT:    [[DIV:%.*]] = fdiv nnan double 1.000000e+00, [[X:%.*]]
+; CHECK-NEXT:    [[CMP:%.*]] = fcmp ninf oeq double [[DIV]], 0.000000e+00
+; CHECK-NEXT:    ret i1 [[CMP]]
+;
+  %div = fdiv nnan double 1.0, %x
+  %cmp = fcmp ninf oeq double %div, 0.0
+  ret i1 %cmp
+}