diff --git a/idea/src/org/jetbrains/kotlin/idea/inspections/conventionNameCalls/ReplaceCallWithBinaryOperatorInspection.kt b/idea/src/org/jetbrains/kotlin/idea/inspections/conventionNameCalls/ReplaceCallWithBinaryOperatorInspection.kt
index faf127c96ad..4e5eda16b39 100644
--- a/idea/src/org/jetbrains/kotlin/idea/inspections/conventionNameCalls/ReplaceCallWithBinaryOperatorInspection.kt
+++ b/idea/src/org/jetbrains/kotlin/idea/inspections/conventionNameCalls/ReplaceCallWithBinaryOperatorInspection.kt
@@ -21,20 +21,25 @@ import com.intellij.openapi.editor.Editor
 import com.intellij.openapi.project.Project
 import com.intellij.psi.PsiElement
 import com.intellij.psi.tree.IElementType
+import org.jetbrains.kotlin.codegen.kotlinType
+import org.jetbrains.kotlin.idea.caches.resolve.analyze
+import org.jetbrains.kotlin.idea.caches.resolve.resolveToCall
 import org.jetbrains.kotlin.idea.inspections.AbstractApplicabilityBasedInspection
-import org.jetbrains.kotlin.idea.intentions.callExpression
+import org.jetbrains.kotlin.idea.intentions.*
 import org.jetbrains.kotlin.idea.intentions.conventionNameCalls.isAnyEquals
-import org.jetbrains.kotlin.idea.intentions.isReceiverExpressionWithValue
-import org.jetbrains.kotlin.idea.intentions.toResolvedCall
 import org.jetbrains.kotlin.lexer.KtSingleValueToken
 import org.jetbrains.kotlin.lexer.KtTokens
 import org.jetbrains.kotlin.psi.*
 import org.jetbrains.kotlin.psi.psiUtil.getLastParentOfTypeInRow
 import org.jetbrains.kotlin.psi.psiUtil.getParentOfType
+import org.jetbrains.kotlin.resolve.calls.callUtil.getFirstArgumentExpression
+import org.jetbrains.kotlin.resolve.calls.callUtil.getReceiverExpression
 import org.jetbrains.kotlin.resolve.calls.model.ArgumentMatch
 import org.jetbrains.kotlin.resolve.calls.model.isReallySuccess
 import org.jetbrains.kotlin.resolve.lazy.BodyResolveMode
+import org.jetbrains.kotlin.types.KotlinType
 import org.jetbrains.kotlin.types.expressions.OperatorConventions
+import org.jetbrains.kotlin.types.typeUtil.*
 import org.jetbrains.kotlin.util.OperatorNameConventions
 
 class ReplaceCallWithBinaryOperatorInspection : AbstractApplicabilityBasedInspection<KtDotQualifiedExpression>(
@@ -69,10 +74,13 @@ class ReplaceCallWithBinaryOperatorInspection : AbstractApplicabilityBasedInspec
     override fun inspectionHighlightType(element: KtDotQualifiedExpression): ProblemHighlightType {
         val calleeExpression = element.callExpression?.calleeExpression as? KtSimpleNameExpression
         val identifier = calleeExpression?.getReferencedNameAsName()
-        return if (identifier == OperatorNameConventions.EQUALS || identifier == OperatorNameConventions.COMPARE_TO) {
+        val isFloatingPointNumberEquals = calleeExpression?.isFloatingPointNumberEquals() ?: false
+
+        return if (isFloatingPointNumberEquals) {
+            ProblemHighlightType.INFORMATION
+        } else if (identifier == OperatorNameConventions.EQUALS || identifier == OperatorNameConventions.COMPARE_TO) {
             ProblemHighlightType.GENERIC_ERROR_OR_WARNING
-        }
-        else {
+        } else {
             ProblemHighlightType.INFORMATION
         }
     }
@@ -84,6 +92,10 @@ class ReplaceCallWithBinaryOperatorInspection : AbstractApplicabilityBasedInspec
 
     override fun fixText(element: KtDotQualifiedExpression): String {
         val calleeExpression = element.callExpression?.calleeExpression as? KtSimpleNameExpression ?: return defaultFixText
+        if (calleeExpression.isFloatingPointNumberEquals()) {
+            return "Replace total order equality with IEEE 754 equality"
+        }
+
         val operation = operation(calleeExpression) ?: return defaultFixText
         return "Replace with '${operation.value}'"
     }
@@ -123,7 +135,6 @@ class ReplaceCallWithBinaryOperatorInspection : AbstractApplicabilityBasedInspec
         return when (identifier) {
             OperatorNameConventions.EQUALS -> {
                 if (!dotQualified.isAnyEquals()) return null
-
                 val prefixExpression = dotQualified.getWrappingPrefixExpressionIfAny()
                 if (prefixExpression != null && prefixExpression.operationToken == KtTokens.EXCL) KtTokens.EXCLEQ
                 else KtTokens.EQEQ
@@ -148,4 +159,25 @@ class ReplaceCallWithBinaryOperatorInspection : AbstractApplicabilityBasedInspec
             else -> OperatorConventions.BINARY_OPERATION_NAMES.inverse()[identifier]
         }
     }
-}
+
+    private fun KtDotQualifiedExpression.isFloatingPointNumberEquals(): Boolean {
+        val resolvedCall = resolveToCall() ?: return false
+        val context = analyze(BodyResolveMode.PARTIAL)
+        val receiverType = resolvedCall.getReceiverExpression().kotlinType(context) ?: return false
+        val argumentType = resolvedCall.getFirstArgumentExpression().kotlinType(context) ?: return false
+        return (receiverType.isFpType() && argumentType.isNumericType()) || (argumentType.isFpType() && receiverType.isNumericType())
+    }
+
+    private fun KtSimpleNameExpression.isFloatingPointNumberEquals(): Boolean {
+        val dotQualified = parent.parent as? KtDotQualifiedExpression ?: return false
+        return dotQualified.isFloatingPointNumberEquals()
+    }
+
+    private fun KotlinType.isFpType(): Boolean {
+        return isFloat() || isDouble()
+    }
+
+    private fun KotlinType.isNumericType(): Boolean {
+        return isFpType() || isByte() || isShort() || isInt() || isLong()
+    }
+}
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsDoubleSmartCast.kt b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsDoubleSmartCast.kt
new file mode 100644
index 00000000000..a723f12101f
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsDoubleSmartCast.kt
@@ -0,0 +1,4 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun test(a: Any, b: Any) =
+    a is Double && b is Double && a.<caret>equals(b)
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsDoubleSmartCast.kt.after b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsDoubleSmartCast.kt.after
new file mode 100644
index 00000000000..1432f7eb740
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsDoubleSmartCast.kt.after
@@ -0,0 +1,4 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun test(a: Any, b: Any) =
+    a is Double && b is Double && a == b
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatSmartCast.kt b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatSmartCast.kt
new file mode 100644
index 00000000000..2eec23a5b8e
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatSmartCast.kt
@@ -0,0 +1,4 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun test(a: Any, b: Any) =
+    a is Float && b is Float && a.<caret>equals(b)
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatSmartCast.kt.after b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatSmartCast.kt.after
new file mode 100644
index 00000000000..a0dafe98b4c
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatSmartCast.kt.after
@@ -0,0 +1,4 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun test(a: Any, b: Any) =
+    a is Float && b is Float && a == b
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral1.kt b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral1.kt
new file mode 100644
index 00000000000..95dbe5e0986
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral1.kt
@@ -0,0 +1,3 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun checkPi(x: Double) = x.<caret>equals(3.14)
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral1.kt.after b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral1.kt.after
new file mode 100644
index 00000000000..03cb7fcf364
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral1.kt.after
@@ -0,0 +1,3 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun checkPi(x: Double) = x == 3.14
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral2.kt b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral2.kt
new file mode 100644
index 00000000000..8142ff1b362
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral2.kt
@@ -0,0 +1,3 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun checkPi(x: Double) = 3.14.<caret>equals(x)
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral2.kt.after b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral2.kt.after
new file mode 100644
index 00000000000..c28368a84b6
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral2.kt.after
@@ -0,0 +1,3 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun checkPi(x: Double) = 3.14 == x
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointType.kt b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointType.kt
new file mode 100644
index 00000000000..7c38c0860fc
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointType.kt
@@ -0,0 +1,3 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun test(a: Double, b: Double) = a.<caret>equals(b)
\ No newline at end of file
diff --git a/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointType.kt.after b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointType.kt.after
new file mode 100644
index 00000000000..aefd51507d6
--- /dev/null
+++ b/idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointType.kt.after
@@ -0,0 +1,3 @@
+// FIX: Replace total order equality with IEEE 754 equality
+
+fun test(a: Double, b: Double) = a == b
\ No newline at end of file
diff --git a/idea/tests/org/jetbrains/kotlin/idea/inspections/LocalInspectionTestGenerated.java b/idea/tests/org/jetbrains/kotlin/idea/inspections/LocalInspectionTestGenerated.java
index 0c90a715dee..3265e781c78 100644
--- a/idea/tests/org/jetbrains/kotlin/idea/inspections/LocalInspectionTestGenerated.java
+++ b/idea/tests/org/jetbrains/kotlin/idea/inspections/LocalInspectionTestGenerated.java
@@ -1526,11 +1526,36 @@ public class LocalInspectionTestGenerated extends AbstractLocalInspectionTest {
                 runTest("idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsCompareTo.kt");
             }
 
+            @TestMetadata("equalsDoubleSmartCast.kt")
+            public void testEqualsDoubleSmartCast() throws Exception {
+                runTest("idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsDoubleSmartCast.kt");
+            }
+
             @TestMetadata("equalsExtensionFunction.kt")
             public void testEqualsExtensionFunction() throws Exception {
                 runTest("idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsExtensionFunction.kt");
             }
 
+            @TestMetadata("equalsFloatSmartCast.kt")
+            public void testEqualsFloatSmartCast() throws Exception {
+                runTest("idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatSmartCast.kt");
+            }
+
+            @TestMetadata("equalsFloatingPointLiteral1.kt")
+            public void testEqualsFloatingPointLiteral1() throws Exception {
+                runTest("idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral1.kt");
+            }
+
+            @TestMetadata("equalsFloatingPointLiteral2.kt")
+            public void testEqualsFloatingPointLiteral2() throws Exception {
+                runTest("idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointLiteral2.kt");
+            }
+
+            @TestMetadata("equalsFloatingPointType.kt")
+            public void testEqualsFloatingPointType() throws Exception {
+                runTest("idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/equalsFloatingPointType.kt");
+            }
+
             @TestMetadata("extensionFunction.kt")
             public void testExtensionFunction() throws Exception {
                 runTest("idea/testData/inspectionsLocal/conventionNameCalls/replaceCallWithBinaryOperator/extensionFunction.kt");