diff --git a/src/backend/access/hash/hashfunc.c b/src/backend/access/hash/hashfunc.c
index db20d9d1c14..68c3ebb9bba 100644
--- a/src/backend/access/hash/hashfunc.c
+++ b/src/backend/access/hash/hashfunc.c
@@ -30,6 +30,7 @@
 #include "catalog/pg_collation.h"
 #include "common/hashfn.h"
 #include "utils/builtins.h"
+#include "utils/float.h"
 #include "utils/pg_locale.h"
 
 /*
@@ -150,6 +151,14 @@ hashfloat4(PG_FUNCTION_ARGS)
 	if (key == (float4) 0)
 		PG_RETURN_UINT32(0);
 
+	/*
+	 * Similarly, NaNs can have different bit patterns but they should all
+	 * compare as equal.  For backwards-compatibility reasons we force them to
+	 * have the hash value of a standard NaN.
+	 */
+	if (isnan(key))
+		key = get_float4_nan();
+
 	/*
 	 * To support cross-type hashing of float8 and float4, we want to return
 	 * the same hash value hashfloat8 would produce for an equal float8 value.
@@ -172,6 +181,8 @@ hashfloat4extended(PG_FUNCTION_ARGS)
 	/* Same approach as hashfloat4 */
 	if (key == (float4) 0)
 		PG_RETURN_UINT64(seed);
+	if (isnan(key))
+		key = get_float4_nan();
 	key8 = key;
 
 	return hash_any_extended((unsigned char *) &key8, sizeof(key8), seed);
@@ -190,6 +201,14 @@ hashfloat8(PG_FUNCTION_ARGS)
 	if (key == (float8) 0)
 		PG_RETURN_UINT32(0);
 
+	/*
+	 * Similarly, NaNs can have different bit patterns but they should all
+	 * compare as equal.  For backwards-compatibility reasons we force them to
+	 * have the hash value of a standard NaN.
+	 */
+	if (isnan(key))
+		key = get_float8_nan();
+
 	return hash_any((unsigned char *) &key, sizeof(key));
 }
 
@@ -202,6 +221,8 @@ hashfloat8extended(PG_FUNCTION_ARGS)
 	/* Same approach as hashfloat8 */
 	if (key == (float8) 0)
 		PG_RETURN_UINT64(seed);
+	if (isnan(key))
+		key = get_float8_nan();
 
 	return hash_any_extended((unsigned char *) &key, sizeof(key), seed);
 }
diff --git a/src/test/regress/expected/hash_func.out b/src/test/regress/expected/hash_func.out
index dca31365bcf..61c6cbbf109 100644
--- a/src/test/regress/expected/hash_func.out
+++ b/src/test/regress/expected/hash_func.out
@@ -339,3 +339,36 @@ SELECT v as value, hash_record_extended(v, 0)::bit(32) as extended0
 FROM   (VALUES (row(1, 'aaa')::hash_test_t2)) x(v);
 ERROR:  could not identify an extended hash function for type money
 DROP TYPE hash_test_t2;
+--
+-- Check special cases for specific data types
+--
+SELECT hashfloat4('0'::float4) = hashfloat4('-0'::float4) AS t;
+ t 
+---
+ t
+(1 row)
+
+SELECT hashfloat4('NaN'::float4) = hashfloat4('-NaN'::float4) AS t;
+ t 
+---
+ t
+(1 row)
+
+SELECT hashfloat8('0'::float8) = hashfloat8('-0'::float8) AS t;
+ t 
+---
+ t
+(1 row)
+
+SELECT hashfloat8('NaN'::float8) = hashfloat8('-NaN'::float8) AS t;
+ t 
+---
+ t
+(1 row)
+
+SELECT hashfloat4('NaN'::float4) = hashfloat8('NaN'::float8) AS t;
+ t 
+---
+ t
+(1 row)
+
diff --git a/src/test/regress/sql/hash_func.sql b/src/test/regress/sql/hash_func.sql
index 0292dedd15a..5c994f5de5e 100644
--- a/src/test/regress/sql/hash_func.sql
+++ b/src/test/regress/sql/hash_func.sql
@@ -253,3 +253,12 @@ FROM   (VALUES (row(1, 'aaa')::hash_test_t2)) x(v);
 SELECT v as value, hash_record_extended(v, 0)::bit(32) as extended0
 FROM   (VALUES (row(1, 'aaa')::hash_test_t2)) x(v);
 DROP TYPE hash_test_t2;
+
+--
+-- Check special cases for specific data types
+--
+SELECT hashfloat4('0'::float4) = hashfloat4('-0'::float4) AS t;
+SELECT hashfloat4('NaN'::float4) = hashfloat4('-NaN'::float4) AS t;
+SELECT hashfloat8('0'::float8) = hashfloat8('-0'::float8) AS t;
+SELECT hashfloat8('NaN'::float8) = hashfloat8('-NaN'::float8) AS t;
+SELECT hashfloat4('NaN'::float4) = hashfloat8('NaN'::float8) AS t;