diff --git a/pkgs/racket-test-core/tests/racket/extflonum.rktl b/pkgs/racket-test-core/tests/racket/extflonum.rktl
index 4967dafaa4..838c277c42 100644
--- a/pkgs/racket-test-core/tests/racket/extflonum.rktl
+++ b/pkgs/racket-test-core/tests/racket/extflonum.rktl
@@ -20,6 +20,20 @@
 (when (extflonum-available?)
   ;; ----------------------------------------
 
+  (test #t eqv? +nan.0 (string->number "+nan.0" 10 'read))
+  (test #t eqv? +inf.0 (string->number "+inf.0" 10 'read))
+  (test #t eqv? -inf.0 (string->number "-inf.0" 10 'read))
+  (test #f eqv? -inf.0 (string->number "+nan.0" 10 'read))
+
+  ;; Check JIT-inlined `eqv?`
+  (let ([eqv (lambda (a b)
+               (eqv? a b))])
+    (set! eqv (if (zero? (random 1)) eqv list))
+    (test #t eqv +nan.0 (string->number "+nan.0" 10 'read))
+    (test #t eqv +inf.0 (string->number "+inf.0" 10 'read))
+    (test #t eqv -inf.0 (string->number "-inf.0" 10 'read))
+    (test #f eqv -inf.0 (string->number "+nan.0" 10 'read)))
+
   (define (extflonum-close? fl1 fl2)
     (extfl<= (extflabs (fl- fl1 fl2))
              (real->extfl 1e-8)))
diff --git a/racket/src/racket/src/jitinline.c b/racket/src/racket/src/jitinline.c
index 731210c1a0..3b60f5b6b0 100644
--- a/racket/src/racket/src/jitinline.c
+++ b/racket/src/racket/src/jitinline.c
@@ -3276,7 +3276,7 @@ int scheme_generate_inlined_binary(mz_jit_state *jitter, Scheme_App3_Rec *app, i
 
     /* check in range of type treated by eqv: */
     ref_f4 = jit_blti_i(jit_forward(), JIT_R2, scheme_integer_type);
-    ref_f5 = jit_bgti_i(jit_forward(), JIT_R2, scheme_char_type);
+    ref_f5 = jit_bgti_i(jit_forward(), JIT_R2, scheme_long_double_type);
     CHECK_LIMIT();
     
     /* in range of interesting types, so break out the generic comparison */
diff --git a/racket/src/racket/src/optimize.c b/racket/src/racket/src/optimize.c
index 2d82e4f486..a25554a16c 100644
--- a/racket/src/racket/src/optimize.c
+++ b/racket/src/racket/src/optimize.c
@@ -3618,6 +3618,8 @@ static Scheme_Object *do_expr_implies_predicate(Scheme_Object *expr, Optimize_In
       return scheme_not_proc;
     if (SCHEME_PROCP(expr))
       return scheme_procedure_p_proc;
+    if (SCHEME_LONG_DBLP(expr))
+      return scheme_extflonum_p_proc;
   }
 
   /* This test is slower, so put it at the end */  
@@ -5712,13 +5714,13 @@ static int relevant_predicate(Scheme_Object *pred)
       || SAME_OBJ(pred, scheme_byte_string_p_proc)
       || SAME_OBJ(pred, scheme_vector_p_proc)
       || SAME_OBJ(pred, scheme_procedure_p_proc)
-      || SAME_OBJ(pred, scheme_syntax_p_proc)
-      || SAME_OBJ(pred, scheme_extflonum_p_proc))
+      || SAME_OBJ(pred, scheme_syntax_p_proc))
     return RLV_IS_RELEVANT;
   if (SAME_OBJ(pred, scheme_char_p_proc)
       || SAME_OBJ(pred, scheme_flonum_p_proc)
       || SAME_OBJ(pred, scheme_number_p_proc)
-      || SAME_OBJ(pred, scheme_real_p_proc))
+      || SAME_OBJ(pred, scheme_real_p_proc)
+      || SAME_OBJ(pred, scheme_extflonum_p_proc))
     return RLV_EQV_TESTEABLE;
   if (SAME_OBJ(pred, scheme_symbol_p_proc)
       || SAME_OBJ(pred, scheme_keyword_p_proc)
diff --git a/racket/src/racket/src/stypes.h b/racket/src/racket/src/stypes.h
index 7ba3d51562..dbb5c94895 100644
--- a/racket/src/racket/src/stypes.h
+++ b/racket/src/racket/src/stypes.h
@@ -82,9 +82,9 @@ enum {
 
   /* other eqv?-able values (must be with numbers) */
   scheme_char_type,                     /* 53 */
+  scheme_long_double_type,              /* 54 */
 
   /* other values */
-  scheme_long_double_type,              /* 54 */
   scheme_char_string_type,              /* 55 */
   scheme_byte_string_type,              /* 56 */
   scheme_unix_path_type,                /* 57 */