diff --git a/implementations/racket/preserves/preserves/float-bytes.rkt b/implementations/racket/preserves/preserves/float-bytes.rkt
index b0d43b6..46b0fa5 100644
--- a/implementations/racket/preserves/preserves/float-bytes.rkt
+++ b/implementations/racket/preserves/preserves/float-bytes.rkt
@@ -10,15 +10,92 @@
          double->bytes)
 
 (require "float.rkt")
+(require (only-in racket/math nan? infinite?))
+
+(module binary racket/base
+  (provide (all-defined-out))
+
+  (define (binary32-nan-or-inf? bs)
+    (and (= (bitwise-bit-field (bytes-ref bs 0) 0 7) #x7f)
+         (bitwise-bit-set? (bytes-ref bs 1) 7)))
+
+  (define (binary64-nan-or-inf? bs)
+    (and (= (bitwise-bit-field (bytes-ref bs 0) 0 7) #x7f)
+         (= (bitwise-bit-field (bytes-ref bs 1) 4 8) #x0f)))
+
+  (define (sign-bit-set? bs)
+    (bitwise-bit-set? (bytes-ref bs 0) 0)))
+
+(require (submod "." binary))
 
 (define (bytes->float bs)
-  (float (floating-point-bytes->real bs #t 0 4)))
+  (if (binary32-nan-or-inf? bs)
+      (let* ((vf (integer-bytes->integer bs #f #t))
+             (signexp (bitwise-bit-field vf 23 32))
+             (payload (bitwise-bit-field vf 0 23))
+             (vd (bitwise-ior (arithmetic-shift signexp 55)
+                              #x0070000000000000
+                              (arithmetic-shift payload 29)))
+             (dbs (integer->integer-bytes vd 8 #f #t)))
+        (float (floating-point-bytes->real dbs #t 0 8)))
+      (float (floating-point-bytes->real bs #t 0 4))))
 
 (define (float->bytes v)
-  (real->floating-point-bytes (float-value v) 4 #t))
+  (let ((v (float-value v)))
+    (if (or (nan? v) (infinite? v))
+        (let* ((dbs (real->floating-point-bytes v 8 #t))
+               (vd (integer-bytes->integer dbs #f #t))
+               (signexp (bitwise-bit-field vd 55 64))
+               (payload (bitwise-bit-field vd 29 52))
+               (vf (bitwise-ior (arithmetic-shift signexp 23)
+                                payload))
+               (bs (integer->integer-bytes vf 4 #f #t)))
+          bs)
+        (real->floating-point-bytes v 4 #t))))
 
 (define (bytes->double bs)
   (floating-point-bytes->real bs #t 0 8))
 
 (define (double->bytes v)
   (real->floating-point-bytes v 8 #t))
+
+(module+ test
+  (require rackunit)
+  (require file/sha1)
+
+  (define (check-roundtrip-double hex)
+    (check-equal? (bytes->hex-string (double->bytes (bytes->double (hex-string->bytes hex))))
+                  hex))
+
+  (define (check-roundtrip-float hex)
+    (check-equal? (bytes->hex-string (float->bytes (bytes->float (hex-string->bytes hex))))
+                  hex))
+
+  (check-roundtrip-double "0123456789abcdef")
+  (check-roundtrip-double "7ff0000000000321")
+  (check-roundtrip-double "7ff0000000000001")
+  (check-roundtrip-double "7ff0000000000000")
+  (check-roundtrip-double "fff0000000000321")
+  (check-roundtrip-double "fff0000000000001")
+  (check-roundtrip-double "fff0000000000000")
+  (check-roundtrip-double "7ff8000000000321")
+  (check-roundtrip-double "7ff8000000000001")
+  (check-roundtrip-double "7ff8000000000000")
+  (check-roundtrip-double "fff8000000000321")
+  (check-roundtrip-double "fff8000000000001")
+  (check-roundtrip-double "fff8000000000000")
+
+  (check-roundtrip-float "01234567")
+  (check-roundtrip-float "7f800321")
+  (check-roundtrip-float "7f800001")
+  (check-roundtrip-float "7f800000")
+  (check-roundtrip-float "ff800321")
+  (check-roundtrip-float "ff800001")
+  (check-roundtrip-float "ff800000")
+  (check-roundtrip-float "7fc00321")
+  (check-roundtrip-float "7fc00001")
+  (check-roundtrip-float "7fc00000")
+  (check-roundtrip-float "ffc00321")
+  (check-roundtrip-float "ffc00001")
+  (check-roundtrip-float "ffc00000")
+  )