diff --git a/lisp/international/mule-util.el b/lisp/international/mule-util.el
index 55449599fe97..38d29cb2385b 100644
--- a/lisp/international/mule-util.el
+++ b/lisp/international/mule-util.el
@@ -333,13 +333,20 @@ QUALITY can be:
   `approximate', in which case we may cut some corners to avoid
     excessive work.
   `exact', in which case we may end up re-(en/de)coding a large
-    part of the file/buffer, this can be expensive and slow.
+    part of the file/buffer, this can be expensive and slow.  (It
+    is an error to request the `exact' method when the buffer's
+    EOL format is not yet decided.)
   nil, in which case we may return nil rather than an approximation."
   (unless coding-system (setq coding-system buffer-file-coding-system))
   (let ((eol (coding-system-eol-type coding-system))
         (type (coding-system-type coding-system))
         (base (coding-system-base coding-system))
         (pm (save-restriction (widen) (point-min))))
+    ;; Handle EOL edge cases.
+    (unless (numberp eol)
+      (if (eq quality 'exact)
+          (error "Unknown EOL format in coding system: %s" coding-system)
+        (setq eol 0)))
     (and (eq type 'utf-8)
          ;; Any post-read/pre-write conversions mean it's not really UTF-8.
          (not (null (coding-system-get coding-system :post-read-conversion)))
@@ -409,14 +416,24 @@ QUALITY can be:
   `approximate', in which case we may cut some corners to avoid
     excessive work.
   `exact', in which case we may end up re-(en/de)coding a large
-    part of the file/buffer, this can be expensive and slow.
+    part of the file/buffer, this can be expensive and slow.  (It
+    is an error to request the `exact' method when the buffer's
+    EOL format is not yet decided.)
   nil, in which case we may return nil rather than an approximation."
   (unless coding-system (setq coding-system buffer-file-coding-system))
   (let* ((eol (coding-system-eol-type coding-system))
-         (lineno (if (= eol 1) (1- (line-number-at-pos position)) 0))
          (type (coding-system-type coding-system))
          (base (coding-system-base coding-system))
-         (point-min 1))                 ;Clarify what the `1' means.
+         (point-min 1)                  ;Clarify what the `1' means.
+         lineno)
+    ;; Handle EOL edge cases.
+    (unless (numberp eol)
+      (if (eq quality 'exact)
+          (error "Unknown EOL format in coding system: %s" coding-system)
+        (setq eol 0)))
+    (setq lineno (if (= eol 1)
+                     (1- (line-number-at-pos position))
+                   0))
     (and (eq type 'utf-8)
          ;; Any post-read/pre-write conversions mean it's not really UTF-8.
          (not (null (coding-system-get coding-system :post-read-conversion)))
diff --git a/test/lisp/international/mule-util-resources/utf-8.txt b/test/lisp/international/mule-util-resources/utf-8.txt
new file mode 100644
index 000000000000..385bbb4ba806
--- /dev/null
+++ b/test/lisp/international/mule-util-resources/utf-8.txt
@@ -0,0 +1,2 @@
+Thís is a test line 1.
+Line 2.
diff --git a/test/lisp/international/mule-util-tests.el b/test/lisp/international/mule-util-tests.el
index 6518be66dbe0..0fcff9d02dd0 100644
--- a/test/lisp/international/mule-util-tests.el
+++ b/test/lisp/international/mule-util-tests.el
@@ -22,6 +22,7 @@
 ;;; Code:
 
 (require 'ert)
+(require 'ert-x)
 (require 'mule-util)
 
 (defconst mule-util-test-truncate-data
@@ -82,4 +83,43 @@
 (dotimes (i (length mule-util-test-truncate-data))
   (mule-util-test-truncate-create i))
 
+(ert-deftest filepos/bufferpos-tests-utf-8 ()
+  (let ((coding-system-for-read 'utf-8-unix))
+    (with-temp-buffer
+      (insert-file-contents (ert-resource-file "utf-8.txt"))
+      (should (eq buffer-file-coding-system 'utf-8-unix))
+      ;; First line is "Thís is a test line 1.".
+      ;; Bytes start counting at 0; chars at 1.
+      (should (= (filepos-to-bufferpos 1 'exact) 2))
+      (should (= (bufferpos-to-filepos 2 'exact) 1))
+      ;; After non-ASCII.
+      (should (= (filepos-to-bufferpos 4 'exact) 4))
+      (should (= (bufferpos-to-filepos 4 'exact) 4)))))
+
+(ert-deftest filepos/bufferpos-tests-binary ()
+  (let ((coding-system-for-read 'binary))
+    (with-temp-buffer
+      (insert-file-contents (ert-resource-file "utf-8.txt"))
+      (should (eq buffer-file-coding-system 'no-conversion))
+      ;; First line is "Thís is a test line 1.".
+      ;; Bytes start counting at 0; chars at 1.
+      (should (= (filepos-to-bufferpos 1 'exact) 2))
+      (should (= (bufferpos-to-filepos 2 'exact) 1))
+      ;; After non-ASCII.
+      (should (= (filepos-to-bufferpos 4 'exact) 5))
+      (should (= (bufferpos-to-filepos 5 'exact) 4)))))
+
+(ert-deftest filepos/bufferpos-tests-undecided ()
+  (let ((coding-system-for-read 'binary))
+    (with-temp-buffer
+      (insert-file-contents (ert-resource-file "utf-8.txt"))
+      (setq buffer-file-coding-system 'undecided)
+      (should-error (filepos-to-bufferpos 1 'exact))
+      (should-error (bufferpos-to-filepos 2 'exact))
+      (should (= (filepos-to-bufferpos 1 'approximate) 2))
+      (should (= (bufferpos-to-filepos 2 'approximate) 1))
+      ;; After non-ASCII.
+      (should (= (filepos-to-bufferpos 4 'approximate) 5))
+      (should (= (bufferpos-to-filepos 5 'approximate) 4)))))
+
 ;;; mule-util-tests.el ends here