diff --git a/lib-src/make-docfile.c b/lib-src/make-docfile.c
index 05a08473c3..c68173eb66 100644
--- a/lib-src/make-docfile.c
+++ b/lib-src/make-docfile.c
@@ -700,7 +700,7 @@ write_globals (void)
       switch (globals[i].type)
 	{
 	case EMACS_INTEGER:
-	  type = "intmax_t";
+	  type = "EMACS_INT";
 	  break;
 	case BOOLEAN:
 	  type = "bool";
diff --git a/src/data.c b/src/data.c
index 15b6106cfe..9718e2f5b4 100644
--- a/src/data.c
+++ b/src/data.c
@@ -1079,7 +1079,8 @@ store_symval_forwarding (union Lisp_Fwd *valcontents, register Lisp_Object newva
       {
 	intmax_t i;
 	CHECK_INTEGER (newval);
-	if (! integer_to_intmax (newval, &i))
+	if (! (integer_to_intmax (newval, &i)
+	       && TYPE_MINIMUM (EMACS_INT) <= i && i <= EMACS_INT_MAX))
 	  xsignal1 (Qoverflow_error, newval);
 	*XFIXNUMFWD (valcontents)->intvar = i;
       }
diff --git a/src/eval.c b/src/eval.c
index bf16a709b1..aa4ee3abc9 100644
--- a/src/eval.c
+++ b/src/eval.c
@@ -63,7 +63,7 @@ Lisp_Object Vrun_hooks;
    signal the error instead of entering an infinite loop of debugger
    invocations.  */
 
-static intmax_t when_entered_debugger;
+static EMACS_INT when_entered_debugger;
 
 /* The function from which the last `signal' was called.  Set in
    Fsignal.  */
@@ -269,9 +269,9 @@ init_eval (void)
    value otherwise.  */
 
 static void
-max_ensure_room (intmax_t *m, intmax_t a, intmax_t b)
+max_ensure_room (EMACS_INT *m, intmax_t a, int b)
 {
-  intmax_t sum = INT_ADD_WRAPV (a, b, &sum) ? INTMAX_MAX : sum;
+  EMACS_INT sum = INT_ADD_WRAPV (a, b, &sum) ? EMACS_INT_MAX : sum;
   *m = max (*m, sum);
 }
 
@@ -280,8 +280,9 @@ max_ensure_room (intmax_t *m, intmax_t a, intmax_t b)
 static void
 restore_stack_limits (Lisp_Object data)
 {
-  integer_to_intmax (XCAR (data), &max_specpdl_size);
-  integer_to_intmax (XCDR (data), &max_lisp_eval_depth);
+  intmax_t i;
+  integer_to_intmax (XCAR (data), &i); max_specpdl_size = i;
+  integer_to_intmax (XCDR (data), &i); max_lisp_eval_depth = i;
 }
 
 static void grow_specpdl (void);
@@ -294,9 +295,9 @@ call_debugger (Lisp_Object arg)
   bool debug_while_redisplaying;
   ptrdiff_t count = SPECPDL_INDEX ();
   Lisp_Object val;
-  intmax_t old_depth = max_lisp_eval_depth;
+  EMACS_INT old_depth = max_lisp_eval_depth;
   /* Do not allow max_specpdl_size less than actual depth (Bug#16603).  */
-  intmax_t old_max = max (max_specpdl_size, count);
+  EMACS_INT old_max = max (max_specpdl_size, count);
 
   /* The previous value of 40 is too small now that the debugger
      prints using cl-prin1 instead of prin1.  Printing lists nested 8
diff --git a/src/fileio.c b/src/fileio.c
index cac8ed0aee..0eb7058ddd 100644
--- a/src/fileio.c
+++ b/src/fileio.c
@@ -5706,7 +5706,7 @@ A non-nil CURRENT-ONLY argument means save only current buffer.  */)
   bool old_message_p = 0;
   struct auto_save_unwind auto_save_unwind;
 
-  intmax_t sum = INT_ADD_WRAPV (specpdl_size, 40, &sum) ? INTMAX_MAX : sum;
+  EMACS_INT sum = INT_ADD_WRAPV (specpdl_size, 40, &sum) ? EMACS_INT_MAX : sum;
   if (max_specpdl_size < sum)
     max_specpdl_size = sum;
 
diff --git a/src/frame.h b/src/frame.h
index 544e0bef17..f53a3bb65a 100644
--- a/src/frame.h
+++ b/src/frame.h
@@ -580,7 +580,7 @@ struct frame
   int config_scroll_bar_lines;
 
   /* The baud rate that was used to calculate costs for this frame.  */
-  intmax_t cost_calculation_baud_rate;
+  EMACS_INT cost_calculation_baud_rate;
 
   /* Frame opacity
      alpha[0]: alpha transparency of the active frame
diff --git a/src/keyboard.c b/src/keyboard.c
index 3af487cf07..38a84d6c4c 100644
--- a/src/keyboard.c
+++ b/src/keyboard.c
@@ -208,7 +208,7 @@ struct buffer *buffer_before_last_command_or_undo;
 
 /* Value of num_nonmacro_input_events as of last auto save.  */
 
-static intmax_t last_auto_save;
+static EMACS_INT last_auto_save;
 
 /* The value of point when the last command was started. */
 static ptrdiff_t last_point_position;
@@ -1966,7 +1966,7 @@ void
 bind_polling_period (int n)
 {
 #ifdef POLL_FOR_INPUT
-  intmax_t new = polling_period;
+  EMACS_INT new = polling_period;
 
   if (n > new)
     new = n;
@@ -5585,7 +5585,7 @@ make_lispy_event (struct input_event *event)
 	     double-click-fuzz as is.  On other frames, interpret it
 	     as a multiple of 1/8 characters.  */
 	  struct frame *f;
-	  intmax_t fuzz;
+	  EMACS_INT fuzz;
 
 	  if (WINDOWP (event->frame_or_window))
 	    f = XFRAME (XWINDOW (event->frame_or_window)->frame);
@@ -5651,7 +5651,7 @@ make_lispy_event (struct input_event *event)
 	    else
 	      {
 		Lisp_Object new_down, down;
-		intmax_t xdiff = double_click_fuzz, ydiff = double_click_fuzz;
+		EMACS_INT xdiff = double_click_fuzz, ydiff = double_click_fuzz;
 
 		/* The third element of every position
 		   should be the (x,y) pair.  */
@@ -5744,7 +5744,7 @@ make_lispy_event (struct input_event *event)
 	     double-click-fuzz as is.  On other frames, interpret it
 	     as a multiple of 1/8 characters.  */
 	  struct frame *fr;
-	  intmax_t fuzz;
+	  EMACS_INT fuzz;
 	  int symbol_num;
 	  bool is_double;
 
diff --git a/src/lisp.h b/src/lisp.h
index 388cd04163..0e25ecc6ad 100644
--- a/src/lisp.h
+++ b/src/lisp.h
@@ -2664,7 +2664,7 @@ make_uint (uintmax_t n)
 struct Lisp_Intfwd
   {
     enum Lisp_Fwd_Type type;	/* = Lisp_Fwd_Int */
-    intmax_t *intvar;
+    EMACS_INT *intvar;
   };
 
 /* Boolean forwarding pointer to an int variable.
@@ -3099,7 +3099,7 @@ enum maxargs
 extern void defvar_lisp (struct Lisp_Objfwd *, const char *, Lisp_Object *);
 extern void defvar_lisp_nopro (struct Lisp_Objfwd *, const char *, Lisp_Object *);
 extern void defvar_bool (struct Lisp_Boolfwd *, const char *, bool *);
-extern void defvar_int (struct Lisp_Intfwd *, const char *, intmax_t *);
+extern void defvar_int (struct Lisp_Intfwd *, const char *, EMACS_INT *);
 extern void defvar_kboard (struct Lisp_Kboard_Objfwd *, const char *, int);
 
 /* Macros we use to define forwarded Lisp variables.
diff --git a/src/lread.c b/src/lread.c
index 8b0d693daf..6389e3ed48 100644
--- a/src/lread.c
+++ b/src/lread.c
@@ -4422,11 +4422,11 @@ defalias (struct Lisp_Subr *sname, char *string)
 #endif /* NOTDEF */
 
 /* Define an "integer variable"; a symbol whose value is forwarded to a
-   C variable of type intmax_t.  Sample call (with "xx" to fool make-docfile):
+   C variable of type EMACS_INT.  Sample call (with "xx" to fool make-docfile):
    DEFxxVAR_INT ("emacs-priority", &emacs_priority, "Documentation");  */
 void
 defvar_int (struct Lisp_Intfwd *i_fwd,
-	    const char *namestring, intmax_t *address)
+	    const char *namestring, EMACS_INT *address)
 {
   Lisp_Object sym;
   sym = intern_c_string (namestring);
diff --git a/src/macros.c b/src/macros.c
index 2d927ffc40..9f6b4ade94 100644
--- a/src/macros.c
+++ b/src/macros.c
@@ -267,7 +267,9 @@ pop_kbd_macro (Lisp_Object info)
   Lisp_Object tem;
   Vexecuting_kbd_macro = XCAR (info);
   tem = XCDR (info);
-  integer_to_intmax (XCAR (tem), &executing_kbd_macro_index);
+  intmax_t i;
+  integer_to_intmax (XCAR (tem), &i);
+  executing_kbd_macro_index = i;
   Vreal_this_command = XCDR (tem);
   run_hook (Qkbd_macro_termination_hook);
 }
diff --git a/src/pdumper.c b/src/pdumper.c
index 2f5c719803..af526d2a80 100644
--- a/src/pdumper.c
+++ b/src/pdumper.c
@@ -1615,7 +1615,7 @@ dump_emacs_reloc_immediate (struct dump_context *ctx,
 
 DEFINE_EMACS_IMMEDIATE_FN (dump_emacs_reloc_immediate_lv, Lisp_Object);
 DEFINE_EMACS_IMMEDIATE_FN (dump_emacs_reloc_immediate_ptrdiff_t, ptrdiff_t);
-DEFINE_EMACS_IMMEDIATE_FN (dump_emacs_reloc_immediate_intmax_t, intmax_t);
+DEFINE_EMACS_IMMEDIATE_FN (dump_emacs_reloc_immediate_emacs_int, EMACS_INT);
 DEFINE_EMACS_IMMEDIATE_FN (dump_emacs_reloc_immediate_int, int);
 DEFINE_EMACS_IMMEDIATE_FN (dump_emacs_reloc_immediate_bool, bool);
 
@@ -2286,10 +2286,10 @@ dump_float (struct dump_context *ctx, const struct Lisp_Float *lfloat)
 static dump_off
 dump_fwd_int (struct dump_context *ctx, const struct Lisp_Intfwd *intfwd)
 {
-#if CHECK_STRUCTS && !defined HASH_Lisp_Intfwd_4D887A7387
+#if CHECK_STRUCTS && !defined HASH_Lisp_Intfwd_1225FA32CC
 # error "Lisp_Intfwd changed. See CHECK_STRUCTS comment."
 #endif
-  dump_emacs_reloc_immediate_intmax_t (ctx, intfwd->intvar, *intfwd->intvar);
+  dump_emacs_reloc_immediate_emacs_int (ctx, intfwd->intvar, *intfwd->intvar);
   struct Lisp_Intfwd out;
   dump_object_start (ctx, &out, sizeof (out));
   DUMP_FIELD_COPY (&out, intfwd, type);
diff --git a/src/thread.h b/src/thread.h
index e46545baf2..5e003761e8 100644
--- a/src/thread.h
+++ b/src/thread.h
@@ -104,7 +104,7 @@ struct thread_state
 #define specpdl_ptr (current_thread->m_specpdl_ptr)
 
   /* Depth in Lisp evaluations and function calls.  */
-  intmax_t m_lisp_eval_depth;
+  EMACS_INT m_lisp_eval_depth;
 #define lisp_eval_depth (current_thread->m_lisp_eval_depth)
 
   /* This points to the current buffer.  */
diff --git a/src/undo.c b/src/undo.c
index 3c1251dae6..27238e6e93 100644
--- a/src/undo.c
+++ b/src/undo.c
@@ -291,7 +291,7 @@ truncate_undo_list (struct buffer *b)
 {
   Lisp_Object list;
   Lisp_Object prev, next, last_boundary;
-  intmax_t size_so_far = 0;
+  EMACS_INT size_so_far = 0;
 
   /* Make sure that calling undo-outer-limit-function
      won't cause another GC.  */
diff --git a/src/xdisp.c b/src/xdisp.c
index 760c31c676..8d16d3891c 100644
--- a/src/xdisp.c
+++ b/src/xdisp.c
@@ -15767,7 +15767,7 @@ enum
 
 static int
 try_scrolling (Lisp_Object window, bool just_this_one_p,
-	       intmax_t arg_scroll_conservatively, intmax_t scroll_step,
+	       EMACS_INT arg_scroll_conservatively, EMACS_INT scroll_step,
 	       bool temp_scroll_step, bool last_line_misfit)
 {
   struct window *w = XWINDOW (window);
@@ -15803,7 +15803,7 @@ try_scrolling (Lisp_Object window, bool just_this_one_p,
     /* Compute how much we should try to scroll maximally to bring
        point into view.  */
     {
-      intmax_t scroll_lines_max
+      EMACS_INT scroll_lines_max
 	= max (scroll_step, max (arg_scroll_conservatively, temp_scroll_step));
       int scroll_lines = clip_to_bounds (0, scroll_lines_max, 1000000);
       scroll_max = scroll_lines * frame_line_height;
diff --git a/src/xselect.c b/src/xselect.c
index 5f0bb44cc9..24d5595af5 100644
--- a/src/xselect.c
+++ b/src/xselect.c
@@ -1085,10 +1085,10 @@ wait_for_property_change (struct prop_location *location)
      property_change_reply, because property_change_reply_object says so.  */
   if (! location->arrived)
     {
-      intmax_t timeout = max (0, x_selection_timeout);
-      intmax_t secs = timeout / 1000;
+      EMACS_INT timeout = max (0, x_selection_timeout);
+      EMACS_INT secs = timeout / 1000;
       int nsecs = (timeout % 1000) * 1000000;
-      TRACE2 ("  Waiting %"PRIdMAX" secs, %d nsecs", secs, nsecs);
+      TRACE2 ("  Waiting %"pI" secs, %d nsecs", secs, nsecs);
       wait_reading_process_output (secs, nsecs, 0, false,
 				   property_change_reply, NULL, 0);
 
@@ -1193,10 +1193,10 @@ x_get_foreign_selection (Lisp_Object selection_symbol, Lisp_Object target_type,
   unblock_input ();
 
   /* This allows quits.  Also, don't wait forever.  */
-  intmax_t timeout = max (0, x_selection_timeout);
-  intmax_t secs = timeout / 1000;
+  EMACS_INT timeout = max (0, x_selection_timeout);
+  EMACS_INT secs = timeout / 1000;
   int nsecs = (timeout % 1000) * 1000000;
-  TRACE1 ("  Start waiting %"PRIdMAX" secs for SelectionNotify", secs);
+  TRACE1 ("  Start waiting %"pI" secs for SelectionNotify", secs);
   wait_reading_process_output (secs, nsecs, 0, false,
 			       reading_selection_reply, NULL, 0);
   TRACE1 ("  Got event = %d", !NILP (XCAR (reading_selection_reply)));
diff --git a/src/xterm.c b/src/xterm.c
index 453669f6e0..c072d17553 100644
--- a/src/xterm.c
+++ b/src/xterm.c
@@ -4886,7 +4886,7 @@ x_x_to_emacs_modifiers (struct x_display_info *dpyinfo, int state)
 }
 
 static int
-x_emacs_to_x_modifiers (struct x_display_info *dpyinfo, intmax_t state)
+x_emacs_to_x_modifiers (struct x_display_info *dpyinfo, EMACS_INT state)
 {
   EMACS_INT mod_ctrl = ctrl_modifier;
   EMACS_INT mod_meta = meta_modifier;