diff --git a/README.md b/README.md
index ba5d185..f98fb79 100644
--- a/README.md
+++ b/README.md
@@ -79,6 +79,11 @@ Some features that are a part of the SDL3 build:
   fullscreen.
 - **Screenshot capture** - F10 writes the framebuffer to disk.
 - **Gamepad support** - cross-platform SDL_Gamepad mapped to the IIgs joystick.
+  A connected gamepad is used automatically (with hotplug); without one, the
+  numeric keypad emulates the joystick. The stick's circular travel is remapped
+  to the square range Apple joysticks have, so games can reach the corners.
+  Override either behavior in the config menu (F4) under Joystick
+  Configuration.
 - **Terminal debugger** - a REPL for the built-in 65816 debugger from the
   controlling terminal.
 - **Drag-and-drop disk loading** - drop a disk image on the window and GSplus
diff --git a/gsplus/src/CMakeLists.txt b/gsplus/src/CMakeLists.txt
index ebb0cea..d7ff1ea 100644
--- a/gsplus/src/CMakeLists.txt
+++ b/gsplus/src/CMakeLists.txt
@@ -266,6 +266,11 @@ add_executable(gsplus-sdl
 )
 target_link_libraries(gsplus-sdl PRIVATE gsplus_core_sdl SDL3::SDL3)
 
+if(UNIX AND NOT APPLE)
+    # paddles.c uses sqrt(); glibc keeps it in libm
+    target_link_libraries(gsplus-sdl PRIVATE m)
+endif()
+
 if(APPLE)
     # macOS-only: retune SDL's default menu bar so ⌘ combos pass through to the
     # emulated IIgs and GSplus quits on ⌥⌘Q. The Objective-C source needs Cocoa.
diff --git a/gsplus/src/adb.c b/gsplus/src/adb.c
index a43a5b3..fb5407e 100644
--- a/gsplus/src/adb.c
+++ b/gsplus/src/adb.c
@@ -2126,7 +2126,7 @@ adb_physical_key_update(Kimage *kimage_ptr, int raw_a2code, word32 unicode_c,
 		if(ascii > 0x30 && ascii <= 0x39) {
 			g_keypad_key_is_down[ascii - 0x30] = !is_up;
 		}
-		if(g_joystick_type == 0) {
+		if(paddle_effective_joystick_type() == 0) {
 			/* If Joystick type is keypad, then do not let these */
 			/*  keypress pass on further, except for cmd/opt */
 			if(ascii == 0x30) {
diff --git a/gsplus/src/config.c b/gsplus/src/config.c
index 3d0ab74..dfe1943 100644
--- a/gsplus/src/config.c
+++ b/gsplus/src/config.c
@@ -57,6 +57,7 @@ extern word32 g_mem_size_exp;
 extern int g_video_line_update_interval;
 extern int g_user_halt_bad;
 extern int g_joystick_type;
+extern int g_joystick_square_range;
 extern int g_joystick_scale_factor_x;
 extern int g_joystick_scale_factor_y;
 extern int g_joystick_trim_amount_x;
@@ -250,8 +251,11 @@ Cfg_menu g_cfg_newslot7_menu[] = {
 
 Cfg_menu g_cfg_joystick_menu[] = {
 { "Joystick Configuration", g_cfg_joystick_menu, 0, 0, CFGTYPE_MENU },
-{ "Joystick Emulation,0,Keypad Joystick,1,Mouse Joystick,2,Native Joystick 1,"
-	"3,Native Joystick 2", KNMP(g_joystick_type), CFGTYPE_INT },
+{ "Joystick Emulation,4,Auto (Gamepad or Keypad),0,Keypad Joystick,"
+	"1,Mouse Joystick,2,Native Joystick 1,3,Native Joystick 2",
+	KNMP(g_joystick_type), CFGTYPE_INT },
+{ "Gamepad Range,1,Square (Full Corners),0,Circular (Raw)",
+	KNMP(g_joystick_square_range), CFGTYPE_INT },
 { "Joystick Scale X,0x100,Standard,0x119,+10%,0x133,+20%,"
 	"0x150,+30%,0xb0,-30%,0xcd,-20%,0xe7,-10%",
 		KNMP(g_joystick_scale_factor_x), CFGTYPE_INT },
diff --git a/gsplus/src/paddles.c b/gsplus/src/paddles.c
index 66c90f0..0f52989 100644
--- a/gsplus/src/paddles.c
+++ b/gsplus/src/paddles.c
@@ -9,6 +9,7 @@
 /**********************************************************************/
 
 #include "defc.h"
+#include <math.h>
 
 extern int g_mouse_raw_x;	/* from adb.c */
 extern int g_mouse_raw_y;
@@ -21,7 +22,8 @@ int	g_joystick_scale_factor_y = 0x100;
 int	g_joystick_trim_amount_x = 0;
 int	g_joystick_trim_amount_y = 0;
 
-int	g_joystick_type = 0;	/* 0 = Keypad Joystick */
+int	g_joystick_type = 4;	/* 4 = Auto (gamepad if present, else keypad) */
+int	g_joystick_square_range = 1;	/* remap circular stick gate to square */
 int	g_joystick_native_type1 = -1;
 int	g_joystick_native_type2 = -1;
 int	g_joystick_native_type = -1;
@@ -35,17 +37,72 @@ dword64	g_paddle_dfcyc[4] = { 0, 0, 0, 0 };
 		/* g_paddle_dfcyc are the dfcyc the paddle goes to 0 */
 
 
+#define STICK_DEADZONE	0.08	/* radial, as a fraction of full deflection */
+
+void
+paddle_map_circle_to_square(int *xptr, int *yptr)
+{
+	double	x, y, r, m, scale;
+
+	/* A modern gamepad stick travels in a circle, so a full diagonal
+	 *  only reaches ~71% on each axis and games expecting the square
+	 *  range of Apple joysticks never see the corners.  Stretch each
+	 *  sample along its own direction -- identity on the axes, up to
+	 *  sqrt(2) at the diagonals -- so the circular rim lands exactly on
+	 *  the square's perimeter. */
+	x = *xptr / 32767.0;
+	y = *yptr / 32767.0;
+	r = sqrt((x * x) + (y * y));
+	if(r < STICK_DEADZONE) {
+		/* Radial deadzone: sticks do not rest at exactly 0, and the
+		 *  stretch below would amplify the drift */
+		*xptr = 0;
+		*yptr = 0;
+		return;
+	}
+	/* Rescale magnitude so travel is continuous at the deadzone edge */
+	scale = (r - STICK_DEADZONE) / (1.0 - STICK_DEADZONE);
+	x = (x / r) * scale;
+	y = (y / r) * scale;
+	m = (fabs(x) > fabs(y)) ? fabs(x) : fabs(y);
+	if(m > 0.0) {
+		x = x * (scale / m);
+		y = y * (scale / m);
+	}
+	/* Clamp: some pads overshoot the unit circle near the diagonals */
+	x = (x > 1.0) ? 1.0 : ((x < -1.0) ? -1.0 : x);
+	y = (y > 1.0) ? 1.0 : ((y < -1.0) ? -1.0 : y);
+	*xptr = (int)(x * 32767.0);
+	*yptr = (int)(y * 32767.0);
+}
+
+int
+paddle_effective_joystick_type()
+{
+	/* Auto (type 4) is resolved every time it's sampled, never stored:
+	 *  use the native joystick/gamepad if one is connected, else the
+	 *  keypad.  g_joystick_native_type1 tracks hotplug, so connecting
+	 *  or removing a gamepad mid-game switches modes automatically. */
+	if(g_joystick_type == 4) {
+		return (g_joystick_native_type1 >= 0) ? 2 : 0;
+	}
+	return g_joystick_type;
+}
+
 void
 paddle_fixup_joystick_type()
 {
+	int	type;
+
 	/* If g_joystick_type points to an illegal value, change it */
-	if(g_joystick_type == 2) {
+	type = paddle_effective_joystick_type();
+	if(type == 2) {
 		g_joystick_native_type = g_joystick_native_type1;
 		if(g_joystick_native_type1 < 0) {
 			g_joystick_type = 0;
 		}
 	}
-	if(g_joystick_type == 3) {
+	if(type == 3) {
 		g_joystick_native_type = g_joystick_native_type2;
 		if(g_joystick_native_type2 < 0) {
 			g_joystick_type = 0;
@@ -62,7 +119,7 @@ paddle_trigger(dword64 dfcyc)
 	/* Determine what all the paddle values are right now */
 	paddle_fixup_joystick_type();
 
-	switch(g_joystick_type) {
+	switch(paddle_effective_joystick_type()) {
 	case 0:		/* Keypad Joystick */
 		paddle_trigger_keypad(dfcyc);
 		break;
@@ -121,15 +178,27 @@ void
 paddle_update_trigger_dcycs(dword64 dfcyc)
 {
 	dword64	trig_dfcyc;
+	int	xy_val[2];
 	int	val, paddle_num, scale, trim;
 	int	i;
 
+	xy_val[0] = g_paddle_val[0];
+	xy_val[1] = g_paddle_val[1];
+	if(g_joystick_square_range &&
+				(paddle_effective_joystick_type() >= 2)) {
+		/* Work on a copy: some backends keep g_paddle_val[] between
+		 *  samples, so remapping in place would compound */
+		paddle_map_circle_to_square(&xy_val[0], &xy_val[1]);
+	}
 	for(i = 0; i < 4; i++) {
 		paddle_num = i;
 		if(g_swap_paddles) {
 			paddle_num = i ^ 1;
 		}
 		val = g_paddle_val[paddle_num];
+		if(paddle_num < 2) {
+			val = xy_val[paddle_num];
+		}
 		if(g_invert_paddles) {
 			val = -val;
 		}
@@ -183,5 +252,12 @@ void
 paddle_update_buttons()
 {
 	paddle_fixup_joystick_type();
-	joystick_update_buttons();
+	if(paddle_effective_joystick_type() >= 2) {
+		joystick_update_buttons();
+	} else {
+		/* In keypad/mouse modes a connected gamepad must not drive
+		 *  the buttons either (half-working input is confusing);
+		 *  also clears bits latched before a mode switch */
+		g_paddle_buttons &= ~3;
+	}
 }
diff --git a/gsplus/src/protos_base.h b/gsplus/src/protos_base.h
index d5e589c..306a813 100644
--- a/gsplus/src/protos_base.h
+++ b/gsplus/src/protos_base.h
@@ -483,6 +483,8 @@ int read_vid_counters(int loc, dword64 dfcyc);
 
 
 /* paddles.c */
+void paddle_map_circle_to_square(int *xptr, int *yptr);
+int paddle_effective_joystick_type(void);
 void paddle_fixup_joystick_type(void);
 void paddle_trigger(dword64 dfcyc);
 void paddle_trigger_mouse(dword64 dfcyc);
diff --git a/gsplus/src/vars_x86linux b/gsplus/src/vars_x86linux
index ac985a5..e66c85c 100644
--- a/gsplus/src/vars_x86linux
+++ b/gsplus/src/vars_x86linux
@@ -3,7 +3,7 @@ OBJECTS1 = pulseaudio_driver.o xdriver.o
 CCOPTS = -O2 -Wall -fomit-frame-pointer -DPULSE_AUDIO
 NAME = gsplus
 LD = $(CC)
-EXTRA_LIBS = -lXext -lpulse
+EXTRA_LIBS = -lXext -lpulse -lm
 EXTRA_SPECIALS =
 
 XOPTS = -I/usr/X11R6/include