DDA: convert um_to_steps_* to generic implementation.

A generic implementation here will allow callers to pass the
target axis in as a parameter so the callers can also be made more
generic.

Traumflug notes:

Split out application of the new implementation in dda.c into its
own commit.

This actually costs 128 bytes, but as we can access axes from within
a loop now, I expect to get more savings elsewhere.

Interestingly, binary size is raised by another 18 bytes if

  um_to_steps(int32_t, enum axis_e)

is changed to

  um_to_steps(enum axis_e, int32_t)

even on the 8-bit ATmega. While putting the axis number to the
front might be a bit more logical (think of additional parameters,
the axis number position would move), NXP application note
AN10963 states on page 10ff, 16-bit data should be 16-bit aligned
and 32-bit data should be 32-bit aligned for best performance.
Well, so let's do it this way.

dda.h

@@ -11,6 +11,12 @@
 	#endif
 #endif
 
+#ifndef SIMULATOR
+  #include <avr/pgmspace.h>
+#else
+  #define PROGMEM
+#endif
+
 /*
 	types
 */

dda_maths.c

@@ -8,6 +8,26 @@
 #include <stdlib.h>
 #include <stdint.h>
 
+/*!
+  Pre-calculated constant values for axis um <=> steps conversions.
+
+  These should be calculated at run-time once in dda_init() if the
+  STEPS_PER_M_* constants are ever replaced with run-time options.
+*/
+const axes_uint32_t PROGMEM axis_qn = {
+  (uint32_t)STEPS_PER_M_X / UM_PER_METER,
+  (uint32_t)STEPS_PER_M_Y / UM_PER_METER,
+  (uint32_t)STEPS_PER_M_Z / UM_PER_METER,
+  (uint32_t)STEPS_PER_M_E / UM_PER_METER
+};
+
+const axes_uint32_t PROGMEM axis_qr = {
+  (uint32_t)STEPS_PER_M_X % UM_PER_METER,
+  (uint32_t)STEPS_PER_M_Y % UM_PER_METER,
+  (uint32_t)STEPS_PER_M_Z % UM_PER_METER,
+  (uint32_t)STEPS_PER_M_E % UM_PER_METER
+};
+
 /*!
   Integer multiply-divide algorithm. Returns the same as muldiv(multiplicand, multiplier, divisor), but also allowing to use precalculated quotients and remainders.
 

dda_maths.h

@@ -4,6 +4,7 @@
 #include	<stdint.h>
 
 #include	"config_wrapper.h"
+#include "dda.h"
 
 // return rounded result of multiplicand * multiplier / divisor
 // this version is with quotient and remainder precalculated elsewhere
@@ -18,36 +19,39 @@ inline int32_t muldiv(int32_t multiplicand, uint32_t multiplier,
                   multiplier % divisor, divisor);
 }
 
-/*
-	micrometer distance <=> motor step distance conversions
+/*!
+  Micrometer distance <=> motor step distance conversions.
 */
-// Like shown in the patch attached to this post:
-// http://forums.reprap.org/read.php?147,89710,130225#msg-130225 ,
-// it might be worth pre-calculating muldivQR()'s qn and rn in dda_init()
-// as soon as STEPS_PER_M_{XYZE} is no longer a compile-time variable.
+
+#define UM_PER_METER (1000000UL)
+
+extern const axes_uint32_t PROGMEM axis_qn;
+extern const axes_uint32_t PROGMEM axis_qr;
+
+static int32_t um_to_steps(int32_t, enum axis_e) __attribute__ ((always_inline));
+inline int32_t um_to_steps(int32_t distance, enum axis_e a) {
+  return muldivQR(distance, pgm_read_dword(&axis_qn[a]),
+                  pgm_read_dword(&axis_qr[a]), UM_PER_METER);
+}
 
 static int32_t um_to_steps_x(int32_t) __attribute__ ((always_inline));
 inline int32_t um_to_steps_x(int32_t distance) {
-    return muldivQR(distance, STEPS_PER_M_X / 1000000UL,
-                    STEPS_PER_M_X % 1000000UL, 1000000UL);
+  return um_to_steps(distance, X);
 }
 
 static int32_t um_to_steps_y(int32_t) __attribute__ ((always_inline));
 inline int32_t um_to_steps_y(int32_t distance) {
-    return muldivQR(distance, STEPS_PER_M_Y / 1000000UL,
-                    STEPS_PER_M_Y % 1000000UL, 1000000UL);
+  return um_to_steps(distance, Y);
 }
 
 static int32_t um_to_steps_z(int32_t) __attribute__ ((always_inline));
 inline int32_t um_to_steps_z(int32_t distance) {
-    return muldivQR(distance, STEPS_PER_M_Z / 1000000UL,
-                    STEPS_PER_M_Z % 1000000UL, 1000000UL);
+  return um_to_steps(distance, Z);
 }
 
 static int32_t um_to_steps_e(int32_t) __attribute__ ((always_inline));
 inline int32_t um_to_steps_e(int32_t distance) {
-    return muldivQR(distance, STEPS_PER_M_E / 1000000UL,
-                    STEPS_PER_M_E % 1000000UL, 1000000UL);
+  return um_to_steps(distance, E);
 }
 
 // approximate 2D distance