Apply sq macro throughout

Marlin/Marlin_main.cpp

@@ -3596,7 +3596,7 @@ inline void gcode_G28() {
          * so Vx = -a Vy = -b Vz = 1 (we want the vector facing towards positive Z
          */
 
-        int abl2 = auto_bed_leveling_grid_points * auto_bed_leveling_grid_points;
+        int abl2 = sq(auto_bed_leveling_grid_points);
 
         double eqnAMatrix[abl2 * 3], // "A" matrix of the linear system of equations
                eqnBVector[abl2],     // "B" vector of Z points
@@ -3629,7 +3629,7 @@ inline void gcode_G28() {
 
           #if ENABLED(DELTA)
             // Avoid probing the corners (outside the round or hexagon print surface) on a delta printer.
-            float distance_from_center = sqrt(xProbe * xProbe + yProbe * yProbe);
+            float distance_from_center = HYPOT(xProbe, yProbe);
             if (distance_from_center > DELTA_PROBEABLE_RADIUS) continue;
           #endif //DELTA
 
@@ -4252,7 +4252,7 @@ inline void gcode_M42() {
         return;
       }
     #else
-      if (sqrt(X_probe_location * X_probe_location + Y_probe_location * Y_probe_location) > DELTA_PROBEABLE_RADIUS) {
+      if (HYPOT(X_probe_location, Y_probe_location) > DELTA_PROBEABLE_RADIUS) {
         SERIAL_PROTOCOLLNPGM("? (X,Y) location outside of probeable radius.");
         return;
       }
@@ -4342,7 +4342,7 @@ inline void gcode_M42() {
           #else
             // If we have gone out too far, we can do a simple fix and scale the numbers
             // back in closer to the origin.
-            while (sqrt(X_current * X_current + Y_current * Y_current) > DELTA_PROBEABLE_RADIUS) {
+            while (HYPOT(X_current, Y_current) > DELTA_PROBEABLE_RADIUS) {
               X_current /= 1.25;
               Y_current /= 1.25;
               if (verbose_level > 3) {
@@ -4378,10 +4378,9 @@ inline void gcode_M42() {
        * data points we have so far
        */
       sum = 0.0;
-      for (uint8_t j = 0; j <= n; j++) {
-        float ss = sample_set[j] - mean;
-        sum += ss * ss;
-      }
+      for (uint8_t j = 0; j <= n; j++)
+        sum += sq(sample_set[j] - mean);
+
       sigma = sqrt(sum / (n + 1));
       if (verbose_level > 0) {
         if (verbose_level > 1) {
@@ -8139,7 +8138,7 @@ void prepare_move_to_destination() {
      * This is important when there are successive arc motions.
      */
     // Vector rotation matrix values
-    float cos_T = 1 - 0.5 * theta_per_segment * theta_per_segment; // Small angle approximation
+    float cos_T = 1 - 0.5 * sq(theta_per_segment); // Small angle approximation
     float sin_T = theta_per_segment;
 
     float arc_target[NUM_AXIS];

Marlin/macros.h

@@ -36,6 +36,7 @@
 // Macros for maths shortcuts
 #define RADIANS(d) ((d)*M_PI/180.0)
 #define DEGREES(r) ((r)*180.0/M_PI)
+#define HYPOT(x,y) sqrt(sq(x)+sq(y))
 
 // Macros to contrain values
 #define NOLESS(v,n) do{ if (v < n) v = n; }while(0)

Marlin/planner.cpp

@@ -171,8 +171,8 @@ void Planner::calculate_trapezoid_for_block(block_t* block, float entry_factor,
   }
 
   #if ENABLED(ADVANCE)
-    volatile long initial_advance = block->advance * entry_factor * entry_factor;
-    volatile long final_advance = block->advance * exit_factor * exit_factor;
+    volatile long initial_advance = block->advance * sq(entry_factor);
+    volatile long final_advance = block->advance * sq(exit_factor);
   #endif // ADVANCE
 
   // block->accelerate_until = accelerate_steps;
@@ -815,13 +815,13 @@ void Planner::check_axes_activity() {
   else {
     block->millimeters = sqrt(
       #if ENABLED(COREXY)
-        square(delta_mm[X_HEAD]) + square(delta_mm[Y_HEAD]) + square(delta_mm[Z_AXIS])
+        sq(delta_mm[X_HEAD]) + sq(delta_mm[Y_HEAD]) + sq(delta_mm[Z_AXIS])
       #elif ENABLED(COREXZ)
-        square(delta_mm[X_HEAD]) + square(delta_mm[Y_AXIS]) + square(delta_mm[Z_HEAD])
+        sq(delta_mm[X_HEAD]) + sq(delta_mm[Y_AXIS]) + sq(delta_mm[Z_HEAD])
       #elif ENABLED(COREYZ)
-        square(delta_mm[X_AXIS]) + square(delta_mm[Y_HEAD]) + square(delta_mm[Z_HEAD])
+        sq(delta_mm[X_AXIS]) + sq(delta_mm[Y_HEAD]) + sq(delta_mm[Z_HEAD])
       #else
-        square(delta_mm[X_AXIS]) + square(delta_mm[Y_AXIS]) + square(delta_mm[Z_AXIS])
+        sq(delta_mm[X_AXIS]) + sq(delta_mm[Y_AXIS]) + sq(delta_mm[Z_AXIS])
       #endif
     );
   }
@@ -1030,7 +1030,7 @@ void Planner::check_axes_activity() {
           dsy = current_speed[Y_AXIS] - previous_speed[Y_AXIS],
           dsz = fabs(csz - previous_speed[Z_AXIS]),
           dse = fabs(cse - previous_speed[E_AXIS]),
-          jerk = sqrt(dsx * dsx + dsy * dsy);
+          jerk = HYPOT(dsx, dsy);
 
     //    if ((fabs(previous_speed[X_AXIS]) > 0.0001) || (fabs(previous_speed[Y_AXIS]) > 0.0001)) {
     vmax_junction = block->nominal_speed;
@@ -1086,7 +1086,7 @@ void Planner::check_axes_activity() {
     }
     else {
       long acc_dist = estimate_acceleration_distance(0, block->nominal_rate, block->acceleration_steps_per_s2);
-      float advance = ((STEPS_PER_CUBIC_MM_E) * (EXTRUDER_ADVANCE_K)) * (cse * cse * (EXTRUSION_AREA) * (EXTRUSION_AREA)) * 256;
+      float advance = ((STEPS_PER_CUBIC_MM_E) * (EXTRUDER_ADVANCE_K)) * HYPOT(cse, EXTRUSION_AREA) * 256;
       block->advance = advance;
       block->advance_rate = acc_dist ? advance / (float)acc_dist : 0;
     }

Marlin/planner.h

@@ -290,7 +290,7 @@ class Planner {
      */
     static float estimate_acceleration_distance(float initial_rate, float target_rate, float accel) {
       if (accel == 0) return 0; // accel was 0, set acceleration distance to 0
-      return (target_rate * target_rate - initial_rate * initial_rate) / (accel * 2);
+      return (sq(target_rate) - sq(initial_rate)) / (accel * 2);
     }
 
     /**
@@ -303,7 +303,7 @@ class Planner {
      */
     static float intersection_distance(float initial_rate, float final_rate, float accel, float distance) {
       if (accel == 0) return 0; // accel was 0, set intersection distance to 0
-      return (accel * 2 * distance - initial_rate * initial_rate + final_rate * final_rate) / (accel * 4);
+      return (accel * 2 * distance - sq(initial_rate) + sq(final_rate)) / (accel * 4);
     }
 
     /**
@@ -312,7 +312,7 @@ class Planner {
      * 'distance'.
      */
     static float max_allowable_speed(float accel, float target_velocity, float distance) {
-      return sqrt(target_velocity * target_velocity - 2 * accel * distance);
+      return sqrt(sq(target_velocity) - 2 * accel * distance);
     }
 
     static void calculate_trapezoid_for_block(block_t* block, float entry_factor, float exit_factor);

Marlin/ultralcd.cpp

@@ -1356,7 +1356,7 @@ void kill_screen(const char* lcd_msg) {
   }
   #if ENABLED(DELTA)
     static float delta_clip_radius_2 =  (DELTA_PRINTABLE_RADIUS) * (DELTA_PRINTABLE_RADIUS);
-    static int delta_clip( float a ) { return sqrt(delta_clip_radius_2 - a*a); }
+    static int delta_clip( float a ) { return sqrt(delta_clip_radius_2 - sq(a)); }
     static void lcd_move_x() { int clip = delta_clip(current_position[Y_AXIS]); _lcd_move_xyz(PSTR(MSG_MOVE_X), X_AXIS, max(sw_endstop_min[X_AXIS], -clip), min(sw_endstop_max[X_AXIS], clip)); }
     static void lcd_move_y() { int clip = delta_clip(current_position[X_AXIS]); _lcd_move_xyz(PSTR(MSG_MOVE_Y), Y_AXIS, max(sw_endstop_min[Y_AXIS], -clip), min(sw_endstop_max[Y_AXIS], clip)); }
   #else