Optimized planner re-write. Significantly faster. Full arc support enabled by rotation matrix approach.

- Significant improvements in the planner. Removed or reordered
repetitive and expensive calculations by order of importance:
recalculating unchanged blocks, trig functions [sin(), cos(), tan()],
sqrt(), divides, and multiplications. Blocks long enough for nominal
speed to be guaranteed to be reached ignored by planner. Done by
introducing two uint8_t flags per block. Reduced computational overhead
by an order of magnitude.   - Arc motion generation completely
re-written and optimized. Now runs with acceleration planner. Removed
all but one trig function (atan2) from initialization. Streamlined
computations. Segment target locations generated by vector
transformation and small angle approximation. Arc path correction
implemented for accumulated error of approximation and single precision
calculation of Arduino. Bug fix in message passing.

planner.h

@@ -3,6 +3,7 @@
   Part of Grbl
 
   Copyright (c) 2009-2011 Simen Svale Skogsrud
+  Modifications Copyright (c) 2011 Sungeun (Sonny) Jeon  
 
   Grbl is free software: you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
@@ -35,9 +36,11 @@ typedef struct {
   // Fields used by the motion planner to manage acceleration
   double speed_x, speed_y, speed_z;   // Nominal mm/minute for each axis
   double nominal_speed;               // The nominal speed for this block in mm/min  
+  double entry_speed_sqr;             // Square of entry speed at previous-current junction in (mm/min)^2
+  double max_entry_speed_sqr;         // Square of maximum allowable entry speed in (mm/min)^2
   double millimeters;                 // The total travel of this block in mm
-  double entry_speed;                 // Entry speed at previous-current junction 
-  double max_entry_speed;             // Maximum allowable entry speed
+  uint8_t recalculate_flag;           // Planner flag to recalculate trapezoids on entry junction
+  uint8_t nominal_length_flag;        // Planner flag for nominal speed always reached
 
   // Settings for the trapezoid generator
   uint32_t initial_rate;              // The jerk-adjusted step rate at start of block  
@@ -54,7 +57,7 @@ void plan_init();
 // Add a new linear movement to the buffer. x, y and z is the signed, absolute target position in 
 // millimaters. Feed rate specifies the speed of the motion. If feed rate is inverted, the feed
 // rate is taken to mean "frequency" and would complete the operation in 1/feed_rate minutes.
-void plan_buffer_line(double x, double y, double z, double feed_rate, int invert_feed_rate);
+void plan_buffer_line(double x, double y, double z, double feed_rate, uint8_t invert_feed_rate);
 
 // Called when the current block is no longer needed. Discards the block and makes the memory
 // availible for new blocks.
@@ -64,7 +67,7 @@ void plan_discard_current_block();
 block_t *plan_get_current_block();
 
 // Enables or disables acceleration-management for upcoming blocks
-void plan_set_acceleration_manager_enabled(int enabled);
+void plan_set_acceleration_manager_enabled(uint8_t enabled);
 
 // Is acceleration-management currently enabled?
 int plan_is_acceleration_manager_enabled();