marlin/Marlin/src/module/planner.cpp

/**
 * Marlin 3D Printer Firmware
 * Copyright (C) 2016 MarlinFirmware [https://github.com/MarlinFirmware/Marlin]
 *
 * Based on Sprinter and grbl.
 * Copyright (C) 2011 Camiel Gubbels / Erik van der Zalm
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 *
 */

/**
 * planner.cpp
 *
 * Buffer movement commands and manage the acceleration profile plan
 *
 * Derived from Grbl
 * Copyright (c) 2009-2011 Simen Svale Skogsrud
 *
 * The ring buffer implementation gleaned from the wiring_serial library by David A. Mellis.
 *
 *
 * Reasoning behind the mathematics in this module (in the key of 'Mathematica'):
 *
 * s == speed, a == acceleration, t == time, d == distance
 *
 * Basic definitions:
 *   Speed[s_, a_, t_] := s + (a*t)
 *   Travel[s_, a_, t_] := Integrate[Speed[s, a, t], t]
 *
 * Distance to reach a specific speed with a constant acceleration:
 *   Solve[{Speed[s, a, t] == m, Travel[s, a, t] == d}, d, t]
 *   d -> (m^2 - s^2)/(2 a) --> estimate_acceleration_distance()
 *
 * Speed after a given distance of travel with constant acceleration:
 *   Solve[{Speed[s, a, t] == m, Travel[s, a, t] == d}, m, t]
 *   m -> Sqrt[2 a d + s^2]
 *
 * DestinationSpeed[s_, a_, d_] := Sqrt[2 a d + s^2]
 *
 * When to start braking (di) to reach a specified destination speed (s2) after accelerating
 * from initial speed s1 without ever stopping at a plateau:
 *   Solve[{DestinationSpeed[s1, a, di] == DestinationSpeed[s2, a, d - di]}, di]
 *   di -> (2 a d - s1^2 + s2^2)/(4 a) --> intersection_distance()
 *
 * IntersectionDistance[s1_, s2_, a_, d_] := (2 a d - s1^2 + s2^2)/(4 a)
 *
 * --
 *
 * The fast inverse function needed for Bézier interpolation for AVR
 * was designed, written and tested by Eduardo José Tagle on April/2018
 */

#include "planner.h"
#include "stepper.h"
#include "motion.h"
#include "../module/temperature.h"
#include "../lcd/ultralcd.h"
#include "../core/language.h"
#include "../gcode/parser.h"

#include "../Marlin.h"

#if HAS_LEVELING
  #include "../feature/bedlevel/bedlevel.h"
#endif

#if ENABLED(FILAMENT_WIDTH_SENSOR)
  #include "../feature/filwidth.h"
#endif

#if ENABLED(BARICUDA)
  #include "../feature/baricuda.h"
#endif

#if ENABLED(MIXING_EXTRUDER)
  #include "../feature/mixing.h"
#endif

#if ENABLED(AUTO_POWER_CONTROL)
  #include "../feature/power.h"
#endif

// Delay for delivery of first block to the stepper ISR, if the queue contains 2 or
// fewer movements. The delay is measured in milliseconds, and must be less than 250ms
#define BLOCK_DELAY_FOR_1ST_MOVE 50

Planner planner;

  // public:

/**
 * A ring buffer of moves described in steps
 */
block_t Planner::block_buffer[BLOCK_BUFFER_SIZE];
volatile uint8_t Planner::block_buffer_head,  // Index of the next block to be pushed
                 Planner::block_buffer_tail;  // Index of the busy block, if any
uint16_t Planner::cleaning_buffer_counter;    // A counter to disable queuing of blocks
uint8_t Planner::delay_before_delivering,     // This counter delays delivery of blocks when queue becomes empty to allow the opportunity of merging blocks
        Planner::block_buffer_planned;        // Index of the optimally planned block

float Planner::max_feedrate_mm_s[XYZE_N],   // Max speeds in mm per second
      Planner::axis_steps_per_mm[XYZE_N],
      Planner::steps_to_mm[XYZE_N];

#if ENABLED(ABORT_ON_ENDSTOP_HIT_FEATURE_ENABLED)
  bool Planner::abort_on_endstop_hit = false;
#endif

#if ENABLED(DISTINCT_E_FACTORS)
  uint8_t Planner::last_extruder = 0;     // Respond to extruder change
#endif

int16_t Planner::flow_percentage[EXTRUDERS] = ARRAY_BY_EXTRUDERS1(100); // Extrusion factor for each extruder

float Planner::e_factor[EXTRUDERS] = ARRAY_BY_EXTRUDERS1(1.0); // The flow percentage and volumetric multiplier combine to scale E movement

#if DISABLED(NO_VOLUMETRICS)
  float Planner::filament_size[EXTRUDERS],          // diameter of filament (in millimeters), typically around 1.75 or 2.85, 0 disables the volumetric calculations for the extruder
        Planner::volumetric_area_nominal = CIRCLE_AREA((DEFAULT_NOMINAL_FILAMENT_DIA) * 0.5), // Nominal cross-sectional area
        Planner::volumetric_multiplier[EXTRUDERS];  // Reciprocal of cross-sectional area of filament (in mm^2). Pre-calculated to reduce computation in the planner
#endif

uint32_t Planner::max_acceleration_steps_per_s2[XYZE_N],
         Planner::max_acceleration_mm_per_s2[XYZE_N]; // Use M201 to override by software

uint32_t Planner::min_segment_time_us;

// Initialized by settings.load()
float Planner::min_feedrate_mm_s,
      Planner::acceleration,         // Normal acceleration mm/s^2  DEFAULT ACCELERATION for all printing moves. M204 SXXXX
      Planner::retract_acceleration, // Retract acceleration mm/s^2 filament pull-back and push-forward while standing still in the other axes M204 TXXXX
      Planner::travel_acceleration,  // Travel acceleration mm/s^2  DEFAULT ACCELERATION for all NON printing moves. M204 MXXXX
      Planner::max_jerk[XYZE],       // The largest speed change requiring no acceleration
      Planner::min_travel_feedrate_mm_s;

#if HAS_LEVELING
  bool Planner::leveling_active = false; // Flag that auto bed leveling is enabled
  #if ABL_PLANAR
    matrix_3x3 Planner::bed_level_matrix; // Transform to compensate for bed level
  #endif
  #if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
    float Planner::z_fade_height,      // Initialized by settings.load()
          Planner::inverse_z_fade_height,
          Planner::last_fade_z;
  #endif
#else
  constexpr bool Planner::leveling_active;
#endif

#if ENABLED(SKEW_CORRECTION)
  #if ENABLED(SKEW_CORRECTION_GCODE)
    float Planner::xy_skew_factor;
  #else
    constexpr float Planner::xy_skew_factor;
  #endif
  #if ENABLED(SKEW_CORRECTION_FOR_Z) && ENABLED(SKEW_CORRECTION_GCODE)
    float Planner::xz_skew_factor, Planner::yz_skew_factor;
  #else
    constexpr float Planner::xz_skew_factor, Planner::yz_skew_factor;
  #endif
#endif

#if ENABLED(AUTOTEMP)
  float Planner::autotemp_max = 250,
        Planner::autotemp_min = 210,
        Planner::autotemp_factor = 0.1;
  bool Planner::autotemp_enabled = false;
#endif

// private:

int32_t Planner::position[NUM_AXIS] = { 0 };

uint32_t Planner::cutoff_long;

float Planner::previous_speed[NUM_AXIS],
      Planner::previous_nominal_speed_sqr;

#if ENABLED(DISABLE_INACTIVE_EXTRUDER)
  uint8_t Planner::g_uc_extruder_last_move[EXTRUDERS] = { 0 };
#endif

#ifdef XY_FREQUENCY_LIMIT
  // Old direction bits. Used for speed calculations
  unsigned char Planner::old_direction_bits = 0;
  // Segment times (in µs). Used for speed calculations
  uint32_t Planner::axis_segment_time_us[2][3] = { { MAX_FREQ_TIME_US + 1, 0, 0 }, { MAX_FREQ_TIME_US + 1, 0, 0 } };
#endif

#if ENABLED(LIN_ADVANCE)
  float Planner::extruder_advance_K; // Initialized by settings.load()
#endif

#if HAS_POSITION_FLOAT
  float Planner::position_float[XYZE]; // Needed for accurate maths. Steps cannot be used!
#endif

#if ENABLED(ULTRA_LCD)
  volatile uint32_t Planner::block_buffer_runtime_us = 0;
#endif

/**
 * Class and Instance Methods
 */

Planner::Planner() { init(); }

void Planner::init() {
  ZERO(position);
  #if HAS_POSITION_FLOAT
    ZERO(position_float);
  #endif
  ZERO(previous_speed);
  previous_nominal_speed_sqr = 0.0;
  #if ABL_PLANAR
    bed_level_matrix.set_to_identity();
  #endif
  clear_block_buffer();
  block_buffer_planned = 0;
  delay_before_delivering = 0;
}

#if ENABLED(BEZIER_JERK_CONTROL)

  #ifdef __AVR__
    // This routine, for AVR, returns 0x1000000 / d, but trying to get the inverse as
    //  fast as possible. A fast converging iterative Newton-Raphson method is able to
    //  reach full precision in just 1 iteration, and takes 211 cycles (worst case, mean
    //  case is less, up to 30 cycles for small divisors), instead of the 500 cycles a
    //  normal division would take.
    //
    // Inspired by the following page,
    //  https://stackoverflow.com/questions/27801397/newton-raphson-division-with-big-integers
    //
    // Suppose we want to calculate
    //  floor(2 ^ k / B)    where B is a positive integer
    // Then
    //  B must be <= 2^k, otherwise, the quotient is 0.
    //
    // The Newton - Raphson iteration for x = B / 2 ^ k yields:
    //  q[n + 1] = q[n] * (2 - q[n] * B / 2 ^ k)
    //
    // We can rearrange it as:
    //  q[n + 1] = q[n] * (2 ^ (k + 1) - q[n] * B) >> k
    //
    //  Each iteration of this kind requires only integer multiplications
    // and bit shifts.
    //  Does it converge to floor(2 ^ k / B) ?:  Not necessarily, but, in
    // the worst case, it eventually alternates between floor(2 ^ k / B)
    // and ceiling(2 ^ k / B)).
    //  So we can use some not-so-clever test to see if we are in this
    // case, and extract floor(2 ^ k / B).
    //  Lastly, a simple but important optimization for this approach is to
    // truncate multiplications (i.e.calculate only the higher bits of the
    // product) in the early iterations of the Newton - Raphson method.The
    // reason to do so, is that the results of the early iterations are far
    // from the quotient, and it doesn't matter to perform them inaccurately.
    //  Finally, we should pick a good starting value for x. Knowing how many
    // digits the divisor has, we can estimate it:
    //
    // 2^k / x = 2 ^ log2(2^k / x)
    // 2^k / x = 2 ^(log2(2^k)-log2(x))
    // 2^k / x = 2 ^(k*log2(2)-log2(x))
    // 2^k / x = 2 ^ (k-log2(x))
    // 2^k / x >= 2 ^ (k-floor(log2(x)))
    // floor(log2(x)) simply is the index of the most significant bit set.
    //
    //  If we could improve this estimation even further, then the number of
    // iterations can be dropped quite a bit, thus saving valuable execution time.
    //  The paper "Software Integer Division" by Thomas L.Rodeheffer, Microsoft
    // Research, Silicon Valley,August 26, 2008, that is available at
    // https://www.microsoft.com/en-us/research/wp-content/uploads/2008/08/tr-2008-141.pdf
    // suggests , for its integer division algorithm, that using a table to supply the
    // first 8 bits of precision, and due to the quadratic convergence nature of the
    // Newton-Raphon iteration, then just 2 iterations should be enough to get
    // maximum precision of the division.
    //  If we precompute values of inverses for small denominator values, then
    // just one Newton-Raphson iteration is enough to reach full precision
    //  We will use the top 9 bits of the denominator as index.
    //
    //  The AVR assembly function is implementing the following C code, included
    // here as reference:
    //
    // uint32_t get_period_inverse(uint32_t d) {
    //  static const uint8_t inv_tab[256] = {
    //    255,253,252,250,248,246,244,242,240,238,236,234,233,231,229,227,
    //    225,224,222,220,218,217,215,213,212,210,208,207,205,203,202,200,
    //    199,197,195,194,192,191,189,188,186,185,183,182,180,179,178,176,
    //    175,173,172,170,169,168,166,165,164,162,161,160,158,157,156,154,
    //    153,152,151,149,148,147,146,144,143,142,141,139,138,137,136,135,
    //    134,132,131,130,129,128,127,126,125,123,122,121,120,119,118,117,
    //    116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,
    //    100,99,98,97,96,95,94,93,92,91,90,89,88,88,87,86,
    //    85,84,83,82,81,80,80,79,78,77,76,75,74,74,73,72,
    //    71,70,70,69,68,67,66,66,65,64,63,62,62,61,60,59,
    //    59,58,57,56,56,55,54,53,53,52,51,50,50,49,48,48,
    //    47,46,46,45,44,43,43,42,41,41,40,39,39,38,37,37,
    //    36,35,35,34,33,33,32,32,31,30,30,29,28,28,27,27,
    //    26,25,25,24,24,23,22,22,21,21,20,19,19,18,18,17,
    //    17,16,15,15,14,14,13,13,12,12,11,10,10,9,9,8,
    //    8,7,7,6,6,5,5,4,4,3,3,2,2,1,0,0
    //  };
    //
    //  // For small denominators, it is cheaper to directly store the result,
    //  //  because those denominators would require 2 Newton-Raphson iterations
    //  //  to converge to the required result precision. For bigger ones, just
    //  //  ONE Newton-Raphson iteration is enough to get maximum precision!
    //  static const uint32_t small_inv_tab[111] PROGMEM = {
    //    16777216,16777216,8388608,5592405,4194304,3355443,2796202,2396745,2097152,1864135,1677721,1525201,1398101,1290555,1198372,1118481,
    //    1048576,986895,932067,883011,838860,798915,762600,729444,699050,671088,645277,621378,599186,578524,559240,541200,
    //    524288,508400,493447,479349,466033,453438,441505,430185,419430,409200,399457,390167,381300,372827,364722,356962,
    //    349525,342392,335544,328965,322638,316551,310689,305040,299593,294337,289262,284359,279620,275036,270600,266305,
    //    262144,258111,254200,250406,246723,243148,239674,236298,233016,229824,226719,223696,220752,217885,215092,212369,
    //    209715,207126,204600,202135,199728,197379,195083,192841,190650,188508,186413,184365,182361,180400,178481,176602,
    //    174762,172960,171196,169466,167772,166111,164482,162885,161319,159783,158275,156796,155344,153919,152520
    //  };
    //
    //  // For small divisors, it is best to directly retrieve the results
    //  if (d <= 110)
    //    return pgm_read_dword(&small_inv_tab[d]);
    //
    //  // Compute initial estimation of 0x1000000/x -
    //  // Get most significant bit set on divider
    //  uint8_t idx = 0;
    //  uint32_t nr = d;
    //  if (!(nr & 0xFF0000)) {
    //    nr <<= 8;
    //    idx += 8;
    //    if (!(nr & 0xFF0000)) {
    //      nr <<= 8;
    //      idx += 8;
    //    }
    //  }
    //  if (!(nr & 0xF00000)) {
    //    nr <<= 4;
    //    idx += 4;
    //  }
    //  if (!(nr & 0xC00000)) {
    //    nr <<= 2;
    //    idx += 2;
    //  }
    //  if (!(nr & 0x800000)) {
    //    nr <<= 1;
    //    idx += 1;
    //  }
    //
    //  // Isolate top 9 bits of the denominator, to be used as index into the initial estimation table
    //  uint32_t tidx = nr >> 15;         // top 9 bits. bit8 is always set
    //  uint32_t ie = inv_tab[tidx & 0xFF] + 256; // Get the table value. bit9 is always set
    //  uint32_t x = idx <= 8 ? (ie >> (8 - idx)) : (ie << (idx - 8)); // Position the estimation at the proper place
    //
    //  // Now, refine estimation by newton-raphson. 1 iteration is enough
    //  x = uint32_t((x * uint64_t((1 << 25) - x * d)) >> 24);
    //
    //  // Estimate remainder
    //  uint32_t r = (1 << 24) - x * d;
    //
    //  // Check if we must adjust result
    //  if (r >= d) x++;
    //
    //  // x holds the proper estimation
    //  return uint32_t(x);
    // }
    //
    static uint32_t get_period_inverse(uint32_t d) {

      static const uint8_t inv_tab[256] PROGMEM = {
        255,253,252,250,248,246,244,242,240,238,236,234,233,231,229,227,
        225,224,222,220,218,217,215,213,212,210,208,207,205,203,202,200,
        199,197,195,194,192,191,189,188,186,185,183,182,180,179,178,176,
        175,173,172,170,169,168,166,165,164,162,161,160,158,157,156,154,
        153,152,151,149,148,147,146,144,143,142,141,139,138,137,136,135,
        134,132,131,130,129,128,127,126,125,123,122,121,120,119,118,117,
        116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,
        100,99,98,97,96,95,94,93,92,91,90,89,88,88,87,86,
        85,84,83,82,81,80,80,79,78,77,76,75,74,74,73,72,
        71,70,70,69,68,67,66,66,65,64,63,62,62,61,60,59,
        59,58,57,56,56,55,54,53,53,52,51,50,50,49,48,48,
        47,46,46,45,44,43,43,42,41,41,40,39,39,38,37,37,
        36,35,35,34,33,33,32,32,31,30,30,29,28,28,27,27,
        26,25,25,24,24,23,22,22,21,21,20,19,19,18,18,17,
        17,16,15,15,14,14,13,13,12,12,11,10,10,9,9,8,
        8,7,7,6,6,5,5,4,4,3,3,2,2,1,0,0
      };

      // For small denominators, it is cheaper to directly store the result.
      //  For bigger ones, just ONE Newton-Raphson iteration is enough to get
      //  maximum precision we need
      static const uint32_t small_inv_tab[111] PROGMEM = {
        16777216,16777216,8388608,5592405,4194304,3355443,2796202,2396745,2097152,1864135,1677721,1525201,1398101,1290555,1198372,1118481,
        1048576,986895,932067,883011,838860,798915,762600,729444,699050,671088,645277,621378,599186,578524,559240,541200,
        524288,508400,493447,479349,466033,453438,441505,430185,419430,409200,399457,390167,381300,372827,364722,356962,
        349525,342392,335544,328965,322638,316551,310689,305040,299593,294337,289262,284359,279620,275036,270600,266305,
        262144,258111,254200,250406,246723,243148,239674,236298,233016,229824,226719,223696,220752,217885,215092,212369,
        209715,207126,204600,202135,199728,197379,195083,192841,190650,188508,186413,184365,182361,180400,178481,176602,
        174762,172960,171196,169466,167772,166111,164482,162885,161319,159783,158275,156796,155344,153919,152520
      };

      // For small divisors, it is best to directly retrieve the results
      if (d <= 110)
        return pgm_read_dword(&small_inv_tab[d]);

      register uint8_t r8 = d & 0xFF;
      register uint8_t r9 = (d >> 8) & 0xFF;
      register uint8_t r10 = (d >> 16) & 0xFF;
      register uint8_t r2,r3,r4,r5,r6,r7,r11,r12,r13,r14,r15,r16,r17,r18;
      register const uint8_t* ptab = inv_tab;

      __asm__ __volatile__(
        // %8:%7:%6 = interval
        // r31:r30: MUST be those registers, and they must point to the inv_tab

        A("clr %13")                       // %13 = 0

        // Now we must compute
        // result = 0xFFFFFF / d
        // %8:%7:%6 = interval
        // %16:%15:%14 = nr
        // %13 = 0

        // A plain division of 24x24 bits should take 388 cycles to complete. We will
        // use Newton-Raphson for the calculation, and will strive to get way less cycles
        // for the same result - Using C division, it takes 500cycles to complete .

        A("clr %3")                        // idx = 0
        A("mov %14,%6")
        A("mov %15,%7")
        A("mov %16,%8")                    // nr = interval
        A("tst %16")                       // nr & 0xFF0000 == 0 ?
        A("brne 2f")                       // No, skip this
        A("mov %16,%15")
        A("mov %15,%14")                   // nr <<= 8, %14 not needed
        A("subi %3,-8")                    // idx += 8
        A("tst %16")                       // nr & 0xFF0000 == 0 ?
        A("brne 2f")                       // No, skip this
        A("mov %16,%15")                   // nr <<= 8, %14 not needed
        A("clr %15")                       // We clear %14
        A("subi %3,-8")                    // idx += 8

        // here %16 != 0 and %16:%15 contains at least 9 MSBits, or both %16:%15 are 0
        L("2")
        A("cpi %16,0x10")                  // (nr & 0xF00000) == 0 ?
        A("brcc 3f")                       // No, skip this
        A("swap %15")                      // Swap nibbles
        A("swap %16")                      // Swap nibbles. Low nibble is 0
        A("mov %14, %15")
        A("andi %14,0x0F")                 // Isolate low nibble
        A("andi %15,0xF0")                 // Keep proper nibble in %15
        A("or %16, %14")                   // %16:%15 <<= 4
        A("subi %3,-4")                    // idx += 4

        L("3")
        A("cpi %16,0x40")                  // (nr & 0xC00000) == 0 ?
        A("brcc 4f")                       // No, skip this
        A("add %15,%15")
        A("adc %16,%16")
        A("add %15,%15")
        A("adc %16,%16")                   // %16:%15 <<= 2
        A("subi %3,-2")                    // idx += 2

        L("4")
        A("cpi %16,0x80")                  // (nr & 0x800000) == 0 ?
        A("brcc 5f")                       // No, skip this
        A("add %15,%15")
        A("adc %16,%16")                   // %16:%15 <<= 1
        A("inc %3")                        // idx += 1

        // Now %16:%15 contains its MSBit set to 1, or %16:%15 is == 0. We are now absolutely sure
        // we have at least 9 MSBits available to enter the initial estimation table
        L("5")
        A("add %15,%15")
        A("adc %16,%16")                   // %16:%15 = tidx = (nr <<= 1), we lose the top MSBit (always set to 1, %16 is the index into the inverse table)
        A("add r30,%16")                   // Only use top 8 bits
        A("adc r31,%13")                   // r31:r30 = inv_tab + (tidx)
        A("lpm %14, Z")                    // %14 = inv_tab[tidx]
        A("ldi %15, 1")                    // %15 = 1  %15:%14 = inv_tab[tidx] + 256

        // We must scale the approximation to the proper place
        A("clr %16")                       // %16 will always be 0 here
        A("subi %3,8")                     // idx == 8 ?
        A("breq 6f")                       // yes, no need to scale
        A("brcs 7f")                       // If C=1, means idx < 8, result was negative!

        // idx > 8, now %3 = idx - 8. We must perform a left shift. idx range:[1-8]
        A("sbrs %3,0")                     // shift by 1bit position?
        A("rjmp 8f")                       // No
        A("add %14,%14")
        A("adc %15,%15")                   // %15:16 <<= 1
        L("8")
        A("sbrs %3,1")                     // shift by 2bit position?
        A("rjmp 9f")                       // No
        A("add %14,%14")
        A("adc %15,%15")
        A("add %14,%14")
        A("adc %15,%15")                   // %15:16 <<= 1
        L("9")
        A("sbrs %3,2")                     // shift by 4bits position?
        A("rjmp 16f")                      // No
        A("swap %15")                      // Swap nibbles. lo nibble of %15 will always be 0
        A("swap %14")                      // Swap nibbles
        A("mov %12,%14")
        A("andi %12,0x0F")                 // isolate low nibble
        A("andi %14,0xF0")                 // and clear it
        A("or %15,%12")                    // %15:%16 <<= 4
        L("16")
        A("sbrs %3,3")                     // shift by 8bits position?
        A("rjmp 6f")                       // No, we are done
        A("mov %16,%15")
        A("mov %15,%14")
        A("clr %14")
        A("jmp 6f")

        // idx < 8, now %3 = idx - 8. Get the count of bits
        L("7")
        A("neg %3")                        // %3 = -idx = count of bits to move right. idx range:[1...8]
        A("sbrs %3,0")                     // shift by 1 bit position ?
        A("rjmp 10f")                      // No, skip it
        A("asr %15")                       // (bit7 is always 0 here)
        A("ror %14")
        L("10")
        A("sbrs %3,1")                     // shift by 2 bit position ?
        A("rjmp 11f")                      // No, skip it
        A("asr %15")                       // (bit7 is always 0 here)
        A("ror %14")
        A("asr %15")                       // (bit7 is always 0 here)
        A("ror %14")
        L("11")
        A("sbrs %3,2")                     // shift by 4 bit position ?
        A("rjmp 12f")                      // No, skip it
        A("swap %15")                      // Swap nibbles
        A("andi %14, 0xF0")                // Lose the lowest nibble
        A("swap %14")                      // Swap nibbles. Upper nibble is 0
        A("or %14,%15")                    // Pass nibble from upper byte
        A("andi %15, 0x0F")                // And get rid of that nibble
        L("12")
        A("sbrs %3,3")                     // shift by 8 bit position ?
        A("rjmp 6f")                       // No, skip it
        A("mov %14,%15")
        A("clr %15")
        L("6")                       // %16:%15:%14 = initial estimation of 0x1000000 / d

        // Now, we must refine the estimation present on %16:%15:%14 using 1 iteration
        // of Newton-Raphson. As it has a quadratic convergence, 1 iteration is enough
        // to get more than 18bits of precision (the initial table lookup gives 9 bits of
        // precision to start from). 18bits of precision is all what is needed here for result

        // %8:%7:%6 = d = interval
        // %16:%15:%14 = x = initial estimation of 0x1000000 / d
        // %13 = 0
        // %3:%2:%1:%0 = working accumulator

        // Compute 1<<25 - x*d. Result should never exceed 25 bits and should always be positive
        A("clr %0")
        A("clr %1")
        A("clr %2")
        A("ldi %3,2")                      // %3:%2:%1:%0 = 0x2000000
        A("mul %6,%14")                    // r1:r0 = LO(d) * LO(x)
        A("sub %0,r0")
        A("sbc %1,r1")
        A("sbc %2,%13")
        A("sbc %3,%13")                    // %3:%2:%1:%0 -= LO(d) * LO(x)
        A("mul %7,%14")                    // r1:r0 = MI(d) * LO(x)
        A("sub %1,r0")
        A("sbc %2,r1" )
        A("sbc %3,%13")                    // %3:%2:%1:%0 -= MI(d) * LO(x) << 8
        A("mul %8,%14")                    // r1:r0 = HI(d) * LO(x)
        A("sub %2,r0")
        A("sbc %3,r1")                     // %3:%2:%1:%0 -= MIL(d) * LO(x) << 16
        A("mul %6,%15")                    // r1:r0 = LO(d) * MI(x)
        A("sub %1,r0")
        A("sbc %2,r1")
        A("sbc %3,%13")                    // %3:%2:%1:%0 -= LO(d) * MI(x) << 8
        A("mul %7,%15")                    // r1:r0 = MI(d) * MI(x)
        A("sub %2,r0")
        A("sbc %3,r1")                     // %3:%2:%1:%0 -= MI(d) * MI(x) << 16
        A("mul %8,%15")                    // r1:r0 = HI(d) * MI(x)
        A("sub %3,r0")                     // %3:%2:%1:%0 -= MIL(d) * MI(x) << 24
        A("mul %6,%16")                    // r1:r0 = LO(d) * HI(x)
        A("sub %2,r0")
        A("sbc %3,r1")                     // %3:%2:%1:%0 -= LO(d) * HI(x) << 16
        A("mul %7,%16")                    // r1:r0 = MI(d) * HI(x)
        A("sub %3,r0")                     // %3:%2:%1:%0 -= MI(d) * HI(x) << 24
        // %3:%2:%1:%0 = (1<<25) - x*d     [169]

        // We need to multiply that result by x, and we are only interested in the top 24bits of that multiply

        // %16:%15:%14 = x = initial estimation of 0x1000000 / d
        // %3:%2:%1:%0 = (1<<25) - x*d = acc
        // %13 = 0

        // result = %11:%10:%9:%5:%4
        A("mul %14,%0")                    // r1:r0 = LO(x) * LO(acc)
        A("mov %4,r1")
        A("clr %5")
        A("clr %9")
        A("clr %10")
        A("clr %11")                       // %11:%10:%9:%5:%4 = LO(x) * LO(acc) >> 8
        A("mul %15,%0")                    // r1:r0 = MI(x) * LO(acc)
        A("add %4,r0")
        A("adc %5,r1")
        A("adc %9,%13")
        A("adc %10,%13")
        A("adc %11,%13")                   // %11:%10:%9:%5:%4 += MI(x) * LO(acc)
        A("mul %16,%0")                    // r1:r0 = HI(x) * LO(acc)
        A("add %5,r0")
        A("adc %9,r1")
        A("adc %10,%13")
        A("adc %11,%13")                   // %11:%10:%9:%5:%4 += MI(x) * LO(acc) << 8

        A("mul %14,%1")                    // r1:r0 = LO(x) * MIL(acc)
        A("add %4,r0")
        A("adc %5,r1")
        A("adc %9,%13")
        A("adc %10,%13")
        A("adc %11,%13")                   // %11:%10:%9:%5:%4 = LO(x) * MIL(acc)
        A("mul %15,%1")                    // r1:r0 = MI(x) * MIL(acc)
        A("add %5,r0")
        A("adc %9,r1")
        A("adc %10,%13")
        A("adc %11,%13")                   // %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 8
        A("mul %16,%1")                    // r1:r0 = HI(x) * MIL(acc)
        A("add %9,r0")
        A("adc %10,r1")
        A("adc %11,%13")                   // %11:%10:%9:%5:%4 += MI(x) * MIL(acc) << 16

        A("mul %14,%2")                    // r1:r0 = LO(x) * MIH(acc)
        A("add %5,r0")
        A("adc %9,r1")
        A("adc %10,%13")
        A("adc %11,%13")                   // %11:%10:%9:%5:%4 = LO(x) * MIH(acc) << 8
        A("mul %15,%2")                    // r1:r0 = MI(x) * MIH(acc)
        A("add %9,r0")
        A("adc %10,r1")
        A("adc %11,%13")                   // %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 16
        A("mul %16,%2")                    // r1:r0 = HI(x) * MIH(acc)
        A("add %10,r0")
        A("adc %11,r1")                    // %11:%10:%9:%5:%4 += MI(x) * MIH(acc) << 24

        A("mul %14,%3")                    // r1:r0 = LO(x) * HI(acc)
        A("add %9,r0")
        A("adc %10,r1")
        A("adc %11,%13")                   // %11:%10:%9:%5:%4 = LO(x) * HI(acc) << 16
        A("mul %15,%3")                    // r1:r0 = MI(x) * HI(acc)
        A("add %10,r0")
        A("adc %11,r1")                    // %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 24
        A("mul %16,%3")                    // r1:r0 = HI(x) * HI(acc)
        A("add %11,r0")                    // %11:%10:%9:%5:%4 += MI(x) * HI(acc) << 32

        // At this point, %11:%10:%9 contains the new estimation of x.

        // Finally, we must correct the result. Estimate remainder as
        // (1<<24) - x*d
        // %11:%10:%9 = x
        // %8:%7:%6 = d = interval" "\n\t"
        A("ldi %3,1")
        A("clr %2")
        A("clr %1")
        A("clr %0")                        // %3:%2:%1:%0 = 0x1000000
        A("mul %6,%9")                     // r1:r0 = LO(d) * LO(x)
        A("sub %0,r0")
        A("sbc %1,r1")
        A("sbc %2,%13")
        A("sbc %3,%13")                    // %3:%2:%1:%0 -= LO(d) * LO(x)
        A("mul %7,%9")                     // r1:r0 = MI(d) * LO(x)
        A("sub %1,r0")
        A("sbc %2,r1")
        A("sbc %3,%13")                    // %3:%2:%1:%0 -= MI(d) * LO(x) << 8
        A("mul %8,%9")                     // r1:r0 = HI(d) * LO(x)
        A("sub %2,r0")
        A("sbc %3,r1")                     // %3:%2:%1:%0 -= MIL(d) * LO(x) << 16
        A("mul %6,%10")                    // r1:r0 = LO(d) * MI(x)
        A("sub %1,r0")
        A("sbc %2,r1")
        A("sbc %3,%13")                    // %3:%2:%1:%0 -= LO(d) * MI(x) << 8
        A("mul %7,%10")                    // r1:r0 = MI(d) * MI(x)
        A("sub %2,r0")
        A("sbc %3,r1")                     // %3:%2:%1:%0 -= MI(d) * MI(x) << 16
        A("mul %8,%10")                    // r1:r0 = HI(d) * MI(x)
        A("sub %3,r0")                     // %3:%2:%1:%0 -= MIL(d) * MI(x) << 24
        A("mul %6,%11")                    // r1:r0 = LO(d) * HI(x)
        A("sub %2,r0")
        A("sbc %3,r1")                     // %3:%2:%1:%0 -= LO(d) * HI(x) << 16
        A("mul %7,%11")                    // r1:r0 = MI(d) * HI(x)
        A("sub %3,r0")                     // %3:%2:%1:%0 -= MI(d) * HI(x) << 24
        // %3:%2:%1:%0 = r = (1<<24) - x*d
        // %8:%7:%6 = d = interval

        // Perform the final correction
        A("sub %0,%6")
        A("sbc %1,%7")
        A("sbc %2,%8")                     // r -= d
        A("brcs 14f")                      // if ( r >= d)

        // %11:%10:%9 = x
        A("ldi %3,1")
        A("add %9,%3")
        A("adc %10,%13")
        A("adc %11,%13")                   // x++
        L("14")

        // Estimation is done. %11:%10:%9 = x
        A("clr __zero_reg__")              // Make C runtime happy
        // [211 cycles total]
        : "=r" (r2),
          "=r" (r3),
          "=r" (r4),
          "=d" (r5),
          "=r" (r6),
          "=r" (r7),
          "+r" (r8),
          "+r" (r9),
          "+r" (r10),
          "=d" (r11),
          "=r" (r12),
          "=r" (r13),
          "=d" (r14),
          "=d" (r15),
          "=d" (r16),
          "=d" (r17),
          "=d" (r18),
          "+z" (ptab)
        :
        : "r0", "r1", "cc"
      );

      // Return the result
      return r11 | (uint16_t(r12) << 8) | (uint32_t(r13) << 16);
    }
  #else
    // All the other 32 CPUs can easily perform the inverse using hardware division,
    // so we don't need to reduce precision or to use assembly language at all.
    // This routine, for all the other archs, returns 0x100000000 / d ~= 0xFFFFFFFF / d
    static FORCE_INLINE uint32_t get_period_inverse(const uint32_t d) { return 0xFFFFFFFF / d; }
  #endif
#endif

#define MINIMAL_STEP_RATE 120

/**
 * Calculate trapezoid parameters, multiplying the entry- and exit-speeds
 * by the provided factors.
 */
void Planner::calculate_trapezoid_for_block(block_t* const block, const float &entry_factor, const float &exit_factor) {

  uint32_t initial_rate = CEIL(block->nominal_rate * entry_factor),
           final_rate = CEIL(block->nominal_rate * exit_factor); // (steps per second)

  // Limit minimal step rate (Otherwise the timer will overflow.)
  NOLESS(initial_rate, uint32_t(MINIMAL_STEP_RATE));
  NOLESS(final_rate, uint32_t(MINIMAL_STEP_RATE));

  #if ENABLED(BEZIER_JERK_CONTROL)
    uint32_t cruise_rate = initial_rate;
  #endif

  const int32_t accel = block->acceleration_steps_per_s2;

          // Steps required for acceleration, deceleration to/from nominal rate
  uint32_t accelerate_steps = CEIL(estimate_acceleration_distance(initial_rate, block->nominal_rate, accel)),
           decelerate_steps = FLOOR(estimate_acceleration_distance(block->nominal_rate, final_rate, -accel));
          // Steps between acceleration and deceleration, if any
  int32_t plateau_steps = block->step_event_count - accelerate_steps - decelerate_steps;

  // Does accelerate_steps + decelerate_steps exceed step_event_count?
  // Then we can't possibly reach the nominal rate, there will be no cruising.
  // Use intersection_distance() to calculate accel / braking time in order to
  // reach the final_rate exactly at the end of this block.
  if (plateau_steps < 0) {
    const float accelerate_steps_float = CEIL(intersection_distance(initial_rate, final_rate, accel, block->step_event_count));
    accelerate_steps = MIN(uint32_t(MAX(accelerate_steps_float, 0)), block->step_event_count);
    plateau_steps = 0;

    #if ENABLED(BEZIER_JERK_CONTROL)
      // We won't reach the cruising rate. Let's calculate the speed we will reach
      cruise_rate = final_speed(initial_rate, accel, accelerate_steps);
    #endif
  }
  #if ENABLED(BEZIER_JERK_CONTROL)
    else // We have some plateau time, so the cruise rate will be the nominal rate
      cruise_rate = block->nominal_rate;
  #endif

  // block->accelerate_until = accelerate_steps;
  // block->decelerate_after = accelerate_steps+plateau_steps;

  #if ENABLED(BEZIER_JERK_CONTROL)
    // Jerk controlled speed requires to express speed versus time, NOT steps
    uint32_t acceleration_time = ((float)(cruise_rate - initial_rate) / accel) * (HAL_STEPPER_TIMER_RATE),
             deceleration_time = ((float)(cruise_rate - final_rate) / accel) * (HAL_STEPPER_TIMER_RATE);

    // And to offload calculations from the ISR, we also calculate the inverse of those times here
    uint32_t acceleration_time_inverse = get_period_inverse(acceleration_time);
    uint32_t deceleration_time_inverse = get_period_inverse(deceleration_time);

  #endif

  // Fill variables used by the stepper in a critical section
  const bool was_enabled = STEPPER_ISR_ENABLED();
  if (was_enabled) DISABLE_STEPPER_DRIVER_INTERRUPT();

  // Don't update variables if block is busy: It is being interpreted by the planner
  if (!TEST(block->flag, BLOCK_BIT_BUSY)) {
    block->accelerate_until = accelerate_steps;
    block->decelerate_after = accelerate_steps + plateau_steps;
    block->initial_rate = initial_rate;
    #if ENABLED(BEZIER_JERK_CONTROL)
      block->acceleration_time = acceleration_time;
      block->deceleration_time = deceleration_time;
      block->acceleration_time_inverse = acceleration_time_inverse;
      block->deceleration_time_inverse = deceleration_time_inverse;
      block->cruise_rate = cruise_rate;
    #endif
    block->final_rate = final_rate;
  }
  if (was_enabled) ENABLE_STEPPER_DRIVER_INTERRUPT();
}

/*                            PLANNER SPEED DEFINITION
                                     +--------+   <- current->nominal_speed
                                    /          \
         current->entry_speed ->   +            \
                                   |             + <- next->entry_speed (aka exit speed)
                                   +-------------+
                                       time -->

  Recalculates the motion plan according to the following basic guidelines:

    1. Go over every feasible block sequentially in reverse order and calculate the junction speeds
        (i.e. current->entry_speed) such that:
      a. No junction speed exceeds the pre-computed maximum junction speed limit or nominal speeds of
         neighboring blocks.
      b. A block entry speed cannot exceed one reverse-computed from its exit speed (next->entry_speed)
         with a maximum allowable deceleration over the block travel distance.
      c. The last (or newest appended) block is planned from a complete stop (an exit speed of zero).
    2. Go over every block in chronological (forward) order and dial down junction speed values if
      a. The exit speed exceeds the one forward-computed from its entry speed with the maximum allowable
         acceleration over the block travel distance.

  When these stages are complete, the planner will have maximized the velocity profiles throughout the all
  of the planner blocks, where every block is operating at its maximum allowable acceleration limits. In
  other words, for all of the blocks in the planner, the plan is optimal and no further speed improvements
  are possible. If a new block is added to the buffer, the plan is recomputed according to the said
  guidelines for a new optimal plan.

  To increase computational efficiency of these guidelines, a set of planner block pointers have been
  created to indicate stop-compute points for when the planner guidelines cannot logically make any further
  changes or improvements to the plan when in normal operation and new blocks are streamed and added to the
  planner buffer. For example, if a subset of sequential blocks in the planner have been planned and are
  bracketed by junction velocities at their maximums (or by the first planner block as well), no new block
  added to the planner buffer will alter the velocity profiles within them. So we no longer have to compute
  them. Or, if a set of sequential blocks from the first block in the planner (or a optimal stop-compute
  point) are all accelerating, they are all optimal and can not be altered by a new block added to the
  planner buffer, as this will only further increase the plan speed to chronological blocks until a maximum
  junction velocity is reached. However, if the operational conditions of the plan changes from infrequently
  used feed holds or feedrate overrides, the stop-compute pointers will be reset and the entire plan is
  recomputed as stated in the general guidelines.

  Planner buffer index mapping:
  - block_buffer_tail: Points to the beginning of the planner buffer. First to be executed or being executed.
  - block_buffer_head: Points to the buffer block after the last block in the buffer. Used to indicate whether
      the buffer is full or empty. As described for standard ring buffers, this block is always empty.
  - block_buffer_planned: Points to the first buffer block after the last optimally planned block for normal
      streaming operating conditions. Use for planning optimizations by avoiding recomputing parts of the
      planner buffer that don't change with the addition of a new block, as describe above. In addition,
      this block can never be less than block_buffer_tail and will always be pushed forward and maintain
      this requirement when encountered by the plan_discard_current_block() routine during a cycle.

  NOTE: Since the planner only computes on what's in the planner buffer, some motions with lots of short
  line segments, like G2/3 arcs or complex curves, may seem to move slow. This is because there simply isn't
  enough combined distance traveled in the entire buffer to accelerate up to the nominal speed and then
  decelerate to a complete stop at the end of the buffer, as stated by the guidelines. If this happens and
  becomes an annoyance, there are a few simple solutions: (1) Maximize the machine acceleration. The planner
  will be able to compute higher velocity profiles within the same combined distance. (2) Maximize line
  motion(s) distance per block to a desired tolerance. The more combined distance the planner has to use,
  the faster it can go. (3) Maximize the planner buffer size. This also will increase the combined distance
  for the planner to compute over. It also increases the number of computations the planner has to perform
  to compute an optimal plan, so select carefully.
*/

// The kernel called by recalculate() when scanning the plan from last to first entry.
void Planner::reverse_pass_kernel(block_t* const current, const block_t * const next) {
  if (current) {
    // If entry speed is already at the maximum entry speed, and there was no change of speed
    // in the next block, there is no need to recheck. Block is cruising and there is no need to
    // compute anything for this block,
    // If not, block entry speed needs to be recalculated to ensure maximum possible planned speed.
    const float max_entry_speed_sqr = current->max_entry_speed_sqr;

    // Compute maximum entry speed decelerating over the current block from its exit speed.
    // If not at the maximum entry speed, or the previous block entry speed changed
    if (current->entry_speed_sqr != max_entry_speed_sqr || (next && TEST(next->flag, BLOCK_BIT_RECALCULATE))) {

      // If nominal length true, max junction speed is guaranteed to be reached.
      // If a block can de/ac-celerate from nominal speed to zero within the length of the block, then
      // the current block and next block junction speeds are guaranteed to always be at their maximum
      // junction speeds in deceleration and acceleration, respectively. This is due to how the current
      // block nominal speed limits both the current and next maximum junction speeds. Hence, in both
      // the reverse and forward planners, the corresponding block junction speed will always be at the
      // the maximum junction speed and may always be ignored for any speed reduction checks.

      const float new_entry_speed_sqr = TEST(current->flag, BLOCK_BIT_NOMINAL_LENGTH)
        ? max_entry_speed_sqr
        : MIN(max_entry_speed_sqr, max_allowable_speed_sqr(-current->acceleration, next ? next->entry_speed_sqr : sq(MINIMUM_PLANNER_SPEED), current->millimeters));
      if (current->entry_speed_sqr != new_entry_speed_sqr) {
        current->entry_speed_sqr = new_entry_speed_sqr;

        // Need to recalculate the block speed
        SBI(current->flag, BLOCK_BIT_RECALCULATE);
      }
    }
  }
}

/**
 * recalculate() needs to go over the current plan twice.
 * Once in reverse and once forward. This implements the reverse pass.
 */
void Planner::reverse_pass() {
  // Initialize block index to the last block in the planner buffer.
  uint8_t block_index = prev_block_index(block_buffer_head);

  // Read the index of the last buffer planned block.
  // The ISR may change it so get a stable local copy.
  uint8_t planned_block_index = block_buffer_planned;

  // If there was a race condition and block_buffer_planned was incremented
  //  or was pointing at the head (queue empty) break loop now and avoid
  //  planning already consumed blocks
  if (planned_block_index == block_buffer_head) return;

  // Reverse Pass: Coarsely maximize all possible deceleration curves back-planning from the last
  // block in buffer. Cease planning when the last optimal planned or tail pointer is reached.
  // NOTE: Forward pass will later refine and correct the reverse pass to create an optimal plan.
  block_t *current;
  const block_t *next = NULL;
  while (block_index != planned_block_index) {

    // Perform the reverse pass
    current = &block_buffer[block_index];

    // Only consider non sync blocks
    if (!TEST(current->flag, BLOCK_BIT_SYNC_POSITION)) {
      reverse_pass_kernel(current, next);
      next = current;
    }

    // Advance to the next
    block_index = prev_block_index(block_index);
  }
}

// The kernel called by recalculate() when scanning the plan from first to last entry.
void Planner::forward_pass_kernel(const block_t * const previous, block_t* const current, uint8_t block_index) {
  if (previous) {
    // If the previous block is an acceleration block, too short to complete the full speed
    // change, adjust the entry speed accordingly. Entry speeds have already been reset,
    // maximized, and reverse-planned. If nominal length is set, max junction speed is
    // guaranteed to be reached. No need to recheck.
    if (!TEST(previous->flag, BLOCK_BIT_NOMINAL_LENGTH) &&
      previous->entry_speed_sqr < current->entry_speed_sqr) {

      // Compute the maximum allowable speed
      const float new_entry_speed_sqr = max_allowable_speed_sqr(-previous->acceleration, previous->entry_speed_sqr, previous->millimeters);

      // If true, current block is full-acceleration and we can move the planned pointer forward.
      if (new_entry_speed_sqr < current->entry_speed_sqr) {

        // Always <= max_entry_speed_sqr. Backward pass sets this.
        current->entry_speed_sqr = new_entry_speed_sqr; // Always <= max_entry_speed_sqr. Backward pass sets this.

        // Set optimal plan pointer.
        block_buffer_planned = block_index;

        // And mark we need to recompute the trapezoidal shape
        SBI(current->flag, BLOCK_BIT_RECALCULATE);
      }
    }

    // Any block set at its maximum entry speed also creates an optimal plan up to this
    // point in the buffer. When the plan is bracketed by either the beginning of the
    // buffer and a maximum entry speed or two maximum entry speeds, every block in between
    // cannot logically be further improved. Hence, we don't have to recompute them anymore.
    if (current->entry_speed_sqr == current->max_entry_speed_sqr)
      block_buffer_planned = block_index;
  }
}

/**
 * recalculate() needs to go over the current plan twice.
 * Once in reverse and once forward. This implements the forward pass.
 */
void Planner::forward_pass() {

  // Forward Pass: Forward plan the acceleration curve from the planned pointer onward.
  // Also scans for optimal plan breakpoints and appropriately updates the planned pointer.

  // Begin at buffer planned pointer. Note that block_buffer_planned can be modified
  //  by the stepper ISR,  so read it ONCE. It it guaranteed that block_buffer_planned
  //  will never lead head, so the loop is safe to execute. Also note that the forward
  //  pass will never modify the values at the tail.
  uint8_t block_index = block_buffer_planned;

  block_t *current;
  const block_t * previous = NULL;
  while (block_index != block_buffer_head) {

    // Perform the forward pass
    current = &block_buffer[block_index];

    // Skip SYNC blocks
    if (!TEST(current->flag, BLOCK_BIT_SYNC_POSITION)) {
      forward_pass_kernel(previous, current, block_index);
      previous = current;
    }
    // Advance to the previous
    block_index = next_block_index(block_index);
  }
}

/**
 * Recalculate the trapezoid speed profiles for all blocks in the plan
 * according to the entry_factor for each junction. Must be called by
 * recalculate() after updating the blocks.
 */
void Planner::recalculate_trapezoids() {
  // The tail may be changed by the ISR so get a local copy.
  uint8_t block_index = block_buffer_tail;

  // As there could be a sync block in the head of the queue, and the next loop must not
  // recalculate the head block (as it needs to be specially handled), scan backwards until
  // we find the first non SYNC block
  uint8_t head_block_index = block_buffer_head;
  while (head_block_index != block_index) {

    // Go back (head always point to the first free block)
    uint8_t prev_index = prev_block_index(head_block_index);

    // Get the pointer to the block
    block_t *prev = &block_buffer[prev_index];

    // If not dealing with a sync block, we are done. The last block is not a SYNC block
    if (!TEST(prev->flag, BLOCK_BIT_SYNC_POSITION)) break;

    // Examine the previous block. This and all following are SYNC blocks
    head_block_index = prev_index;
  };

  // Go from the tail (currently executed block) to the first block, without including it)
  block_t *current = NULL, *next = NULL;
  float current_entry_speed = 0.0, next_entry_speed = 0.0;
  while (block_index != head_block_index) {

    next = &block_buffer[block_index];

    // Skip sync blocks
    if (!TEST(next->flag, BLOCK_BIT_SYNC_POSITION)) {
      next_entry_speed = SQRT(next->entry_speed_sqr);

      if (current) {
        // Recalculate if current block entry or exit junction speed has changed.
        if (TEST(current->flag, BLOCK_BIT_RECALCULATE) || TEST(next->flag, BLOCK_BIT_RECALCULATE)) {
          // NOTE: Entry and exit factors always > 0 by all previous logic operations.
          const float current_nominal_speed = SQRT(current->nominal_speed_sqr),
                      nomr = 1.0 / current_nominal_speed;
          calculate_trapezoid_for_block(current, current_entry_speed * nomr, next_entry_speed * nomr);
          #if ENABLED(LIN_ADVANCE)
            if (current->use_advance_lead) {
              const float comp = current->e_D_ratio * extruder_advance_K * axis_steps_per_mm[E_AXIS];
              current->max_adv_steps = current_nominal_speed * comp;
              current->final_adv_steps = next_entry_speed * comp;
            }
          #endif
          CBI(current->flag, BLOCK_BIT_RECALCULATE); // Reset current only to ensure next trapezoid is computed
        }
      }

      current = next;
      current_entry_speed = next_entry_speed;
    }

    block_index = next_block_index(block_index);
  }

  // Last/newest block in buffer. Exit speed is set with MINIMUM_PLANNER_SPEED. Always recalculated.
  if (next) {
    const float next_nominal_speed = SQRT(next->nominal_speed_sqr),
                nomr = 1.0 / next_nominal_speed;
    calculate_trapezoid_for_block(next, next_entry_speed * nomr, (MINIMUM_PLANNER_SPEED) * nomr);
    #if ENABLED(LIN_ADVANCE)
      if (next->use_advance_lead) {
        const float comp = next->e_D_ratio * extruder_advance_K * axis_steps_per_mm[E_AXIS];
        next->max_adv_steps = next_nominal_speed * comp;
        next->final_adv_steps = (MINIMUM_PLANNER_SPEED) * comp;
      }
    #endif
    CBI(next->flag, BLOCK_BIT_RECALCULATE);
  }
}

void Planner::recalculate() {
  // Initialize block index to the last block in the planner buffer.
  const uint8_t block_index = prev_block_index(block_buffer_head);
  // If there is just one block, no planning can be done. Avoid it!
  if (block_index != block_buffer_planned) {
    reverse_pass();
    forward_pass();
  }
  recalculate_trapezoids();
}

#if ENABLED(AUTOTEMP)

  void Planner::getHighESpeed() {
    static float oldt = 0;

    if (!autotemp_enabled) return;
    if (thermalManager.degTargetHotend(0) + 2 < autotemp_min) return; // probably temperature set to zero.

    float high = 0.0;
    for (uint8_t b = block_buffer_tail; b != block_buffer_head; b = next_block_index(b)) {
      block_t* block = &block_buffer[b];
      if (block->steps[X_AXIS] || block->steps[Y_AXIS] || block->steps[Z_AXIS]) {
        const float se = (float)block->steps[E_AXIS] / block->step_event_count * SQRT(block->nominal_speed_sqr); // mm/sec;
        NOLESS(high, se);
      }
    }

    float t = autotemp_min + high * autotemp_factor;
    t = constrain(t, autotemp_min, autotemp_max);
    if (t < oldt) t = t * (1 - (AUTOTEMP_OLDWEIGHT)) + oldt * (AUTOTEMP_OLDWEIGHT);
    oldt = t;
    thermalManager.setTargetHotend(t, 0);
  }

#endif // AUTOTEMP

/**
 * Maintain fans, paste extruder pressure,
 */
void Planner::check_axes_activity() {
  unsigned char axis_active[NUM_AXIS] = { 0 },
                tail_fan_speed[FAN_COUNT];

  #if ENABLED(BARICUDA)
    #if HAS_HEATER_1
      uint8_t tail_valve_pressure;
    #endif
    #if HAS_HEATER_2
      uint8_t tail_e_to_p_pressure;
    #endif
  #endif

  if (has_blocks_queued()) {

    #if FAN_COUNT > 0
      for (uint8_t i = 0; i < FAN_COUNT; i++)
        tail_fan_speed[i] = block_buffer[block_buffer_tail].fan_speed[i];
    #endif

    block_t* block;

    #if ENABLED(BARICUDA)
      block = &block_buffer[block_buffer_tail];
      #if HAS_HEATER_1
        tail_valve_pressure = block->valve_pressure;
      #endif
      #if HAS_HEATER_2
        tail_e_to_p_pressure = block->e_to_p_pressure;
      #endif
    #endif

    for (uint8_t b = block_buffer_tail; b != block_buffer_head; b = next_block_index(b)) {
      block = &block_buffer[b];
      LOOP_XYZE(i) if (block->steps[i]) axis_active[i]++;
    }
  }
  else {
    #if FAN_COUNT > 0
      for (uint8_t i = 0; i < FAN_COUNT; i++) tail_fan_speed[i] = fanSpeeds[i];
    #endif

    #if ENABLED(BARICUDA)
      #if HAS_HEATER_1
        tail_valve_pressure = baricuda_valve_pressure;
      #endif
      #if HAS_HEATER_2
        tail_e_to_p_pressure = baricuda_e_to_p_pressure;
      #endif
    #endif
  }

  #if ENABLED(DISABLE_X)
    if (!axis_active[X_AXIS]) disable_X();
  #endif
  #if ENABLED(DISABLE_Y)
    if (!axis_active[Y_AXIS]) disable_Y();
  #endif
  #if ENABLED(DISABLE_Z)
    if (!axis_active[Z_AXIS]) disable_Z();
  #endif
  #if ENABLED(DISABLE_E)
    if (!axis_active[E_AXIS]) disable_e_steppers();
  #endif

  #if FAN_COUNT > 0

    #if FAN_KICKSTART_TIME > 0

      static millis_t fan_kick_end[FAN_COUNT] = { 0 };

      #define KICKSTART_FAN(f) \
        if (tail_fan_speed[f]) { \
          millis_t ms = millis(); \
          if (fan_kick_end[f] == 0) { \
            fan_kick_end[f] = ms + FAN_KICKSTART_TIME; \
            tail_fan_speed[f] = 255; \
          } else if (PENDING(ms, fan_kick_end[f])) \
            tail_fan_speed[f] = 255; \
        } else fan_kick_end[f] = 0

      #if HAS_FAN0
        KICKSTART_FAN(0);
      #endif
      #if HAS_FAN1
        KICKSTART_FAN(1);
      #endif
      #if HAS_FAN2
        KICKSTART_FAN(2);
      #endif

    #endif // FAN_KICKSTART_TIME > 0

    #if FAN_MIN_PWM != 0 || FAN_MAX_PWM != 255
      #define CALC_FAN_SPEED(f) (tail_fan_speed[f] ? map(tail_fan_speed[f], 1, 255, FAN_MIN_PWM, FAN_MAX_PWM) : 0)
    #else
      #define CALC_FAN_SPEED(f) tail_fan_speed[f]
    #endif

    #if ENABLED(FAN_SOFT_PWM)
      #if HAS_FAN0
        thermalManager.soft_pwm_amount_fan[0] = CALC_FAN_SPEED(0);
      #endif
      #if HAS_FAN1
        thermalManager.soft_pwm_amount_fan[1] = CALC_FAN_SPEED(1);
      #endif
      #if HAS_FAN2
        thermalManager.soft_pwm_amount_fan[2] = CALC_FAN_SPEED(2);
      #endif
    #else
      #if HAS_FAN0
        analogWrite(FAN_PIN, CALC_FAN_SPEED(0));
      #endif
      #if HAS_FAN1
        analogWrite(FAN1_PIN, CALC_FAN_SPEED(1));
      #endif
      #if HAS_FAN2
        analogWrite(FAN2_PIN, CALC_FAN_SPEED(2));
      #endif
    #endif

  #endif // FAN_COUNT > 0

  #if ENABLED(AUTOTEMP)
    getHighESpeed();
  #endif

  #if ENABLED(BARICUDA)
    #if HAS_HEATER_1
      analogWrite(HEATER_1_PIN, tail_valve_pressure);
    #endif
    #if HAS_HEATER_2
      analogWrite(HEATER_2_PIN, tail_e_to_p_pressure);
    #endif
  #endif
}

#if DISABLED(NO_VOLUMETRICS)

  /**
   * Get a volumetric multiplier from a filament diameter.
   * This is the reciprocal of the circular cross-section area.
   * Return 1.0 with volumetric off or a diameter of 0.0.
   */
  inline float calculate_volumetric_multiplier(const float &diameter) {
    return (parser.volumetric_enabled && diameter) ? 1.0 / CIRCLE_AREA(diameter * 0.5) : 1.0;
  }

  /**
   * Convert the filament sizes into volumetric multipliers.
   * The multiplier converts a given E value into a length.
   */
  void Planner::calculate_volumetric_multipliers() {
    for (uint8_t i = 0; i < COUNT(filament_size); i++) {
      volumetric_multiplier[i] = calculate_volumetric_multiplier(filament_size[i]);
      refresh_e_factor(i);
    }
  }

#endif // !NO_VOLUMETRICS

#if ENABLED(FILAMENT_WIDTH_SENSOR)
  /**
   * Convert the ratio value given by the filament width sensor
   * into a volumetric multiplier. Conversion differs when using
   * linear extrusion vs volumetric extrusion.
   */
  void Planner::calculate_volumetric_for_width_sensor(const int8_t encoded_ratio) {
    // Reconstitute the nominal/measured ratio
    const float nom_meas_ratio = 1.0 + 0.01 * encoded_ratio,
                ratio_2 = sq(nom_meas_ratio);

    volumetric_multiplier[FILAMENT_SENSOR_EXTRUDER_NUM] = parser.volumetric_enabled
      ? ratio_2 / CIRCLE_AREA(filament_width_nominal * 0.5) // Volumetric uses a true volumetric multiplier
      : ratio_2;                                            // Linear squares the ratio, which scales the volume

    refresh_e_factor(FILAMENT_SENSOR_EXTRUDER_NUM);
  }
#endif

#if PLANNER_LEVELING || HAS_UBL_AND_CURVES
  /**
   * rx, ry, rz - Cartesian positions in mm
   *              Leveled XYZ on completion
   */
  void Planner::apply_leveling(float &rx, float &ry, float &rz) {

    #if ENABLED(SKEW_CORRECTION)
      skew(rx, ry, rz);
    #endif

    if (!leveling_active) return;

    #if ABL_PLANAR

      float dx = rx - (X_TILT_FULCRUM),
            dy = ry - (Y_TILT_FULCRUM);

      apply_rotation_xyz(bed_level_matrix, dx, dy, rz);

      rx = dx + X_TILT_FULCRUM;
      ry = dy + Y_TILT_FULCRUM;

    #elif HAS_MESH

      #if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
        const float fade_scaling_factor = fade_scaling_factor_for_z(rz);
      #else
        constexpr float fade_scaling_factor = 1.0;
      #endif

      #if ENABLED(AUTO_BED_LEVELING_BILINEAR)
        const float raw[XYZ] = { rx, ry, 0 };
      #endif

      rz += (
        #if ENABLED(MESH_BED_LEVELING)
          mbl.get_z(rx, ry
            #if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
              , fade_scaling_factor
            #endif
          )
        #elif ENABLED(AUTO_BED_LEVELING_UBL)
          fade_scaling_factor ? fade_scaling_factor * ubl.get_z_correction(rx, ry) : 0.0
        #elif ENABLED(AUTO_BED_LEVELING_BILINEAR)
          fade_scaling_factor ? fade_scaling_factor * bilinear_z_offset(raw) : 0.0
        #endif
      );

    #endif
  }

#endif

#if PLANNER_LEVELING

  void Planner::unapply_leveling(float raw[XYZ]) {

    if (leveling_active) {

      #if ABL_PLANAR

        matrix_3x3 inverse = matrix_3x3::transpose(bed_level_matrix);

        float dx = raw[X_AXIS] - (X_TILT_FULCRUM),
              dy = raw[Y_AXIS] - (Y_TILT_FULCRUM);

        apply_rotation_xyz(inverse, dx, dy, raw[Z_AXIS]);

        raw[X_AXIS] = dx + X_TILT_FULCRUM;
        raw[Y_AXIS] = dy + Y_TILT_FULCRUM;

      #elif HAS_MESH

        #if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
          const float fade_scaling_factor = fade_scaling_factor_for_z(raw[Z_AXIS]);
        #else
          constexpr float fade_scaling_factor = 1.0;
        #endif

        raw[Z_AXIS] -= (
          #if ENABLED(MESH_BED_LEVELING)
            mbl.get_z(raw[X_AXIS], raw[Y_AXIS]
              #if ENABLED(ENABLE_LEVELING_FADE_HEIGHT)
                , fade_scaling_factor
              #endif
            )
          #elif ENABLED(AUTO_BED_LEVELING_UBL)
            fade_scaling_factor ? fade_scaling_factor * ubl.get_z_correction(raw[X_AXIS], raw[Y_AXIS]) : 0.0
          #elif ENABLED(AUTO_BED_LEVELING_BILINEAR)
            fade_scaling_factor ? fade_scaling_factor * bilinear_z_offset(raw) : 0.0
          #endif
        );

      #endif
    }

    #if ENABLED(SKEW_CORRECTION)
      unskew(raw[X_AXIS], raw[Y_AXIS], raw[Z_AXIS]);
    #endif
  }

#endif // PLANNER_LEVELING

void Planner::quick_stop() {

  // Remove all the queued blocks. Note that this function is NOT
  // called from the Stepper ISR, so we must consider tail as readonly!
  // that is why we set head to tail - But there is a race condition that
  // must be handled: The tail could change between the read and the assignment
  // so this must be enclosed in a critical section

  const bool was_enabled = STEPPER_ISR_ENABLED();
  if (was_enabled) DISABLE_STEPPER_DRIVER_INTERRUPT();

  // Drop all queue entries
  block_buffer_planned = block_buffer_head = block_buffer_tail;

  // Restart the block delay for the first movement - As the queue was
  // forced to empty, there's no risk the ISR will touch this.
  delay_before_delivering = BLOCK_DELAY_FOR_1ST_MOVE;

  #if ENABLED(ULTRA_LCD)
    // Clear the accumulated runtime
    clear_block_buffer_runtime();
  #endif

  // Make sure to drop any attempt of queuing moves for at least 1 second
  cleaning_buffer_counter = 1000;

  // Reenable Stepper ISR
  if (was_enabled) ENABLE_STEPPER_DRIVER_INTERRUPT();

  // And stop the stepper ISR
  stepper.quick_stop();
}

void Planner::endstop_triggered(const AxisEnum axis) {
  // Record stepper position and discard the current block
  stepper.endstop_triggered(axis);
}

float Planner::triggered_position_mm(const AxisEnum axis) {
  return stepper.triggered_position(axis) * steps_to_mm[axis];
}

void Planner::finish_and_disable() {
  while (has_blocks_queued() || cleaning_buffer_counter) idle();
  disable_all_steppers();
}

/**
 * Get an axis position according to stepper position(s)
 * For CORE machines apply translation from ABC to XYZ.
 */
float Planner::get_axis_position_mm(const AxisEnum axis) {
  float axis_steps;
  #if IS_CORE
    // Requesting one of the "core" axes?
    if (axis == CORE_AXIS_1 || axis == CORE_AXIS_2) {

      // Protect the access to the position.
      const bool was_enabled = STEPPER_ISR_ENABLED();
      if (was_enabled) DISABLE_STEPPER_DRIVER_INTERRUPT();

      // ((a1+a2)+(a1-a2))/2 -> (a1+a2+a1-a2)/2 -> (a1+a1)/2 -> a1
      // ((a1+a2)-(a1-a2))/2 -> (a1+a2-a1+a2)/2 -> (a2+a2)/2 -> a2
      axis_steps = 0.5f * (
        axis == CORE_AXIS_2 ? CORESIGN(stepper.position(CORE_AXIS_1) - stepper.position(CORE_AXIS_2))
                            : stepper.position(CORE_AXIS_1) + stepper.position(CORE_AXIS_2)
      );

      if (was_enabled) ENABLE_STEPPER_DRIVER_INTERRUPT();
    }
    else
      axis_steps = stepper.position(axis);
  #else
    axis_steps = stepper.position(axis);
  #endif
  return axis_steps * steps_to_mm[axis];
}

/**
 * Block until all buffered steps are executed / cleaned
 */
void Planner::synchronize() { while (has_blocks_queued() || cleaning_buffer_counter) idle(); }

/**
 * Planner::_buffer_steps
 *
 * Add a new linear movement to the planner queue (in terms of steps).
 *
 *  target      - target position in steps units
 *  fr_mm_s     - (target) speed of the move
 *  extruder    - target extruder
 *  millimeters - the length of the movement, if known
 *
 * Returns true if movement was properly queued, false otherwise
 */
bool Planner::_buffer_steps(const int32_t (&target)[XYZE]
  #if HAS_POSITION_FLOAT
    , const float (&target_float)[XYZE]
  #endif
  , float fr_mm_s, const uint8_t extruder, const float &millimeters
) {

  // If we are cleaning, do not accept queuing of movements
  if (cleaning_buffer_counter) return false;

  // Wait for the next available block
  uint8_t next_buffer_head;
  block_t * const block = get_next_free_block(next_buffer_head);

  // Fill the block with the specified movement
  if (!_populate_block(block, false, target
  #if HAS_POSITION_FLOAT
    , target_float
  #endif
    , fr_mm_s, extruder, millimeters
  )) {
    // Movement was not queued, probably because it was too short.
    //  Simply accept that as movement queued and done
    return true;
  }

  // If this is the first added movement, reload the delay, otherwise, cancel it.
  if (block_buffer_head == block_buffer_tail) {
    // If it was the first queued block, restart the 1st block delivery delay, to
    // give the planner an opportunity to queue more movements and plan them
    // As there are no queued movements, the Stepper ISR will not touch this
    // variable, so there is no risk setting this here (but it MUST be done
    // before the following line!!)
    delay_before_delivering = BLOCK_DELAY_FOR_1ST_MOVE;
  }

  // Move buffer head
  block_buffer_head = next_buffer_head;

  // Recalculate and optimize trapezoidal speed profiles
  recalculate();

  // Movement successfully queued!
  return true;
}

/**
 * Planner::_populate_block
 *
 * Fills a new linear movement in the block (in terms of steps).
 *
 *  target      - target position in steps units
 *  fr_mm_s     - (target) speed of the move
 *  extruder    - target extruder
 *
 * Returns true is movement is acceptable, false otherwise
 */
bool Planner::_populate_block(block_t * const block, bool split_move,
    const int32_t (&target)[XYZE]
  #if HAS_POSITION_FLOAT
    , const float (&target_float)[XYZE]
  #endif
  , float fr_mm_s, const uint8_t extruder, const float &millimeters/*=0.0*/
) {

  const int32_t da = target[A_AXIS] - position[A_AXIS],
                db = target[B_AXIS] - position[B_AXIS],
                dc = target[C_AXIS] - position[C_AXIS];

  int32_t de = target[E_AXIS] - position[E_AXIS];

  /* <-- add a slash to enable
    SERIAL_ECHOPAIR("  _populate_block FR:", fr_mm_s);
    SERIAL_ECHOPAIR(" A:", target[A_AXIS]);
    SERIAL_ECHOPAIR(" (", da);
    SERIAL_ECHOPAIR(" steps) B:", target[B_AXIS]);
    SERIAL_ECHOPAIR(" (", db);
    SERIAL_ECHOPAIR(" steps) C:", target[C_AXIS]);
    SERIAL_ECHOPAIR(" (", dc);
    SERIAL_ECHOPAIR(" steps) E:", target[E_AXIS]);
    SERIAL_ECHOPAIR(" (", de);
    SERIAL_ECHOLNPGM(" steps)");
  //*/

  #if ENABLED(PREVENT_COLD_EXTRUSION) || ENABLED(PREVENT_LENGTHY_EXTRUDE)
    if (de) {
      #if ENABLED(PREVENT_COLD_EXTRUSION)
        if (thermalManager.tooColdToExtrude(extruder)) {
          position[E_AXIS] = target[E_AXIS]; // Behave as if the move really took place, but ignore E part
          #if HAS_POSITION_FLOAT
            position_float[E_AXIS] = target_float[E_AXIS];
          #endif
          de = 0; // no difference
          SERIAL_ECHO_START();
          SERIAL_ECHOLNPGM(MSG_ERR_COLD_EXTRUDE_STOP);
        }
      #endif // PREVENT_COLD_EXTRUSION
      #if ENABLED(PREVENT_LENGTHY_EXTRUDE)
        if (ABS(de * e_factor[extruder]) > (int32_t)axis_steps_per_mm[E_AXIS_N] * (EXTRUDE_MAXLENGTH)) { // It's not important to get max. extrusion length in a precision < 1mm, so save some cycles and cast to int
          position[E_AXIS] = target[E_AXIS]; // Behave as if the move really took place, but ignore E part
          #if HAS_POSITION_FLOAT
            position_float[E_AXIS] = target_float[E_AXIS];
          #endif
          de = 0; // no difference
          SERIAL_ECHO_START();
          SERIAL_ECHOLNPGM(MSG_ERR_LONG_EXTRUDE_STOP);
        }
      #endif // PREVENT_LENGTHY_EXTRUDE
    }
  #endif // PREVENT_COLD_EXTRUSION || PREVENT_LENGTHY_EXTRUDE

  // Compute direction bit-mask for this block
  uint8_t dm = 0;
  #if CORE_IS_XY
    if (da < 0) SBI(dm, X_HEAD);                // Save the real Extruder (head) direction in X Axis
    if (db < 0) SBI(dm, Y_HEAD);                // ...and Y
    if (dc < 0) SBI(dm, Z_AXIS);
    if (da + db < 0) SBI(dm, A_AXIS);           // Motor A direction
    if (CORESIGN(da - db) < 0) SBI(dm, B_AXIS); // Motor B direction
  #elif CORE_IS_XZ
    if (da < 0) SBI(dm, X_HEAD);                // Save the real Extruder (head) direction in X Axis
    if (db < 0) SBI(dm, Y_AXIS);
    if (dc < 0) SBI(dm, Z_HEAD);                // ...and Z
    if (da + dc < 0) SBI(dm, A_AXIS);           // Motor A direction
    if (CORESIGN(da - dc) < 0) SBI(dm, C_AXIS); // Motor C direction
  #elif CORE_IS_YZ
    if (da < 0) SBI(dm, X_AXIS);
    if (db < 0) SBI(dm, Y_HEAD);                // Save the real Extruder (head) direction in Y Axis
    if (dc < 0) SBI(dm, Z_HEAD);                // ...and Z
    if (db + dc < 0) SBI(dm, B_AXIS);           // Motor B direction
    if (CORESIGN(db - dc) < 0) SBI(dm, C_AXIS); // Motor C direction
  #else
    if (da < 0) SBI(dm, X_AXIS);
    if (db < 0) SBI(dm, Y_AXIS);
    if (dc < 0) SBI(dm, Z_AXIS);
  #endif
  if (de < 0) SBI(dm, E_AXIS);

  const float esteps_float = de * e_factor[extruder];
  const uint32_t esteps = ABS(esteps_float) + 0.5;

  // Clear all flags, including the "busy" bit
  block->flag = 0x00;

  // Set direction bits
  block->direction_bits = dm;

  // Number of steps for each axis
  // See http://www.corexy.com/theory.html
  #if CORE_IS_XY
    block->steps[A_AXIS] = ABS(da + db);
    block->steps[B_AXIS] = ABS(da - db);
    block->steps[Z_AXIS] = ABS(dc);
  #elif CORE_IS_XZ
    block->steps[A_AXIS] = ABS(da + dc);
    block->steps[Y_AXIS] = ABS(db);
    block->steps[C_AXIS] = ABS(da - dc);
  #elif CORE_IS_YZ
    block->steps[X_AXIS] = ABS(da);
    block->steps[B_AXIS] = ABS(db + dc);
    block->steps[C_AXIS] = ABS(db - dc);
  #elif IS_SCARA
    block->steps[A_AXIS] = ABS(da);
    block->steps[B_AXIS] = ABS(db);
    block->steps[Z_AXIS] = ABS(dc);
  #else
    // default non-h-bot planning
    block->steps[A_AXIS] = ABS(da);
    block->steps[B_AXIS] = ABS(db);
    block->steps[C_AXIS] = ABS(dc);
  #endif

  block->steps[E_AXIS] = esteps;
  block->step_event_count = MAX4(block->steps[A_AXIS], block->steps[B_AXIS], block->steps[C_AXIS], esteps);

  // Bail if this is a zero-length block
  if (block->step_event_count < MIN_STEPS_PER_SEGMENT) return false;

  // For a mixing extruder, get a magnified step_event_count for each
  #if ENABLED(MIXING_EXTRUDER)
    for (uint8_t i = 0; i < MIXING_STEPPERS; i++)
      block->mix_event_count[i] = mixing_factor[i] * block->step_event_count;
  #endif

  #if FAN_COUNT > 0
    for (uint8_t i = 0; i < FAN_COUNT; i++) block->fan_speed[i] = fanSpeeds[i];
  #endif

  #if ENABLED(BARICUDA)
    block->valve_pressure = baricuda_valve_pressure;
    block->e_to_p_pressure = baricuda_e_to_p_pressure;
  #endif

  block->active_extruder = extruder;

  #if ENABLED(AUTO_POWER_CONTROL)
    if (block->steps[X_AXIS] || block->steps[Y_AXIS] || block->steps[Z_AXIS])
      powerManager.power_on();
  #endif

  // Enable active axes
  #if CORE_IS_XY
    if (block->steps[A_AXIS] || block->steps[B_AXIS]) {
      enable_X();
      enable_Y();
    }
    #if DISABLED(Z_LATE_ENABLE)
      if (block->steps[Z_AXIS]) enable_Z();
    #endif
  #elif CORE_IS_XZ
    if (block->steps[A_AXIS] || block->steps[C_AXIS]) {
      enable_X();
      enable_Z();
    }
    if (block->steps[Y_AXIS]) enable_Y();
  #elif CORE_IS_YZ
    if (block->steps[B_AXIS] || block->steps[C_AXIS]) {
      enable_Y();
      enable_Z();
    }
    if (block->steps[X_AXIS]) enable_X();
  #else
    if (block->steps[X_AXIS]) enable_X();
    if (block->steps[Y_AXIS]) enable_Y();
    #if DISABLED(Z_LATE_ENABLE)
      if (block->steps[Z_AXIS]) enable_Z();
    #endif
  #endif

  // Enable extruder(s)
  if (esteps) {
    #if ENABLED(AUTO_POWER_CONTROL)
      powerManager.power_on();
    #endif

    #if ENABLED(DISABLE_INACTIVE_EXTRUDER) // Enable only the selected extruder

      #define DISABLE_IDLE_E(N) if (!g_uc_extruder_last_move[N]) disable_E##N();

      for (uint8_t i = 0; i < EXTRUDERS; i++)
        if (g_uc_extruder_last_move[i] > 0) g_uc_extruder_last_move[i]--;

      switch (extruder) {
        case 0:
          #if EXTRUDERS > 1
            DISABLE_IDLE_E(1);
            #if EXTRUDERS > 2
              DISABLE_IDLE_E(2);
              #if EXTRUDERS > 3
                DISABLE_IDLE_E(3);
                #if EXTRUDERS > 4
                  DISABLE_IDLE_E(4);
                #endif // EXTRUDERS > 4
              #endif // EXTRUDERS > 3
            #endif // EXTRUDERS > 2
          #endif // EXTRUDERS > 1
          enable_E0();
          g_uc_extruder_last_move[0] = (BLOCK_BUFFER_SIZE) * 2;
          #if ENABLED(DUAL_X_CARRIAGE) || ENABLED(DUAL_NOZZLE_DUPLICATION_MODE)
            if (extruder_duplication_enabled) {
              enable_E1();
              g_uc_extruder_last_move[1] = (BLOCK_BUFFER_SIZE) * 2;
            }
          #endif
        break;
        #if EXTRUDERS > 1
          case 1:
            DISABLE_IDLE_E(0);
            #if EXTRUDERS > 2
              DISABLE_IDLE_E(2);
              #if EXTRUDERS > 3
                DISABLE_IDLE_E(3);
                #if EXTRUDERS > 4
                  DISABLE_IDLE_E(4);
                #endif // EXTRUDERS > 4
              #endif // EXTRUDERS > 3
            #endif // EXTRUDERS > 2
            enable_E1();
            g_uc_extruder_last_move[1] = (BLOCK_BUFFER_SIZE) * 2;
          break;
          #if EXTRUDERS > 2
            case 2:
              DISABLE_IDLE_E(0);
              DISABLE_IDLE_E(1);
              #if EXTRUDERS > 3
                DISABLE_IDLE_E(3);
                #if EXTRUDERS > 4
                  DISABLE_IDLE_E(4);
                #endif
              #endif
              enable_E2();
              g_uc_extruder_last_move[2] = (BLOCK_BUFFER_SIZE) * 2;
            break;
            #if EXTRUDERS > 3
              case 3:
                DISABLE_IDLE_E(0);
                DISABLE_IDLE_E(1);
                DISABLE_IDLE_E(2);
                #if EXTRUDERS > 4
                  DISABLE_IDLE_E(4);
                #endif
                enable_E3();
                g_uc_extruder_last_move[3] = (BLOCK_BUFFER_SIZE) * 2;
              break;
              #if EXTRUDERS > 4
                case 4:
                  DISABLE_IDLE_E(0);
                  DISABLE_IDLE_E(1);
                  DISABLE_IDLE_E(2);
                  DISABLE_IDLE_E(3);
                  enable_E4();
                  g_uc_extruder_last_move[4] = (BLOCK_BUFFER_SIZE) * 2;
                break;
              #endif // EXTRUDERS > 4
            #endif // EXTRUDERS > 3
          #endif // EXTRUDERS > 2
        #endif // EXTRUDERS > 1
      }
    #else
      enable_E0();
      enable_E1();
      enable_E2();
      enable_E3();
      enable_E4();
    #endif
  }

  if (esteps)
    NOLESS(fr_mm_s, min_feedrate_mm_s);
  else
    NOLESS(fr_mm_s, min_travel_feedrate_mm_s);

  /**
   * This part of the code calculates the total length of the movement.
   * For cartesian bots, the X_AXIS is the real X movement and same for Y_AXIS.
   * But for corexy bots, that is not true. The "X_AXIS" and "Y_AXIS" motors (that should be named to A_AXIS
   * and B_AXIS) cannot be used for X and Y length, because A=X+Y and B=X-Y.
   * So we need to create other 2 "AXIS", named X_HEAD and Y_HEAD, meaning the real displacement of the Head.
   * Having the real displacement of the head, we can calculate the total movement length and apply the desired speed.
   */
  #if IS_CORE
    float delta_mm[Z_HEAD + 1];
    #if CORE_IS_XY
      delta_mm[X_HEAD] = da * steps_to_mm[A_AXIS];
      delta_mm[Y_HEAD] = db * steps_to_mm[B_AXIS];
      delta_mm[Z_AXIS] = dc * steps_to_mm[Z_AXIS];
      delta_mm[A_AXIS] = (da + db) * steps_to_mm[A_AXIS];
      delta_mm[B_AXIS] = CORESIGN(da - db) * steps_to_mm[B_AXIS];
    #elif CORE_IS_XZ
      delta_mm[X_HEAD] = da * steps_to_mm[A_AXIS];
      delta_mm[Y_AXIS] = db * steps_to_mm[Y_AXIS];
      delta_mm[Z_HEAD] = dc * steps_to_mm[C_AXIS];
      delta_mm[A_AXIS] = (da + dc) * steps_to_mm[A_AXIS];
      delta_mm[C_AXIS] = CORESIGN(da - dc) * steps_to_mm[C_AXIS];
    #elif CORE_IS_YZ
      delta_mm[X_AXIS] = da * steps_to_mm[X_AXIS];
      delta_mm[Y_HEAD] = db * steps_to_mm[B_AXIS];
      delta_mm[Z_HEAD] = dc * steps_to_mm[C_AXIS];
      delta_mm[B_AXIS] = (db + dc) * steps_to_mm[B_AXIS];
      delta_mm[C_AXIS] = CORESIGN(db - dc) * steps_to_mm[C_AXIS];
    #endif
  #else
    float delta_mm[ABCE];
    delta_mm[A_AXIS] = da * steps_to_mm[A_AXIS];
    delta_mm[B_AXIS] = db * steps_to_mm[B_AXIS];
    delta_mm[C_AXIS] = dc * steps_to_mm[C_AXIS];
  #endif
  delta_mm[E_AXIS] = esteps_float * steps_to_mm[E_AXIS_N];

  if (block->steps[A_AXIS] < MIN_STEPS_PER_SEGMENT && block->steps[B_AXIS] < MIN_STEPS_PER_SEGMENT && block->steps[C_AXIS] < MIN_STEPS_PER_SEGMENT) {
    block->millimeters = ABS(delta_mm[E_AXIS]);
  }
  else if (!millimeters) {
    block->millimeters = SQRT(
      #if CORE_IS_XY
        sq(delta_mm[X_HEAD]) + sq(delta_mm[Y_HEAD]) + sq(delta_mm[Z_AXIS])
      #elif CORE_IS_XZ
        sq(delta_mm[X_HEAD]) + sq(delta_mm[Y_AXIS]) + sq(delta_mm[Z_HEAD])
      #elif CORE_IS_YZ
        sq(delta_mm[X_AXIS]) + sq(delta_mm[Y_HEAD]) + sq(delta_mm[Z_HEAD])
      #else
        sq(delta_mm[X_AXIS]) + sq(delta_mm[Y_AXIS]) + sq(delta_mm[Z_AXIS])
      #endif
    );
  }
  else
    block->millimeters = millimeters;

  const float inverse_millimeters = 1.0 / block->millimeters;  // Inverse millimeters to remove multiple divides

  // Calculate inverse time for this move. No divide by zero due to previous checks.
  // Example: At 120mm/s a 60mm move takes 0.5s. So this will give 2.0.
  float inverse_secs = fr_mm_s * inverse_millimeters;

  const uint8_t moves_queued = movesplanned();

  // Slow down when the buffer starts to empty, rather than wait at the corner for a buffer refill
  #if ENABLED(SLOWDOWN) || ENABLED(ULTRA_LCD) || defined(XY_FREQUENCY_LIMIT)
    // Segment time im micro seconds
    uint32_t segment_time_us = LROUND(1000000.0 / inverse_secs);
  #endif

  #if ENABLED(SLOWDOWN)
    if (WITHIN(moves_queued, 2, (BLOCK_BUFFER_SIZE) / 2 - 1)) {
      if (segment_time_us < min_segment_time_us) {
        // buffer is draining, add extra time.  The amount of time added increases if the buffer is still emptied more.
        const uint32_t nst = segment_time_us + LROUND(2 * (min_segment_time_us - segment_time_us) / moves_queued);
        inverse_secs = 1000000.0 / nst;
        #if defined(XY_FREQUENCY_LIMIT) || ENABLED(ULTRA_LCD)
          segment_time_us = nst;
        #endif
      }
    }
  #endif

  #if ENABLED(ULTRA_LCD)
    // Protect the access to the position.
    const bool was_enabled = STEPPER_ISR_ENABLED();
    if (was_enabled) DISABLE_STEPPER_DRIVER_INTERRUPT();

    block_buffer_runtime_us += segment_time_us;

    if (was_enabled) ENABLE_STEPPER_DRIVER_INTERRUPT();
  #endif

  block->nominal_speed_sqr = sq(block->millimeters * inverse_secs);   //   (mm/sec)^2 Always > 0
  block->nominal_rate = CEIL(block->step_event_count * inverse_secs); // (step/sec) Always > 0

  #if ENABLED(FILAMENT_WIDTH_SENSOR)
    static float filwidth_e_count = 0, filwidth_delay_dist = 0;

    //FMM update ring buffer used for delay with filament measurements
    if (extruder == FILAMENT_SENSOR_EXTRUDER_NUM && filwidth_delay_index[1] >= 0) {  //only for extruder with filament sensor and if ring buffer is initialized

      constexpr int MMD_CM = MAX_MEASUREMENT_DELAY + 1, MMD_MM = MMD_CM * 10;

      // increment counters with next move in e axis
      filwidth_e_count += delta_mm[E_AXIS];
      filwidth_delay_dist += delta_mm[E_AXIS];

      // Only get new measurements on forward E movement
      if (!UNEAR_ZERO(filwidth_e_count)) {

        // Loop the delay distance counter (modulus by the mm length)
        while (filwidth_delay_dist >= MMD_MM) filwidth_delay_dist -= MMD_MM;

        // Convert into an index into the measurement array
        filwidth_delay_index[0] = int8_t(filwidth_delay_dist * 0.1);

        // If the index has changed (must have gone forward)...
        if (filwidth_delay_index[0] != filwidth_delay_index[1]) {
          filwidth_e_count = 0; // Reset the E movement counter
          const int8_t meas_sample = thermalManager.widthFil_to_size_ratio();
          do {
            filwidth_delay_index[1] = (filwidth_delay_index[1] + 1) % MMD_CM; // The next unused slot
            measurement_delay[filwidth_delay_index[1]] = meas_sample;         // Store the measurement
          } while (filwidth_delay_index[0] != filwidth_delay_index[1]);       // More slots to fill?
        }
      }
    }
  #endif

  // Calculate and limit speed in mm/sec for each axis
  float current_speed[NUM_AXIS], speed_factor = 1.0; // factor <1 decreases speed
  LOOP_XYZE(i) {
    const float cs = ABS((current_speed[i] = delta_mm[i] * inverse_secs));
    #if ENABLED(DISTINCT_E_FACTORS)
      if (i == E_AXIS) i += extruder;
    #endif
    if (cs > max_feedrate_mm_s[i]) NOMORE(speed_factor, max_feedrate_mm_s[i] / cs);
  }

  // Max segment time in µs.
  #ifdef XY_FREQUENCY_LIMIT

    // Check and limit the xy direction change frequency
    const unsigned char direction_change = block->direction_bits ^ old_direction_bits;
    old_direction_bits = block->direction_bits;
    segment_time_us = LROUND((float)segment_time_us / speed_factor);

    uint32_t xs0 = axis_segment_time_us[X_AXIS][0],
             xs1 = axis_segment_time_us[X_AXIS][1],
             xs2 = axis_segment_time_us[X_AXIS][2],
             ys0 = axis_segment_time_us[Y_AXIS][0],
             ys1 = axis_segment_time_us[Y_AXIS][1],
             ys2 = axis_segment_time_us[Y_AXIS][2];

    if (TEST(direction_change, X_AXIS)) {
      xs2 = axis_segment_time_us[X_AXIS][2] = xs1;
      xs1 = axis_segment_time_us[X_AXIS][1] = xs0;
      xs0 = 0;
    }
    xs0 = axis_segment_time_us[X_AXIS][0] = xs0 + segment_time_us;

    if (TEST(direction_change, Y_AXIS)) {
      ys2 = axis_segment_time_us[Y_AXIS][2] = axis_segment_time_us[Y_AXIS][1];
      ys1 = axis_segment_time_us[Y_AXIS][1] = axis_segment_time_us[Y_AXIS][0];
      ys0 = 0;
    }
    ys0 = axis_segment_time_us[Y_AXIS][0] = ys0 + segment_time_us;

    const uint32_t max_x_segment_time = MAX3(xs0, xs1, xs2),
                   max_y_segment_time = MAX3(ys0, ys1, ys2),
                   min_xy_segment_time = MIN(max_x_segment_time, max_y_segment_time);
    if (min_xy_segment_time < MAX_FREQ_TIME_US) {
      const float low_sf = speed_factor * min_xy_segment_time / (MAX_FREQ_TIME_US);
      NOMORE(speed_factor, low_sf);
    }
  #endif // XY_FREQUENCY_LIMIT

  // Correct the speed
  if (speed_factor < 1.0) {
    LOOP_XYZE(i) current_speed[i] *= speed_factor;
    block->nominal_rate *= speed_factor;
    block->nominal_speed_sqr = block->nominal_speed_sqr * sq(speed_factor);
  }

  // Compute and limit the acceleration rate for the trapezoid generator.
  const float steps_per_mm = block->step_event_count * inverse_millimeters;
  uint32_t accel;
  if (!block->steps[A_AXIS] && !block->steps[B_AXIS] && !block->steps[C_AXIS]) {
    // convert to: acceleration steps/sec^2
    accel = CEIL(retract_acceleration * steps_per_mm);
    #if ENABLED(LIN_ADVANCE)
      block->use_advance_lead = false;
    #endif
  }
  else {
    #define LIMIT_ACCEL_LONG(AXIS,INDX) do{ \
      if (block->steps[AXIS] && max_acceleration_steps_per_s2[AXIS+INDX] < accel) { \
        const uint32_t comp = max_acceleration_steps_per_s2[AXIS+INDX] * block->step_event_count; \
        if (accel * block->steps[AXIS] > comp) accel = comp / block->steps[AXIS]; \
      } \
    }while(0)

    #define LIMIT_ACCEL_FLOAT(AXIS,INDX) do{ \
      if (block->steps[AXIS] && max_acceleration_steps_per_s2[AXIS+INDX] < accel) { \
        const float comp = (float)max_acceleration_steps_per_s2[AXIS+INDX] * (float)block->step_event_count; \
        if ((float)accel * (float)block->steps[AXIS] > comp) accel = comp / (float)block->steps[AXIS]; \
      } \
    }while(0)

    // Start with print or travel acceleration
    accel = CEIL((esteps ? acceleration : travel_acceleration) * steps_per_mm);

    #if ENABLED(LIN_ADVANCE)
      /**
       *
       * Use LIN_ADVANCE for blocks if all these are true:
       *
       * esteps             : This is a print move, because we checked for A, B, C steps before.
       *
       * extruder_advance_K : There is an advance factor set.
       *
       * de > 0             : Extruder is running forward (e.g., for "Wipe while retracting" (Slic3r) or "Combing" (Cura) moves)
       */
      block->use_advance_lead =  esteps
                              && extruder_advance_K
                              && de > 0;

      if (block->use_advance_lead) {
        block->e_D_ratio = (target_float[E_AXIS] - position_float[E_AXIS]) /
          #if IS_KINEMATIC
            block->millimeters
          #else
            SQRT(sq(target_float[X_AXIS] - position_float[X_AXIS])
               + sq(target_float[Y_AXIS] - position_float[Y_AXIS])
               + sq(target_float[Z_AXIS] - position_float[Z_AXIS]))
          #endif
        ;

        // Check for unusual high e_D ratio to detect if a retract move was combined with the last print move due to min. steps per segment. Never execute this with advance!
        // This assumes no one will use a retract length of 0mm < retr_length < ~0.2mm and no one will print 100mm wide lines using 3mm filament or 35mm wide lines using 1.75mm filament.
        if (block->e_D_ratio > 3.0)
          block->use_advance_lead = false;
        else {
          const uint32_t max_accel_steps_per_s2 = max_jerk[E_AXIS] / (extruder_advance_K * block->e_D_ratio) * steps_per_mm;
          #if ENABLED(LA_DEBUG)
            if (accel > max_accel_steps_per_s2)
              SERIAL_ECHOLNPGM("Acceleration limited.");
          #endif
          NOMORE(accel, max_accel_steps_per_s2);
        }
      }
    #endif

    #if ENABLED(DISTINCT_E_FACTORS)
      #define ACCEL_IDX extruder
    #else
      #define ACCEL_IDX 0
    #endif

    // Limit acceleration per axis
    if (block->step_event_count <= cutoff_long) {
      LIMIT_ACCEL_LONG(A_AXIS, 0);
      LIMIT_ACCEL_LONG(B_AXIS, 0);
      LIMIT_ACCEL_LONG(C_AXIS, 0);
      LIMIT_ACCEL_LONG(E_AXIS, ACCEL_IDX);
    }
    else {
      LIMIT_ACCEL_FLOAT(A_AXIS, 0);
      LIMIT_ACCEL_FLOAT(B_AXIS, 0);
      LIMIT_ACCEL_FLOAT(C_AXIS, 0);
      LIMIT_ACCEL_FLOAT(E_AXIS, ACCEL_IDX);
    }
  }
  block->acceleration_steps_per_s2 = accel;
  block->acceleration = accel / steps_per_mm;
  #if DISABLED(BEZIER_JERK_CONTROL)
    block->acceleration_rate = (uint32_t)(accel * (4096.0 * 4096.0 / (HAL_STEPPER_TIMER_RATE)));
  #endif
  #if ENABLED(LIN_ADVANCE)
    if (block->use_advance_lead) {
      block->advance_speed = (HAL_STEPPER_TIMER_RATE) / (extruder_advance_K * block->e_D_ratio * block->acceleration * axis_steps_per_mm[E_AXIS_N]);
      #if ENABLED(LA_DEBUG)
        if (extruder_advance_K * block->e_D_ratio * block->acceleration * 2 < SQRT(block->nominal_speed_sqr) * block->e_D_ratio)
          SERIAL_ECHOLNPGM("More than 2 steps per eISR loop executed.");
        if (block->advance_speed < 200)
          SERIAL_ECHOLNPGM("eISR running at > 10kHz.");
      #endif
    }
  #endif

  float vmax_junction_sqr; // Initial limit on the segment entry velocity (mm/s)^2

  #if ENABLED(JUNCTION_DEVIATION)

    /**
     * Compute maximum allowable entry speed at junction by centripetal acceleration approximation.
     * Let a circle be tangent to both previous and current path line segments, where the junction
     * deviation is defined as the distance from the junction to the closest edge of the circle,
     * colinear with the circle center. The circular segment joining the two paths represents the
     * path of centripetal acceleration. Solve for max velocity based on max acceleration about the
     * radius of the circle, defined indirectly by junction deviation. This may be also viewed as
     * path width or max_jerk in the previous Grbl version. This approach does not actually deviate
     * from path, but used as a robust way to compute cornering speeds, as it takes into account the
     * nonlinearities of both the junction angle and junction velocity.
     *
     * NOTE: If the junction deviation value is finite, Grbl executes the motions in an exact path
     * mode (G61). If the junction deviation value is zero, Grbl will execute the motion in an exact
     * stop mode (G61.1) manner. In the future, if continuous mode (G64) is desired, the math here
     * is exactly the same. Instead of motioning all the way to junction point, the machine will
     * just follow the arc circle defined here. The Arduino doesn't have the CPU cycles to perform
     * a continuous mode path, but ARM-based microcontrollers most certainly do.
     *
     * NOTE: The max junction speed is a fixed value, since machine acceleration limits cannot be
     * changed dynamically during operation nor can the line move geometry. This must be kept in
     * memory in the event of a feedrate override changing the nominal speeds of blocks, which can
     * change the overall maximum entry speed conditions of all blocks.
     *
     * #######
     * https://github.com/MarlinFirmware/Marlin/issues/10341#issuecomment-388191754
     *
     * hoffbaked: on May 10 2018 tuned and improved the GRBL algorithm for Marlin:
          Okay! It seems to be working good. I somewhat arbitrarily cut it off at 1mm
          on then on anything with less sides than an octagon. With this, and the
          reverse pass actually recalculating things, a corner acceleration value
          of 1000 junction deviation of .05 are pretty reasonable. If the cycles
          can be spared, a better acos could be used. For all I know, it may be
          already calculated in a different place. */

    // Unit vector of previous path line segment
    static float previous_unit_vec[
      #if ENABLED(JUNCTION_DEVIATION_INCLUDE_E)
        XYZE
      #else
        XYZ
      #endif
    ];

    float unit_vec[] = {
      delta_mm[A_AXIS] * inverse_millimeters,
      delta_mm[B_AXIS] * inverse_millimeters,
      delta_mm[C_AXIS] * inverse_millimeters
      #if ENABLED(JUNCTION_DEVIATION_INCLUDE_E)
        , delta_mm[E_AXIS] * inverse_millimeters
      #endif
    };

    // Skip first block or when previous_nominal_speed is used as a flag for homing and offset cycles.
    if (moves_queued && !UNEAR_ZERO(previous_nominal_speed_sqr)) {
      // Compute cosine of angle between previous and current path. (prev_unit_vec is negative)
      // NOTE: Max junction velocity is computed without sin() or acos() by trig half angle identity.
      float junction_cos_theta = -previous_unit_vec[X_AXIS] * unit_vec[X_AXIS]
                                 -previous_unit_vec[Y_AXIS] * unit_vec[Y_AXIS]
                                 -previous_unit_vec[Z_AXIS] * unit_vec[Z_AXIS]
                                  #if ENABLED(JUNCTION_DEVIATION_INCLUDE_E)
                                    -previous_unit_vec[E_AXIS] * unit_vec[E_AXIS]
                                  #endif
                                ;

      // NOTE: Computed without any expensive trig, sin() or acos(), by trig half angle identity of cos(theta).
      if (junction_cos_theta > 0.999999) {
        // For a 0 degree acute junction, just set minimum junction speed.
        vmax_junction_sqr = sq(MINIMUM_PLANNER_SPEED);
      }
      else {
        NOLESS(junction_cos_theta, -0.999999); // Check for numerical round-off to avoid divide by zero.
        const float sin_theta_d2 = SQRT(0.5 * (1.0 - junction_cos_theta)); // Trig half angle identity. Always positive.

        // TODO: Technically, the acceleration used in calculation needs to be limited by the minimum of the
        // two junctions. However, this shouldn't be a significant problem except in extreme circumstances.
        vmax_junction_sqr = (JUNCTION_ACCELERATION_FACTOR * JUNCTION_DEVIATION_FACTOR * sin_theta_d2) / (1.0 - sin_theta_d2);
        if (block->millimeters < 1.0) {

          // Fast acos approximation, minus the error bar to be safe
          float junction_theta = (RADIANS(-40) * sq(junction_cos_theta) - RADIANS(50)) * junction_cos_theta + RADIANS(90) - 0.18;

          // If angle is greater than 135 degrees (octagon), find speed for approximate arc
          if (junction_theta > RADIANS(135)) {
            const float limit_sqr = block->millimeters / (RADIANS(180) - junction_theta) * JUNCTION_ACCELERATION_FACTOR;
            NOMORE(vmax_junction_sqr, limit_sqr);
          }
        }
      }

      // Get the lowest speed
      vmax_junction_sqr = MIN3(vmax_junction_sqr, block->nominal_speed_sqr, previous_nominal_speed_sqr);
    }
    else // Init entry speed to zero. Assume it starts from rest. Planner will correct this later.
      vmax_junction_sqr = 0.0;

    COPY(previous_unit_vec, unit_vec);

  #else // Classic Jerk Limiting

    /**
     * Adapted from Průša MKS firmware
     * https://github.com/prusa3d/Prusa-Firmware
     *
     * Start with a safe speed (from which the machine may halt to stop immediately).
     */

    // Exit speed limited by a jerk to full halt of a previous last segment
    static float previous_safe_speed;

    const float nominal_speed = SQRT(block->nominal_speed_sqr);
    float safe_speed = nominal_speed;

    uint8_t limited = 0;
    LOOP_XYZE(i) {
      const float jerk = ABS(current_speed[i]), maxj = max_jerk[i];
      if (jerk > maxj) {
        if (limited) {
          const float mjerk = maxj * nominal_speed;
          if (jerk * safe_speed > mjerk) safe_speed = mjerk / jerk;
        }
        else {
          ++limited;
          safe_speed = maxj;
        }
      }
    }

    float vmax_junction;
    if (moves_queued && !UNEAR_ZERO(previous_nominal_speed_sqr)) {
      // Estimate a maximum velocity allowed at a joint of two successive segments.
      // If this maximum velocity allowed is lower than the minimum of the entry / exit safe velocities,
      // then the machine is not coasting anymore and the safe entry / exit velocities shall be used.

      // Factor to multiply the previous / current nominal velocities to get componentwise limited velocities.
      float v_factor = 1;
      limited = 0;

      // The junction velocity will be shared between successive segments. Limit the junction velocity to their minimum.
      // Pick the smaller of the nominal speeds. Higher speed shall not be achieved at the junction during coasting.
      const float previous_nominal_speed = SQRT(previous_nominal_speed_sqr);
      vmax_junction = MIN(nominal_speed, previous_nominal_speed);

      // Now limit the jerk in all axes.
      const float smaller_speed_factor = vmax_junction / previous_nominal_speed;
      LOOP_XYZE(axis) {
        // Limit an axis. We have to differentiate: coasting, reversal of an axis, full stop.
        float v_exit = previous_speed[axis] * smaller_speed_factor,
              v_entry = current_speed[axis];
        if (limited) {
          v_exit *= v_factor;
          v_entry *= v_factor;
        }

        // Calculate jerk depending on whether the axis is coasting in the same direction or reversing.
        const float jerk = (v_exit > v_entry)
            ? //                                  coasting             axis reversal
              ( (v_entry > 0 || v_exit < 0) ? (v_exit - v_entry) : MAX(v_exit, -v_entry) )
            : // v_exit <= v_entry                coasting             axis reversal
              ( (v_entry < 0 || v_exit > 0) ? (v_entry - v_exit) : MAX(-v_exit, v_entry) );

        if (jerk > max_jerk[axis]) {
          v_factor *= max_jerk[axis] / jerk;
          ++limited;
        }
      }
      if (limited) vmax_junction *= v_factor;
      // Now the transition velocity is known, which maximizes the shared exit / entry velocity while
      // respecting the jerk factors, it may be possible, that applying separate safe exit / entry velocities will achieve faster prints.
      const float vmax_junction_threshold = vmax_junction * 0.99f;
      if (previous_safe_speed > vmax_junction_threshold && safe_speed > vmax_junction_threshold)
        vmax_junction = safe_speed;
    }
    else
      vmax_junction = safe_speed;

    previous_safe_speed = safe_speed;
    vmax_junction_sqr = sq(vmax_junction);

  #endif // Classic Jerk Limiting

  // Max entry speed of this block equals the max exit speed of the previous block.
  block->max_entry_speed_sqr = vmax_junction_sqr;

  // Initialize block entry speed. Compute based on deceleration to user-defined MINIMUM_PLANNER_SPEED.
  const float v_allowable_sqr = max_allowable_speed_sqr(-block->acceleration, sq(MINIMUM_PLANNER_SPEED), block->millimeters);

  // If we are trying to add a split block, start with the
  // max. allowed speed to avoid an interrupted first move.
  block->entry_speed_sqr = !split_move ? sq(MINIMUM_PLANNER_SPEED) : MIN(vmax_junction_sqr, v_allowable_sqr);

  // Initialize planner efficiency flags
  // Set flag if block will always reach maximum junction speed regardless of entry/exit speeds.
  // If a block can de/ac-celerate from nominal speed to zero within the length of the block, then
  // the current block and next block junction speeds are guaranteed to always be at their maximum
  // junction speeds in deceleration and acceleration, respectively. This is due to how the current
  // block nominal speed limits both the current and next maximum junction speeds. Hence, in both
  // the reverse and forward planners, the corresponding block junction speed will always be at the
  // the maximum junction speed and may always be ignored for any speed reduction checks.
  block->flag |= block->nominal_speed_sqr <= v_allowable_sqr ? BLOCK_FLAG_RECALCULATE | BLOCK_FLAG_NOMINAL_LENGTH : BLOCK_FLAG_RECALCULATE;

  // Update previous path unit_vector and nominal speed
  COPY(previous_speed, current_speed);
  previous_nominal_speed_sqr = block->nominal_speed_sqr;

  // Update the position
  static_assert(COUNT(target) > 1, "Parameter to _buffer_steps must be (&target)[XYZE]!");
  COPY(position, target);
  #if HAS_POSITION_FLOAT
    COPY(position_float, target_float);
  #endif

  // Movement was accepted
  return true;
} // _populate_block()

/**
 * Planner::buffer_sync_block
 * Add a block to the buffer that just updates the position
 */
void Planner::buffer_sync_block() {
  // Wait for the next available block
  uint8_t next_buffer_head;
  block_t * const block = get_next_free_block(next_buffer_head);

  // Clear block
  memset(block, 0, sizeof(block_t));

  block->flag = BLOCK_FLAG_SYNC_POSITION;

  block->position[A_AXIS] = position[A_AXIS];
  block->position[B_AXIS] = position[B_AXIS];
  block->position[C_AXIS] = position[C_AXIS];
  block->position[E_AXIS] = position[E_AXIS];

  // If this is the first added movement, reload the delay, otherwise, cancel it.
  if (block_buffer_head == block_buffer_tail) {
    // If it was the first queued block, restart the 1st block delivery delay, to
    // give the planner an opportunity to queue more movements and plan them
    // As there are no queued movements, the Stepper ISR will not touch this
    // variable, so there is no risk setting this here (but it MUST be done
    // before the following line!!)
    delay_before_delivering = BLOCK_DELAY_FOR_1ST_MOVE;
  }

  block_buffer_head = next_buffer_head;

  stepper.wake_up();
} // buffer_sync_block()

/**
 * Planner::buffer_segment
 *
 * Add a new linear movement to the buffer in axis units.
 *
 * Leveling and kinematics should be applied ahead of calling this.
 *
 *  a,b,c,e     - target positions in mm and/or degrees
 *  fr_mm_s     - (target) speed of the move
 *  extruder    - target extruder
 *  millimeters - the length of the movement, if known
 */
bool Planner::buffer_segment(const float &a, const float &b, const float &c, const float &e, const float &fr_mm_s, const uint8_t extruder, const float &millimeters/*=0.0*/) {

  // If we are cleaning, do not accept queuing of movements
  if (cleaning_buffer_counter) return false;

  // When changing extruders recalculate steps corresponding to the E position
  #if ENABLED(DISTINCT_E_FACTORS)
    if (last_extruder != extruder && axis_steps_per_mm[E_AXIS_N] != axis_steps_per_mm[E_AXIS + last_extruder]) {
      position[E_AXIS] = LROUND(position[E_AXIS] * axis_steps_per_mm[E_AXIS_N] * steps_to_mm[E_AXIS + last_extruder]);
      last_extruder = extruder;
    }
  #endif

  // The target position of the tool in absolute steps
  // Calculate target position in absolute steps
  const int32_t target[ABCE] = {
    LROUND(a * axis_steps_per_mm[A_AXIS]),
    LROUND(b * axis_steps_per_mm[B_AXIS]),
    LROUND(c * axis_steps_per_mm[C_AXIS]),
    LROUND(e * axis_steps_per_mm[E_AXIS_N])
  };

  #if HAS_POSITION_FLOAT
    const float target_float[XYZE] = { a, b, c, e };
  #endif

  // DRYRUN prevents E moves from taking place
  if (DEBUGGING(DRYRUN)) {
    position[E_AXIS] = target[E_AXIS];
    #if HAS_POSITION_FLOAT
      position_float[E_AXIS] = e;
    #endif
  }

  /* <-- add a slash to enable
    SERIAL_ECHOPAIR("  buffer_segment FR:", fr_mm_s);
    #if IS_KINEMATIC
      SERIAL_ECHOPAIR(" A:", a);
      SERIAL_ECHOPAIR(" (", position[A_AXIS]);
      SERIAL_ECHOPAIR("->", target[A_AXIS]);
      SERIAL_ECHOPAIR(") B:", b);
    #else
      SERIAL_ECHOPAIR(" X:", a);
      SERIAL_ECHOPAIR(" (", position[X_AXIS]);
      SERIAL_ECHOPAIR("->", target[X_AXIS]);
      SERIAL_ECHOPAIR(") Y:", b);
    #endif
    SERIAL_ECHOPAIR(" (", position[Y_AXIS]);
    SERIAL_ECHOPAIR("->", target[Y_AXIS]);
    #if ENABLED(DELTA)
      SERIAL_ECHOPAIR(") C:", c);
    #else
      SERIAL_ECHOPAIR(") Z:", c);
    #endif
    SERIAL_ECHOPAIR(" (", position[Z_AXIS]);
    SERIAL_ECHOPAIR("->", target[Z_AXIS]);
    SERIAL_ECHOPAIR(") E:", e);
    SERIAL_ECHOPAIR(" (", position[E_AXIS]);
    SERIAL_ECHOPAIR("->", target[E_AXIS]);
    SERIAL_ECHOLNPGM(")");
  //*/

  // Queue the movement
    if (
    !_buffer_steps(target
      #if HAS_POSITION_FLOAT
        , target_float
      #endif
      , fr_mm_s, extruder, millimeters
    )
  ) return false;

  stepper.wake_up();
  return true;
} // buffer_segment()

/**
 * Directly set the planner XYZ position (and stepper positions)
 * converting mm (or angles for SCARA) into steps.
 *
 * On CORE machines stepper ABC will be translated from the given XYZ.
 */

void Planner::_set_position_mm(const float &a, const float &b, const float &c, const float &e) {
  #if ENABLED(DISTINCT_E_FACTORS)
    #define _EINDEX (E_AXIS + active_extruder)
    last_extruder = active_extruder;
  #else
    #define _EINDEX E_AXIS
  #endif
  position[A_AXIS] = LROUND(a * axis_steps_per_mm[A_AXIS]),
  position[B_AXIS] = LROUND(b * axis_steps_per_mm[B_AXIS]),
  position[C_AXIS] = LROUND(c * axis_steps_per_mm[C_AXIS]),
  position[E_AXIS] = LROUND(e * axis_steps_per_mm[_EINDEX]);
  #if HAS_POSITION_FLOAT
    position_float[A_AXIS] = a;
    position_float[B_AXIS] = b;
    position_float[C_AXIS] = c;
    position_float[E_AXIS] = e;
  #endif
  previous_nominal_speed_sqr = 0.0; // Resets planner junction speeds. Assumes start from rest.
  ZERO(previous_speed);
  buffer_sync_block();
}

void Planner::set_position_mm_kinematic(const float (&cart)[XYZE]) {
  #if PLANNER_LEVELING
    float raw[XYZ] = { cart[X_AXIS], cart[Y_AXIS], cart[Z_AXIS] };
    apply_leveling(raw);
  #else
    const float (&raw)[XYZE] = cart;
  #endif
  #if IS_KINEMATIC
    inverse_kinematics(raw);
    _set_position_mm(delta[A_AXIS], delta[B_AXIS], delta[C_AXIS], cart[E_AXIS]);
  #else
    _set_position_mm(raw[X_AXIS], raw[Y_AXIS], raw[Z_AXIS], cart[E_AXIS]);
  #endif
}

/**
 * Setters for planner position (also setting stepper position).
 */
void Planner::set_position_mm(const AxisEnum axis, const float &v) {
  #if ENABLED(DISTINCT_E_FACTORS)
    const uint8_t axis_index = axis + (axis == E_AXIS ? active_extruder : 0);
    last_extruder = active_extruder;
  #else
    const uint8_t axis_index = axis;
  #endif
  position[axis] = LROUND(v * axis_steps_per_mm[axis_index]);
  #if HAS_POSITION_FLOAT
    position_float[axis] = v;
  #endif
  previous_speed[axis] = 0.0;
  buffer_sync_block();
}

// Recalculate the steps/s^2 acceleration rates, based on the mm/s^2
void Planner::reset_acceleration_rates() {
  #if ENABLED(DISTINCT_E_FACTORS)
    #define AXIS_CONDITION (i < E_AXIS || i == E_AXIS + active_extruder)
  #else
    #define AXIS_CONDITION true
  #endif
  uint32_t highest_rate = 1;
  LOOP_XYZE_N(i) {
    max_acceleration_steps_per_s2[i] = max_acceleration_mm_per_s2[i] * axis_steps_per_mm[i];
    if (AXIS_CONDITION) NOLESS(highest_rate, max_acceleration_steps_per_s2[i]);
  }
  cutoff_long = 4294967295UL / highest_rate; // 0xFFFFFFFFUL
}

// Recalculate position, steps_to_mm if axis_steps_per_mm changes!
void Planner::refresh_positioning() {
  LOOP_XYZE_N(i) steps_to_mm[i] = 1.0 / axis_steps_per_mm[i];
  set_position_mm_kinematic(current_position);
  reset_acceleration_rates();
}

#if ENABLED(AUTOTEMP)

  void Planner::autotemp_M104_M109() {
    if ((autotemp_enabled = parser.seen('F'))) autotemp_factor = parser.value_float();
    if (parser.seen('S')) autotemp_min = parser.value_celsius();
    if (parser.seen('B')) autotemp_max = parser.value_celsius();
  }

#endif