path: root/src/Movement/DriveMovement.cpp

/*
 * DriveMovement.cpp
 *
 *  Created on: 17 Jan 2015
 *      Author: David
 */

#include "DriveMovement.h"
#include "DDA.h"
#include "Move.h"
#include "StepTimer.h"
#include <Platform/RepRap.h>
#include <Math/Isqrt.h>
#include "Kinematics/LinearDeltaKinematics.h"

// Static members

DriveMovement *DriveMovement::freeList = nullptr;
unsigned int DriveMovement::numCreated = 0;

void DriveMovement::InitialAllocate(unsigned int num) noexcept
{
	while (num > numCreated)
	{
		freeList = new DriveMovement(freeList);
		++numCreated;
	}
}

// Allocate a DM, from the freelist if possible, else create a new one
DriveMovement *DriveMovement::Allocate(size_t p_drive, DMState st) noexcept
{
	DriveMovement * dm = freeList;
	if (dm != nullptr)
	{
		freeList = dm->nextDM;
		dm->nextDM = nullptr;
	}
	else
	{
		dm = new DriveMovement(nullptr);
		++numCreated;
	}
	dm->drive = (uint8_t)p_drive;
	dm->state = st;
	return dm;
}

// Constructors
DriveMovement::DriveMovement(DriveMovement *next) noexcept : nextDM(next)
{
}

// Non static members

void DriveMovement::DebugPrint() const noexcept
{
	const char c = (drive < reprap.GetGCodes().GetTotalAxes()) ? reprap.GetGCodes().GetAxisLetters()[drive] : (char)('0' + LogicalDriveToExtruder(drive));
	if (state != DMState::idle)
	{
		debugPrintf("DM%c%s dir=%c steps=%" PRIu32 " next=%" PRIu32 " rev=%" PRIu32 " interval=%" PRIu32 " ssl=%" PRIu32 " A=%.4e B=%.4e C=%.4e dsf=%.4e tsf=%.1f",
						c, (state == DMState::stepError) ? " ERR:" : ":", (direction) ? 'F' : 'B', totalSteps, nextStep, reverseStartStep, stepInterval, segmentStepLimit,
							(double)pA, (double)pB, (double)pC, (double)distanceSoFar, (double)timeSoFar);
		if (isDelta)
		{
			debugPrintf(" hmz0s=%.4e minusAaPlusBbTimesS=%.4e dSquaredMinusAsquaredMinusBsquared=%.4e drev=%.4e\n",
							(double)mp.delta.fHmz0s, (double)mp.delta.fMinusAaPlusBbTimesS, (double)mp.delta.fDSquaredMinusAsquaredMinusBsquaredTimesSsquared, (double)mp.delta.reverseStartDistance);
		}
		else if (isExtruder)
		{
			debugPrintf(" pa=%" PRIu32 " eed=%.4e ebf=%.4e\n", (uint32_t)mp.cart.pressureAdvanceK, (double)mp.cart.extraExtrusionDistance, (double)mp.cart.extrusionBroughtForwards);
		}
		else
		{
			debugPrintf("\n");
		}
	}
	else
	{
		debugPrintf("DM%c: not moving\n", c);
	}
}

// This is called when currentSegment has just been changed to a new segment. Return true if there is a new segment to execute.
bool DriveMovement::NewCartesianSegment() noexcept
{
	while (true)
	{
		if (currentSegment == nullptr)
		{
			return false;
		}

		// Work out the movement limit in steps
		pC = currentSegment->CalcC(mp.cart.effectiveMmPerStep);
		if (currentSegment->IsLinear())
		{
			// Set up pB, pC such that for forward motion, time = pB + pC * stepNumber
			pB = currentSegment->CalcLinearB(distanceSoFar, timeSoFar);
			state = DMState::cartLinear;
		}
		else
		{
			// Set up pA, pB, pC such that for forward motion, time = pB + sqrt(pA + pC * stepNumber)
			pA = currentSegment->CalcNonlinearA(distanceSoFar);
			pB = currentSegment->CalcNonlinearB(timeSoFar);
			state = (currentSegment->IsAccelerating()) ? DMState::cartAccel : DMState::cartDecelNoReverse;
		}

		distanceSoFar += currentSegment->GetSegmentLength();
		timeSoFar += currentSegment->GetSegmentTime();

		segmentStepLimit = (currentSegment->GetNext() == nullptr) ? totalSteps + 1 : (uint32_t)(distanceSoFar * mp.cart.effectiveStepsPerMm) + 1;

		if (nextStep < segmentStepLimit)
		{
			return true;
		}

		currentSegment = currentSegment->GetNext();						// skip this segment
	}
}

#if SUPPORT_LINEAR_DELTA

// This is called when currentSegment has just been changed to a new segment. Return true if there is a new segment to execute.
bool DriveMovement::NewDeltaSegment(const DDA& dda) noexcept
{
	while (true)
	{
		if (currentSegment == nullptr)
		{
			return false;
		}

		const float stepsPerMm = reprap.GetPlatform().DriveStepsPerUnit(drive);
		pC = currentSegment->GetC()/stepsPerMm;		//TODO store the reciprocal to avoid the division
		if (currentSegment->IsLinear())
		{
			// Set up pB, pC such that for forward motion, time = pB + pC * (distanceMoved * steps/mm)
			pB = currentSegment->CalcLinearB(distanceSoFar, timeSoFar);
		}
		else
		{
			// Set up pA, pB, pC such that for forward motion, time = pB + sqrt(pA + pC * (distanceMoved * steps/mm))
			pA = currentSegment->CalcNonlinearA(distanceSoFar);
			pB = currentSegment->CalcNonlinearB(timeSoFar);
		}

		distanceSoFar += currentSegment->GetSegmentLength();
		timeSoFar += currentSegment->GetSegmentTime();

		// Work out whether we reverse in this segment and the movement limit in steps.
		// First check whether the first step in this segment is the previously-calculated reverse start step, and if so then do the reversal.
		if (nextStep == reverseStartStep)
		{
			direction = false;					// we must have been going up, so now we are going down
			directionChanged = true;
		}

		if (currentSegment->GetNext() == nullptr)
		{
			// This is the last segment, so the phase step limit is the number of total steps, and we can avoid some calculation
			segmentStepLimit = totalSteps + 1;
			state = (reverseStartStep <= totalSteps && nextStep < reverseStartStep) ? DMState::deltaForwardsReversing : DMState::deltaNormal;
		}
		else
		{
			// Work out how many whole steps we have moved up or down at the end of this segment
			const float sDx = distanceSoFar * dda.directionVector[0];
			const float sDy = distanceSoFar * dda.directionVector[1];
			int32_t netStepsAtEnd = (int32_t)floorf(fastSqrtf(mp.delta.fDSquaredMinusAsquaredMinusBsquaredTimesSsquared - fsquare(stepsPerMm) * (sDx * (sDx + mp.delta.fTwoA) + sDy * (sDy + mp.delta.fTwoB)))
												+ (distanceSoFar * dda.directionVector[2] - mp.delta.h0MinusZ0) * stepsPerMm);

			// If there is a reversal then we only ever move up by (reverseStartStep - 1) steps, so netStepsAtEnd should be less than reverseStartStep.
			// However, because of rounding error, it might possibly be equal.
			// If there is no reversal then reverseStartStep is set to totalSteps + 1, so netStepsAtEnd must again be less than reverseStartStep.
			if (netStepsAtEnd >= (int32_t)reverseStartStep)
			{
				netStepsAtEnd = (int32_t)(reverseStartStep - 1);			// correct the rounding error - we know that reverseStartStep cannot be 0 so subtracting 1 is safe
			}

			if (!direction)
			{
				// We are going down so any reversal has already happened
				state = DMState::deltaNormal;
				segmentStepLimit = (nextStep >= reverseStartStep)
									? (uint32_t)((int32_t)(2 * reverseStartStep) - netStepsAtEnd)		// we went up (reverseStartStep-1) steps, now we are going down to netStepsAtEnd
										: (uint32_t)(-netStepsAtEnd);									// we are just going down to netStepsAtEnd
			}
			else if (distanceSoFar <= mp.delta.reverseStartDistance)
			{
				// This segment is purely upwards motion of the tower
				state = DMState::deltaNormal;
				segmentStepLimit = (uint32_t)(netStepsAtEnd + 1);
			}
			else
			{
				// This segment ends with reverse motion
				segmentStepLimit = (uint32_t)((int32_t)(2 * reverseStartStep) - netStepsAtEnd);
				state = DMState::deltaForwardsReversing;
			}
		}

		if (segmentStepLimit > nextStep)
		{
			return true;
		}

		currentSegment = currentSegment->GetNext();
	}
}

#endif // SUPPORT_LINEAR_DELTA

// This is called when currentSegment has just been changed to a new segment. Return true if there is a new segment to execute.
bool DriveMovement::NewExtruderSegment() noexcept
{
	while (true)
	{
		if (currentSegment == nullptr)
		{
			return false;
		}

		const float startDistance = distanceSoFar;
		const float startTime = timeSoFar;

		distanceSoFar += currentSegment->GetSegmentLength();
		timeSoFar += currentSegment->GetSegmentTime();

		pC = currentSegment->CalcC(mp.cart.effectiveMmPerStep);
		if (currentSegment->IsLinear())
		{
			// Set up pB, pC such that for forward motion, time = pB + pC * stepNumber
			pB = currentSegment->CalcLinearB(startDistance, startTime);
			state = DMState::cartLinear;
		}
		else
		{
			// Set up pA, pB, pC such that for forward motion, time = pB + sqrt(pA + pC * stepNumber)
			pA = currentSegment->CalcNonlinearA(startDistance, mp.cart.pressureAdvanceK);
			pB = currentSegment->CalcNonlinearB(startTime, mp.cart.pressureAdvanceK);
			if (currentSegment->IsAccelerating())
			{
				// Extruders have a single acceleration segment. We need to add the extra extrusion distance due to pressure advance to the extrusion distance.
				distanceSoFar += mp.cart.extraExtrusionDistance;
				state = DMState::cartAccel;
			}
			else
			{
				// This is the single decelerating segment. If it includes pressure advance then it may include reversal.
				state = (reverseStartStep <= totalSteps) ? DMState::cartDecelForwardsReversing : DMState::cartDecelNoReverse;
			}
		}

		// Work out the movement limit in steps
		segmentStepLimit = ((currentSegment->GetNext() == nullptr) ? totalSteps : (uint32_t)(distanceSoFar * mp.cart.effectiveStepsPerMm)) + 1;

		if (nextStep < segmentStepLimit)
		{
			return true;
		}

		currentSegment = currentSegment->GetNext();						// skip this segment
	}
}

// Prepare this DM for a Cartesian axis move, returning true if there are steps to do
bool DriveMovement::PrepareCartesianAxis(const DDA& dda, const PrepParams& params) noexcept
{
	distanceSoFar = 0.0;
	timeSoFar = 0.0;
	mp.cart.pressureAdvanceK = 0.0;
	// We can't use directionVector here because those values relate to Cartesian space, whereas we may be CoreXY etc.
	mp.cart.effectiveStepsPerMm = (float)totalSteps/dda.totalDistance;
	mp.cart.effectiveMmPerStep = 1.0/mp.cart.effectiveStepsPerMm;
	isDelta = false;
	isExtruder = false;
	currentSegment = (dda.shapedSegments != nullptr) ? dda.shapedSegments : dda.unshapedSegments;
	nextStep = 0;									// must do this before calling NewCartesianSegment

	if (!NewCartesianSegment())
	{
		return false;
	}

	// Prepare for the first step
	nextStepTime = 0;
	stepsTakenThisSegment = 0;						// no steps taken yet since the start of the segment
	stepsTillRecalc = 0;							// so that we don't skip the calculation
	reverseStartStep = totalSteps + 1;				// no reverse phase
	return CalcNextStepTime(dda);
}

#if SUPPORT_LINEAR_DELTA

// Prepare this DM for a Delta axis move, returning true if there are steps to do
bool DriveMovement::PrepareDeltaAxis(const DDA& dda, const PrepParams& params) noexcept
{
	const float stepsPerMm = reprap.GetPlatform().DriveStepsPerUnit(drive);
	const float A = params.initialX - params.dparams->GetTowerX(drive);
	const float B = params.initialY - params.dparams->GetTowerY(drive);
	const float aAplusbB = A * dda.directionVector[X_AXIS] + B * dda.directionVector[Y_AXIS];
	const float dSquaredMinusAsquaredMinusBsquared = params.dparams->GetDiagonalSquared(drive) - fsquare(A) - fsquare(B);
	const float h0MinusZ0 = fastSqrtf(dSquaredMinusAsquaredMinusBsquared);

	mp.delta.h0MinusZ0 = h0MinusZ0;
	mp.delta.fTwoA = 2.0 * A;
	mp.delta.fTwoB = 2.0 * B;
	mp.delta.fHmz0s = h0MinusZ0 * stepsPerMm;
	mp.delta.fMinusAaPlusBbTimesS = -(aAplusbB * stepsPerMm);
	mp.delta.fDSquaredMinusAsquaredMinusBsquaredTimesSsquared = dSquaredMinusAsquaredMinusBsquared * fsquare(stepsPerMm);

	// Calculate the distance at which we need to reverse direction.
	if (params.a2plusb2 <= 0.0)
	{
		// Pure Z movement. We can't use the main calculation because it divides by params.a2plusb2.
		direction = (dda.directionVector[Z_AXIS] >= 0.0);
		mp.delta.reverseStartDistance = (direction) ? dda.totalDistance + 1.0 : -1.0;	// so that we never reverse and NewDeltaSegment knows which way we are going
		reverseStartStep = totalSteps + 1;
	}
	else
	{
		// The distance to reversal is the solution to a quadratic equation. One root corresponds to the carriages being below the bed,
		// the other root corresponds to the carriages being above the bed.
		const float drev = ((dda.directionVector[Z_AXIS] * fastSqrtf(params.a2plusb2 * params.dparams->GetDiagonalSquared(drive) - fsquare(A * dda.directionVector[Y_AXIS] - B * dda.directionVector[X_AXIS])))
							- aAplusbB)/params.a2plusb2;
		mp.delta.reverseStartDistance = drev;
		if (drev <= 0.0)
		{
			// No reversal, going down
			reverseStartStep = totalSteps + 1;
			direction = false;
		}
		else if (drev >= dda.totalDistance)
		{
			// No reversal, going up
			reverseStartStep = totalSteps + 1;
			direction = true;
		}
		else																	// the reversal point is within range
		{
			// Calculate how many steps we need to move up before reversing
			const float hrev = dda.directionVector[Z_AXIS] * drev + fastSqrtf(dSquaredMinusAsquaredMinusBsquared - 2 * drev * aAplusbB - params.a2plusb2 * fsquare(drev));
			const int32_t numStepsUp = (int32_t)((hrev - mp.delta.h0MinusZ0) * stepsPerMm);

			// We may be going down but almost at the peak height already, in which case we don't really have a reversal.
			// However, we could be going up by a whole step due to rounding, so we need to check the direction
			if (numStepsUp < 1)
			{
				if (direction)
				{
					mp.delta.reverseStartDistance = dda.totalDistance + 1.0;	// indicate that there is no reversal
				}
				else
				{
					mp.delta.reverseStartDistance = -1.0;						// so that we know we have reversed already
					reverseStartStep = totalSteps + 1;
				}
			}
			else if (direction && (uint32_t)numStepsUp <= totalSteps)
			{
				// If numStepsUp == totalSteps then the reverse segment is too small to do.
				// If numStepsUp < totalSteps then there has been a rounding error, because we are supposed to move up more than the calculated number of steps we move up.
				// This can happen if the calculated reversal is very close to the end of the move, because we round the final step positions to the nearest step, which may be up.
				// Either way, don't do a reverse segment.
				reverseStartStep = totalSteps + 1;
				mp.delta.reverseStartDistance = dda.totalDistance + 1.0;
			}
			else
			{
				reverseStartStep = (uint32_t)numStepsUp + 1;

				// Correct the initial direction and the total number of steps
				if (direction)
				{
					// Net movement is up, so we will go up first and then down by a lesser amount
					totalSteps = (2 * (uint32_t)numStepsUp) - totalSteps;
				}
				else
				{
					// Net movement is down, so we will go up first and then down by a greater amount
					direction = true;
					totalSteps = (2 * (uint32_t)numStepsUp) + totalSteps;
				}
			}
		}
	}

	distanceSoFar = 0.0;
	timeSoFar = 0.0;

	isDelta = true;
	currentSegment = (dda.shapedSegments != nullptr) ? dda.shapedSegments : dda.unshapedSegments;

	nextStep = 0;									// must do this before calling NewDeltaSegment
	if (!NewDeltaSegment(dda))
	{
		return false;
	}

	// Prepare for the first step
	nextStepTime = 0;
	stepsTakenThisSegment = 0;						// no steps taken yet since the start of the segment
	stepsTillRecalc = 0;							// so that we don't skip the calculation
	return CalcNextStepTime(dda);
}

#endif	// SUPPORT_LINEAR_DELTA

// Prepare this DM for an extruder move, returning true if there are steps to do
// If there are no steps to do, set nextStep = 0 so that DDARing::CurrentMoveCompleted doesn't add any steps to the movement accumulator
// We have already generated the extruder segments and we know that there are some
bool DriveMovement::PrepareExtruder(const DDA& dda, const PrepParams& params) noexcept
{
	const float stepsPerMm = reprap.GetPlatform().DriveStepsPerUnit(drive);
	const float effStepsPerMm = stepsPerMm * fabsf(dda.directionVector[drive]);
	const float effMmPerStep = 1.0/effStepsPerMm;

	ExtruderShaper& shaper = reprap.GetMove().GetExtruderShaper(
#if SUPPORT_REMOTE_COMMANDS
																(dda.flags.isRemote) ? drive :
#endif
																	LogicalDriveToExtruder(drive)
															   );
	float forwardDistance =	mp.cart.extrusionBroughtForwards =
#if SUPPORT_REMOTE_COMMANDS
			(dda.flags.isRemote) ? 0.0 :
#endif
				shaper.GetExtrusionPending()/dda.directionVector[drive];
	float reverseDistance;

	mp.cart.effectiveStepsPerMm = effStepsPerMm;
	mp.cart.effectiveMmPerStep = effMmPerStep;
	distanceSoFar = forwardDistance;
	timeSoFar = 0.0;

	// Calculate the total forward and reverse movement distances
	if (dda.flags.usePressureAdvance && shaper.GetKclocks() > 0.0)
	{
		// We are using nonzero pressure advance. Movement must be forwards.
		mp.cart.pressureAdvanceK = shaper.GetKclocks();
		mp.cart.extraExtrusionDistance = mp.cart.pressureAdvanceK * (dda.topSpeed - dda.startSpeed);
		forwardDistance += mp.cart.extraExtrusionDistance;

# if 0 //SHAPE_EXTRUSION
		forwardDistance += params.shaped.decelStartDistance;
		reverseDistance = 0.0;

		// Find the deceleration segments
		const MoveSegment *decelSeg = dda.unshapedSegments;
		while (decelSeg != nullptr && (decelSeg->IsLinear() || decelSeg->IsAccelerating()))
		{
			decelSeg = decelSeg->GetNext();
		}

		float lastUncorrectedSpeed = dda.topSpeed;
		float lastDistance = forwardDistance;
		while (decelSeg != nullptr)
		{
			const float initialDecelSpeed = lastUncorrectedSpeed - mp.cart.pressureAdvanceK * decelSeg->deceleration;
			if (initialDecelSpeed <= 0.0)
			{
				// This entire deceleration segment is in reverse
				reverseDistance += ((0.5 * params.unshaped.deceleration * params.unshaped.decelClocks) - initialDecelSpeed) * params.unshaped.decelClocks;
			}
			else
			{
				const float timeToReverse = initialDecelSpeed * ((-0.5) * decelSeg->GetC());	// 'c' is -2/deceleration, so -0.5*c is 1/deceleration
				if (timeToReverse < params.unshaped.decelClocks)
				{
					// There is a reversal, although it could be tiny
					const float distanceToReverse = fsquare(initialDecelSpeed) * decelSeg->GetC() * (-0.25);	// because (v^2-u^2) = 2as, so if v=0 then s=-u^2/2a = u^2/2d = -0.25*u^2*c
					forwardDistance += params.unshaped.decelStartDistance + distanceToReverse;
					reverseDistance = 0.5 * params.unshaped.deceleration * fsquare(params.unshaped.decelClocks - timeToReverse);	// because s = 0.5*a*t^2
				}
				else
				{
					// No reversal
					forwardDistance += dda.totalDistance - (mp.cart.pressureAdvanceK * params.unshaped.deceleration * params.unshaped.decelClocks);
					reverseDistance = 0.0;
				}
			}

		}
# else
		// Check if there is a reversal in the deceleration segment
		// There is at most one deceleration segment in the unshaped segments
		const MoveSegment *decelSeg = dda.unshapedSegments;
		while (decelSeg != nullptr && (decelSeg->IsLinear() || decelSeg->IsAccelerating()))
		{
			decelSeg = decelSeg->GetNext();
		}

		if (decelSeg == nullptr)
		{
			forwardDistance += dda.totalDistance;			// no deceleration segment
			reverseDistance = 0.0;
		}
		else
		{
			const float initialDecelSpeed = dda.topSpeed - mp.cart.pressureAdvanceK * params.unshaped.deceleration;
			if (initialDecelSpeed <= 0.0)
			{
				// The entire deceleration segment is in reverse
				forwardDistance += params.unshaped.decelStartDistance;
				reverseDistance = ((0.5 * params.unshaped.deceleration * params.unshaped.decelClocks) - initialDecelSpeed) * params.unshaped.decelClocks;
			}
			else
			{
				const float timeToReverse = initialDecelSpeed * ((-0.5) * decelSeg->GetC());	// 'c' is -2/deceleration, so -0.5*c is 1/deceleration
				if (timeToReverse < params.unshaped.decelClocks)
				{
					// There is a reversal, although it could be tiny
					const float distanceToReverse = fsquare(initialDecelSpeed) * decelSeg->GetC() * (-0.25);	// because (v^2-u^2) = 2as, so if v=0 then s=-u^2/2a = u^2/2d = -0.25*u^2*c
					forwardDistance += params.unshaped.decelStartDistance + distanceToReverse;
					reverseDistance = 0.5 * params.unshaped.deceleration * fsquare(params.unshaped.decelClocks - timeToReverse);	// because s = 0.5*a*t^2
				}
				else
				{
					// No reversal
					forwardDistance += dda.totalDistance - (mp.cart.pressureAdvanceK * params.unshaped.deceleration * params.unshaped.decelClocks);
					reverseDistance = 0.0;
				}
			}
		}
# endif
	}
	else
	{
		// No pressure advance. Movement may be backwards but this still counts as forward distance in the calculations.
		mp.cart.pressureAdvanceK = mp.cart.extraExtrusionDistance = 0.0;
		forwardDistance += dda.totalDistance;
		reverseDistance = 0.0;
	}

	// Check whether there are any steps at all
	const float forwardSteps = forwardDistance * effStepsPerMm;
	if (reverseDistance > 0.0)
	{
		const float netDistance = forwardDistance - reverseDistance;
		const int32_t iFwdSteps = (int32_t)forwardSteps;
		int32_t netSteps = (int32_t)(netDistance * effStepsPerMm);
		if (netSteps == 0 && iFwdSteps == 0)
		{
			// No movement at all
			nextStep = totalSteps = 0;
			reverseStartStep = 1;
#if SUPPORT_REMOTE_COMMANDS
			if (!dda.flags.isRemote)
#endif
			{
				shaper.SetExtrusionPending(netDistance * dda.directionVector[drive]);
			}
			return false;
		}

		// Note, netSteps may be negative for e.g. a deceleration-only move
		if (netSteps == iFwdSteps)
		{
			// The reverse segment is very small, so ignore it
			totalSteps = (uint32_t)iFwdSteps;
			reverseStartStep = totalSteps + 1;
		}
		else
		{
			// We know that netSteps <= iFwdSteps
			reverseStartStep = iFwdSteps + 1;
			// Round up netSteps because we don't want to overshoot the reverse movement.
			const float extrusionPending = netDistance - (float)netSteps * effMmPerStep;
			if (extrusionPending > 0.05 * effMmPerStep)
			{
				++netSteps;
			}
			totalSteps = (uint32_t)((int32_t)(2 * reverseStartStep) - netSteps - 2);
		}
#if SUPPORT_REMOTE_COMMANDS
		if (!dda.flags.isRemote)
#endif
		{
			shaper.SetExtrusionPending((netDistance - (float)netSteps * effMmPerStep) * dda.directionVector[drive]);
		}
	}
	else
	{
		if (forwardSteps >= 1.0)
		{
			totalSteps = (uint32_t)forwardSteps;
#if SUPPORT_REMOTE_COMMANDS
			if (!dda.flags.isRemote)
#endif
			{
				shaper.SetExtrusionPending((forwardDistance - (float)totalSteps * effMmPerStep) * dda.directionVector[drive]);
			}
		}
		else
		{
			// No steps at all, or negative forward steps which I think should be impossible unless the steps/mm is changed
			nextStep = totalSteps = 0;
			reverseStartStep = 1;
#if SUPPORT_REMOTE_COMMANDS
			if (!dda.flags.isRemote)
#endif
			{
				shaper.SetExtrusionPending(forwardDistance * dda.directionVector[drive]);
			}
			return false;
		}
		reverseStartStep = totalSteps + 1;			// no reverse phase
	}

	currentSegment = dda.unshapedSegments;
	isDelta = false;
	isExtruder = true;

	nextStep = 0;									// must do this before calling NewExtruderSegment
	if (!NewExtruderSegment())
	{
		return false;								// this should not happen because we have already determined that there are steps to do
	}

	// Prepare for the first step
	nextStepTime = 0;
	stepsTakenThisSegment = 0;						// no steps taken yet since the start of the segment
	stepsTillRecalc = 0;							// so that we don't skip the calculation
	return CalcNextStepTime(dda);
}

// Version of fastSqrtf that allows for slightly negative operands caused by rounding error
static inline float fastLimSqrtf(float f) noexcept
{
	return (f > 0.0) ? fastSqrtf(f) : 0.0;
}

// Calculate and store the time since the start of the move when the next step for the specified DriveMovement is due.
// We have already incremented nextStep and checked that it does not exceed totalSteps, so at least one more step is due
// Return true if all OK, false to abort this move because the calculation has gone wrong
bool DriveMovement::CalcNextStepTimeFull(const DDA &dda) noexcept
pre(nextStep <= totalSteps; stepsTillRecalc == 0)
{
	uint32_t shiftFactor = 0;									// assume single stepping

	{
		uint32_t stepsToLimit = segmentStepLimit - nextStep;
		// If there are no more steps left in this segment, skip to the next segment and use single stepping
		if (stepsToLimit == 0)
		{
			currentSegment = currentSegment->GetNext();
			const bool more =
#if SUPPORT_LINEAR_DELTA
								(isDelta) ? NewDeltaSegment(dda) :
#endif
									(isExtruder) ? NewExtruderSegment()
										: NewCartesianSegment();
			if (!more)
			{
				state = DMState::stepError;
				nextStep += 100000000;							// so we can tell what happened in the debug print
				return false;
			}
			// Leave shiftFactor set to 0 so that we compute a single step time, because the interval will have changed
			stepsTakenThisSegment = 1;							// this will be the first step in this segment
		}
		else if (stepsTakenThisSegment < 2)
		{
			// Reasons why we always use single stepping until we are on the third step in a segment:
			// 1. On the very first step of a move we don't know what the step interval is, so we must use single stepping for the first step.
			// 2. For extruders the step interval calculated for the very first step may be very small because of overdue extrusion,
			//    so we don't have a reliable step interval until we have calculated 2 steps.
			// 3. When starting a subsequent segment there may be a discontinuity due to rounding error,
			//    so the step interval calculated after the first step in a subsequent phase is not reliable.
			++stepsTakenThisSegment;
		}
		else
		{
			if (reverseStartStep < segmentStepLimit && nextStep < reverseStartStep)
			{
				stepsToLimit = reverseStartStep - nextStep;
			}

			if (stepsToLimit > 1 && stepInterval < DDA::MinCalcInterval)
			{
				if (stepInterval < DDA::MinCalcInterval/4 && stepsToLimit > 8)
				{
					shiftFactor = 3;							// octal stepping
				}
				else if (stepInterval < DDA::MinCalcInterval/2 && stepsToLimit > 4)
				{
					shiftFactor = 2;							// quad stepping
				}
				else if (stepsToLimit > 2)
				{
					shiftFactor = 1;							// double stepping
				}
			}
		}
	}

	stepsTillRecalc = (1u << shiftFactor) - 1u;					// store number of additional steps to generate

	float nextCalcStepTime;

	// Work out the time of the step
	switch (state)
	{
	case DMState::cartLinear:									// linear steady speed
		nextCalcStepTime = pB + (float)(nextStep + stepsTillRecalc) * pC;
		break;

	case DMState::cartAccel:									// Cartesian accelerating
		nextCalcStepTime = pB + fastLimSqrtf(pA + pC * (float)(nextStep + stepsTillRecalc));
		break;

	case DMState::cartDecelForwardsReversing:
		if (nextStep + stepsTillRecalc < reverseStartStep)
		{
			nextCalcStepTime = pB - fastLimSqrtf(pA + pC * (float)(nextStep + stepsTillRecalc));
			break;
		}

		direction = false;
		directionChanged = true;
		state = DMState::cartDecelReverse;
		// no break
	case DMState::cartDecelReverse:								// Cartesian decelerating, reverse motion. Convert the steps to int32_t because the net steps may be negative.
		nextCalcStepTime = pB + fastLimSqrtf(pA + pC * (float)((2 * (int32_t)(reverseStartStep - 1)) - (int32_t)(nextStep + stepsTillRecalc)));
		break;

	case DMState::cartDecelNoReverse:							// Cartesian accelerating with no reversal
		nextCalcStepTime = pB - fastLimSqrtf(pA + pC * (float)(nextStep + stepsTillRecalc));
		break;

	case DMState::deltaForwardsReversing:						// moving forwards
		if (nextStep == reverseStartStep)
		{
			direction = false;
			directionChanged = true;
			state = DMState::deltaNormal;
		}
		// no break
	case DMState::deltaNormal:
		// Calculate d*s where d = distance the head has travelled, s = steps/mm for this drive
		{
			const float steps = (float)(1u << shiftFactor);
			if (direction)
			{
				mp.delta.fHmz0s += steps;						// get new carriage height above Z in steps
			}
			else
			{
				mp.delta.fHmz0s -= steps;						// get new carriage height above Z in steps
			}

			const float hmz0sc = mp.delta.fHmz0s * dda.directionVector[Z_AXIS];
			const float t1 = mp.delta.fMinusAaPlusBbTimesS + hmz0sc;
			const float t2a = mp.delta.fDSquaredMinusAsquaredMinusBsquaredTimesSsquared - fsquare(mp.delta.fHmz0s) + fsquare(t1);
			// Due to rounding error we can end up trying to take the square root of a negative number if we do not take precautions here
			const float t2 = fastLimSqrtf(t2a);
			const float ds = (direction) ? t1 - t2 : t1 + t2;

			// Now feed ds into the step algorithm for Cartesian motion
			if (ds < 0.0)
			{
				state = DMState::stepError;
				nextStep += 110000000;							// so that we can tell what happened in the debug print
				return false;
			}

			const float pCds = pC * ds;
			nextCalcStepTime = (currentSegment->IsLinear()) ? pB + pCds
								: (currentSegment->IsAccelerating()) ? pB + fastLimSqrtf(pA + pCds)
									 : pB - fastLimSqrtf(pA + pCds);
			//if (currentSegment->IsLinear()) { pA = ds; }	//DEBUG
		}
		break;

	default:
		return false;
	}

#if 0	//DEBUG
	if (std::isnan(nextCalcStepTime) || nextCalcStepTime < 0.0)
	{
		state = DMState::stepError;
		nextStep += 140000000 + stepsTillRecalc;			// so we can tell what happened in the debug print
		distanceSoFar = nextCalcStepTime;					//DEBUG
		return false;
	}
#endif

	uint32_t iNextCalcStepTime = (uint32_t)nextCalcStepTime;

	if (iNextCalcStepTime > dda.clocksNeeded)
	{
		// The calculation makes this step late.
		// When the end speed is very low, calculating the time of the last step is very sensitive to rounding error.
		// So if this is the last step and it is late, bring it forward to the expected finish time.
		// Very rarely on a delta, the penultimate step may also be calculated late. Allow for that here in case it affects Cartesian axes too.
		if (nextStep + stepsTillRecalc + 1 >= totalSteps)
		{
			iNextCalcStepTime = dda.clocksNeeded;
		}
		else
		{
			// We don't expect any step except the last to be late
			state = DMState::stepError;
			nextStep += 120000000 + stepsTillRecalc;		// so we can tell what happened in the debug print
			stepInterval = iNextCalcStepTime;				//DEBUG
			return false;
		}
	}

	// When crossing between movement phases with high microstepping, due to rounding errors the next step may appear to be due before the last one
	stepInterval = (iNextCalcStepTime > nextStepTime)
					? (iNextCalcStepTime - nextStepTime) >> shiftFactor	// calculate the time per step, ready for next time
					: 0;

#if 0	//DEBUG
	if (isExtruder && stepInterval < 20 /*&& nextStep + stepsTillRecalc + 1 < totalSteps*/)
	{
		state = DMState::stepError;
		nextStep += 130000000 + stepsTillRecalc;			// so we can tell what happened in the debug print
		return false;
	}
#endif

#if EVEN_STEPS
	nextStepTime = iNextCalcStepTime - (stepsTillRecalc * stepInterval);
#else
	nextStepTime = iNextCalcStepTime;
#endif

	return true;
}

// End