reprapfirmware-dc42/src/Movement/DDA.cpp

/*
 * DDA.cpp
 *
 *  Created on: 7 Dec 2014
 *      Author: David
 */

#include "RepRapFirmware.h"

#ifdef DUET_NG
# define DDA_MOVE_DEBUG	(1)
#else
// On the wired Duets we don't have enough RAM to support this
# define DDA_MOVE_DEBUG	(0)
#endif

#if DDA_MOVE_DEBUG

// Structure to hold the essential parameters of a move, for debugging
struct MoveParameters
{
	float accelDistance;
	float steadyDistance;
	float decelDistance;
	float startSpeed;
	float topSpeed;
	float endSpeed;

	MoveParameters()
	{
		accelDistance = steadyDistance = decelDistance = startSpeed = topSpeed = endSpeed = 0.0;
	}
};

const size_t NumSavedMoves = 256;

static MoveParameters savedMoves[NumSavedMoves];
static size_t savedMovePointer = 0;

// Print the saved moves in CSV format for analysis
/*static*/ void DDA::PrintMoves()
{
	// Print the saved moved in CSV format
	for (size_t i = 0; i < NumSavedMoves; ++i)
	{
		const MoveParameters& m = savedMoves[savedMovePointer];
		reprap.GetPlatform()->MessageF(DEBUG_MESSAGE, "%f,%f,%f,%f,%f,%f\n", m.accelDistance, m.steadyDistance, m.decelDistance, m.startSpeed, m.topSpeed, m.endSpeed);
		savedMovePointer = (savedMovePointer + 1) % NumSavedMoves;
	}
}

#else

/*static*/ void DDA::PrintMoves() { }

#endif

DDA::DDA(DDA* n) : next(n), prev(nullptr), state(empty)
{
	memset(ddm, 0, sizeof(ddm));	//DEBUG to clear stepError field
}

// Return the number of clocks this DDA still needs to execute.
// This could be slightly negative, if the move is overdue for completion.
int32_t DDA::GetTimeLeft() const
pre(state == executing || state == frozen || state == completed)
{
	return (state == completed) ? 0
			: (state == executing) ? (int32_t)(moveStartTime + clocksNeeded - Platform::GetInterruptClocks())
			: (int32_t)clocksNeeded;
}

void DDA::DebugPrintVector(const char *name, const float *vec, size_t len) const
{
	debugPrintf("%s=", name);
	for (size_t i = 0; i < len; ++i)
	{
		debugPrintf("%c%f", ((i == 0) ? '[' : ' '), vec[i]);
	}
	debugPrintf("]");
}

void DDA::DebugPrint() const
{
	const size_t numAxes = reprap.GetGCodes()->GetNumAxes();
	debugPrintf("DDA:");
	if (endCoordinatesValid)
	{
		float startCoordinates[MAX_AXES];
		for (size_t i = 0; i < numAxes; ++i)
		{
			startCoordinates[i] = endCoordinates[i] - (totalDistance * directionVector[i]);
		}
		DebugPrintVector(" start", startCoordinates, numAxes);
		DebugPrintVector(" end", endCoordinates, numAxes);
	}

	debugPrintf(" d=%f", totalDistance);
	DebugPrintVector(" vec", directionVector, 5);
	debugPrintf("\na=%f reqv=%f topv=%f startv=%f endv=%f\n"
				"daccel=%f ddecel=%f cks=%u\n",
				acceleration, requestedSpeed, topSpeed, startSpeed, endSpeed,
				accelDistance, decelDistance, clocksNeeded);
	for (size_t axis = 0; axis < numAxes; ++axis)
	{
		ddm[axis].DebugPrint(reprap.GetGCodes()->axisLetters[axis], isDeltaMovement);
	}
	for (size_t i = numAxes; i < DRIVES; ++i)
	{
		if (ddm[i].state != DMState::idle)
		{
			ddm[i].DebugPrint((char)('0' + (i - numAxes)), false);
		}
	}
}

// This is called by Move to initialize all DDAs
void DDA::Init()
{
	// Set the endpoints to zero, because Move asks for them.
	// They will be wrong if we are on a delta. We take care of that when we process the M665 command in config.g.
	for (size_t drive = 0; drive < DRIVES; ++drive)
	{
		endPoint[drive] = 0;
		ddm[drive].state = DMState::idle;
	}
	state = empty;
	endCoordinatesValid = false;
}

// Set up a real move. Return true if it represents real movement, else false.
bool DDA::Init(const GCodes::RawMove &nextMove, bool doMotorMapping)
{
	// 1. Compute the new endpoints and the movement vector
	const int32_t *positionNow = prev->DriveCoordinates();
	const Move *move = reprap.GetMove();
	if (doMotorMapping)
	{
		move->MotorTransform(nextMove.coords, endPoint);			// transform the axis coordinates if on a delta or CoreXY printer
		isDeltaMovement = move->IsDeltaMode()
							&& (endPoint[X_AXIS] != positionNow[X_AXIS] || endPoint[Y_AXIS] != positionNow[Y_AXIS] || endPoint[Z_AXIS] != positionNow[Z_AXIS]);
	}
	else
	{
		isDeltaMovement = false;
	}

	isPrintingMove = false;
	bool realMove = false, xyMoving = false;
	const bool isSpecialDeltaMove = (move->IsDeltaMode() && !doMotorMapping);
	float accelerations[DRIVES];
	const float *normalAccelerations = reprap.GetPlatform()->Accelerations();
	const size_t numAxes = reprap.GetGCodes()->GetNumAxes();
	for (size_t drive = 0; drive < DRIVES; drive++)
	{
		accelerations[drive] = normalAccelerations[drive];
		if (drive >= numAxes || !doMotorMapping)
		{
			endPoint[drive] = Move::MotorEndPointToMachine(drive, nextMove.coords[drive]);
		}

		int32_t delta;
		if (drive < numAxes)
		{
			endCoordinates[drive] = nextMove.coords[drive];
			delta = endPoint[drive] - positionNow[drive];
		}
		else
		{
			delta = endPoint[drive];
		}

		DriveMovement& dm = ddm[drive];
		if (drive < numAxes && !isSpecialDeltaMove)
		{
			directionVector[drive] = nextMove.coords[drive] - prev->GetEndCoordinate(drive, false);
			dm.state = (isDeltaMovement || delta != 0)
						? DMState::moving				// on a delta printer, if one tower moves then we assume they all do
						: DMState::idle;
		}
		else
		{
			directionVector[drive] = (float)delta/reprap.GetPlatform()->DriveStepsPerUnit(drive);
			dm.state = (delta != 0) ? DMState::moving : DMState::idle;
		}

		if (dm.state == DMState::moving)
		{
			dm.totalSteps = labs(delta);				// for now this is the number of net steps, but gets adjusted later if there is a reverse in direction
			dm.direction = (delta >= 0);				// for now this is the direction of net movement, but gets adjusted later if it is a delta movement
			realMove = true;

			if (drive < numAxes && drive != Z_AXIS)
			{
				xyMoving = true;
			}

			if (drive >= numAxes && xyMoving)
			{
				if (delta > 0)
				{
					isPrintingMove = true;				// we have both movement and extrusion
				}
				const float compensationTime = reprap.GetPlatform()->GetPressureAdvance(drive);
				if (compensationTime > 0.0)
				{
					// Compensation causes instant velocity changes equal to acceleration * k, so we may need to limit the acceleration
					accelerations[drive] = min<float>(accelerations[drive], reprap.GetPlatform()->ConfiguredInstantDv(drive)/compensationTime);
				}
			}
		}
	}

	// 2. Throw it away if there's no real movement.
	if (!realMove)
	{
		return false;
	}

	// 3. Store some values
	endStopsToCheck = nextMove.endStopsToCheck;
	filePos = nextMove.filePos;
	usePressureAdvance = nextMove.usePressureAdvance;
	hadLookaheadUnderrun = false;

	// The end coordinates will be valid at the end of this move if it does not involve endstop checks and is not a special move on a delta printer
	endCoordinatesValid = (endStopsToCheck == 0) && (doMotorMapping || !move->IsDeltaMode());

	// 4. Normalise the direction vector and compute the amount of motion.
	// If there is any XYZ movement, then we normalise it so that the total XYZ movement has unit length.
	// This means that the user gets the feed rate that he asked for. It also makes the delta calculations simpler.
	if (xyMoving || ddm[Z_AXIS].state == DMState::moving)
	{
		if (isDeltaMovement)
		{
			// Add on the Z movement needed to compensate for bed tilt
			const DeltaParameters& dparams = move->GetDeltaParams();
			directionVector[Z_AXIS] += (directionVector[X_AXIS] * dparams.GetXTilt()) + (directionVector[Y_AXIS] * dparams.GetYTilt());
		}

		totalDistance = Normalise(directionVector, DRIVES, numAxes);
		if (isDeltaMovement)
		{
			// The following are only needed when doing delta movements. We could defer computing them until Prepare(), which would make simulation faster.
			a2plusb2 = fsquare(directionVector[X_AXIS]) + fsquare(directionVector[Y_AXIS]);
			cKc = (int32_t)(directionVector[Z_AXIS] * DriveMovement::Kc);

			const float initialX = prev->GetEndCoordinate(X_AXIS, false);
			const float initialY = prev->GetEndCoordinate(Y_AXIS, false);
			const DeltaParameters& dparams = move->GetDeltaParams();
			const float diagonalSquared = fsquare(dparams.GetDiagonal());
			const float a2b2D2 = a2plusb2 * diagonalSquared;

			for (size_t drive = 0; drive < DELTA_AXES; ++drive)
			{
				const float A = initialX - dparams.GetTowerX(drive);
				const float B = initialY - dparams.GetTowerY(drive);
				const float stepsPerMm = reprap.GetPlatform()->DriveStepsPerUnit(drive);
				DriveMovement& dm = ddm[drive];
				const float aAplusbB = A * directionVector[X_AXIS] + B * directionVector[Y_AXIS];
				const float dSquaredMinusAsquaredMinusBsquared = diagonalSquared - fsquare(A) - fsquare(B);
				float h0MinusZ0 = sqrtf(dSquaredMinusAsquaredMinusBsquared);
				dm.mp.delta.hmz0sK = (int32_t)(h0MinusZ0 * stepsPerMm * DriveMovement::K2);
				dm.mp.delta.minusAaPlusBbTimesKs = -(int32_t)(aAplusbB * stepsPerMm * DriveMovement::K2);
				dm.mp.delta.dSquaredMinusAsquaredMinusBsquaredTimesKsquaredSsquared =
						(int64_t)(dSquaredMinusAsquaredMinusBsquared * fsquare(stepsPerMm * DriveMovement::K2));

				// Calculate the distance at which we need to reverse direction.
				if (a2plusb2 <= 0.0)
				{
					// Pure Z movement. We can't use the main calculation because it divides by a2plusb2.
					dm.direction = (directionVector[Z_AXIS] >= 0.0);
					dm.mp.delta.reverseStartStep = dm.totalSteps + 1;
				}
				else
				{
					// The distance to reversal is the solution to a quadratic equation. One root corresponds to the carriages being above the bed,
					// the other root corresponds to the carriages being above the bed.
					const float drev = ((directionVector[Z_AXIS] * sqrt(a2b2D2 - fsquare(A * directionVector[Y_AXIS] - B * directionVector[X_AXIS])))
										- aAplusbB)/a2plusb2;
					if (drev > 0.0 && drev < totalDistance)		// if the reversal point is within range
					{
						// Calculate how many steps we need to move up before reversing
						const float hrev = directionVector[Z_AXIS] * drev + sqrt(dSquaredMinusAsquaredMinusBsquared - 2 * drev * aAplusbB - a2plusb2 * fsquare(drev));
						int32_t numStepsUp = (int32_t)((hrev - h0MinusZ0) * stepsPerMm);

						// We may be almost at the peak height already, in which case we don't really have a reversal.
						if (numStepsUp < 1 || (dm.direction && (uint32_t)numStepsUp <= dm.totalSteps))
						{
							dm.mp.delta.reverseStartStep = dm.totalSteps + 1;
						}
						else
						{
							dm.mp.delta.reverseStartStep = (uint32_t)numStepsUp + 1;

							// Correct the initial direction and the total number of steps
							if (dm.direction)
							{
								// Net movement is up, so we will go up a bit and then down by a lesser amount
								dm.totalSteps = (2 * numStepsUp) - dm.totalSteps;
							}
							else
							{
								// Net movement is down, so we will go up first and then down by a greater amount
								dm.direction = true;
								dm.totalSteps = (2 * numStepsUp) + dm.totalSteps;
							}
						}
					}
					else
					{
						dm.mp.delta.reverseStartStep = dm.totalSteps + 1;
					}
				}
			}
		}
	}
	else
	{
		totalDistance = Normalise(directionVector, DRIVES, DRIVES);
	}

	// 5. Compute the maximum acceleration available and maximum top speed
	float normalisedDirectionVector[DRIVES];			// Used to hold a unit-length vector in the direction of motion
	memcpy(normalisedDirectionVector, directionVector, sizeof(normalisedDirectionVector));
	Absolute(normalisedDirectionVector, DRIVES);
	acceleration = VectorBoxIntersection(normalisedDirectionVector, accelerations, DRIVES);

	// Set the speed to the smaller of the requested and maximum speed.
	// Also enforce a minimum speed of 0.5mm/sec. We need a minimum speed to avoid overflow in the movement calculations.
	float reqSpeed = nextMove.feedRate;
	if (isSpecialDeltaMove)
	{
		// Special case of a raw or homing move on a delta printer
		// We use the Cartesian motion system to implement these moves, so the feed rate will be interpreted in Cartesian coordinates.
		// This is wrong, we want the feed rate to apply to the drive that is moving the farthest.
		float maxDistance = 0.0;
		for (size_t axis = 0; axis < DELTA_AXES; ++axis)
		{
			if (normalisedDirectionVector[axis] > maxDistance)
			{
				maxDistance = normalisedDirectionVector[axis];
			}
		}
		if (maxDistance != 0.0)				// should always be true
		{
			reqSpeed /= maxDistance;		// because normalisedDirectionVector is unit-normalised
		}
	}
	requestedSpeed = max<float>(0.5, min<float>(reqSpeed, VectorBoxIntersection(normalisedDirectionVector, reprap.GetPlatform()->MaxFeedrates(), DRIVES)));

	// On a Cartesian or CoreXY printer, it is OK to limit the X and Y speeds and accelerations independently, and in consequence to allow greater values
	// for diagonal moves. On a delta, this is not OK and any movement in the XY plane should be limited to the X/Y axis values, which we assume to be equal.
	if (isDeltaMovement)
	{
		const float xyFactor = sqrt(fsquare(normalisedDirectionVector[X_AXIS]) + fsquare(normalisedDirectionVector[X_AXIS]));
		const float maxSpeed = reprap.GetPlatform()->MaxFeedrates()[X_AXIS];
		if (requestedSpeed * xyFactor > maxSpeed)
		{
			requestedSpeed = maxSpeed/xyFactor;
		}

		const float maxAcceleration = normalAccelerations[X_AXIS];
		if (acceleration * xyFactor > maxAcceleration)
		{
			acceleration = maxAcceleration/xyFactor;
		}
	}

	// 6. Calculate the provisional accelerate and decelerate distances and the top speed
	endSpeed = 0.0;					// until the next move asks us to adjust it

	if (prev->state != provisional)
	{
		// There is no previous move that we can adjust, so this move must start at zero speed.
		startSpeed = 0.0;
	}
	else
	{
		// Try to meld this move to the previous move to avoid stop/start
		// Assuming that this move ends with zero speed, calculate the maximum possible starting speed: u^2 = v^2 - 2as
		prev->targetNextSpeed = min<float>(sqrtf(acceleration * totalDistance * 2.0), requestedSpeed);
		DoLookahead(prev);
		startSpeed = prev->targetNextSpeed;
	}

	RecalculateMove();
	state = provisional;
	return true;
}

float DDA::GetMotorPosition(size_t drive) const
{
	return Move::MotorEndpointToPosition(endPoint[drive], drive);
}

// Return true if this move is or might have been intended to be a deceleration-only move
// A move planned as a deceleration-only move may have a short acceleration segment at the start because of rounding error
// We declare this inline because it is only used once, in DDA::DoLookahead
inline bool DDA::IsDecelerationMove() const
{
	return decelDistance == totalDistance					// the simple case - is a deceleration-only move
			|| (topSpeed < requestedSpeed					// can't have been intended as deceleration-only if it reaches the requested speed
				&& decelDistance > 0.98 * totalDistance		// rounding error can only go so far
				&& prev->state == DDA::provisional			// if we can't adjust the previous move then we don't care (and its figures may not be reliable if it has been recycled already)
				&& prev->decelDistance > 0.0);				// if the previous move has no deceleration phase then no point in adjus6ting it
}

// Try to increase the ending speed of this move to allow the next move to start at targetNextSpeed
/*static*/ void DDA::DoLookahead(DDA *laDDA)
pre(state == provisional)
{
//	if (reprap.Debug(moduleDda)) debugPrintf("Adjusting, %f\n", laDDA->targetNextSpeed);
	unsigned int laDepth = 0;
	bool goingUp = true;

	for(;;)					// this loop is used to nest lookahead without making recursive calls
	{
		bool recurse = false;
		if (goingUp)
		{
			// We have been asked to adjust the end speed of this move to match the next move starting at targetNextSpeed
			if (laDDA->topSpeed >= laDDA->requestedSpeed)
			{
				// This move already reaches its top speed, so just need to adjust the deceleration part
				laDDA->endSpeed = laDDA->requestedSpeed;		// remove the deceleration phase
				laDDA->CalcNewSpeeds();							// put it back if necessary
			}
			else if (laDDA->IsDecelerationMove())
			{
				// This is a deceleration-only move, so we may have to adjust the previous move as well to get optimum behaviour
				if (laDDA->prev->state == provisional)
				{
					laDDA->endSpeed = laDDA->requestedSpeed;
					laDDA->CalcNewSpeeds();
					const float maxStartSpeed = sqrtf(fsquare(laDDA->endSpeed) + (2 * laDDA->acceleration * laDDA->totalDistance));
					if (maxStartSpeed < laDDA->requestedSpeed)
					{
						laDDA->prev->targetNextSpeed = maxStartSpeed;
						// Still provisionally a decelerate-only move
					}
					else
					{
						laDDA->prev->targetNextSpeed = laDDA->requestedSpeed;
					}
					recurse = true;
				}
				else
				{
					// This move is a deceleration-only move but we can't adjust the previous one
					laDDA->hadLookaheadUnderrun = true;
					laDDA->endSpeed = min<float>(sqrtf(fsquare(laDDA->startSpeed) + (2 * laDDA->acceleration * laDDA->totalDistance)),
													laDDA->requestedSpeed);
					laDDA->CalcNewSpeeds();
				}
			}
			else
			{
				// This move doesn't reach its requested speed, but it isn't a deceleration-only move
				// Set its end speed to the minimum of the requested speed and the highest we can reach
				laDDA->endSpeed = min<float>(sqrtf(fsquare(laDDA->startSpeed) + (2 * laDDA->acceleration * laDDA->totalDistance)),
												laDDA->requestedSpeed);
				laDDA->CalcNewSpeeds();
			}
		}
		else
		{
			// Going back down the list
			// We have adjusted the end speed of the previous move as much as is possible and it has adjusted its targetNextSpeed accordingly.
			// Adjust this move to match it.
			laDDA->startSpeed = laDDA->prev->targetNextSpeed;
			const float maxEndSpeed = sqrtf(fsquare(laDDA->startSpeed) + (2 * laDDA->acceleration * laDDA->totalDistance));
			if (maxEndSpeed < laDDA->endSpeed)
			{
				// Oh dear, we were too optimistic! Have another go.
				laDDA->endSpeed = maxEndSpeed;
				laDDA->CalcNewSpeeds();
			}
		}

		if (recurse)
		{
			// Still going up
			laDDA = laDDA->prev;
			++laDepth;
			if (reprap.Debug(moduleDda)) debugPrintf("Recursion start %u\n", laDepth);
		}
		else
		{
			// Either just stopped going up. or going down
			laDDA->RecalculateMove();

			if (laDepth == 0)
			{
//				if (reprap.Debug(moduleDda)) debugPrintf("Complete, %f\n", laDDA->targetNextSpeed);
				return;
			}

			laDDA = laDDA->next;
			--laDepth;
			goingUp = false;
		}
	}
}

// Recalculate the top speed, acceleration distance and deceleration distance, and whether we can pause after this move
// This may cause a move that we intended to be a deceleration-only move to have a tiny acceleration segment at the start
void DDA::RecalculateMove()
{
	accelDistance = (fsquare(requestedSpeed) - fsquare(startSpeed))/(2.0 * acceleration);
	decelDistance = (fsquare(requestedSpeed) - fsquare(endSpeed))/(2.0 * acceleration);
	if (accelDistance + decelDistance >= totalDistance)
	{
		// This move has no steady-speed phase, so it's accelerate-decelerate or accelerate-only move.
		// If V is the peak speed, then (V^2 - u^2)/2a + (V^2 - v^2)/2a = distance.
		// So (2V^2 - u^2 - v^2)/2a = distance
		// So V^2 = a * distance + 0.5(u^2 + v^2)
		float vsquared = (acceleration * totalDistance) + 0.5 * (fsquare(startSpeed) + fsquare(endSpeed));
		// Calculate accelerate distance from: V^2 = u^2 + 2as
		if (vsquared >= 0.0)
		{
			accelDistance = max<float>((vsquared - fsquare(startSpeed))/(2.0 * acceleration), 0.0);
			decelDistance = totalDistance - accelDistance;
			topSpeed = sqrtf(vsquared);
		}
		else if (startSpeed < endSpeed)
		{
			// This would ideally never happen, but might because of rounding errors
			accelDistance = totalDistance;
			decelDistance = 0.0;
			topSpeed = endSpeed;
		}
		else
		{
			// This would ideally never happen, but might because of rounding errors
			accelDistance = 0.0;
			decelDistance = totalDistance;
			topSpeed = startSpeed;
		}
	}
	else
	{
		topSpeed = requestedSpeed;
	}

	canPause = (endStopsToCheck == 0);
	if (canPause && endSpeed != 0.0)
	{
		const Platform *p = reprap.GetPlatform();
		for (size_t drive = 0; drive < DRIVES; ++drive)
		{
			if (ddm[drive].state == DMState::moving && endSpeed * fabsf(directionVector[drive]) > p->ActualInstantDv(drive))
			{
				canPause = false;
				break;
			}
		}
	}
}

// Decide what speed we would really like this move to end at.
// On entry, endSpeed is our proposed ending speed and targetNextSpeed is the proposed starting speed of the next move
// On return, targetNextSpeed is the speed we would like the next move to start at, and endSpeed is the corresponding end speed of this move.
void DDA::CalcNewSpeeds()
{
	// We may have to make multiple passes, because reducing one of the speeds may solve some problems but actually make matters worse on another axis.
	bool limited;
	do
	{
//		debugPrintf("  Pass, start=%f end=%f\n", targetStartSpeed, endSpeed);
		limited = false;
		for (size_t drive = 0; drive < DRIVES; ++drive)
		{
			const float thisMoveFraction = directionVector[drive];
			const float nextMoveFraction = next->directionVector[drive];
			const DriveMovement& thisMoveDm = ddm[drive];
			const DriveMovement& nextMoveDm = next->ddm[drive];
			if (thisMoveDm.state == DMState::moving || nextMoveDm.state == DMState::moving)
			{
				const float thisMoveSpeed = endSpeed * thisMoveFraction;
				const float nextMoveSpeed = targetNextSpeed * nextMoveFraction;
				const float idealDeltaV = fabsf(thisMoveSpeed - nextMoveSpeed);
				float maxDeltaV = reprap.GetPlatform()->ActualInstantDv(drive);
				if (idealDeltaV > maxDeltaV)
				{
					// This drive can't change speed fast enough, so reduce the start and/or end speeds
					// This algorithm sometimes converges very slowly, requiring many passes.
					// To ensure it converges at all, and to speed up convergence, we over-adjust the speed to achieve an even lower deltaV.
					maxDeltaV *= 0.8;
					if ((thisMoveFraction >= 0.0) == (nextMoveFraction >= 0.0))
					{
						// Drive moving in the same direction for this move and the next one, so we must reduce speed of the faster one
						if (fabsf(thisMoveSpeed) > fabsf(nextMoveSpeed))
						{
							endSpeed = (fabsf(nextMoveSpeed) + maxDeltaV)/fabsf(thisMoveFraction);
						}
						else
						{
							targetNextSpeed = (fabsf(thisMoveSpeed) + maxDeltaV)/fabsf(nextMoveFraction);
						}
					}
					else if (fabsf(thisMoveSpeed) * 2 < maxDeltaV)
					{
						targetNextSpeed = (maxDeltaV - fabsf(thisMoveSpeed))/fabsf(nextMoveFraction);
					}
					else if (fabsf(nextMoveSpeed) * 2 < maxDeltaV)
					{
						endSpeed = (maxDeltaV - fabsf(nextMoveSpeed))/fabsf(thisMoveFraction);
					}
					else
					{
						targetNextSpeed = maxDeltaV/(2 * fabsf(nextMoveFraction));
						endSpeed = maxDeltaV/(2 * fabsf(thisMoveFraction));
					}
					limited = true;
					// Most conflicts are between X and Y. So if we just did Y, start another pass immediately to save time.
					if (drive == 1)
					{
						break;
					}
				}
			}
		}
	} while (limited);
}

// This is called by Move::CurrentMoveCompleted to update the live coordinates from the move that has just finished
bool DDA::FetchEndPosition(volatile int32_t ep[DRIVES], volatile float endCoords[MAX_AXES])
{
	for (size_t drive = 0; drive < DRIVES; ++drive)
	{
		ep[drive] = endPoint[drive];
	}
	if (endCoordinatesValid)
	{
		const size_t numAxes = reprap.GetGCodes()->GetNumAxes();
		for (size_t axis = 0; axis < numAxes; ++axis)
		{
			endCoords[axis] = endCoordinates[axis];
		}
	}
	return endCoordinatesValid;
}

void DDA::SetPositions(const float move[DRIVES], size_t numDrives)
{
	reprap.GetMove()->EndPointToMachine(move, endPoint, numDrives);
	const size_t numAxes = reprap.GetGCodes()->GetNumAxes();
	for (size_t axis = 0; axis < numAxes; ++axis)
	{
		endCoordinates[axis] = move[axis];
	}
	endCoordinatesValid = true;
}

// Get a Cartesian end coordinate from this move
float DDA::GetEndCoordinate(size_t drive, bool disableDeltaMapping)
pre(disableDeltaMapping || drive < MAX_AXES)
{
	if (disableDeltaMapping)
	{
		return Move::MotorEndpointToPosition(endPoint[drive], drive);
	}
	else
	{
		const size_t numAxes = reprap.GetGCodes()->GetNumAxes();
		if (drive < numAxes && !endCoordinatesValid)
		{
			reprap.GetMove()->MachineToEndPoint(endPoint, endCoordinates, numAxes);
			endCoordinatesValid = true;
		}
		return endCoordinates[drive];
	}
}

// Calculate the time needed for this move. Called instead of Prepare when we are in simulation mode.
float DDA::CalcTime() const
{
	return (topSpeed - startSpeed)/acceleration								// acceleration time
			+ (totalDistance - accelDistance - decelDistance)/topSpeed		// steady speed time
			+ (topSpeed - endSpeed)/acceleration;							// deceleration time
}

// Prepare this DDA for execution.
// This must not be called with interrupts disabled, because it calls Platform::EnableDrive.
void DDA::Prepare()
{
//debugPrintf("Prep\n");

	PrepParams params;
	params.decelStartDistance = totalDistance - decelDistance;

	// Convert the accelerate/decelerate distances to times
	float accelStopTime = (topSpeed - startSpeed)/acceleration;
	float decelStartTime = accelStopTime + (params.decelStartDistance - accelDistance)/topSpeed;
	float totalTime = decelStartTime + (topSpeed - endSpeed)/acceleration;

	// Enforce the maximum average acceleration
	if (isPrintingMove && topSpeed > startSpeed && topSpeed > endSpeed)
	{
		const float maxAverageAcceleration = reprap.GetPlatform()->GetMaxAverageAcceleration();
		if (2 * topSpeed - startSpeed - endSpeed > totalTime * maxAverageAcceleration)
		{
			// Reduce the top speed to comply with the maximum average acceleration
			const float a2 = fsquare(acceleration);
			const float am2 = fsquare(maxAverageAcceleration);
			const float aam = acceleration * maxAverageAcceleration;
			const float discriminant = (a2 + (2 * aam) - am2) * (fsquare(startSpeed) + fsquare(endSpeed))
					+ (2 * a2 + 2 * am2 - 4 * aam) * startSpeed * endSpeed
					+ (8 * a2 * maxAverageAcceleration - 4 * acceleration * am2) * totalDistance;
			const float oldTopSpeed = topSpeed;
			if (discriminant < 0.0)
			{
				topSpeed = max<float>(startSpeed, endSpeed);
			}
			else
			{
				const float temp =  (sqrtf(discriminant) + (acceleration - maxAverageAcceleration) * (startSpeed + endSpeed))
										/(4 * acceleration - 2 * maxAverageAcceleration);
				topSpeed = max<float>(max<float>(temp, startSpeed), endSpeed);
			}

			//DEBUG
			debugPrintf("ots %f nts %f ss %f es %f\n", oldTopSpeed, topSpeed, startSpeed, endSpeed);

			// Recalculate parameters
			accelDistance = (fsquare(topSpeed) - fsquare(startSpeed))/(2 * acceleration);
			decelDistance = (fsquare(topSpeed) - fsquare(endSpeed))/(2 * acceleration);
			params.decelStartDistance = totalDistance - decelDistance;
			accelStopTime = (topSpeed - startSpeed)/acceleration;
			decelStartTime = accelStopTime + (params.decelStartDistance - accelDistance)/topSpeed;
			totalTime = decelStartTime + (topSpeed - endSpeed)/acceleration;
		}
	}

	clocksNeeded = (uint32_t)(totalTime * stepClockRate);

	params.startSpeedTimesCdivA = (uint32_t)((startSpeed * stepClockRate)/acceleration);
	params.topSpeedTimesCdivA = (uint32_t)((topSpeed * stepClockRate)/acceleration);
	params.decelStartClocks = (uint32_t)(decelStartTime * stepClockRate);
	params.topSpeedTimesCdivAPlusDecelStartClocks = params.topSpeedTimesCdivA + params.decelStartClocks;
	params.accelClocksMinusAccelDistanceTimesCdivTopSpeed = (uint32_t)((accelStopTime - (accelDistance/topSpeed)) * stepClockRate);
	params.compFactor = 1.0 - startSpeed/topSpeed;

	goingSlow = false;
	firstDM = nullptr;

	const size_t numAxes = reprap.GetGCodes()->GetNumAxes();
	for (size_t drive = 0; drive < DRIVES; ++drive)
	{
		DriveMovement& dm = ddm[drive];
		if (dm.state == DMState::moving)
		{
			dm.drive = drive;
			reprap.GetPlatform()->EnableDrive(drive);
			if (drive >= numAxes)
			{
				dm.PrepareExtruder(*this, params, usePressureAdvance);

				// Check for sensible values, print them if they look dubious
				if (reprap.Debug(moduleDda)
					&& (   dm.totalSteps > 1000000
						|| dm.mp.cart.reverseStartStep < dm.mp.cart.decelStartStep
						|| (dm.mp.cart.reverseStartStep <= dm.totalSteps
								&& dm.mp.cart.fourMaxStepDistanceMinusTwoDistanceToStopTimesCsquaredDivA > (int64_t)(dm.mp.cart.twoCsquaredTimesMmPerStepDivA * dm.mp.cart.reverseStartStep))
					  )
				   )
				{
					DebugPrint();
				}
			}
			else if (isDeltaMovement)
			{
				dm.PrepareDeltaAxis(*this, params);

				// Check for sensible values, print them if they look dubious
				if (reprap.Debug(moduleDda) && dm.totalSteps > 1000000)
				{
					DebugPrint();
				}
			}
			else
			{
				dm.PrepareCartesianAxis(*this, params);

				// Check for sensible values, print them if they look dubious
				if (reprap.Debug(moduleDda) && dm.totalSteps > 1000000)
				{
					DebugPrint();
				}
			}

			// Prepare for the first step
			dm.nextStep = 0;
			dm.nextStepTime = 0;
			dm.stepInterval = 999999;						// initialise to a large value so that we will calculate the time for just one step
			dm.stepsTillRecalc = 0;							// so that we don't skip the calculation
			bool stepsToDo = (isDeltaMovement && drive < numAxes)
							? dm.CalcNextStepTimeDelta(*this, false)
							: dm.CalcNextStepTimeCartesian(*this, false);
			if (stepsToDo)
			{
				InsertDM(&dm);
			}
			else
			{
				dm.state = DMState::idle;
			}
		}
	}

	if (reprap.Debug(moduleDda) && reprap.Debug(moduleMove))	// temp show the prepared DDA if debug enabled for both modules
	{
		DebugPrint();
	}

#if DDA_MOVE_DEBUG
	MoveParameters& m = savedMoves[savedMovePointer];
	m.accelDistance = accelDistance;
	m.decelDistance = decelDistance;
	m.steadyDistance = totalDistance - accelDistance - decelDistance;
	m.startSpeed = startSpeed;
	m.topSpeed = topSpeed;
	m.endSpeed = endSpeed;
	savedMovePointer = (savedMovePointer + 1) % NumSavedMoves;
#endif

	state = frozen;					// must do this last so that the ISR doesn't start executing it before we have finished setting it up
}

// The remaining functions are speed-critical, so use full optimisation
#pragma GCC optimize ("O3")

// Start executing this move, returning true if Step() needs to be called immediately. Must be called with interrupts disabled, to avoid a race condition.
// Returns true if the caller needs to call the step ISR immediately.
bool DDA::Start(uint32_t tim)
pre(state == frozen)
{
	moveStartTime = tim;
	state = executing;

	if (firstDM == nullptr)
	{
		// No steps are pending. This should not happen!
		return true;	// schedule another interrupt immediately
	}
	else
	{
		unsigned int extrusions = 0, retractions = 0;		// bitmaps of extruding and retracting drives
		const size_t numAxes = reprap.GetGCodes()->GetNumAxes();
		for (size_t i = 0; i < DRIVES; ++i)
		{
			DriveMovement& dm = ddm[i];
			if (dm.state == DMState::moving)
			{
				reprap.GetPlatform()->SetDirection(i, dm.direction);
				if (i >= numAxes)
				{
					if (dm.direction == FORWARDS)
					{
						extrusions |= (1 << (i - numAxes));
					}
					else
					{
						retractions |= (1 << (i - numAxes));
					}
				}
			}
		}

		bool extruding = false;
		if (extrusions != 0 || retractions != 0)
		{
			const unsigned int prohibitedMovements = reprap.GetProhibitedExtruderMovements(extrusions, retractions);
			for (DriveMovement **dmpp = &firstDM; *dmpp != nullptr; )
			{
				bool thisDriveExtruding = (*dmpp)->drive >= numAxes;
				if (thisDriveExtruding && (prohibitedMovements & (1 << ((*dmpp)->drive - numAxes))) != 0)
				{
					*dmpp = (*dmpp)->nextDM;
				}
				else
				{
					extruding = extruding || thisDriveExtruding;
					dmpp = &((*dmpp)->nextDM);
				}
			}
		}

		Platform *platform = reprap.GetPlatform();
		if (extruding)
		{
			platform->ExtrudeOn();
		}
		else
		{
			platform->ExtrudeOff();
		}

		if (firstDM != nullptr)
		{
			return platform->ScheduleInterrupt(firstDM->nextStepTime + moveStartTime);
		}
		else
		{
			return true;
		}
	}
}

extern uint32_t maxReps;

// This is called by the interrupt service routine to execute steps.
// It returns true if it needs to be called again on the DDA of the new current move, otherwise false.
// This must be as fast as possible, because it determines the maximum movement speed.
bool DDA::Step()
{
	Platform *platform = reprap.GetPlatform();
	uint32_t lastStepPulseTime = platform->GetInterruptClocks();
	bool repeat;
	uint32_t numReps = 0;
	do
	{
		// Keep this loop as fast as possible, in the case that there are no endstops to check!

		// 1. Check endstop switches and Z probe if asked. This is not speed critical because fast moves do not use endstops or the Z probe.
		if (endStopsToCheck != 0)											// if any homing switches or the Z probe is enabled in this move
		{
			if ((endStopsToCheck & ZProbeActive) != 0)						// if the Z probe is enabled in this move
			{
				// Check whether the Z probe has been triggered. On a delta at least, this must be done separately from endstop checks,
				// because we have both a high endstop and a Z probe, and the Z motor is not the same thing as the Z axis.
				switch (platform->GetZProbeResult())
				{
				case EndStopHit::lowHit:
					MoveAborted();											// set the state to completed and recalculate the endpoints
					reprap.GetMove()->ZProbeTriggered(this);
					break;

				case EndStopHit::lowNear:
					ReduceHomingSpeed();
					break;

				default:
					break;
				}
			}

			const size_t numAxes = reprap.GetGCodes()->GetNumAxes();
			for (size_t drive = 0; drive < numAxes; ++drive)
			{
				if ((endStopsToCheck & (1 << drive)) != 0)
				{
					switch(platform->Stopped(drive))
					{
					case EndStopHit::lowHit:
						endStopsToCheck &= ~(1 << drive);					// clear this check so that we can check for more
						if (endStopsToCheck == 0 || reprap.GetMove()->IsCoreXYAxis(drive))	// if no more endstops to check, or this axis uses shared motors
						{
							MoveAborted();
						}
						else
						{
							StopDrive(drive);
						}
						reprap.GetMove()->HitLowStop(drive, this);
						break;

					case EndStopHit::highHit:
						endStopsToCheck &= ~(1 << drive);					// clear this check so that we can check for more
						if (endStopsToCheck == 0 || reprap.GetMove()->IsCoreXYAxis(drive))	// if no more endstops to check, or this axis uses shared motors
						{
							MoveAborted();
						}
						else
						{
							StopDrive(drive);
						}
						reprap.GetMove()->HitHighStop(drive, this);
						break;

					case EndStopHit::lowNear:
						// Only reduce homing speed if there are no more axes to be homed.
						// This allows us to home X and Y simultaneously.
						if (endStopsToCheck == (1 << drive))
						{
							ReduceHomingSpeed();
						}
						break;

					default:
						break;
					}
				}
			}

			if (state == completed)		// we may have completed the move due to triggering an endstop switch or Z probe
			{
				break;
			}
		}

		// 2. Determine which drivers are due for stepping, overdue, or will be due very shortly
		DriveMovement* dm = firstDM;
		const uint32_t elapsedTime = (Platform::GetInterruptClocks() - moveStartTime) + minInterruptInterval;
		uint32_t driversStepping = 0;
		while (dm != nullptr && elapsedTime >= dm->nextStepTime)		// if the next step is due
		{
			++numReps;
			driversStepping |= platform->GetDriversBitmap(dm->drive);
			dm = dm->nextDM;

//uint32_t t3 = Platform::GetInterruptClocks() - t2;
//if (t3 > maxCalcTime) maxCalcTime = t3;
//if (t3 < minCalcTime) minCalcTime = t3;
		}

		// 3. Step the drivers
		if ((driversStepping & platform->GetSlowDrivers()) != 0)
		{
			while (Platform::GetInterruptClocks() - lastStepPulseTime < platform->GetSlowDriverClocks()) {}
			Platform::StepDriversHigh(driversStepping);					// generate the steps
			lastStepPulseTime = Platform::GetInterruptClocks();
		}
		else
		{
			Platform::StepDriversHigh(driversStepping);					// generate the steps
		}

		// 4. Remove those drives from the list, calculate the next step times, update the direction pins where necessary,
		//    and re-insert them so as to keep the list in step-time order. We assume that meeting the direction pin hold time
		//    is not a problem for any driver type. This is not necessarily true.
		DriveMovement *dmToInsert = firstDM;							// head of the chain we need to re-insert
		firstDM = dm;													// remove the chain from the list
		while (dmToInsert != dm)										// note that both of these may be nullptr
		{
			const bool hasMoreSteps = (isDeltaMovement && dmToInsert->drive < DELTA_AXES)
					? dmToInsert->CalcNextStepTimeDelta(*this, true)
					: dmToInsert->CalcNextStepTimeCartesian(*this, true);
			DriveMovement * const nextToInsert = dmToInsert->nextDM;
			if (hasMoreSteps)
			{
				InsertDM(dmToInsert);
			}
			dmToInsert = nextToInsert;
		}

		// 5. Reset all step pins low
		if ((driversStepping & platform->GetSlowDrivers()) != 0)
		{
			while (Platform::GetInterruptClocks() - lastStepPulseTime < platform->GetSlowDriverClocks()) {}
			Platform::StepDriversLow();									// set all step pins low
			lastStepPulseTime = Platform::GetInterruptClocks();
		}
		else
		{
			Platform::StepDriversLow();									// set all step pins low
		}

		// 6. Check for move completed
		if (firstDM == nullptr)
		{
			state = completed;
			break;
		}

		// 7. Schedule next interrupt, or if it would be too soon, generate more steps immediately
		repeat = platform->ScheduleInterrupt(firstDM->nextStepTime + moveStartTime);
	} while (repeat);

	if (numReps > maxReps)
	{
		maxReps = numReps;
	}

	if (state == completed)
	{
		uint32_t finishTime = moveStartTime + clocksNeeded;		// calculate how long this move should take
		Move *move = reprap.GetMove();
		move->CurrentMoveCompleted();							// tell Move that the current move is complete
		return move->TryStartNextMove(finishTime);				// schedule the next move
	}
	return false;
}

// Stop a drive and re-calculate the corresponding endpoint
void DDA::StopDrive(size_t drive)
{
	DriveMovement& dm = ddm[drive];
	if (dm.state == DMState::moving)
	{
		int32_t stepsLeft = dm.totalSteps - dm.nextStep + 1;
		if (dm.direction)
		{
			endPoint[drive] -= stepsLeft;			// we were going forwards
		}
		else
		{
			endPoint[drive] += stepsLeft;			// we were going backwards
		}
		dm.state = DMState::idle;
		if (drive < reprap.GetGCodes()->GetNumAxes())
		{
			endCoordinatesValid = false;			// the XYZ position is no longer valid
		}
		RemoveDM(drive);
		if (firstDM == nullptr)
		{
			state = completed;
		}
	}
}

// This is called when we abort a move because we have hit an endstop.
// It adjusts the end points of the current move to account for how far through the move we got.
void DDA::MoveAborted()
{
	for (size_t drive = 0; drive < DRIVES; ++drive)
	{
		StopDrive(drive);
	}
	state = completed;
}

// Reduce the speed of this move to the indicated speed.
// This is called from the ISR, so interrupts are disabled and nothing else can mess with us.
// As this is only called for homing moves and with very low speeds, we assume that we don't need acceleration or deceleration phases.
void DDA::ReduceHomingSpeed()
{
	if (!goingSlow)
	{
		goingSlow = true;
		const float factor = 3.0;				// the factor by which we are reducing the speed
		topSpeed /= factor;
		for (size_t drive = 0; drive < DRIVES; ++drive)
		{
			DriveMovement& dm = ddm[drive];
			if (dm.state == DMState::moving)
			{
				dm.ReduceSpeed(*this, factor);
				RemoveDM(dm.drive);
				InsertDM(&dm);
			}
		}

		// We also need to adjust the total clocks needed, to prevent step errors being recorded
		const uint32_t clocksSoFar = Platform::GetInterruptClocks() - moveStartTime;
		if (clocksSoFar < clocksNeeded)
		{
			const uint32_t clocksLeft = clocksNeeded - clocksSoFar;
			clocksNeeded += (uint32_t)(clocksLeft * (factor - 1.0));
		}
	}
}

bool DDA::HasStepError() const
{
	for (size_t drive = 0; drive < DRIVES; ++drive)
	{
		const DriveMovement& dm = ddm[drive];
		if (dm.state == DMState::stepError)
		{
			return true;
		}
	}
	return false;
}

// Remove this drive from the list of drives with steps due, and return its DM or nullptr if not there
// Called from the step ISR only.
DriveMovement *DDA::RemoveDM(size_t drive)
{
	DriveMovement **dmp = &firstDM;
	while (*dmp != nullptr)
	{
		DriveMovement *dm = *dmp;
		if (dm->drive == drive)
		{
			(*dmp) = dm->nextDM;
			return dm;
		}
		dmp = &(dm->nextDM);
	}
	return nullptr;
}

// Take a unit positive-hyperquadrant vector, and return the factor needed to obtain
// length of the vector as projected to touch box[].
float DDA::VectorBoxIntersection(const float v[], const float box[], size_t dimensions)
{
	// Generate a vector length that is guaranteed to exceed the size of the box
	float biggerThanBoxDiagonal = 2.0*Magnitude(box, dimensions);
	float magnitude = biggerThanBoxDiagonal;
	for (size_t d = 0; d < dimensions; d++)
	{
		if (biggerThanBoxDiagonal*v[d] > box[d])
		{
			float a = box[d]/v[d];
			if (a < magnitude)
			{
				magnitude = a;
			}
		}
	}
	return magnitude;
}

// Normalise a vector with dim1 dimensions so that it is unit in the first dim2 dimensions, and also return its previous magnitude in dim2 dimensions
float DDA::Normalise(float v[], size_t dim1, size_t dim2)
{
	float magnitude = Magnitude(v, dim2);
	if (magnitude <= 0.0)
	{
		return 0.0;
	}
	Scale(v, 1.0/magnitude, dim1);
	return magnitude;
}

// Return the magnitude of a vector
float DDA::Magnitude(const float v[], size_t dimensions)
{
	float magnitude = 0.0;
	for (size_t d = 0; d < dimensions; d++)
	{
		magnitude += v[d]*v[d];
	}
	magnitude = sqrtf(magnitude);
	return magnitude;
}

// Multiply a vector by a scalar
void DDA::Scale(float v[], float scale, size_t dimensions)
{
	for(size_t d = 0; d < dimensions; d++)
	{
		v[d] = scale*v[d];
	}
}

// Move a vector into the positive hyperquadrant
void DDA::Absolute(float v[], size_t dimensions)
{
	for(size_t d = 0; d < dimensions; d++)
	{
		v[d] = fabsf(v[d]);
	}
}

// End