teensy-audio/synth_waveform.cpp

/* Audio Library for Teensy 3.X
 * Copyright (c) 2018, Paul Stoffregen, paul@pjrc.com
 *
 * Development of this audio library was funded by PJRC.COM, LLC by sales of
 * Teensy and Audio Adaptor boards.  Please support PJRC's efforts to develop
 * open source software by purchasing Teensy or other PJRC products.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice, development funding notice, and this permission
 * notice shall be included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

#include <Arduino.h>
#include "synth_waveform.h"
#include "arm_math.h"
#include "utility/dspinst.h"


// uncomment for more accurate but more computationally expensive frequency modulation
//#define IMPROVE_EXPONENTIAL_ACCURACY
#define BASE_AMPLITUDE 0x6000  // 0x7fff won't work due to Gibb's phenomenon, so use 3/4 of full range.



void AudioSynthWaveform::update(void)
{
	audio_block_t *block;
	int16_t *bp, *end;
	int32_t val1, val2;
	int16_t magnitude15;
	uint32_t i, ph, index, index2, scale;
	const uint32_t inc = phase_increment;

	ph = phase_accumulator + phase_offset;
	if (magnitude == 0) {
		phase_accumulator += inc * AUDIO_BLOCK_SAMPLES;
		return;
	}
	block = allocate();
	if (!block) {
		phase_accumulator += inc * AUDIO_BLOCK_SAMPLES;
		return;
	}
	bp = block->data;

	switch(tone_type) {
	case WAVEFORM_SINE:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			index = ph >> 24;
			val1 = AudioWaveformSine[index];
			val2 = AudioWaveformSine[index+1];
			scale = (ph >> 8) & 0xFFFF;
			val2 *= scale;
			val1 *= 0x10000 - scale;
			*bp++ = multiply_32x32_rshift32(val1 + val2, magnitude);
			ph += inc;
		}
		break;

	case WAVEFORM_ARBITRARY:
		if (!arbdata) {
			release(block);
			phase_accumulator += inc * AUDIO_BLOCK_SAMPLES;
			return;
		}
		// len = 256
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			index = ph >> 24;
			index2 = index + 1;
			if (index2 >= 256) index2 = 0;
			val1 = *(arbdata + index);
			val2 = *(arbdata + index2);
			scale = (ph >> 8) & 0xFFFF;
			val2 *= scale;
			val1 *= 0x10000 - scale;
			*bp++ = multiply_32x32_rshift32(val1 + val2, magnitude);
			ph += inc;
		}
		break;

	case WAVEFORM_SQUARE:
		magnitude15 = signed_saturate_rshift(magnitude, 16, 1);
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			if (ph & 0x80000000) {
				*bp++ = -magnitude15;
			} else {
				*bp++ = magnitude15;
			}
			ph += inc;
		}
		break;

	case WAVEFORM_BANDLIMIT_SQUARE:
		for (int i = 0 ; i < AUDIO_BLOCK_SAMPLES ; i++)
		{
		  uint32_t new_ph = ph + inc ;
		  int16_t val = band_limit_waveform.generate_square (new_ph, i) ;
		  *bp++ = (val * magnitude) >> 16 ;
		  ph = new_ph ;
		}
		break;

	case WAVEFORM_SAWTOOTH:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			*bp++ = signed_multiply_32x16t(magnitude, ph);
			ph += inc;
		}
		break;

	case WAVEFORM_SAWTOOTH_REVERSE:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			*bp++ = signed_multiply_32x16t(0xFFFFFFFFu - magnitude, ph);
			ph += inc;
		}
		break;

	case WAVEFORM_BANDLIMIT_SAWTOOTH:
	case WAVEFORM_BANDLIMIT_SAWTOOTH_REVERSE:
		for (i = 0 ; i < AUDIO_BLOCK_SAMPLES; i++)
		{
		  uint32_t new_ph = ph + inc ;
		  int16_t val = band_limit_waveform.generate_sawtooth (new_ph, i) ;
		  if (tone_type == WAVEFORM_BANDLIMIT_SAWTOOTH_REVERSE)
		    *bp++ = (val * -magnitude) >> 16 ;
		  else
		    *bp++ = (val * magnitude) >> 16 ;
		  ph = new_ph ;
		}
		break;

	case WAVEFORM_TRIANGLE:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			uint32_t phtop = ph >> 30;
			if (phtop == 1 || phtop == 2) {
				*bp++ = ((0xFFFF - (ph >> 15)) * magnitude) >> 16;
			} else {
				*bp++ = (((int32_t)ph >> 15) * magnitude) >> 16;
			}
			ph += inc;
		}
		break;

	case WAVEFORM_TRIANGLE_VARIABLE:
		do {
		uint32_t rise = 0xFFFFFFFF / (pulse_width >> 16);
		uint32_t fall = 0xFFFFFFFF / (0xFFFF - (pulse_width >> 16));
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			if (ph < pulse_width/2) {
				uint32_t n = (ph >> 16) * rise;
				*bp++ = ((n >> 16) * magnitude) >> 16;
			} else if (ph < 0xFFFFFFFF - pulse_width/2) {
				uint32_t n = 0x7FFFFFFF - (((ph - pulse_width/2) >> 16) * fall);
				*bp++ = (((int32_t)n >> 16) * magnitude) >> 16;
			} else {
				uint32_t n = ((ph + pulse_width/2) >> 16) * rise + 0x80000000;
				*bp++ = (((int32_t)n >> 16) * magnitude) >> 16;
			}
			ph += inc;
		}
		} while (0);
		break;

	case WAVEFORM_PULSE:
		magnitude15 = signed_saturate_rshift(magnitude, 16, 1);
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			if (ph < pulse_width) {
				*bp++ = magnitude15;
			} else {
				*bp++ = -magnitude15;
			}
			ph += inc;
		}
		break;

	case WAVEFORM_BANDLIMIT_PULSE:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++)
		{
		  int32_t new_ph = ph + inc ;
		  int32_t val = band_limit_waveform.generate_pulse (new_ph, pulse_width, i) ;
		  *bp++ = (int16_t) ((val * magnitude) >> 16) ;
		  ph = new_ph ;
		}
		break;

	case WAVEFORM_SAMPLE_HOLD:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			*bp++ = sample;
			uint32_t newph = ph + inc;
			if (newph < ph) {
				sample = random(magnitude) - (magnitude >> 1);
			}
			ph = newph;
		}
		break;
	}
	phase_accumulator = ph - phase_offset;

	if (tone_offset) {
		bp = block->data;
		end = bp + AUDIO_BLOCK_SAMPLES;
		do {
			val1 = *bp;
			*bp++ = signed_saturate_rshift(val1 + tone_offset, 16, 0);
		} while (bp < end);
	}
	transmit(block, 0);
	release(block);
}

//--------------------------------------------------------------------------------

void AudioSynthWaveformModulated::update(void)
{
	audio_block_t *block, *moddata, *shapedata;
	int16_t *bp, *end;
	int32_t val1, val2;
	int16_t magnitude15;
	uint32_t i, ph, index, index2, scale, priorphase;
	const uint32_t inc = phase_increment;

	moddata = receiveReadOnly(0);
	shapedata = receiveReadOnly(1);

	// Pre-compute the phase angle for every output sample of this update
	ph = phase_accumulator;
	priorphase = phasedata[AUDIO_BLOCK_SAMPLES-1];
	if (moddata && modulation_type == 0) {
		// Frequency Modulation
		bp = moddata->data;
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			int32_t n = (*bp++) * modulation_factor; // n is # of octaves to mod
			int32_t ipart = n >> 27; // 4 integer bits
			n &= 0x7FFFFFF;          // 27 fractional bits
			#ifdef IMPROVE_EXPONENTIAL_ACCURACY
			// exp2 polynomial suggested by Stefan Stenzel on "music-dsp"
			// mail list, Wed, 3 Sep 2014 10:08:55 +0200
			int32_t x = n << 3;
			n = multiply_accumulate_32x32_rshift32_rounded(536870912, x, 1494202713);
			int32_t sq = multiply_32x32_rshift32_rounded(x, x);
			n = multiply_accumulate_32x32_rshift32_rounded(n, sq, 1934101615);
			n = n + (multiply_32x32_rshift32_rounded(sq,
				multiply_32x32_rshift32_rounded(x, 1358044250)) << 1);
			n = n << 1;
			#else
			// exp2 algorithm by Laurent de Soras
			// https://www.musicdsp.org/en/latest/Other/106-fast-exp2-approximation.html
			n = (n + 134217728) << 3;

			n = multiply_32x32_rshift32_rounded(n, n);
			n = multiply_32x32_rshift32_rounded(n, 715827883) << 3;
			n = n + 715827882;
			#endif
			uint32_t scale = n >> (14 - ipart);
			uint64_t phstep = (uint64_t)inc * scale;
			uint32_t phstep_msw = phstep >> 32;
			if (phstep_msw < 0x7FFE) {
				ph += phstep >> 16;
			} else {
				ph += 0x7FFE0000;
			}
			phasedata[i] = ph;
		}
		release(moddata);
	} else if (moddata) {
		// Phase Modulation
		bp = moddata->data;
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			// more than +/- 180 deg shift by 32 bit overflow of "n"
			uint32_t n = (uint16_t)(*bp++) * modulation_factor;
			phasedata[i] = ph + n;
			ph += inc;
		}
		release(moddata);
	} else {
		// No Modulation Input
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			phasedata[i] = ph;
			ph += inc;
		}
	}
	phase_accumulator = ph;

	// If the amplitude is zero, no output, but phase still increments properly
	if (magnitude == 0) {
		if (shapedata) release(shapedata);
		return;
	}
	block = allocate();
	if (!block) {
		if (shapedata) release(shapedata);
		return;
	}
	bp = block->data;

	// Now generate the output samples using the pre-computed phase angles
	switch(tone_type) {
	case WAVEFORM_SINE:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			ph = phasedata[i];
			index = ph >> 24;
			val1 = AudioWaveformSine[index];
			val2 = AudioWaveformSine[index+1];
			scale = (ph >> 8) & 0xFFFF;
			val2 *= scale;
			val1 *= 0x10000 - scale;
			*bp++ = multiply_32x32_rshift32(val1 + val2, magnitude);
		}
		break;

	case WAVEFORM_ARBITRARY:
		if (!arbdata) {
			release(block);
			if (shapedata) release(shapedata);
			return;
		}
		// len = 256
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			ph = phasedata[i];
			index = ph >> 24;
			index2 = index + 1;
			if (index2 >= 256) index2 = 0;
			val1 = *(arbdata + index);
			val2 = *(arbdata + index2);
			scale = (ph >> 8) & 0xFFFF;
			val2 *= scale;
			val1 *= 0x10000 - scale;
			*bp++ = multiply_32x32_rshift32(val1 + val2, magnitude);
		}
		break;

	case WAVEFORM_PULSE:
		if (shapedata) {
			magnitude15 = signed_saturate_rshift(magnitude, 16, 1);
			for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
				uint32_t width = ((shapedata->data[i] + 0x8000) & 0xFFFF) << 16;
				if (phasedata[i] < width) {
					*bp++ = magnitude15;
				} else {
					*bp++ = -magnitude15;
				}
			}
			break;
		} // else fall through to orginary square without shape modulation

	case WAVEFORM_SQUARE:
		magnitude15 = signed_saturate_rshift(magnitude, 16, 1);
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			if (phasedata[i] & 0x80000000) {
				*bp++ = -magnitude15;
			} else {
				*bp++ = magnitude15;
			}
		}
		break;

	case WAVEFORM_BANDLIMIT_PULSE:
		if (shapedata)
		{
		  for (i=0; i < AUDIO_BLOCK_SAMPLES; i++)
		  {
		    uint32_t width = ((shapedata->data[i] + 0x8000) & 0xFFFF) << 16;
		    int32_t val = band_limit_waveform.generate_pulse (phasedata[i], width, i) ;
		    *bp++ = (int16_t) ((val * magnitude) >> 16) ;
		  }
		  break;
		} // else fall through to orginary square without shape modulation

	case WAVEFORM_BANDLIMIT_SQUARE:
		for (i = 0 ; i < AUDIO_BLOCK_SAMPLES ; i++)
		{
		  int32_t val = band_limit_waveform.generate_square (phasedata[i], i) ;
		  *bp++ = (int16_t) ((val * magnitude) >> 16) ;
		}
		break;

	case WAVEFORM_SAWTOOTH:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			*bp++ = signed_multiply_32x16t(magnitude, phasedata[i]);
		}
		break;

	case WAVEFORM_SAWTOOTH_REVERSE:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			*bp++ = signed_multiply_32x16t(0xFFFFFFFFu - magnitude, phasedata[i]);
		}
		break;

	case WAVEFORM_BANDLIMIT_SAWTOOTH:
	case WAVEFORM_BANDLIMIT_SAWTOOTH_REVERSE:
		for (i = 0 ; i < AUDIO_BLOCK_SAMPLES ; i++)
		{
		  int16_t val = band_limit_waveform.generate_sawtooth (phasedata[i], i) ;
		  val = (int16_t) ((val * magnitude) >> 16) ;
		  *bp++ = tone_type == WAVEFORM_BANDLIMIT_SAWTOOTH_REVERSE ? (int16_t) -val : (int16_t) +val ;
		}
		break;

	case WAVEFORM_TRIANGLE_VARIABLE:
		if (shapedata) {
			for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
				uint32_t width = (shapedata->data[i] + 0x8000) & 0xFFFF;
				uint32_t rise = 0xFFFFFFFF / width;
				uint32_t fall = 0xFFFFFFFF / (0xFFFF - width);
				uint32_t halfwidth = width << 15;
				uint32_t n;
				ph = phasedata[i];
				if (ph < halfwidth) {
					n = (ph >> 16) * rise;
					*bp++ = ((n >> 16) * magnitude) >> 16;
				} else if (ph < 0xFFFFFFFF - halfwidth) {
					n = 0x7FFFFFFF - (((ph - halfwidth) >> 16) * fall);
					*bp++ = (((int32_t)n >> 16) * magnitude) >> 16;
				} else {
					n = ((ph + halfwidth) >> 16) * rise + 0x80000000;
					*bp++ = (((int32_t)n >> 16) * magnitude) >> 16;
				}
				ph += inc;
			}
			break;
		} // else fall through to orginary triangle without shape modulation

	case WAVEFORM_TRIANGLE:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			ph = phasedata[i];
			uint32_t phtop = ph >> 30;
			if (phtop == 1 || phtop == 2) {
				*bp++ = ((0xFFFF - (ph >> 15)) * magnitude) >> 16;
			} else {
				*bp++ = (((int32_t)ph >> 15) * magnitude) >> 16;
			}
		}
		break;
	case WAVEFORM_SAMPLE_HOLD:
		for (i=0; i < AUDIO_BLOCK_SAMPLES; i++) {
			ph = phasedata[i];
			if (ph < priorphase) { // does not work for phase modulation
				sample = random(magnitude) - (magnitude >> 1);
			}
			priorphase = ph;
			*bp++ = sample;
		}
		break;
	}

	if (tone_offset) {
		bp = block->data;
		end = bp + AUDIO_BLOCK_SAMPLES;
		do {
			val1 = *bp;
			*bp++ = signed_saturate_rshift(val1 + tone_offset, 16, 0);
		} while (bp < end);
	}
	if (shapedata) release(shapedata);
	transmit(block, 0);
	release(block);
}


// BandLimitedWaveform


#define SUPPORT_SHIFT 4
#define SUPPORT (1 << SUPPORT_SHIFT)
#define PTRMASK ((2 << SUPPORT_SHIFT) - 1)

#define SCALE 16
#define SCALE_MASK (SCALE-1)
#define N (SCALE * SUPPORT * 2)

#define GUARD_BITS 8
#define GUARD      (1 << GUARD_BITS)
#define HALF_GUARD (1 << (GUARD_BITS-1))


#define DEG180 0x80000000u

#define PHASE_SCALE (0x100000000L / (2 * BASE_AMPLITUDE))


extern "C"
{
  extern const int16_t step_table [258] ;
}

int32_t BandLimitedWaveform::lookup (int offset)
{
  int off = offset >> GUARD_BITS ;
  int frac = offset & (GUARD-1) ;

  int32_t a, b ;
  if (off < N/2)   // handle odd symmetry by reflecting table
  {
    a = step_table [off+1] ;
    b = step_table [off+2] ;
  }
  else
  {
    a = - step_table [N-off] ;
    b = - step_table [N-off-1] ;
  }
  return  BASE_AMPLITUDE + ((frac * b + (GUARD - frac) * a + HALF_GUARD) >> GUARD_BITS) ; // interpolated
}

// create a new step, apply its past waveform into the cyclic sample buffer
// and add a step_state object into active list so it can be added for the future samples
void BandLimitedWaveform::insert_step (int offset, bool rising, int i)
{
  while (offset <= (N/2-SCALE)<<GUARD_BITS)
  {
    if (offset >= 0)
      cyclic [i & 15] += rising ? lookup (offset) : -lookup (offset) ;
    offset += SCALE<<GUARD_BITS ;
    i ++ ;
  }

  states[newptr].offset = offset ;
  states[newptr].positive = rising ;
  newptr = (newptr+1) & PTRMASK ;
}

// generate value for current sample from one active step, checking for the
// dc_offset adjustment at the end of the table.
int32_t BandLimitedWaveform::process_step (int i)
{
  int off = states[i].offset ;
  bool positive = states[i].positive ;

  int32_t entry = lookup (off) ;
  off += SCALE<<GUARD_BITS ;
  states[i].offset = off ;  // update offset in table for next sample
  if (off >= N<<GUARD_BITS)             // at end of step table we alter dc_offset to extend the step into future
    dc_offset += positive ? 2*BASE_AMPLITUDE : -2*BASE_AMPLITUDE ;

  return positive ? entry : -entry ;
}

// process all active steps for current sample, basically generating the waveform portion
// due only to steps
// square waves use this directly.
int32_t BandLimitedWaveform::process_active_steps (uint32_t new_phase)
{
  int32_t sample = dc_offset ;
  
  int step_count = (newptr - delptr) & PTRMASK ;
  if (step_count > 0)        // for any steps in-flight we sum in table entry and update its state
  {
    int i = newptr ;
    do
    {
      i = (i-1) & PTRMASK ;
      sample += process_step (i) ;
    } while (i != delptr) ;
    if (states[delptr].offset >= N<<GUARD_BITS)  // remove any finished entries from the buffer.
    {
      delptr = (delptr+1) & PTRMASK ;
      // can be upto two steps per sample now for pulses
      if (newptr != delptr && states[delptr].offset >= N<<GUARD_BITS)
	delptr = (delptr+1) & PTRMASK ;
    }
  }
  return sample ;
}

// for sawtooth need to add in the slope and compensate for all the steps being one way
int32_t BandLimitedWaveform::process_active_steps_saw (uint32_t new_phase)
{
  int32_t sample = process_active_steps (new_phase) ;

  sample += (int16_t) ((((uint64_t)phase_word * (2*BASE_AMPLITUDE)) >> 32) - BASE_AMPLITUDE) ;  // generate the sloped part of the wave

  if (new_phase < DEG180 && phase_word >= DEG180) // detect wrap around, correct dc offset
    dc_offset += 2*BASE_AMPLITUDE ;

  return sample ;
}

// for pulse need to adjust the baseline according to the pulse width to cancel the DC component.
int32_t BandLimitedWaveform::process_active_steps_pulse (uint32_t new_phase, uint32_t pulse_width)
{
  int32_t sample = process_active_steps (new_phase) ;

  return sample + BASE_AMPLITUDE/2 - pulse_width / (0x80000000u / BASE_AMPLITUDE) ; // correct DC offset for duty cycle
}

// Check for new steps using the phase update for the current sample for a square wave
void BandLimitedWaveform::new_step_check_square (uint32_t new_phase, int i)
{
  if (new_phase >= DEG180 && phase_word < DEG180) // detect falling step
  {
    int32_t offset = (int32_t) ((uint64_t) (SCALE<<GUARD_BITS) * (sampled_width - phase_word) / (new_phase - phase_word)) ;
    if (offset == SCALE<<GUARD_BITS)
      offset -- ;
    if (pulse_state) // guard against two falling steps in a row (if pulse width changing for instance)
    {
      insert_step (- offset, false, i) ;
      pulse_state = false ;
    }
  }
  else if (new_phase < DEG180 && phase_word >= DEG180) // detect wrap around, rising step
  {
    int32_t offset = (int32_t) ((uint64_t) (SCALE<<GUARD_BITS) * (- phase_word) / (new_phase - phase_word)) ;
    if (offset == SCALE<<GUARD_BITS)
      offset -- ;
    if (!pulse_state) // guard against two rising steps in a row (if pulse width changing for instance)
    {
      insert_step (- offset, true, i) ;
      pulse_state = true ;
    }
  }
}

// Checking for new steps for pulse waveform has to deal with changing frequency and pulse width and
// not letting a pulse glitch out of existence as these change across a single period of the waveform
// now we detect the rising edge just like for a square wave and use that to sample the pulse width
// parameter, which then has to be checked against the instantaneous frequency every sample.
void BandLimitedWaveform::new_step_check_pulse (uint32_t new_phase, uint32_t pulse_width, int i)
{
  if (pulse_state && phase_word < sampled_width && (new_phase >= sampled_width || new_phase < phase_word))  // falling edge
  {
    int32_t offset = (int32_t) ((uint64_t) (SCALE<<GUARD_BITS) * (sampled_width - phase_word) / (new_phase - phase_word)) ;
    if (offset == SCALE<<GUARD_BITS)
      offset -- ;
    insert_step (- offset, false, i) ;
    pulse_state = false ;
  }
  if ((!pulse_state) && phase_word >= DEG180 && new_phase < DEG180) // detect wrap around, rising step
  {
    // sample the pulse width value so its not changing under our feet later in cycle due to modulation
    sampled_width = pulse_width ;

    int32_t offset = (int32_t) ((uint64_t) (SCALE<<GUARD_BITS) * (- phase_word) / (new_phase - phase_word)) ;
    if (offset == SCALE<<GUARD_BITS)
      offset -- ;
    insert_step (- offset, true, i) ;
    pulse_state = true ;
    
    if (pulse_state && new_phase >= sampled_width) // detect falling step directly after a rising edge
    //if (new_phase - sampled_width < DEG180) // detect falling step directly after a rising edge
    {
      int32_t offset = (int32_t) ((uint64_t) (SCALE<<GUARD_BITS) * (sampled_width - phase_word) / (new_phase - phase_word)) ;
      if (offset == SCALE<<GUARD_BITS)
	offset -- ;
      insert_step (- offset, false, i) ;
      pulse_state = false ;
    }
  }
}

// new steps for sawtooth are at 180 degree point, always falling.
void BandLimitedWaveform::new_step_check_saw (uint32_t new_phase, int i)
{
  if (new_phase >= DEG180 && phase_word < DEG180) // detect falling step
  {
    int32_t offset = (int32_t) ((uint64_t) (SCALE<<GUARD_BITS) * (DEG180 - phase_word) / (new_phase - phase_word)) ;
    if (offset == SCALE<<GUARD_BITS)
      offset -- ;
    insert_step (- offset, false, i) ;
  }
}
  
// the generation function pushd new sample into cyclic buffer, having taken out the oldest entry
// to return.  The output is thus 16 samples behind, which allows the non-casual step function to
// work in real time.
int16_t BandLimitedWaveform::generate_sawtooth (uint32_t new_phase, int i)
{
  new_step_check_saw (new_phase, i) ;
  int32_t val = process_active_steps_saw (new_phase) ;
  int16_t sample = (int16_t) cyclic [i&15] ;
  cyclic [i&15] = val ;
  phase_word = new_phase ;
  return sample ;
}

int16_t BandLimitedWaveform::generate_square (uint32_t new_phase, int i)
{
  new_step_check_square (new_phase, i) ;
  int32_t val = process_active_steps (new_phase) ;
  int16_t sample = (int16_t) cyclic [i&15] ;
  cyclic [i&15] = val ;
  phase_word = new_phase ;
  return sample ;
}

int16_t BandLimitedWaveform::generate_pulse (uint32_t new_phase, uint32_t pulse_width, int i)
{
  new_step_check_pulse (new_phase, pulse_width, i) ;
  int32_t val = process_active_steps_pulse (new_phase, pulse_width) ;
  int32_t sample = cyclic [i&15] ;
  cyclic [i&15] = val ;
  phase_word = new_phase ;
  return (int16_t) ((sample >> 1) - (sample >> 5)) ; // scale down to avoid overflow on narrow pulses, where the DC shift is big
}

void BandLimitedWaveform::init_sawtooth (uint32_t freq_word)
{
  phase_word = 0 ;
  newptr = 0 ;
  delptr = 0 ;
  for (int i = 0 ; i < 2*SUPPORT ; i++)
    phase_word -= freq_word ;
  dc_offset = phase_word < DEG180 ? BASE_AMPLITUDE : -BASE_AMPLITUDE ;
  for (int i = 0 ; i < 2*SUPPORT ; i++)
  {
    uint32_t new_phase = phase_word + freq_word ;
    new_step_check_saw (new_phase, i) ;
    cyclic [i & 15] = (int16_t) process_active_steps_saw (new_phase) ;
    phase_word = new_phase ;
  }
}


void BandLimitedWaveform::init_square (uint32_t freq_word)
{
  init_pulse (freq_word, DEG180) ;
}

void BandLimitedWaveform::init_pulse (uint32_t freq_word, uint32_t pulse_width)
{
  phase_word = 0 ;
  sampled_width = pulse_width ;
  newptr = 0 ;
  delptr = 0 ;
  for (int i = 0 ; i < 2*SUPPORT ; i++)
    phase_word -= freq_word ;

  if (phase_word < pulse_width)
  {
    dc_offset = BASE_AMPLITUDE ;
    pulse_state = true ;
  }
  else
  {
    dc_offset = -BASE_AMPLITUDE ;
    pulse_state = false ;
  }
  
  for (int i = 0 ; i < 2*SUPPORT ; i++)
  {
    uint32_t new_phase = phase_word + freq_word ;
    new_step_check_pulse (new_phase, pulse_width, i) ;
    cyclic [i & 15] = (int16_t) process_active_steps_pulse (new_phase, pulse_width) ;
    phase_word = new_phase ;
  }
}

BandLimitedWaveform::BandLimitedWaveform()
{
  newptr = 0 ;
  delptr = 0 ;
  dc_offset = BASE_AMPLITUDE ;
  phase_word = 0 ;
}