Quadratic approximation of sine

readme.md

Tried converting this to fixed-point:

http://www.dspguru.com/dsp/tricks/parabolic-approximation-of-sin-and-cos

Don't bother with this; it's so distorted (-28 dB THD) you can tell it's not a sine wave by looking at it.

Uses slightly more CPU than AudioSynthWaveformSine, but I didn't bother trying to optimize it. Would need to break into octants instead of quadrants and use at least 5th order polynomial to get 16-bit quality? Doesn't seem like it would be any faster.

quadratic.cpp

#include "quadratic.h"
#include "utility/dspinst.h"

void AudioSynthWaveformRes::update(void)
{
  audio_block_t *block;
  uint32_t i, inc;
  int32_t ph, modph;
  int32_t y, tmp;
  uint32_t quadrant;

  if (magnitude)
  {
    block = allocate();
    if (block)
    {
      ph = phase_accumulator;
      inc = phase_increment;
      for (i = 0; i < AUDIO_BLOCK_SAMPLES; i++)
      {
        quadrant = ph bitand (3 << 30);
        modph = ph bitand ~(3 << 30);

        if (quadrant == (2 << 30)) // 1: -sin
        {
          y = (multiply_32x32_rshift32_rounded(modph, modph) << 1) - modph;
        }
        else if (quadrant == (3 << 30)) // 2: -cos
        {
          y = (multiply_32x32_rshift32_rounded(modph, modph) << 1) - (1 << 29);
        }
        else if (quadrant == (0 << 30)) // 3: sin
        {
          y = modph - (multiply_32x32_rshift32_rounded(modph, modph) << 1);
        }
        else if (quadrant == (1 << 30)) // 4: cos
        {
          y = (1 << 29) - (multiply_32x32_rshift32_rounded(modph, modph) << 1);
        }
        block->data[i] = multiply_32x32_rshift32_rounded(y, magnitude);
        ph += inc;
      }
      phase_accumulator = ph;
      transmit(block);
      release(block);
      return;
    }
  }
  phase_accumulator += phase_increment * AUDIO_BLOCK_SAMPLES;
}

quadratic.h

#ifndef quadratic_h_
#define quadratic_h_

#include "AudioStream.h"
#include "arm_math.h"

class AudioSynthWaveformRes : public AudioStream
{
  public:
    AudioSynthWaveformRes() : AudioStream(0, NULL), magnitude(16384) {}
    void frequency(float freq)
    {
      if (freq < 0.0) freq = 0.0;
      else if (freq > AUDIO_SAMPLE_RATE_EXACT / 2) freq = AUDIO_SAMPLE_RATE_EXACT / 2;
      phase_increment = freq * (4294967296.0 / AUDIO_SAMPLE_RATE_EXACT);
    }
    void phase(float angle)
    {
      if (angle < 0.0) angle = 0.0;
      else if (angle > 360.0)
      {
        angle = angle - 360.0;
        if (angle >= 360.0) return;
      }
      phase_accumulator = angle * (4294967296.0 / 360.0);
    }
    void amplitude(float n)
    {
      if (n < 0) n = 0;
      else if (n > 1.0) n = 1.0;
      magnitude = n * 262139.0;  // why does 262144 cause overflow??
    }
    virtual void update(void);
  private:
    uint32_t phase_accumulator;
    uint32_t phase_increment;
    int32_t magnitude;
};

#endif

quadratic_sine.ino

#include <Audio.h>
#include <Wire.h>
#include <SD.h>
#include <SPI.h>

#include <math.h>
#include "quadratic.h"

AudioSynthWaveformRes    waveform1;      //xy=188,240
AudioOutputI2S           i2s1;           //xy=565,241
AudioConnection          patchCord2(waveform1, 0, i2s1, 0);
AudioConnection          patchCord3(waveform1, 0, i2s1, 1);
AudioControlSGTL5000     audioShield;     //xy=586,175

void setup()
{
  Serial.begin(9600);

  AudioMemory(80);
  audioShield.enable();
  audioShield.volume(0.3);

  waveform1.amplitude(1.0);  // 1.26 Vpp for 1.0
  waveform1.frequency(997.1);
}

void loop()
{
  Serial.print(AudioProcessorUsage());
  Serial.print(",");
  Serial.println(AudioProcessorUsageMax());
  delay(500);
}