monostep/Source/dsp/WaveTables.h

#pragma once

#include <cmath>
#include <algorithm>
#include <cstdint>
#include <random>

namespace monostep
{

enum class Waveform : int
{
    sine = 0,
    triangle = 1,
    saw = 2,
    square = 3,
    pulse = 4,
    noise = 5,
    sub = 6,
    pluck = 7,
    super = 8,
    sah = 9,
    formant = 10,
    pwm = 11
};

static constexpr int numWaveforms = 12;

inline float frac (float x)
{
    return x - std::floor (x);
}

inline float polyBlep (float t, float dt)
{
    if (t < dt)
    {
        t /= dt;
        return t + t - t * t - 1.0f;
    }

    if (t > 1.0f - dt)
    {
        t = (t - 1.0f) / dt;
        return t * t + t + t + 1.0f;
    }

    return 0.0f;
}

inline float renderWave (Waveform w, float phase, float inc)
{
    switch (w)
    {
        case Waveform::sine:
            return std::sin (phase * 6.283185307179586f);

        case Waveform::triangle:
        {
            const float f = frac (phase);
            return 4.0f * std::min (f, 1.0f - f) - 1.0f;
        }

        case Waveform::saw:
        {
            const float f = frac (phase);
            return (2.0f * f - 1.0f) - polyBlep (f, inc);
        }

        case Waveform::square:
        {
            const float f = frac (phase);
            float v = (f < 0.5f) ? 1.0f : -1.0f;
            v += polyBlep (f, inc);
            v -= polyBlep (frac (f + 0.5f), inc);
            return v;
        }

        case Waveform::pulse:
        {
            const float f = frac (phase);
            return (f < 0.3f) ? 1.0f : -1.0f;
        }

        case Waveform::sub:
        {
            const float f = frac (phase * 0.25f);
            return 4.0f * std::min (f, 1.0f - f) - 1.0f;
        }

        case Waveform::noise:
        {
            thread_local static std::mt19937 rng { std::random_device {}() };
            thread_local static std::uniform_real_distribution<float> dist (-1.0f, 1.0f);
            return dist (rng);
        }

        case Waveform::pluck:
        {
            const float f = frac (phase);
            return 2.0f * std::sin (f * 6.283185307179586f * 2.0f) * std::exp (-10.0f * f);
        }

        case Waveform::super:
        {
            float sum = 0.0f;
            const float detunes[3] = { -0.01f, 0.0f, 0.01f };

            for (const float d : detunes)
            {
                const float f = frac (phase + d);
                sum += (2.0f * f - 1.0f) - polyBlep (f, inc);
            }

            return sum / 3.0f;
        }

        case Waveform::sah:
        {
            const int steps = 16;
            const float f = frac (phase);
            int s = static_cast<int> (std::floor (f * (float) steps));
            if (s >= steps) s = steps - 1;
            if (s < 0)      s = 0;

            std::uint32_t h = static_cast<std::uint32_t> (s);
            h ^= h << 13;  h ^= h >> 17;  h ^= h << 5;
            const float r = static_cast<float> (h & 0xffffff) / 16777215.0f;

            return r * 2.0f - 1.0f;
        }

        case Waveform::formant:
        {
            const float w = phase * 6.283185307179586f;
            const float env = 0.5f + 0.3f * std::cos (w * 0.5f) + 0.2f * std::cos (w * 0.25f);
            return std::sin (w) * env;
        }

        case Waveform::pwm:
        {
            const float width = 0.2f;
            const float f = frac (phase);
            float v = (f < width) ? 1.0f : -1.0f;
            v += polyBlep (f, inc);
            v -= polyBlep (frac (f + 1.0f - width), inc);
            return v;
        }
    }

    return 0.0f;
}

} // namespace monostep