mayhem-firmware/firmware/common/sine_table.hpp

/*
 * Copyright (C) 2015 Jared Boone, ShareBrained Technology, Inc.
 *
 * This file is part of PortaPack.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2, or (at your option)
 * any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; see the file COPYING.  If not, write to
 * the Free Software Foundation, Inc., 51 Franklin Street,
 * Boston, MA 02110-1301, USA.
 */

#ifndef __SINE_TABLE_H__
#define __SINE_TABLE_H__

// TODO: Including only for pi. Need separate math.hpp...
#include "complex.hpp"

#include <array>
#include <cmath>

/*
import numpy
length = 256
w = numpy.arange(length, dtype=numpy.float64) * (2 * numpy.pi / length)
v = numpy.sin(w)
print(v)
*/
constexpr uint16_t sine_table_f32_period = 256;
// periode is 256 . means sine_table_f32[0]= sine_table_f32[0+256], sine_table_f32[1]=sine_table_f32[1+256] (those two added manualy)
// Then table has 258 values ,256:[0,..255] + [256] and [257], those two are  used when we interpolate[255] with [255+1], and [256] with [256+1]
// [256] index is needed in the function sin_f32() when we are inputing very small radian values , example , sin_f32((-1e-14) in radians)

static constexpr std::array<float, sine_table_f32_period + 2> sine_table_f32{
    0.00000000e+00, 2.45412285e-02, 4.90676743e-02,
    7.35645636e-02, 9.80171403e-02, 1.22410675e-01,
    1.46730474e-01, 1.70961889e-01, 1.95090322e-01,
    2.19101240e-01, 2.42980180e-01, 2.66712757e-01,
    2.90284677e-01, 3.13681740e-01, 3.36889853e-01,
    3.59895037e-01, 3.82683432e-01, 4.05241314e-01,
    4.27555093e-01, 4.49611330e-01, 4.71396737e-01,
    4.92898192e-01, 5.14102744e-01, 5.34997620e-01,
    5.55570233e-01, 5.75808191e-01, 5.95699304e-01,
    6.15231591e-01, 6.34393284e-01, 6.53172843e-01,
    6.71558955e-01, 6.89540545e-01, 7.07106781e-01,
    7.24247083e-01, 7.40951125e-01, 7.57208847e-01,
    7.73010453e-01, 7.88346428e-01, 8.03207531e-01,
    8.17584813e-01, 8.31469612e-01, 8.44853565e-01,
    8.57728610e-01, 8.70086991e-01, 8.81921264e-01,
    8.93224301e-01, 9.03989293e-01, 9.14209756e-01,
    9.23879533e-01, 9.32992799e-01, 9.41544065e-01,
    9.49528181e-01, 9.56940336e-01, 9.63776066e-01,
    9.70031253e-01, 9.75702130e-01, 9.80785280e-01,
    9.85277642e-01, 9.89176510e-01, 9.92479535e-01,
    9.95184727e-01, 9.97290457e-01, 9.98795456e-01,
    9.99698819e-01, 1.00000000e+00, 9.99698819e-01,
    9.98795456e-01, 9.97290457e-01, 9.95184727e-01,
    9.92479535e-01, 9.89176510e-01, 9.85277642e-01,
    9.80785280e-01, 9.75702130e-01, 9.70031253e-01,
    9.63776066e-01, 9.56940336e-01, 9.49528181e-01,
    9.41544065e-01, 9.32992799e-01, 9.23879533e-01,
    9.14209756e-01, 9.03989293e-01, 8.93224301e-01,
    8.81921264e-01, 8.70086991e-01, 8.57728610e-01,
    8.44853565e-01, 8.31469612e-01, 8.17584813e-01,
    8.03207531e-01, 7.88346428e-01, 7.73010453e-01,
    7.57208847e-01, 7.40951125e-01, 7.24247083e-01,
    7.07106781e-01, 6.89540545e-01, 6.71558955e-01,
    6.53172843e-01, 6.34393284e-01, 6.15231591e-01,
    5.95699304e-01, 5.75808191e-01, 5.55570233e-01,
    5.34997620e-01, 5.14102744e-01, 4.92898192e-01,
    4.71396737e-01, 4.49611330e-01, 4.27555093e-01,
    4.05241314e-01, 3.82683432e-01, 3.59895037e-01,
    3.36889853e-01, 3.13681740e-01, 2.90284677e-01,
    2.66712757e-01, 2.42980180e-01, 2.19101240e-01,
    1.95090322e-01, 1.70961889e-01, 1.46730474e-01,
    1.22410675e-01, 9.80171403e-02, 7.35645636e-02,
    4.90676743e-02, 2.45412285e-02, 1.22464680e-16,
    -2.45412285e-02, -4.90676743e-02, -7.35645636e-02,
    -9.80171403e-02, -1.22410675e-01, -1.46730474e-01,
    -1.70961889e-01, -1.95090322e-01, -2.19101240e-01,
    -2.42980180e-01, -2.66712757e-01, -2.90284677e-01,
    -3.13681740e-01, -3.36889853e-01, -3.59895037e-01,
    -3.82683432e-01, -4.05241314e-01, -4.27555093e-01,
    -4.49611330e-01, -4.71396737e-01, -4.92898192e-01,
    -5.14102744e-01, -5.34997620e-01, -5.55570233e-01,
    -5.75808191e-01, -5.95699304e-01, -6.15231591e-01,
    -6.34393284e-01, -6.53172843e-01, -6.71558955e-01,
    -6.89540545e-01, -7.07106781e-01, -7.24247083e-01,
    -7.40951125e-01, -7.57208847e-01, -7.73010453e-01,
    -7.88346428e-01, -8.03207531e-01, -8.17584813e-01,
    -8.31469612e-01, -8.44853565e-01, -8.57728610e-01,
    -8.70086991e-01, -8.81921264e-01, -8.93224301e-01,
    -9.03989293e-01, -9.14209756e-01, -9.23879533e-01,
    -9.32992799e-01, -9.41544065e-01, -9.49528181e-01,
    -9.56940336e-01, -9.63776066e-01, -9.70031253e-01,
    -9.75702130e-01, -9.80785280e-01, -9.85277642e-01,
    -9.89176510e-01, -9.92479535e-01, -9.95184727e-01,
    -9.97290457e-01, -9.98795456e-01, -9.99698819e-01,
    -1.00000000e+00, -9.99698819e-01, -9.98795456e-01,
    -9.97290457e-01, -9.95184727e-01, -9.92479535e-01,
    -9.89176510e-01, -9.85277642e-01, -9.80785280e-01,
    -9.75702130e-01, -9.70031253e-01, -9.63776066e-01,
    -9.56940336e-01, -9.49528181e-01, -9.41544065e-01,
    -9.32992799e-01, -9.23879533e-01, -9.14209756e-01,
    -9.03989293e-01, -8.93224301e-01, -8.81921264e-01,
    -8.70086991e-01, -8.57728610e-01, -8.44853565e-01,
    -8.31469612e-01, -8.17584813e-01, -8.03207531e-01,
    -7.88346428e-01, -7.73010453e-01, -7.57208847e-01,
    -7.40951125e-01, -7.24247083e-01, -7.07106781e-01,
    -6.89540545e-01, -6.71558955e-01, -6.53172843e-01,
    -6.34393284e-01, -6.15231591e-01, -5.95699304e-01,
    -5.75808191e-01, -5.55570233e-01, -5.34997620e-01,
    -5.14102744e-01, -4.92898192e-01, -4.71396737e-01,
    -4.49611330e-01, -4.27555093e-01, -4.05241314e-01,
    -3.82683432e-01, -3.59895037e-01, -3.36889853e-01,
    -3.13681740e-01, -2.90284677e-01, -2.66712757e-01,
    -2.42980180e-01, -2.19101240e-01, -1.95090322e-01,
    -1.70961889e-01, -1.46730474e-01, -1.22410675e-01,
    -9.80171403e-02, -7.35645636e-02, -4.90676743e-02,
    -2.45412285e-02, 0.00000000e+00, 2.45412285e-02};

inline float sin_f32(const float w) {
    const float x = w / (2 * pi);            // normalization
    const float x_frac = x - std::floor(x);  // [0, 1]

    const float n = x_frac * sine_table_f32_period;
    const uint16_t n_int = static_cast<uint16_t>(n);
    const float n_frac = n - n_int;

    const float p0 = sine_table_f32[n_int];
    const float p1 = sine_table_f32[n_int + 1];
    const float diff = p1 - p0;
    const float result = p0 + n_frac * diff;  // linear interpolation

    return result;
}

#endif /*__SINE_TABLE_H__*/