MicroDexed is a compatible 6-operator-FM-synth based on the Teensy(-3.6/-4.x) Microcontroller. https://www.parasitstudio.de
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/*
* Copyright 2012 Google Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#define _USE_MATH_DEFINES
#include <math.h>
#include "synth.h"
#include "sin.h"
#define R (1 << 29)
#ifdef SIN_DELTA
int32_t sintab[SIN_N_SAMPLES << 1];
#else
int32_t sintab[SIN_N_SAMPLES + 1];
#endif
void Sin::init() {
FRAC_NUM dphase = 2 * M_PI / SIN_N_SAMPLES;
//int32_t c = (int32_t)floor(cos(dphase) * (1 << 30) + 0.5);
int32_t c = (int32_t)floor(COS_FUNC(dphase) * (1 << 30) + 0.5);
//int32_t s = (int32_t)floor(sin(dphase) * (1 << 30) + 0.5);
int32_t s = (int32_t)floor(SIN_FUNC(dphase) * (1 << 30) + 0.5);
int32_t u = 1 << 30;
int32_t v = 0;
for (int i = 0; i < SIN_N_SAMPLES / 2; i++) {
#ifdef SIN_DELTA
sintab[(i << 1) + 1] = (v + 32) >> 6;
sintab[((i + SIN_N_SAMPLES / 2) << 1) + 1] = -((v + 32) >> 6);
#else
sintab[i] = (v + 32) >> 6;
sintab[i + SIN_N_SAMPLES / 2] = -((v + 32) >> 6);
#endif
int32_t t = ((int64_t)u * (int64_t)s + (int64_t)v * (int64_t)c + R) >> 30;
u = ((int64_t)u * (int64_t)c - (int64_t)v * (int64_t)s + R) >> 30;
v = t;
}
#ifdef SIN_DELTA
for (int i = 0; i < SIN_N_SAMPLES - 1; i++) {
sintab[i << 1] = sintab[(i << 1) + 3] - sintab[(i << 1) + 1];
}
sintab[(SIN_N_SAMPLES << 1) - 2] = -sintab[(SIN_N_SAMPLES << 1) - 1];
#else
sintab[SIN_N_SAMPLES] = 0;
#endif
}
#ifndef SIN_INLINE
int32_t Sin::lookup(int32_t phase) {
const int SHIFT = 24 - SIN_LG_N_SAMPLES;
int lowbits = phase & ((1 << SHIFT) - 1);
#ifdef SIN_DELTA
int phase_int = (phase >> (SHIFT - 1)) & ((SIN_N_SAMPLES - 1) << 1);
int dy = sintab[phase_int];
int y0 = sintab[phase_int + 1];
return y0 + (((int64_t)dy * (int64_t)lowbits) >> SHIFT);
#else
int phase_int = (phase >> SHIFT) & (SIN_N_SAMPLES - 1);
int y0 = sintab[phase_int];
int y1 = sintab[phase_int + 1];
return y0 + (((int64_t)(y1 - y0) * (int64_t)lowbits) >> SHIFT);
#endif
}
#endif
#if 0
// The following is an implementation designed not to use any lookup tables,
// based on the following implementation by Basile Graf:
// http://www.rossbencina.com/static/code/sinusoids/even_polynomial_sin_approximation.txt
#define C0 (1 << 24)
#define C1 (331121857 >> 2)
#define C2 (1084885537 >> 4)
#define C3 (1310449902 >> 6)
int32_t Sin::compute(int32_t phase) {
int32_t x = (phase & ((1 << 23) - 1)) - (1 << 22);
int32_t x2 = ((int64_t)x * (int64_t)x) >> 22;
int32_t x4 = ((int64_t)x2 * (int64_t)x2) >> 24;
int32_t x6 = ((int64_t)x2 * (int64_t)x4) >> 24;
int32_t y = C0 -
(((int64_t)C1 * (int64_t)x2) >> 24) +
(((int64_t)C2 * (int64_t)x4) >> 24) -
(((int64_t)C3 * (int64_t)x6) >> 24);
y ^= -((phase >> 23) & 1);
return y;
}
#endif
#if 1
// coefficients are Chebyshev polynomial, computed by compute_cos_poly.py
#define C8_0 16777216
#define C8_2 -331168742
#define C8_4 1089453524
#define C8_6 -1430910663
#define C8_8 950108533
int32_t Sin::compute(int32_t phase) {
int32_t x = (phase & ((1 << 23) - 1)) - (1 << 22);
int32_t x2 = ((int64_t)x * (int64_t)x) >> 16;
int32_t y = (((((((((((((int64_t)C8_8
* (int64_t)x2) >> 32) + C8_6)
* (int64_t)x2) >> 32) + C8_4)
* (int64_t)x2) >> 32) + C8_2)
* (int64_t)x2) >> 32) + C8_0);
y ^= -((phase >> 23) & 1);
return y;
}
#endif
#define C10_0 (1 << 30)
#define C10_2 -1324675874 // scaled * 4
#define C10_4 1089501821
#define C10_6 -1433689867
#define C10_8 1009356886
#define C10_10 -421101352
int32_t Sin::compute10(int32_t phase) {
int32_t x = (phase & ((1 << 29) - 1)) - (1 << 28);
int32_t x2 = ((int64_t)x * (int64_t)x) >> 26;
int32_t y = ((((((((((((((((int64_t)C10_10
* (int64_t)x2) >> 34) + C10_8)
* (int64_t)x2) >> 34) + C10_6)
* (int64_t)x2) >> 34) + C10_4)
* (int64_t)x2) >> 32) + C10_2)
* (int64_t)x2) >> 30) + C10_0);
y ^= -((phase >> 29) & 1);
return y;
}