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+/*
+ * Copyright 2009 Phil Burk, Mobileer 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.
+ */
+
+package com.jsyn.engine;
+
+/*
+ * Multiple tables of sawtooth data.
+ * organized by octaves below the Nyquist Rate.
+ * used to generate band-limited Sawtooth, Impulse, Pulse, Square and Triangle BL waveforms
+ *
+ <pre>
+ Analysis of octave requirements for tables.
+
+ OctavesIndex Frequency Partials
+ 0 N/2 11025 1
+ 1 N/4 5512 2
+ 2 N/8 2756 4
+ 3 N/16 1378 8
+ 4 N/32 689 16
+ 5 N/64 344 32
+ 6 N/128 172 64
+ 7 N/256 86 128
+ </pre>
+ *
+ * @author Phil Burk (C) 2009 Mobileer Inc
+ */
+public class MultiTable {
+
+ public final static int NUM_TABLES = 8;
+ public final static int CYCLE_SIZE = (1 << 10);
+
+ private static MultiTable instance = new MultiTable(NUM_TABLES, CYCLE_SIZE);
+ private double phaseScalar;
+ private float[][] tables; // array of array of tables
+
+ /**************************************************************************
+ * Initialize sawtooth wavetables. Table[0] should contain a pure sine wave. Succeeding tables
+ * should have increasing numbers of partials.
+ */
+ public MultiTable(int numTables, int cycleSize) {
+ int tableSize = cycleSize + 1;
+
+ // Allocate array of arrays.
+ tables = new float[numTables][tableSize];
+
+ float[] sineTable = tables[0];
+
+ phaseScalar = (float) (cycleSize * 0.5);
+
+ /* Fill initial sine table with values for -PI to PI. */
+ for (int j = 0; j < tableSize; j++) {
+ sineTable[j] = (float) Math.sin(((((double) j) / (double) cycleSize) * Math.PI * 2.0)
+ - Math.PI);
+ }
+
+ /*
+ * Build each table from scratch and scale partials by raised cosine* to eliminate Gibbs
+ * effect.
+ */
+ for (int i = 1; i < numTables; i++) {
+ int numPartials;
+ double kGibbs;
+ float[] table = tables[i];
+
+ /* Add together partials for this table. */
+ numPartials = 1 << i;
+ kGibbs = Math.PI / (2 * numPartials);
+ for (int k = 0; k < numPartials; k++) {
+ double ampl, cGibbs;
+ int sineIndex = 0;
+ int partial = k + 1;
+ cGibbs = Math.cos(k * kGibbs);
+ /* Calculate amplitude for Nth partial */
+ ampl = cGibbs * cGibbs / partial;
+
+ for (int j = 0; j < tableSize; j++) {
+ table[j] += (float) ampl * sineTable[sineIndex];
+ sineIndex += partial;
+ /* Wrap index at end of table.. */
+ if (sineIndex >= cycleSize) {
+ sineIndex -= cycleSize;
+ }
+ }
+ }
+ }
+
+ /* Normalize after */
+ for (int i = 1; i < numTables; i++) {
+ normalizeArray(tables[i]);
+ }
+ }
+
+ /**************************************************************************/
+ public static float normalizeArray(float[] fdata) {
+ float max, val, gain;
+ int i;
+
+ // determine maximum value.
+ max = 0.0f;
+ for (i = 0; i < fdata.length; i++) {
+ val = Math.abs(fdata[i]);
+ if (val > max)
+ max = val;
+ }
+ if (max < 0.0000001f)
+ max = 0.0000001f;
+ // scale array
+ gain = 1.0f / max;
+ for (i = 0; i < fdata.length; i++)
+ fdata[i] *= gain;
+ return gain;
+ }
+
+ /*****************************************************************************
+ * When the phaseInc maps to the highest level table, then we start interpolating between the
+ * highest table and the raw sawtooth value (phase). When phaseInc points to highest table:
+ * flevel = NUM_TABLES - 1 = -1 - log2(pInc); log2(pInc) = - NUM_TABLES pInc = 2**(-NUM_TABLES)
+ */
+ private final static double LOWEST_PHASE_INC_INV = (1 << NUM_TABLES);
+
+ /**************************************************************************/
+ /* Phase ranges from -1.0 to +1.0 */
+ public double calculateSawtooth(double currentPhase, double positivePhaseIncrement,
+ double flevel) {
+ float[] tableBase;
+ double val;
+ double hiSam; /* Use when verticalFraction is 1.0 */
+ double loSam; /* Use when verticalFraction is 0.0 */
+ double sam1, sam2;
+
+ /* Use Phase to determine sampleIndex into table. */
+ double findex = ((phaseScalar * currentPhase) + phaseScalar);
+ // findex is > 0 so we do not need to call floor().
+ int sampleIndex = (int) findex;
+ double horizontalFraction = findex - sampleIndex;
+ int tableIndex = (int) flevel;
+
+ if (tableIndex > (NUM_TABLES - 2)) {
+ /*
+ * Just use top table and mix with arithmetic sawtooth if below lowest frequency.
+ * Generate new fraction for interpolating between 0.0 and lowest table frequency.
+ */
+ double fraction = positivePhaseIncrement * LOWEST_PHASE_INC_INV;
+ tableBase = tables[(NUM_TABLES - 1)];
+
+ /* Get adjacent samples. Assume guard point present. */
+ sam1 = tableBase[sampleIndex];
+ sam2 = tableBase[sampleIndex + 1];
+ /* Interpolate between adjacent samples. */
+ loSam = sam1 + (horizontalFraction * (sam2 - sam1));
+
+ /* Use arithmetic version for low frequencies. */
+ /* fraction is 0.0 at 0 Hz */
+ val = currentPhase + (fraction * (loSam - currentPhase));
+ } else {
+
+ double verticalFraction = flevel - tableIndex;
+
+ if (tableIndex < 0) {
+ if (tableIndex < -1) // above Nyquist!
+ {
+ val = 0.0;
+ } else {
+ /*
+ * At top of supported range, interpolate between 0.0 and first partial.
+ */
+ tableBase = tables[0]; /* Sine wave table. */
+
+ /* Get adjacent samples. Assume guard point present. */
+ sam1 = tableBase[sampleIndex];
+ sam2 = tableBase[sampleIndex + 1];
+
+ /* Interpolate between adjacent samples. */
+ hiSam = sam1 + (horizontalFraction * (sam2 - sam1));
+ /* loSam = 0.0 */
+ // verticalFraction is 0.0 at Nyquist
+ val = verticalFraction * hiSam;
+ }
+ } else {
+ /*
+ * Interpolate between adjacent levels to prevent harmonics from popping.
+ */
+ tableBase = tables[tableIndex + 1];
+
+ /* Get adjacent samples. Assume guard point present. */
+ sam1 = tableBase[sampleIndex];
+ sam2 = tableBase[sampleIndex + 1];
+
+ /* Interpolate between adjacent samples. */
+ hiSam = sam1 + (horizontalFraction * (sam2 - sam1));
+
+ /* Get adjacent samples. Assume guard point present. */
+ tableBase = tables[tableIndex];
+ sam1 = tableBase[sampleIndex];
+ sam2 = tableBase[sampleIndex + 1];
+
+ /* Interpolate between adjacent samples. */
+ loSam = sam1 + (horizontalFraction * (sam2 - sam1));
+
+ val = loSam + (verticalFraction * (hiSam - loSam));
+ }
+ }
+ return val;
+ }
+
+ public double convertPhaseIncrementToLevel(double positivePhaseIncrement) {
+ if (positivePhaseIncrement < 1.0e-30) {
+ positivePhaseIncrement = 1.0e-30;
+ }
+ return -1.0 - (Math.log(positivePhaseIncrement) / Math.log(2.0));
+ }
+
+ public static MultiTable getInstance() {
+ return instance;
+ }
+
+}
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