From 2916efee213d0d0c6fe67669bf666141e6149f27 Mon Sep 17 00:00:00 2001
From: Chris Robinson <chris.kcat@gmail.com>
Date: Mon, 28 Aug 2017 10:31:23 -0700
Subject: Automatically generate the bsinc table when building
This makes bsincgen a native tool like bin2h, so it can run automatically when
compiling.
---
native-tools/CMakeLists.txt | 15 ++
native-tools/bsincgen.c | 404 ++++++++++++++++++++++++++++++++++++++++++++
2 files changed, 419 insertions(+)
create mode 100644 native-tools/bsincgen.c
(limited to 'native-tools')
diff --git a/native-tools/CMakeLists.txt b/native-tools/CMakeLists.txt
index bb8c677e..3c66c8bc 100644
--- a/native-tools/CMakeLists.txt
+++ b/native-tools/CMakeLists.txt
@@ -2,9 +2,24 @@ cmake_minimum_required(VERSION 3.0.2)
project(native-tools)
+include(CheckLibraryExists)
+
+check_library_exists(m pow "" HAVE_LIBM)
+
add_executable(bin2h bin2h.c)
# Enforce no dressing for executable names, so the main script can find it
set_target_properties(bin2h PROPERTIES OUTPUT_NAME bin2h)
# Avoid configuration-dependent subdirectories while building with Visual Studio
set_target_properties(bin2h PROPERTIES RUNTIME_OUTPUT_DIRECTORY_DEBUG "${CMAKE_BINARY_DIR}")
set_target_properties(bin2h PROPERTIES RUNTIME_OUTPUT_DIRECTORY_RELEASE "${CMAKE_BINARY_DIR}")
+
+add_executable(bsincgen bsincgen.c)
+set_target_properties(bsincgen PROPERTIES OUTPUT_NAME bsincgen)
+set_target_properties(bsincgen PROPERTIES RUNTIME_OUTPUT_DIRECTORY_DEBUG "${CMAKE_BINARY_DIR}")
+set_target_properties(bsincgen PROPERTIES RUNTIME_OUTPUT_DIRECTORY_RELEASE "${CMAKE_BINARY_DIR}")
+if(HAVE_LIBM)
+ target_link_libraries(bsincgen m)
+endif(HAVE_LIBM)
+if(WIN32 AND CMAKE_COMPILER_IS_GNUCC)
+ set_property(TARGET bsincgen APPEND_STRING PROPERTY LINK_FLAGS " -municode")
+endif(WIN32 AND CMAKE_COMPILER_IS_GNUCC)
diff --git a/native-tools/bsincgen.c b/native-tools/bsincgen.c
new file mode 100644
index 00000000..754e0709
--- /dev/null
+++ b/native-tools/bsincgen.c
@@ -0,0 +1,404 @@
+/*
+ * Sinc interpolator coefficient and delta generator for the OpenAL Soft
+ * cross platform audio library.
+ *
+ * Copyright (C) 2015 by Christopher Fitzgerald.
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Library General Public
+ * License as published by the Free Software Foundation; either
+ * version 2 of the License, or (at your option) any later version.
+ *
+ * This library 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
+ * Library General Public License for more details.
+ *
+ * You should have received a copy of the GNU Library General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
+ * MA 02110-1301 USA
+ *
+ * Or visit: http://www.gnu.org/licenses/old-licenses/lgpl-2.0.html
+ *
+ * --------------------------------------------------------------------------
+ *
+ * This is a modified version of the bandlimited windowed sinc interpolator
+ * algorithm presented here:
+ *
+ * Smith, J.O. "Windowed Sinc Interpolation", in
+ * Physical Audio Signal Processing,
+ * https://ccrma.stanford.edu/~jos/pasp/Windowed_Sinc_Interpolation.html,
+ * online book,
+ * accessed October 2012.
+ */
+
+#define _UNICODE
+#include <stdio.h>
+#include <math.h>
+#include <string.h>
+#include <stdlib.h>
+
+#include "../common/win_main_utf8.h"
+
+
+#ifndef M_PI
+#define M_PI (3.14159265358979323846)
+#endif
+
+#if defined(__ANDROID__) && !(defined(_ISOC99_SOURCE) || (defined(_POSIX_C_SOURCE) && _POSIX_C_SOURCE >= 200112L))
+#define log2(x) (log(x) / log(2.0))
+#endif
+
+// The number of distinct scale and phase intervals within the filter table.
+// Must be the same as in alu.h!
+#define BSINC_SCALE_COUNT (16)
+#define BSINC_PHASE_COUNT (16)
+
+/* 48 points includes the doubling for downsampling, so the maximum number of
+ * base sample points is 24, which is 23rd order.
+ */
+#define BSINC_POINTS_MAX (48)
+
+static double MinDouble(double a, double b)
+{ return (a <= b) ? a : b; }
+
+static double MaxDouble(double a, double b)
+{ return (a >= b) ? a : b; }
+
+/* NOTE: This is the normalized (instead of just sin(x)/x) cardinal sine
+ * function.
+ * 2 f_t sinc(2 f_t x)
+ * f_t -- normalized transition frequency (0.5 is nyquist)
+ * x -- sample index (-N to N)
+ */
+static double Sinc(const double x)
+{
+ if(fabs(x) < 1e-15)
+ return 1.0;
+ return sin(M_PI * x) / (M_PI * x);
+}
+
+static double BesselI_0(const double x)
+{
+ double term, sum, last_sum, x2, y;
+ int i;
+
+ term = 1.0;
+ sum = 1.0;
+ x2 = x / 2.0;
+ i = 1;
+
+ do {
+ y = x2 / i;
+ i++;
+ last_sum = sum;
+ term *= y * y;
+ sum += term;
+ } while(sum != last_sum);
+
+ return sum;
+}
+
+/* NOTE: k is assumed normalized (-1 to 1)
+ * beta is equivalent to 2 alpha
+ */
+static double Kaiser(const double b, const double k)
+{
+ if(!(k >= -1.0 && k <= 1.0))
+ return 0.0;
+ return BesselI_0(b * sqrt(1.0 - k*k)) / BesselI_0(b);
+}
+
+/* Calculates the (normalized frequency) transition width of the Kaiser window.
+ * Rejection is in dB.
+ */
+static double CalcKaiserWidth(const double rejection, const int order)
+{
+ double w_t = 2.0 * M_PI;
+
+ if(rejection > 21.0)
+ return (rejection - 7.95) / (order * 2.285 * w_t);
+ /* This enforces a minimum rejection of just above 21.18dB */
+ return 5.79 / (order * w_t);
+}
+
+static double CalcKaiserBeta(const double rejection)
+{
+ if(rejection > 50.0)
+ return 0.1102 * (rejection - 8.7);
+ else if(rejection >= 21.0)
+ return (0.5842 * pow(rejection - 21.0, 0.4)) +
+ (0.07886 * (rejection - 21.0));
+ return 0.0;
+}
+
+/* Generates the coefficient, delta, and index tables required by the bsinc resampler */
+static void BsiGenerateTables(FILE *output, const char *tabname, const double rejection, const int order)
+{
+ static double filter[BSINC_SCALE_COUNT][BSINC_PHASE_COUNT + 1][BSINC_POINTS_MAX];
+ static double scDeltas[BSINC_SCALE_COUNT][BSINC_PHASE_COUNT ][BSINC_POINTS_MAX];
+ static double phDeltas[BSINC_SCALE_COUNT][BSINC_PHASE_COUNT + 1][BSINC_POINTS_MAX];
+ static double spDeltas[BSINC_SCALE_COUNT][BSINC_PHASE_COUNT ][BSINC_POINTS_MAX];
+ static int mt[BSINC_SCALE_COUNT];
+ static double at[BSINC_SCALE_COUNT];
+ const int num_points_min = order + 1;
+ double width, beta, scaleBase, scaleRange;
+ int si, pi, i;
+
+ memset(filter, 0, sizeof(filter));
+ memset(scDeltas, 0, sizeof(scDeltas));
+ memset(phDeltas, 0, sizeof(phDeltas));
+ memset(spDeltas, 0, sizeof(spDeltas));
+
+ /* Calculate windowing parameters. The width describes the transition
+ band, but it may vary due to the linear interpolation between scales
+ of the filter.
+ */
+ width = CalcKaiserWidth(rejection, order);
+ beta = CalcKaiserBeta(rejection);
+ scaleBase = width / 2.0;
+ scaleRange = 1.0 - scaleBase;
+
+ // Determine filter scaling.
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ {
+ const double scale = scaleBase + (scaleRange * si / (BSINC_SCALE_COUNT - 1));
+ const double a = MinDouble(floor(num_points_min / (2.0 * scale)), num_points_min);
+ const int m = 2 * (int)a;
+
+ mt[si] = m;
+ at[si] = a;
+ }
+
+ /* Calculate the Kaiser-windowed Sinc filter coefficients for each scale
+ and phase.
+ */
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ {
+ const int m = mt[si];
+ const int o = num_points_min - (m / 2);
+ const int l = (m / 2) - 1;
+ const double a = at[si];
+ const double scale = scaleBase + (scaleRange * si / (BSINC_SCALE_COUNT - 1));
+ const double cutoff = (0.5 * scale) - (scaleBase * MaxDouble(0.5, scale));
+
+ for(pi = 0; pi <= BSINC_PHASE_COUNT; pi++)
+ {
+ const double phase = l + ((double)pi / BSINC_PHASE_COUNT);
+
+ for(i = 0; i < m; i++)
+ {
+ const double x = i - phase;
+ filter[si][pi][o + i] = Kaiser(beta, x / a) * 2.0 * cutoff * Sinc(2.0 * cutoff * x);
+ }
+ }
+ }
+
+ /* Linear interpolation between scales is simplified by pre-calculating
+ the delta (b - a) in: x = a + f (b - a)
+
+ Given a difference in points between scales, the destination points
+ will be 0, thus: x = a + f (-a)
+ */
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ {
+ const int m = mt[si];
+ const int o = num_points_min - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ for(i = 0; i < m; i++)
+ scDeltas[si][pi][o + i] = filter[si + 1][pi][o + i] - filter[si][pi][o + i];
+ }
+ }
+
+ // Linear interpolation between phases is also simplified.
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ {
+ const int m = mt[si];
+ const int o = num_points_min - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ for(i = 0; i < m; i++)
+ phDeltas[si][pi][o + i] = filter[si][pi + 1][o + i] - filter[si][pi][o + i];
+ }
+ }
+
+ /* This last simplification is done to complete the bilinear equation for
+ the combination of scale and phase.
+ */
+ for(si = 0; si < (BSINC_SCALE_COUNT - 1); si++)
+ {
+ const int m = mt[si];
+ const int o = num_points_min - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ for(i = 0; i < m; i++)
+ spDeltas[si][pi][o + i] = phDeltas[si + 1][pi][o + i] - phDeltas[si][pi][o + i];
+ }
+ }
+
+ // Make sure the number of points is a multiple of 4 (for SIMD).
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ mt[si] = (mt[si]+3) & ~3;
+
+ fprintf(output,
+"/* This %d%s order filter has a rejection of -%.0fdB, yielding a transition width\n"
+" * of ~%.3f (normalized frequency). Order increases when downsampling to a\n"
+" * limit of one octave, after which the quality of the filter (transition\n"
+" * width) suffers to reduce the CPU cost. The bandlimiting will cut all sound\n"
+" * after downsampling by ~%.2f octaves.\n"
+" */\n"
+"const BSincTable %s = {\n",
+ order, (((order%100)/10) == 1) ? "th" :
+ ((order%10) == 1) ? "st" :
+ ((order%10) == 2) ? "nd" :
+ ((order%10) == 3) ? "rd" : "th",
+ rejection, width, log2(1.0/scaleBase), tabname);
+
+ /* The scaleBase is calculated from the Kaiser window transition width.
+ It represents the absolute limit to the filter before it fully cuts
+ the signal. The limit in octaves can be calculated by taking the
+ base-2 logarithm of its inverse: log_2(1 / scaleBase)
+ */
+ fprintf(output, " /* scaleBase */ %.9ef, /* scaleRange */ %.9ef,\n", scaleBase, 1.0 / scaleRange);
+
+ fprintf(output, " /* m */ {");
+ fprintf(output, " %d", mt[0]);
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ fprintf(output, ", %d", mt[si]);
+ fprintf(output, " },\n");
+
+ fprintf(output, " /* filterOffset */ {");
+ fprintf(output, " %d", 0);
+ i = mt[0]*4*BSINC_PHASE_COUNT;
+ for(si = 1; si < BSINC_SCALE_COUNT; si++)
+ {
+ fprintf(output, ", %d", i);
+ i += mt[si]*4*BSINC_PHASE_COUNT;
+ }
+
+ fprintf(output, " },\n");
+
+ // Calculate the table size.
+ i = 0;
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ i += 4 * BSINC_PHASE_COUNT * mt[si];
+
+ fprintf(output, "\n /* Tab (%d entries) */ {\n", i);
+ for(si = 0; si < BSINC_SCALE_COUNT; si++)
+ {
+ const int m = mt[si];
+ const int o = num_points_min - (m / 2);
+
+ for(pi = 0; pi < BSINC_PHASE_COUNT; pi++)
+ {
+ fprintf(output, " /* %2d,%2d (%d) */", si, pi, m);
+ fprintf(output, "\n ");
+ for(i = 0; i < m; i++)
+ fprintf(output, " %+14.9ef,", filter[si][pi][o + i]);
+ fprintf(output, "\n ");
+ for(i = 0; i < m; i++)
+ fprintf(output, " %+14.9ef,", scDeltas[si][pi][o + i]);
+ fprintf(output, "\n ");
+ for(i = 0; i < m; i++)
+ fprintf(output, " %+14.9ef,", phDeltas[si][pi][o + i]);
+ fprintf(output, "\n ");
+ for(i = 0; i < m; i++)
+ fprintf(output, " %+14.9ef,", spDeltas[si][pi][o + i]);
+ fprintf(output, "\n");
+ }
+ }
+ fprintf(output, " }\n};\n\n");
+}
+
+
+/* These methods generate a much simplified 4-point sinc interpolator using a
+ * Kaiser window. This is much simpler to process at run-time, but has notably
+ * more aliasing noise.
+ */
+
+/* Same as in alu.h! */
+#define FRACTIONBITS (12)
+#define FRACTIONONE (1<<FRACTIONBITS)
+
+static void Sinc4GenerateTables(FILE *output, const double rejection)
+{
+ static double filter[FRACTIONONE][4];
+
+ const double width = CalcKaiserWidth(rejection, 3);
+ const double beta = CalcKaiserBeta(rejection);
+ const double scaleBase = width / 2.0;
+ const double scaleRange = 1.0 - scaleBase;
+ const double scale = scaleBase + scaleRange;
+ const double a = MinDouble(4.0, floor(4.0 / (2.0*scale)));
+ const int m = 2 * (int)a;
+ const int l = (m/2) - 1;
+ int pi;
+ for(pi = 0;pi < FRACTIONONE;pi++)
+ {
+ const double phase = l + ((double)pi / FRACTIONONE);
+ int i;
+
+ for(i = 0;i < m;i++)
+ {
+ double x = i - phase;
+ filter[pi][i] = Kaiser(beta, x / a) * Sinc(x);
+ }
+ }
+
+ fprintf(output, "alignas(16) static const float sinc4Tab[FRACTIONONE][4] = {\n");
+ for(pi = 0;pi < FRACTIONONE;pi++)
+ fprintf(output, " { %+14.9ef, %+14.9ef, %+14.9ef, %+14.9ef },\n",
+ filter[pi][0], filter[pi][1], filter[pi][2], filter[pi][3]);
+ fprintf(output, "};\n\n");
+}
+
+
+int main(int argc, char *argv[])
+{
+ FILE *output;
+
+ if(argc > 2)
+ {
+ fprintf(stderr, "Usage: %s [output file]\n", argv[0]);
+ return 1;
+ }
+
+ if(argc == 2)
+ {
+ output = fopen(argv[1], "wb");
+ if(!output)
+ {
+ fprintf(stderr, "Failed to open %s for writing\n", argv[1]);
+ return 1;
+ }
+ }
+ else
+ output = stdout;
+
+ fprintf(output, "/* Generated by bsincgen, do not edit! */\n\n"
+"static_assert(BSINC_SCALE_COUNT == %d, \"Unexpected BSINC_SCALE_COUNT value!\");\n"
+"static_assert(BSINC_PHASE_COUNT == %d, \"Unexpected BSINC_PHASE_COUNT value!\");\n"
+"static_assert(FRACTIONONE == %d, \"Unexpected FRACTIONONE value!\");\n\n"
+"typedef struct BSincTable {\n"
+" const float scaleBase, scaleRange;\n"
+" const int m[BSINC_SCALE_COUNT];\n"
+" const int filterOffset[BSINC_SCALE_COUNT];\n"
+" alignas(16) const float Tab[];\n"
+"} BSincTable;\n\n", BSINC_SCALE_COUNT, BSINC_PHASE_COUNT, FRACTIONONE);
+ /* A 23rd order filter with a -60dB drop at nyquist. */
+ BsiGenerateTables(output, "bsinc24", 60.0, 23);
+ /* An 11th order filter with a -60dB drop at nyquist. */
+ BsiGenerateTables(output, "bsinc12", 60.0, 11);
+ Sinc4GenerateTables(output, 60.0);
+
+ if(output != stdout)
+ fclose(output);
+ output = NULL;
+
+ return 0;
+}
--
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