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#define compile \
exec gcc -Wall -pedantic -std=gnu99 -lm lutgen.c -o lutgen || exit 255
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <math.h>
/*
* cubic spline interpolation doc,
* (derived from "digital image warping", g. wolberg)
*
* interpolation polynomial: f(x) = A3*(x-floor(x))**3 + A2*(x-floor(x))**2 + A1*(x-floor(x)) + A0
*
* with Y = equispaced data points (dist=1), YD = first derivates of data points and IP = floor(x)
* the A[0..3] can be found by solving
* A0 = Y[IP]
* A1 = YD[IP]
* A2 = 3*(Y[IP+1]-Y[IP])-2.0*YD[IP]-YD[IP+1]
* A3 = -2.0 * (Y[IP+1]-Y[IP]) + YD[IP] - YD[IP+1]
*
* with the first derivates as
* YD[IP] = 0.5 * (Y[IP+1] - Y[IP-1]);
* YD[IP+1] = 0.5 * (Y[IP+2] - Y[IP])
*
* the coefs becomes
* A0 = Y[IP]
* A1 = YD[IP]
* = 0.5 * (Y[IP+1] - Y[IP-1]);
* A2 = 3.0 * (Y[IP+1]-Y[IP])-2.0*YD[IP]-YD[IP+1]
* = 3.0 * (Y[IP+1] - Y[IP]) - 0.5 * 2.0 * (Y[IP+1] - Y[IP-1]) - 0.5 * (Y[IP+2] - Y[IP])
* = 3.0 * Y[IP+1] - 3.0 * Y[IP] - Y[IP+1] + Y[IP-1] - 0.5 * Y[IP+2] + 0.5 * Y[IP]
* = -0.5 * Y[IP+2] + 2.0 * Y[IP+1] - 2.5 * Y[IP] + Y[IP-1]
* = Y[IP-1] + 2 * Y[IP+1] - 0.5 * (5.0 * Y[IP] + Y[IP+2])
* A3 = -2.0 * (Y[IP+1]-Y[IP]) + YD[IP] + YD[IP+1]
* = -2.0 * Y[IP+1] + 2.0 * Y[IP] + 0.5 * (Y[IP+1] - Y[IP-1]) + 0.5 * (Y[IP+2] - Y[IP])
* = -2.0 * Y[IP+1] + 2.0 * Y[IP] + 0.5 * Y[IP+1] - 0.5 * Y[IP-1] + 0.5 * Y[IP+2] - 0.5 * Y[IP]
* = 0.5 * Y[IP+2] - 1.5 * Y[IP+1] + 1.5 * Y[IP] - 0.5 * Y[IP-1]
* = 0.5 * (3.0 * (Y[IP] - Y[IP+1]) - Y[IP-1] + YP[IP+2])
*
* then interpolated data value is (horner rule)
* out = (((A3*x)+A2)*x+A1)*x+A0
*
* this gives parts of data points Y[IP-1] to Y[IP+2] of
* part x**3 x**2 x**1 x**0
* Y[IP-1] -0.5 1 -0.5 0
* Y[IP] 1.5 -2.5 0 1
* Y[IP+1] -1.5 2 0.5 0
* Y[IP+2] 0.5 -0.5 0 0
*/
// number of bits used to scale spline coefs
#define SPLINE_QUANTBITS 14
#define SPLINE_QUANTSCALE (1L << SPLINE_QUANTBITS)
#define SPLINE_8SHIFT (SPLINE_QUANTBITS - 8)
#define SPLINE_16SHIFT (SPLINE_QUANTBITS)
// forces coefsset to unity gain
#define SPLINE_CLAMPFORUNITY
// log2(number) of precalculated splines (range is [4..14])
#define SPLINE_FRACBITS 10
#define SPLINE_LUTLEN (1L << SPLINE_FRACBITS)
int16_t cubic_spline_lut[4 * SPLINE_LUTLEN];
void cubic_spline_init(void)
{
int i;
int len = SPLINE_LUTLEN;
float flen = 1.0f / (float) SPLINE_LUTLEN;
float scale = (float) SPLINE_QUANTSCALE;
for (i = 0; i < len; i++) {
float LCm1, LC0, LC1, LC2;
float LX = ((float) i) * flen;
int indx = i << 2;
#ifdef SPLINE_CLAMPFORUNITY
int sum;
#endif
LCm1 = (float) floor(0.5 + scale * (-0.5 * LX * LX * LX + 1.0 * LX * LX - 0.5 * LX ));
LC0 = (float) floor(0.5 + scale * ( 1.5 * LX * LX * LX - 2.5 * LX * LX + 1.0));
LC1 = (float) floor(0.5 + scale * (-1.5 * LX * LX * LX + 2.0 * LX * LX + 0.5 * LX ));
LC2 = (float) floor(0.5 + scale * ( 0.5 * LX * LX * LX - 0.5 * LX * LX ));
cubic_spline_lut[indx + 0] = (int16_t) ((LCm1 < -scale) ? -scale : ((LCm1 > scale) ? scale : LCm1));
cubic_spline_lut[indx + 1] = (int16_t) ((LC0 < -scale) ? -scale : ((LC0 > scale) ? scale : LC0 ));
cubic_spline_lut[indx + 2] = (int16_t) ((LC1 < -scale) ? -scale : ((LC1 > scale) ? scale : LC1 ));
cubic_spline_lut[indx + 3] = (int16_t) ((LC2 < -scale) ? -scale : ((LC2 > scale) ? scale : LC2 ));
#ifdef SPLINE_CLAMPFORUNITY
sum = cubic_spline_lut[indx + 0] +
cubic_spline_lut[indx + 1] +
cubic_spline_lut[indx + 2] +
cubic_spline_lut[indx + 3];
if (sum != SPLINE_QUANTSCALE) {
int max = indx;
if (cubic_spline_lut[indx + 1] > cubic_spline_lut[max]) max = indx + 1;
if (cubic_spline_lut[indx + 2] > cubic_spline_lut[max]) max = indx + 2;
if (cubic_spline_lut[indx + 3] > cubic_spline_lut[max]) max = indx + 3;
cubic_spline_lut[max] += (SPLINE_QUANTSCALE - sum);
}
#endif
}
}
/* fir interpolation doc,
* (derived from "an engineer's guide to fir digital filters", n.j. loy)
*
* calculate coefficients for ideal lowpass filter (with cutoff = fc in 0..1 (mapped to 0..nyquist))
* c[-N..N] = (i==0) ? fc : sin(fc*pi*i)/(pi*i)
*
* then apply selected window to coefficients
* c[-N..N] *= w(0..N)
* with n in 2*N and w(n) being a window function (see loy)
*
* then calculate gain and scale filter coefs to have unity gain.
*/
// quantizer scale of window coefs
#define WFIR_QUANTBITS 15
#define WFIR_QUANTSCALE (1L << WFIR_QUANTBITS)
#define WFIR_8SHIFT (WFIR_QUANTBITS - 8)
#define WFIR_16BITSHIFT (WFIR_QUANTBITS)
// log2(number)-1 of precalculated taps range is [4..12]
#define WFIR_FRACBITS 10
#define WFIR_LUTLEN ((1L << (WFIR_FRACBITS + 1)) + 1)
// number of samples in window
#define WFIR_LOG2WIDTH 3
#define WFIR_WIDTH (1L << WFIR_LOG2WIDTH)
#define WFIR_SMPSPERWING ((WFIR_WIDTH - 1) >> 1)
// cutoff (1.0 == pi/2)
#define WFIR_CUTOFF 0.90f
// wfir type
#define WFIR_HANN 0
#define WFIR_HAMMING 1
#define WFIR_BLACKMANEXACT 2
#define WFIR_BLACKMAN3T61 3
#define WFIR_BLACKMAN3T67 4
#define WFIR_BLACKMAN4T92 5
#define WFIR_BLACKMAN4T74 6
#define WFIR_KAISER4T 7
#define WFIR_TYPE WFIR_BLACKMANEXACT
// wfir help
#ifndef M_zPI
#define M_zPI 3.1415926535897932384626433832795
#endif
#define M_zEPS 1e-8
#define M_zBESSELEPS 1e-21
float coef(int pc_nr, float p_ofs, float p_cut, int p_width, int p_type)
{
double width_m1 = p_width - 1;
double width_m1_half = 0.5 * width_m1;
double pos_u = (double) pc_nr - p_ofs;
double pos = pos_u - width_m1_half;
double idl = 2.0 * M_zPI / width_m1;
double wc, si;
if (fabs(pos) < M_zEPS) {
wc = 1.0;
si = p_cut;
return p_cut;
}
switch (p_type) {
case WFIR_HANN:
wc = 0.50 - 0.50 * cos(idl * pos_u);
break;
case WFIR_HAMMING:
wc = 0.54 - 0.46 * cos(idl * pos_u);
break;
case WFIR_BLACKMANEXACT:
wc = 0.42 - 0.50 * cos(idl * pos_u) + 0.08 * cos(2.0 * idl * pos_u);
break;
case WFIR_BLACKMAN3T61:
wc = 0.44959 - 0.49364 * cos(idl * pos_u) + 0.05677 * cos(2.0 * idl * pos_u);
break;
case WFIR_BLACKMAN3T67:
wc = 0.42323 - 0.49755 * cos(idl * pos_u) + 0.07922 * cos(2.0 * idl * pos_u);
break;
case WFIR_BLACKMAN4T92:
wc = 0.35875 - 0.48829 * cos(idl * pos_u) + 0.14128 * cos(2.0 * idl * pos_u) -
0.01168 * cos(3.0 * idl * pos_u);
break;
case WFIR_BLACKMAN4T74:
wc = 0.40217 - 0.49703 * cos(idl * pos_u) + 0.09392 * cos(2.0 * idl * pos_u) -
0.00183 * cos(3.0*idl*pos_u);
break;
case WFIR_KAISER4T:
wc = 0.40243 - 0.49804 * cos(idl * pos_u) + 0.09831 * cos(2.0 * idl * pos_u) -
0.00122 * cos(3.0 * idl * pos_u);
break;
default:
wc = 1.0;
break;
}
pos *= M_zPI;
si = sin(p_cut * pos) / pos;
return (float)(wc * si);
}
int16_t windowed_fir_lut[WFIR_LUTLEN*WFIR_WIDTH];
void windowed_fir_init(void)
{
int pcl;
// number of precalculated lines for 0..1 (-1..0)
float pcllen = (float)(1L << WFIR_FRACBITS);
float norm = 1.0f / (float)(2.0f * pcllen);
float cut = WFIR_CUTOFF;
float scale = (float) WFIR_QUANTSCALE;
for (pcl = 0; pcl < WFIR_LUTLEN; pcl++) {
float gain,coefs[WFIR_WIDTH];
float ofs = ((float) pcl - pcllen) * norm;
int cc, indx = pcl << WFIR_LOG2WIDTH;
for (cc = 0, gain = 0.0f; cc < WFIR_WIDTH; cc++) {
coefs[cc] = coef(cc, ofs, cut, WFIR_WIDTH, WFIR_TYPE);
gain += coefs[cc];
}
gain = 1.0f / gain;
for (cc = 0; cc < WFIR_WIDTH; cc++) {
float coef = (float)floor( 0.5 + scale * coefs[cc] * gain);
windowed_fir_lut[indx + cc] = (signed short)((coef < -scale) ? - scale :
((coef > scale) ? scale : coef));
}
}
}
#define LOOP(x, y) \
printf("static signed short %s[%lu] = {\n", #x, y); \
\
for (int i = 0; i < y; i++) { \
if (i && !(i % 64)) { \
printf("\n"); \
} \
printf(" %d,", x[i]); \
} \
\
printf("\n};\n\n");
int main(int argc, char **argv)
{
cubic_spline_init();
windowed_fir_init();
LOOP(cubic_spline_lut, (4 * SPLINE_LUTLEN));
LOOP(windowed_fir_lut, (WFIR_LUTLEN * WFIR_WIDTH));
return 0;
}
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