/* Maps each possible size (n) in the split k-tokenizer to a different value.
Possible values of n are:
2, 3, 4, 7, 8, 14, 15, 16, 31, 32, 63, 64, 127, 128
Since we don't care about the order (even in the bit-stream) the simplest
ordering (implemented here) is:
14, 2, 3, 4, 7, 8, 15, 16, 31, 32, 63, 64, 127, 128 */
int od_pvq_size_ctx(int n) {
int logn;
int odd;
logn = OD_ILOG(n - 1);
odd = n & 1;
return 2*logn - 1 - odd - 7*(n == 14);
}
int image_init(image *img, jpeg_header *header) {
int hmax;
int vmax;
int i;
memset(img, 0, sizeof(image));
img->width = header->width;
img->height = header->height;
img->nplanes = header->ncomps;
hmax = 0;
vmax = 0;
for (i = 0; i < img->nplanes; i++) {
jpeg_component *comp;
comp = &header->comp[i];
hmax = OD_MAXI(hmax, comp->hsamp);
vmax = OD_MAXI(vmax, comp->vsamp);
}
for (i = 0; i < img->nplanes; i++) {
jpeg_component *comp;
image_plane *plane;
comp = &header->comp[i];
plane = &img->plane[i];
plane->width = comp->hblocks << 3;
plane->height = comp->vblocks << 3;
/* TODO support 16-bit images */
plane->xstride = 1;
plane->ystride = plane->xstride*plane->width;
plane->xdec = OD_ILOG(hmax) - OD_ILOG(comp->hsamp);
plane->ydec = OD_ILOG(vmax) - OD_ILOG(comp->vsamp);
plane->data = od_aligned_malloc(plane->ystride*plane->height, IMAGE_ALIGN);
if (plane->data == NULL) {
image_clear(img);
return EXIT_FAILURE;
}
plane->coef = od_aligned_malloc(plane->width*plane->height*sizeof(short),
IMAGE_ALIGN);
if (plane->coef == NULL) {
image_clear(img);
return EXIT_FAILURE;
}
}
img->pixels = od_aligned_malloc(img->width*img->height*3, IMAGE_ALIGN);
if (img->pixels == NULL) {
image_clear(img);
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
}
/* Computes an upper-bound on the number of bits required to store the L2 norm
of a vector (excluding sign). */
int od_vector_log_mag(const od_coeff *x, int n) {
int i;
int32_t sum;
sum = 0;
for (i = 0; i < n; i++) {
int16_t tmp;
tmp = x[i] >> 8;
sum += tmp*(int32_t)tmp;
}
/* We add one full bit (instead of rounding OD_ILOG() up) for safety because
the >> 8 above causes the sum to be slightly underestimated. */
return 8 + 1 + OD_ILOG(n + sum)/2;
}
static int32_t od_pow(int32_t x, od_val16 beta)
{
int16_t t;
int xshift;
int log2_x;
od_val32 logr;
/*FIXME: this conditional is to avoid doing log2(0).*/
if (x == 0)
return 0;
log2_x = (OD_ILOG(x) - 1);
xshift = log2_x - OD_LOG2_INSHIFT;
/*t should be in range [0.0, 1.0[ in Q(OD_LOG2_INSHIFT).*/
t = OD_VSHR(x, xshift) - (1 << OD_LOG2_INSHIFT);
/*log2(g/OD_COMPAND_SCALE) = log2(x) - OD_COMPAND_SHIFT in
Q(OD_LOG2_OUTSHIFT).*/
logr = od_log2(t) + (log2_x - OD_COMPAND_SHIFT)*OD_LOG2_OUTSCALE;
logr = OD_MULT16_32_QBETA(beta, logr);
return od_exp2(logr);
}
static od_val16 od_rcp(od_val16 x)
{
int i;
od_val16 n;
od_val16 r;
i = OD_ILOG(x) - 1;
/*n is Q15 with range [0,1).*/
n = OD_VSHR_ROUND(x, i - OD_RCP_INSHIFT) - (1 << OD_RCP_INSHIFT);
/*Start with a linear approximation:
r = 1.8823529411764706-0.9411764705882353*n.
The coefficients and the result are Q14 in the range [15420,30840].*/
r = 30840 + OD_MULT16_16_Q15(-15420, n);
/*Perform two Newton iterations:
r -= r*((r*n)-1.Q15)
= r*((r*n)+(r-1.Q15)).*/
r = r - OD_MULT16_16_Q15(r, (OD_MULT16_16_Q15(r, n) + r - 32768));
/*We subtract an extra 1 in the second iteration to avoid overflow; it also
neatly compensates for truncation error in the rest of the process.*/
r = r - (1 + OD_MULT16_16_Q15(r, OD_MULT16_16_Q15(r, n) + r - 32768));
/*r is now the Q15 solution to 2/(n+1), with a maximum relative error
of 7.05346E-5, a (relative) RMSE of 2.14418E-5, and a peak absolute
error of 1.24665/32768.*/
return OD_VSHR_ROUND(r, i - OD_RCP_OUTSHIFT);
}
/** Applies Householder reflection from compute_householder(). The
* reflection is its own inverse.
*
* @param [out] out reflected vector
* @param [in] x vector to be reflected
* @param [in] r reflection
* @param [in] n number of dimensions in x,r
*/
void od_apply_householder(od_val16 *out, const od_val16 *x, const od_val16 *r,
int n) {
int i;
od_val32 proj;
od_val16 proj_1;
od_val32 l2r;
#if !defined(OD_FLOAT_PVQ)
od_val16 proj_norm;
od_val16 l2r_norm;
od_val16 rcp;
int proj_shift;
int l2r_shift;
int outshift;
#endif
/*FIXME: Can we get l2r and/or l2r_shift from an earlier computation?*/
l2r = 0;
for (i = 0; i < n; i++) {
l2r += OD_MULT16_16(r[i], r[i]);
}
/* Apply Householder reflection */
proj = 0;
for (i = 0; i < n; i++) {
proj += OD_MULT16_16(r[i], x[i]);
}
#if defined(OD_FLOAT_PVQ)
proj_1 = proj*2./(1e-100 + l2r);
for (i = 0; i < n; i++) {
out[i] = x[i] - r[i]*proj_1;
}
#else
/*l2r_norm is [0.5, 1.0[ in Q15.*/
l2r_shift = (OD_ILOG(l2r) - 1) - 14;
l2r_norm = OD_VSHR_ROUND(l2r, l2r_shift);
rcp = od_rcp(l2r_norm);
proj_shift = (OD_ILOG(abs(proj)) - 1) - 14;
/*proj_norm is [0.5, 1.0[ in Q15.*/
proj_norm = OD_VSHR_ROUND(proj, proj_shift);
proj_1 = OD_MULT16_16_Q15(proj_norm, rcp);
/*The proj*2. in the float code becomes -1 in the final outshift.
The sign of l2r_shift is positive since we're taking the reciprocal of
l2r_norm and this is a right shift.*/
outshift = OD_MINI(30, OD_RCP_OUTSHIFT - proj_shift - 1 + l2r_shift);
if (outshift >= 0) {
for (i = 0; i < n; i++) {
int32_t tmp;
tmp = OD_MULT16_16(r[i], proj_1);
tmp = OD_SHR_ROUND(tmp, outshift);
out[i] = x[i] - tmp;
}
}
else {
/*FIXME: Can we make this case impossible?
Right now, if r[] is all zeros except for 1, 2, or 3 ones, and
if x[] is all zeros except for large values at the same position as the
ones in r[], then we can end up with a shift of -1.*/
for (i = 0; i < n; i++) {
int32_t tmp;
tmp = OD_MULT16_16(r[i], proj_1);
tmp = OD_SHL(tmp, -outshift);
out[i] = x[i] - tmp;
}
}
#endif
}
