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Simplifying the split delta allocation computation #14

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a1ff0ce
imid/iside are no longer needed
jmvalin Feb 9, 2026
e482e6f
Simplifying the split delta allocation computation
jmvalin Feb 9, 2026
c2ccc64
Allow up to 4096 bits per band (32767>>BITRES)
jmvalin Feb 9, 2026
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78 changes: 36 additions & 42 deletions celt/bands.c
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Original file line number Diff line number Diff line change
Expand Up @@ -106,18 +106,35 @@ oac_int16 oaci_bitexact_cos(oac_int16 x) {
return 1 + x2;
}

int oaci_bitexact_log2tan(int isin, int icos) {
int lc;
int ls;
lc = EC_ILOG(icos);
ls = EC_ILOG(isin);
icos <<= 15 - lc;
isin <<= 15 - ls;
return (ls - lc)*(1<<11)
+ FRAC_MUL16(isin, FRAC_MUL16(isin, -2597) + 7932)
- FRAC_MUL16(icos, FRAC_MUL16(icos, -2597) + 7932);
/* This is a log2() approximation designed to be bit-exact on any platform. Bit exactness
with this approximation is important because it has an impact on the bit allocation */
static oac_int16 oaci_bitexact_log2(oac_int32 x) {
int i;
oac_int16 n, frac;
/* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
0.15530808010959576, -0.08556153059057618 */
static const oac_int16 C[5] = {-6801 + (1<<(14 - 11)), 15746, -5217, 2545, -1401};
if (x == 0)
return -32767;
i = EC_ILOG(x)-1;
n = (x << 15 >> i) - 32768 - 16384;
frac = (C[0] + FRAC_MUL16(n, (C[1] + FRAC_MUL16(n, (C[2] + FRAC_MUL16(n, (C[3] + FRAC_MUL16(n, C[4]))))))));
return ((i - 12) << 11) + (frac >> (14 - 11));
}

/* This is a log2(tan(x)) approximation designed to be bit-exact on any platform. Bit exactness
with this approximation is important because it has an impact on the bit allocation */
int oaci_bitexact_delta(int itheta) {
int sign = 1;
if (itheta > 8192) {
itheta = 16384 - itheta;
sign = -1;
}
/* log2(tan(pi/4*x)) ~= log2(x) -.343 - .061*x + .404*x.^2. */
return sign*(oaci_bitexact_log2(itheta) - 703 - FRAC_MUL16(itheta, (500 - FRAC_MUL16(itheta, 13238))));
}


#ifdef FIXED_POINT
/* Compute the amplitude (sqrt energy) in each of the bands */
void oaci_compute_band_energies(const CELTMode *m, const celt_sig *X, celt_ener *bandE, int end, int C, int LM, int arch) {
Expand Down Expand Up @@ -624,7 +641,7 @@ void oaci_haar1(celt_norm *X, int N0, int stride) {
}
}

static int oaci_compute_qn(int N, int b, int offset, int pulse_cap, int stereo) {
static int oaci_compute_qn(int N, oac_int32 b, int offset, int pulse_cap, int stereo) {
static const oac_int16 exp2_table8[8] =
{16384, 17866, 19483, 21247, 23170, 25267, 27554, 30048};
int qn, qb;
Expand Down Expand Up @@ -669,22 +686,19 @@ struct band_ctx {

struct split_ctx {
int inv;
int imid;
int iside;
int delta;
oac_int32 delta;
int itheta;
int itheta_q30;
};

static void oaci_compute_theta(struct band_ctx *ctx, struct split_ctx *sctx,
celt_norm *X, celt_norm *Y, int N, int *b, int B, int B0,
celt_norm *X, celt_norm *Y, int N, oac_int32 *b, int B, int B0,
int LM,
int stereo, int *fill) {
int qn;
int itheta = 0;
int itheta_q30 = 0;
int delta;
int imid, iside;
int qalloc;
int pulse_cap;
int offset;
Expand Down Expand Up @@ -728,9 +742,7 @@ static void oaci_compute_theta(struct band_ctx *ctx, struct split_ctx *sctx,
to inject noise on one side. If so, make sure the energy of that side
is zero. */
int unquantized = oaci_celt_udiv((oac_int32)itheta*16384, qn);
imid = oaci_bitexact_cos((oac_int16)unquantized);
iside = oaci_bitexact_cos((oac_int16)(16384 - unquantized));
delta = FRAC_MUL16((N - 1)<<7, oaci_bitexact_log2tan(iside, imid));
delta = FRAC_MUL16((N - 1)<<7, oaci_bitexact_delta(unquantized));
if (delta > *b)
itheta = qn;
else if (delta < -*b)
Expand Down Expand Up @@ -843,26 +855,18 @@ static void oaci_compute_theta(struct band_ctx *ctx, struct split_ctx *sctx,
*b -= qalloc;

if (itheta == 0) {
imid = 32767;
iside = 0;
*fill &= (1<<B) - 1;
delta = -16384;
} else if (itheta == 16384) {
imid = 0;
iside = 32767;
*fill &= ((1<<B) - 1)<<B;
delta = 16384;
} else {
imid = oaci_bitexact_cos((oac_int16)itheta);
iside = oaci_bitexact_cos((oac_int16)(16384 - itheta));
/* This is the mid vs side allocation that minimizes squared error
in that band. */
delta = FRAC_MUL16((N - 1)<<7, oaci_bitexact_log2tan(iside, imid));
delta = FRAC_MUL16((N - 1)<<7, oaci_bitexact_delta(itheta));
}

sctx->inv = inv;
sctx->imid = imid;
sctx->iside = iside;
sctx->delta = delta;
sctx->itheta = itheta;
sctx->itheta_q30 = itheta_q30;
Expand Down Expand Up @@ -909,7 +913,6 @@ static unsigned oaci_quant_partition(struct band_ctx *ctx, celt_norm *X,
const unsigned char *cache;
int q;
int curr_bits;
int imid = 0, iside = 0;
int B0 = B;
oac_val32 mid = 0, side = 0;
unsigned cm = 0;
Expand Down Expand Up @@ -944,12 +947,8 @@ static unsigned oaci_quant_partition(struct band_ctx *ctx, celt_norm *X,
B = (B + 1)>>1;

oaci_compute_theta(ctx, &sctx, X, Y, N, &b, B, B0, LM, 0, &fill);
imid = sctx.imid;
iside = sctx.iside;
delta = sctx.delta;
itheta = sctx.itheta;
(void)imid;
(void)iside;
#ifdef FIXED_POINT
mid = oaci_celt_cos_norm32(sctx.itheta_q30);
side = oaci_celt_cos_norm32((1<<30) - sctx.itheta_q30);
Expand Down Expand Up @@ -1124,7 +1123,7 @@ unsigned oaci_cubic_quant_partition(struct band_ctx *ctx, celt_norm *X, int N, i

/* This function is responsible for encoding and decoding a band for the mono case. */
static unsigned oaci_quant_band(struct band_ctx *ctx, celt_norm *X,
int N, int b, int B, celt_norm *lowband,
int N, oac_int32 b, int B, celt_norm *lowband,
int LM, celt_norm *lowband_out,
oac_val32 gain, celt_norm *lowband_scratch, int fill) {
int N0 = N;
Expand Down Expand Up @@ -1245,10 +1244,9 @@ static unsigned oaci_quant_band(struct band_ctx *ctx, celt_norm *X,

/* This function is responsible for encoding and decoding a band for the stereo case. */
static unsigned oaci_quant_band_stereo(struct band_ctx *ctx, celt_norm *X, celt_norm *Y,
int N, int b, int B, celt_norm *lowband,
int N, oac_int32 b, int B, celt_norm *lowband,
int LM, celt_norm *lowband_out,
celt_norm *lowband_scratch, int fill) {
int imid = 0, iside = 0;
int inv = 0;
oac_val32 mid = 0, side = 0;
unsigned cm = 0;
Expand Down Expand Up @@ -1277,12 +1275,8 @@ static unsigned oaci_quant_band_stereo(struct band_ctx *ctx, celt_norm *X, celt_
}
oaci_compute_theta(ctx, &sctx, X, Y, N, &b, B, B, LM, 1, &fill);
inv = sctx.inv;
imid = sctx.imid;
iside = sctx.iside;
delta = sctx.delta;
itheta = sctx.itheta;
(void)imid;
(void)iside;
#ifdef FIXED_POINT
mid = oaci_celt_cos_norm32(sctx.itheta_q30);
side = oaci_celt_cos_norm32((1<<30) - sctx.itheta_q30);
Expand Down Expand Up @@ -1482,7 +1476,7 @@ void oaci_quant_all_bands(int encode, const CELTMode *m, int start, int end,
ctx.avoid_split_noise = B > 1;
for (i = start; i < end; i++) {
oac_int32 tell;
int b;
oac_int32 b;
int N;
oac_int32 curr_balance;
int effective_lowband = -1;
Expand Down Expand Up @@ -1511,7 +1505,7 @@ void oaci_quant_all_bands(int encode, const CELTMode *m, int start, int end,
ctx.total_bits = total_bits;
if (i <= codedBands - 1) {
curr_balance = oaci_celt_sudiv(balance, IMIN(3, codedBands - i));
b = IMAX(0, IMIN(16383, IMIN(remaining_bits, pulses[i] + curr_balance)));
b = IMAX(0, IMIN(32767, IMIN(remaining_bits, pulses[i] + curr_balance)));
} else {
b = 0;
}
Expand Down
3 changes: 1 addition & 2 deletions celt/bands.h
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Original file line number Diff line number Diff line change
Expand Up @@ -69,8 +69,7 @@
#include "entdec.h"
#include "rate.h"

oac_int16 oaci_bitexact_cos(oac_int16 x);
int oaci_bitexact_log2tan(int isin, int icos);
int oaci_bitexact_delta(int itheta);

/** Compute the amplitude (sqrt energy) in each of the bands
* @param m Mode data
Expand Down
52 changes: 13 additions & 39 deletions celt/tests/test_unit_mathops.c
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Original file line number Diff line number Diff line change
Expand Up @@ -119,48 +119,23 @@ void testsqrt(void) {
}
}

void testbitexactcos(void) {
int i;
oac_int32 min_d, max_d, last, chk;
chk = max_d = 0;
last = min_d = 32767;
for (i = 64; i <= 16320; i++) {
oac_int32 d;
oac_int32 q = oaci_bitexact_cos(i);
chk ^= q*i;
d = last - q;
if (d > max_d) max_d = d;
if (d < min_d) min_d = d;
last = q;
}
if ((chk != 89408644) || (max_d != 5) || (min_d != 0) || (oaci_bitexact_cos(64) != 32767)
|| (oaci_bitexact_cos(16320) != 200) || (oaci_bitexact_cos(8192) != 23171)) {
fprintf (stderr, "oaci_bitexact_cos failed\n");
ret = 1;
}
#ifndef DISABLE_FLOAT_API
static int oaci_delta_ground_truth(int itheta) {
return 2048*log2(tan(itheta/8192.*M_PI/4));
}
#endif

void testbitexactlog2tan(void) {
int i, fail;
oac_int32 min_d, max_d, last, chk;
fail = chk = max_d = 0;
last = min_d = 15059;
for (i = 64; i < 8193; i++) {
oac_int32 d;
oac_int32 mid = oaci_bitexact_cos(i);
oac_int32 side = oaci_bitexact_cos(16384 - i);
oac_int32 q = oaci_bitexact_log2tan(mid, side);
chk ^= q*i;
d = last - q;
if (q != -1*oaci_bitexact_log2tan(side, mid))
fail = 1;
if (d > max_d) max_d = d;
if (d < min_d) min_d = d;
last = q;
}
if ((chk != 15821257) || (max_d != 61) || (min_d != -2) || fail
|| (oaci_bitexact_log2tan(32767, 200) != 15059) || (oaci_bitexact_log2tan(30274, 12540) != 2611)
|| (oaci_bitexact_log2tan(23171, 23171) != 0)) {
fail = 0;
for (i = 1; i <= 8192; i++) {
oac_int32 q = oaci_bitexact_delta(i);
#ifndef DISABLE_FLOAT_API
if (abs(q - oaci_delta_ground_truth(i)) > 16) fail=1;
#endif
if (q != -1*oaci_bitexact_delta(16384-i)) fail = 1;
}
if (fail) {
fprintf (stderr, "oaci_bitexact_log2tan failed\n");
ret = 1;
}
Expand Down Expand Up @@ -722,7 +697,6 @@ int main(void) {
int i;
int use_ref_impl[2] = { 0, 1 };

testbitexactcos();
testbitexactlog2tan();
testdiv();
testsqrt();
Expand Down