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Diffstat (limited to 'third_party/aom/av1/common/pvq.c')
| -rw-r--r-- | third_party/aom/av1/common/pvq.c | 1007 |
1 files changed, 1007 insertions, 0 deletions
diff --git a/third_party/aom/av1/common/pvq.c b/third_party/aom/av1/common/pvq.c new file mode 100644 index 0000000000..75fe761d74 --- /dev/null +++ b/third_party/aom/av1/common/pvq.c @@ -0,0 +1,1007 @@ +/* + * Copyright (c) 2001-2016, Alliance for Open Media. All rights reserved + * + * This source code is subject to the terms of the BSD 2 Clause License and + * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License + * was not distributed with this source code in the LICENSE file, you can + * obtain it at www.aomedia.org/license/software. If the Alliance for Open + * Media Patent License 1.0 was not distributed with this source code in the + * PATENTS file, you can obtain it at www.aomedia.org/license/patent. + */ + +/* clang-format off */ + +#ifdef HAVE_CONFIG_H +# include "config.h" +#endif + +#include "odintrin.h" +#include "partition.h" +#include "pvq.h" +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include <string.h> + +/* Imported from encode.c in daala */ +/* These are the PVQ equivalent of quantization matrices, except that + the values are per-band. */ +#define OD_MASKING_DISABLED 0 +#define OD_MASKING_ENABLED 1 + +const unsigned char OD_LUMA_QM_Q4[2][OD_QM_SIZE] = { +/* Flat quantization for PSNR. The DC component isn't 16 because the DC + magnitude compensation is done here for inter (Haar DC doesn't need it). + Masking disabled: */ + { + 16, 16, + 16, 16, 16, 16, + 16, 16, 16, 16, 16, 16, + 16, 16, 16, 16, 16, 16, 16, 16 + }, +/* The non-flat AC coefficients compensate for the non-linear scaling caused + by activity masking. The values are currently hand-tuned so that the rate + of each band remains roughly constant when enabling activity masking + on intra. + Masking enabled: */ + { + 16, 16, + 16, 18, 28, 32, + 16, 14, 20, 20, 28, 32, + 16, 11, 14, 14, 17, 17, 22, 28 + } +}; + +const unsigned char OD_CHROMA_QM_Q4[2][OD_QM_SIZE] = { +/* Chroma quantization is different because of the reduced lapping. + FIXME: Use the same matrix as luma for 4:4:4. + Masking disabled: */ + { + 16, 16, + 16, 16, 16, 16, + 16, 16, 16, 16, 16, 16, + 16, 16, 16, 16, 16, 16, 16, 16 + }, +/* The AC part is flat for chroma because it has no activity masking. + Masking enabled: */ + { + 16, 16, + 16, 16, 16, 16, + 16, 16, 16, 16, 16, 16, + 16, 16, 16, 16, 16, 16, 16, 16 + } +}; + +/* No interpolation, always use od_flat_qm_q4, but use a different scale for + each plane. + FIXME: Add interpolation and properly tune chroma. */ +const od_qm_entry OD_DEFAULT_QMS[2][2][OD_NPLANES_MAX] = { + /* Masking disabled */ + { { { 4, 256, OD_LUMA_QM_Q4[OD_MASKING_DISABLED] }, + { 4, 256, OD_CHROMA_QM_Q4[OD_MASKING_DISABLED] }, + { 4, 256, OD_CHROMA_QM_Q4[OD_MASKING_DISABLED] } }, + { { 0, 0, NULL}, + { 0, 0, NULL}, + { 0, 0, NULL} } }, + /* Masking enabled */ + { { { 4, 256, OD_LUMA_QM_Q4[OD_MASKING_ENABLED] }, + { 4, 256, OD_CHROMA_QM_Q4[OD_MASKING_ENABLED] }, + { 4, 256, OD_CHROMA_QM_Q4[OD_MASKING_ENABLED] } }, + { { 0, 0, NULL}, + { 0, 0, NULL}, + { 0, 0, NULL} } } +}; + +/* Constants for the beta parameter, which controls how activity masking is + used. + beta = 1 / (1 - alpha), so when beta is 1, alpha is 0 and activity + masking is disabled. When beta is 1.5, activity masking is used. Note that + activity masking is neither used for 4x4 blocks nor for chroma. */ +#define OD_BETA(b) OD_QCONST32(b, OD_BETA_SHIFT) +static const od_val16 OD_PVQ_BETA4_LUMA[1] = {OD_BETA(1.)}; +static const od_val16 OD_PVQ_BETA8_LUMA[4] = {OD_BETA(1.), OD_BETA(1.), + OD_BETA(1.), OD_BETA(1.)}; +static const od_val16 OD_PVQ_BETA16_LUMA[7] = {OD_BETA(1.), OD_BETA(1.), + OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.)}; +static const od_val16 OD_PVQ_BETA32_LUMA[10] = {OD_BETA(1.), OD_BETA(1.), + OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), + OD_BETA(1.), OD_BETA(1.)}; + +static const od_val16 OD_PVQ_BETA4_LUMA_MASKING[1] = {OD_BETA(1.)}; +static const od_val16 OD_PVQ_BETA8_LUMA_MASKING[4] = {OD_BETA(1.5), + OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5)}; +static const od_val16 OD_PVQ_BETA16_LUMA_MASKING[7] = {OD_BETA(1.5), + OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), + OD_BETA(1.5)}; +static const od_val16 OD_PVQ_BETA32_LUMA_MASKING[10] = {OD_BETA(1.5), + OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), + OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5), OD_BETA(1.5)}; + +static const od_val16 OD_PVQ_BETA4_CHROMA[1] = {OD_BETA(1.)}; +static const od_val16 OD_PVQ_BETA8_CHROMA[4] = {OD_BETA(1.), OD_BETA(1.), + OD_BETA(1.), OD_BETA(1.)}; +static const od_val16 OD_PVQ_BETA16_CHROMA[7] = {OD_BETA(1.), OD_BETA(1.), + OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.)}; +static const od_val16 OD_PVQ_BETA32_CHROMA[10] = {OD_BETA(1.), OD_BETA(1.), + OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), OD_BETA(1.), + OD_BETA(1.), OD_BETA(1.)}; + +const od_val16 *const OD_PVQ_BETA[2][OD_NPLANES_MAX][OD_TXSIZES + 1] = { + {{OD_PVQ_BETA4_LUMA, OD_PVQ_BETA8_LUMA, + OD_PVQ_BETA16_LUMA, OD_PVQ_BETA32_LUMA}, + {OD_PVQ_BETA4_CHROMA, OD_PVQ_BETA8_CHROMA, + OD_PVQ_BETA16_CHROMA, OD_PVQ_BETA32_CHROMA}, + {OD_PVQ_BETA4_CHROMA, OD_PVQ_BETA8_CHROMA, + OD_PVQ_BETA16_CHROMA, OD_PVQ_BETA32_CHROMA}}, + {{OD_PVQ_BETA4_LUMA_MASKING, OD_PVQ_BETA8_LUMA_MASKING, + OD_PVQ_BETA16_LUMA_MASKING, OD_PVQ_BETA32_LUMA_MASKING}, + {OD_PVQ_BETA4_CHROMA, OD_PVQ_BETA8_CHROMA, + OD_PVQ_BETA16_CHROMA, OD_PVQ_BETA32_CHROMA}, + {OD_PVQ_BETA4_CHROMA, OD_PVQ_BETA8_CHROMA, + OD_PVQ_BETA16_CHROMA, OD_PVQ_BETA32_CHROMA}} +}; + + +void od_interp_qm(unsigned char *out, int q, const od_qm_entry *entry1, + const od_qm_entry *entry2) { + int i; + if (entry2 == NULL || entry2->qm_q4 == NULL + || q < entry1->interp_q << OD_COEFF_SHIFT) { + /* Use entry1. */ + for (i = 0; i < OD_QM_SIZE; i++) { + out[i] = OD_MINI(255, entry1->qm_q4[i]*entry1->scale_q8 >> 8); + } + } + else if (entry1 == NULL || entry1->qm_q4 == NULL + || q > entry2->interp_q << OD_COEFF_SHIFT) { + /* Use entry2. */ + for (i = 0; i < OD_QM_SIZE; i++) { + out[i] = OD_MINI(255, entry2->qm_q4[i]*entry2->scale_q8 >> 8); + } + } + else { + /* Interpolate between entry1 and entry2. The interpolation is linear + in terms of log(q) vs log(m*scale). Considering that we're ultimately + multiplying the result it makes sense, but we haven't tried other + interpolation methods. */ + double x; + const unsigned char *m1; + const unsigned char *m2; + int q1; + int q2; + m1 = entry1->qm_q4; + m2 = entry2->qm_q4; + q1 = entry1->interp_q << OD_COEFF_SHIFT; + q2 = entry2->interp_q << OD_COEFF_SHIFT; + x = (log(q)-log(q1))/(log(q2)-log(q1)); + for (i = 0; i < OD_QM_SIZE; i++) { + out[i] = OD_MINI(255, (int)floor(.5 + (1./256)*exp( + x*log(m2[i]*entry2->scale_q8) + (1 - x)*log(m1[i]*entry1->scale_q8)))); + } + } +} + +void od_adapt_pvq_ctx_reset(od_pvq_adapt_ctx *state, int is_keyframe) { + od_pvq_codeword_ctx *ctx; + int i; + int pli; + int bs; + ctx = &state->pvq_codeword_ctx; + OD_CDFS_INIT_DYNAMIC(state->pvq_param_model[0].cdf); + OD_CDFS_INIT_DYNAMIC(state->pvq_param_model[1].cdf); + OD_CDFS_INIT_DYNAMIC(state->pvq_param_model[2].cdf); + for (i = 0; i < 2*OD_TXSIZES; i++) { + ctx->pvq_adapt[4*i + OD_ADAPT_K_Q8] = 384; + ctx->pvq_adapt[4*i + OD_ADAPT_SUM_EX_Q8] = 256; + ctx->pvq_adapt[4*i + OD_ADAPT_COUNT_Q8] = 104; + ctx->pvq_adapt[4*i + OD_ADAPT_COUNT_EX_Q8] = 128; + } + OD_CDFS_INIT_DYNAMIC(ctx->pvq_k1_cdf); + for (pli = 0; pli < OD_NPLANES_MAX; pli++) { + for (bs = 0; bs < OD_TXSIZES; bs++) + for (i = 0; i < PVQ_MAX_PARTITIONS; i++) { + state->pvq_exg[pli][bs][i] = 2 << 16; + } + } + for (i = 0; i < OD_TXSIZES*PVQ_MAX_PARTITIONS; i++) { + state->pvq_ext[i] = is_keyframe ? 24576 : 2 << 16; + } + OD_CDFS_INIT_DYNAMIC(state->pvq_gaintheta_cdf); + OD_CDFS_INIT_Q15(state->pvq_skip_dir_cdf); + OD_CDFS_INIT_DYNAMIC(ctx->pvq_split_cdf); +} + +/* QMs are arranged from smallest to largest blocksizes, first for + blocks with decimation=0, followed by blocks with decimation=1.*/ +int od_qm_offset(int bs, int xydec) +{ + return xydec*OD_QM_STRIDE + OD_QM_OFFSET(bs); +} + +#if defined(OD_FLOAT_PVQ) +#define OD_DEFAULT_MAG 1.0 +#else +#define OD_DEFAULT_MAG OD_QM_SCALE +#endif + +/* Initialize the quantization matrix. */ +// Note: When hybrid transform and corresponding scan order is used by PVQ, +// we don't need seperate qm and qm_inv for each transform type, +// because AOM does not do magnitude compensation (i.e. simplay x16 for all coeffs). +void od_init_qm(int16_t *x, int16_t *x_inv, const int *qm) { + int i; + int j; + int16_t y[OD_TXSIZE_MAX*OD_TXSIZE_MAX]; + int16_t y_inv[OD_TXSIZE_MAX*OD_TXSIZE_MAX]; + int16_t *x1; + int16_t *x1_inv; + int off; + int bs; + int xydec; + for (bs = 0; bs < OD_TXSIZES; bs++) { + for (xydec = 0; xydec < 2; xydec++) { + off = od_qm_offset(bs, xydec); + x1 = x + off; + x1_inv = x_inv + off; + for (i = 0; i < 4 << bs; i++) { + for (j = 0; j < 4 << bs; j++) { + /*This will ultimately be clamped to fit in 16 bits.*/ + od_val32 mag; + int16_t ytmp; + mag = OD_DEFAULT_MAG; + if (i != 0 || j != 0) { +#if defined(OD_FLOAT_PVQ) + mag /= 0.0625*qm[(i << 1 >> bs)*8 + (j << 1 >> bs)]; +#else + int qmv; + qmv = qm[(i << 1 >> bs)*8 + (j << 1 >> bs)]; + mag *= 16; + mag = (mag + (qmv >> 1))/qmv; +#endif + OD_ASSERT(mag > 0.0); + } + /*Convert to fit in 16 bits.*/ +#if defined(OD_FLOAT_PVQ) + y[i*(4 << bs) + j] = (int16_t)OD_MINI(OD_QM_SCALE_MAX, + (int32_t)floor(.5 + mag*OD_QM_SCALE)); + y_inv[i*(4 << bs) + j] = (int16_t)floor(.5 + + OD_QM_SCALE*OD_QM_INV_SCALE/(double)y[i*(4 << bs) + j]); +#else + y[i*(4 << bs) + j] = (int16_t)OD_MINI(OD_QM_SCALE_MAX, mag); + ytmp = y[i*(4 << bs) + j]; + y_inv[i*(4 << bs) + j] = (int16_t)((OD_QM_SCALE*OD_QM_INV_SCALE + + (ytmp >> 1))/ytmp); +#endif + } + } + od_raster_to_coding_order_16(x1, 4 << bs, y, 4 << bs); + od_raster_to_coding_order_16(x1_inv, 4 << bs, y_inv, 4 << bs); + } + } +} + +/* 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); +} + +/* Maps a length n to a context for the (k=1, n<=16) coder, with a special + case when n is the original length (orig_length=1) of the vector (i.e. we + haven't split it yet). For orig_length=0, we use the same mapping as + od_pvq_size_ctx() up to n=16. When orig_length=1, we map lengths + 7, 8, 14, 15 to contexts 8 to 11. */ +int od_pvq_k1_ctx(int n, int orig_length) { + if (orig_length) return 8 + 2*(n > 8) + (n & 1); + else return od_pvq_size_ctx(n); +} + +/* Indexing for the packed quantization matrices. */ +int od_qm_get_index(int bs, int band) { + /* The -band/3 term is due to the fact that we force corresponding horizontal + and vertical bands to have the same quantization. */ + OD_ASSERT(bs >= 0 && bs < OD_TXSIZES); + return bs*(bs + 1) + band - band/3; +} + +#if !defined(OD_FLOAT_PVQ) +/*See celt/mathops.c in Opus and tools/cos_search.c.*/ +static int16_t od_pvq_cos_pi_2(int16_t x) +{ + int16_t x2; + x2 = OD_MULT16_16_Q15(x, x); + return OD_MINI(32767, (1073758164 - x*x + x2*(-7654 + OD_MULT16_16_Q16(x2, + 16573 + OD_MULT16_16_Q16(-2529, x2)))) >> 15); +} +#endif + +/*Approximates cos(x) for -pi < x < pi. + Input is in OD_THETA_SCALE.*/ +od_val16 od_pvq_cos(od_val32 x) { +#if defined(OD_FLOAT_PVQ) + return cos(x); +#else + /*Wrap x around by masking, since cos is periodic.*/ + x = x & 0x0001ffff; + if (x > (1 << 16)) { + x = (1 << 17) - x; + } + if (x & 0x00007fff) { + if (x < (1 << 15)) { + return od_pvq_cos_pi_2((int16_t)x); + } + else { + return -od_pvq_cos_pi_2((int16_t)(65536 - x)); + } + } + else { + if (x & 0x0000ffff) { + return 0; + } + else if (x & 0x0001ffff) { + return -32767; + } + else { + return 32767; + } + } +#endif +} + +/*Approximates sin(x) for 0 <= x < pi. + Input is in OD_THETA_SCALE.*/ +od_val16 od_pvq_sin(od_val32 x) { +#if defined(OD_FLOAT_PVQ) + return sin(x); +#else + return od_pvq_cos(32768 - x); +#endif +} + +#if !defined(OD_FLOAT_PVQ) +/* 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; +} +#endif + +/** Computes Householder reflection that aligns the reference r to the + * dimension in r with the greatest absolute value. The reflection + * vector is returned in r. + * + * @param [in,out] r reference vector to be reflected, reflection + * also returned in r + * @param [in] n number of dimensions in r + * @param [in] gr gain of reference vector + * @param [out] sign sign of reflection + * @return dimension number to which reflection aligns + **/ +int od_compute_householder(od_val16 *r, int n, od_val32 gr, int *sign, + int shift) { + int m; + int i; + int s; + od_val16 maxr; + OD_UNUSED(shift); + /* Pick component with largest magnitude. Not strictly + * necessary, but it helps numerical stability */ + m = 0; + maxr = 0; + for (i = 0; i < n; i++) { + if (OD_ABS(r[i]) > maxr) { + maxr = OD_ABS(r[i]); + m = i; + } + } + s = r[m] > 0 ? 1 : -1; + /* This turns r into a Householder reflection vector that would reflect + * the original r[] to e_m */ + r[m] += OD_SHR_ROUND(gr*s, shift); + *sign = s; + return m; +} + +#if !defined(OD_FLOAT_PVQ) +#define OD_RCP_INSHIFT 15 +#define OD_RCP_OUTSHIFT 14 +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); +} +#endif + +/** 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 +} + +#if !defined(OD_FLOAT_PVQ) +static od_val16 od_beta_rcp(od_val16 beta){ + if (beta == OD_BETA(1.)) + return OD_BETA(1.); + else if (beta == OD_BETA(1.5)) + return OD_BETA(1./1.5); + else { + od_val16 rcp_beta; + /*Shift by 1 less, transposing beta to range [.5, .75] and thus < 32768.*/ + rcp_beta = od_rcp(beta << (OD_RCP_INSHIFT - 1 - OD_BETA_SHIFT)); + return OD_SHR_ROUND(rcp_beta, OD_RCP_OUTSHIFT + 1 - OD_BETA_SHIFT); + } +} + +#define OD_EXP2_INSHIFT 15 +#define OD_EXP2_FRACSHIFT 15 +#define OD_EXP2_OUTSHIFT 15 +static const int32_t OD_EXP2_C[5] = {32768, 22709, 7913, 1704, 443}; +/*Output is [1.0, 2.0) in Q(OD_EXP2_FRACSHIFT). + It does not include the integer offset, which is added in od_exp2 after the + final shift).*/ +static int32_t od_exp2_frac(int32_t x) +{ + return OD_MULT16_16_Q15(x, (OD_EXP2_C[1] + OD_MULT16_16_Q15(x, + (OD_EXP2_C[2] + OD_MULT16_16_Q15(x, (OD_EXP2_C[3] + + OD_MULT16_16_Q15(x, OD_EXP2_C[4]))))))); +} + +/** Base-2 exponential approximation (2^x) with Q15 input and output.*/ +static int32_t od_exp2(int32_t x) +{ + int integer; + int32_t frac; + integer = x >> OD_EXP2_INSHIFT; + if (integer > 14) + return 0x7f000000; + else if (integer < -15) + return 0; + frac = od_exp2_frac(x - OD_SHL(integer, OD_EXP2_INSHIFT)); + return OD_VSHR_ROUND(OD_EXP2_C[0] + frac, -integer) + 1; +} + +#define OD_LOG2_INSHIFT 15 +#define OD_LOG2_OUTSHIFT 15 +#define OD_LOG2_INSCALE_1 (1./(1 << OD_LOG2_INSHIFT)) +#define OD_LOG2_OUTSCALE (1 << OD_LOG2_OUTSHIFT) +static int16_t od_log2(int16_t x) +{ + return x + OD_MULT16_16_Q15(x, (14482 + OD_MULT16_16_Q15(x, (-23234 + + OD_MULT16_16_Q15(x, (13643 + OD_MULT16_16_Q15(x, (-6403 + + OD_MULT16_16_Q15(x, 1515))))))))); +} + +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); +} +#endif + +/** Gain companding: raises gain to the power 1/beta for activity masking. + * + * @param [in] g real (uncompanded) gain + * @param [in] q0 uncompanded quality parameter + * @param [in] beta activity masking beta param (exponent) + * @return g^(1/beta) + */ +static od_val32 od_gain_compand(od_val32 g, int q0, od_val16 beta) { +#if defined(OD_FLOAT_PVQ) + if (beta == 1) return OD_CGAIN_SCALE*g/(double)q0; + else { + return OD_CGAIN_SCALE*OD_COMPAND_SCALE*pow(g*OD_COMPAND_SCALE_1, + 1./beta)/(double)q0; + } +#else + if (beta == OD_BETA(1)) return (OD_CGAIN_SCALE*g + (q0 >> 1))/q0; + else { + int32_t expr; + expr = od_pow(g, od_beta_rcp(beta)); + expr <<= OD_CGAIN_SHIFT + OD_COMPAND_SHIFT - OD_EXP2_OUTSHIFT; + return (expr + (q0 >> 1))/q0; + } +#endif +} + +#if !defined(OD_FLOAT_PVQ) +#define OD_SQRT_INSHIFT 16 +#define OD_SQRT_OUTSHIFT 15 +static int16_t od_rsqrt_norm(int16_t x); + +static int16_t od_sqrt_norm(int32_t x) +{ + OD_ASSERT(x < 65536); + return OD_MINI(OD_SHR_ROUND(x*od_rsqrt_norm(x), OD_SQRT_OUTSHIFT), 32767); +} + +static int16_t od_sqrt(int32_t x, int *sqrt_shift) +{ + int k; + int s; + int32_t t; + if (x == 0) { + *sqrt_shift = 0; + return 0; + } + OD_ASSERT(x < (1 << 30)); + k = ((OD_ILOG(x) - 1) >> 1); + /*t is x in the range [0.25, 1) in QINSHIFT, or x*2^(-s). + Shift by log2(x) - log2(0.25*(1 << INSHIFT)) to ensure 0.25 lower bound.*/ + s = 2*k - (OD_SQRT_INSHIFT - 2); + t = OD_VSHR(x, s); + /*We want to express od_sqrt() in terms of od_sqrt_norm(), which is + defined as (2^OUTSHIFT)*sqrt(t*(2^-INSHIFT)) with t=x*(2^-s). + This simplifies to 2^(OUTSHIFT-(INSHIFT/2)-(s/2))*sqrt(x), so the caller + needs to shift right by OUTSHIFT - INSHIFT/2 - s/2.*/ + *sqrt_shift = OD_SQRT_OUTSHIFT - ((s + OD_SQRT_INSHIFT) >> 1); + return od_sqrt_norm(t); +} +#endif + +/** Gain expanding: raises gain to the power beta for activity masking. + * + * @param [in] cg companded gain + * @param [in] q0 uncompanded quality parameter + * @param [in] beta activity masking beta param (exponent) + * @return g^beta + */ +od_val32 od_gain_expand(od_val32 cg0, int q0, od_val16 beta) { + if (beta == OD_BETA(1)) { + /*The multiply fits into 28 bits because the expanded gain has a range from + 0 to 2^20.*/ + return OD_SHR_ROUND(cg0*q0, OD_CGAIN_SHIFT); + } + else if (beta == OD_BETA(1.5)) { +#if defined(OD_FLOAT_PVQ) + double cg; + cg = cg0*OD_CGAIN_SCALE_1; + cg *= q0*OD_COMPAND_SCALE_1; + return OD_COMPAND_SCALE*cg*sqrt(cg); +#else + int32_t irt; + int64_t tmp; + int sqrt_inshift; + int sqrt_outshift; + /*cg0 is in Q(OD_CGAIN_SHIFT) and we need to divide it by + 2^OD_COMPAND_SHIFT.*/ + irt = od_sqrt(cg0*q0, &sqrt_outshift); + sqrt_inshift = (OD_CGAIN_SHIFT + OD_COMPAND_SHIFT) >> 1; + /*tmp is in Q(OD_CGAIN_SHIFT + OD_COMPAND_SHIFT).*/ + tmp = cg0*q0*(int64_t)irt; + /*Expanded gain must be in Q(OD_COMPAND_SHIFT), thus OD_COMPAND_SHIFT is + not included here.*/ + return OD_MAXI(1, + OD_VSHR_ROUND(tmp, OD_CGAIN_SHIFT + sqrt_outshift + sqrt_inshift)); +#endif + } + else { +#if defined(OD_FLOAT_PVQ) + /*Expanded gain must be in Q(OD_COMPAND_SHIFT), hence the multiply by + OD_COMPAND_SCALE.*/ + double cg; + cg = cg0*OD_CGAIN_SCALE_1; + return OD_COMPAND_SCALE*pow(cg*q0*OD_COMPAND_SCALE_1, beta); +#else + int32_t expr; + int32_t cg; + cg = OD_SHR_ROUND(cg0*q0, OD_CGAIN_SHIFT); + expr = od_pow(cg, beta); + /*Expanded gain must be in Q(OD_COMPAND_SHIFT), hence the subtraction by + OD_COMPAND_SHIFT.*/ + return OD_MAXI(1, OD_SHR_ROUND(expr, OD_EXP2_OUTSHIFT - OD_COMPAND_SHIFT)); +#endif + } +} + +/** Computes the raw and quantized/companded gain of a given input + * vector + * + * @param [in] x vector of input data + * @param [in] n number of elements in vector x + * @param [in] q0 quantizer + * @param [out] g raw gain + * @param [in] beta activity masking beta param + * @param [in] bshift shift to be applied to raw gain + * @return quantized/companded gain + */ +od_val32 od_pvq_compute_gain(const od_val16 *x, int n, int q0, od_val32 *g, + od_val16 beta, int bshift) { + int i; + od_val32 acc; +#if !defined(OD_FLOAT_PVQ) + od_val32 irt; + int sqrt_shift; +#else + OD_UNUSED(bshift); +#endif + acc = 0; + for (i = 0; i < n; i++) { + acc += x[i]*(od_val32)x[i]; + } +#if defined(OD_FLOAT_PVQ) + *g = sqrt(acc); +#else + irt = od_sqrt(acc, &sqrt_shift); + *g = OD_VSHR_ROUND(irt, sqrt_shift - bshift); +#endif + /* Normalize gain by quantization step size and apply companding + (if ACTIVITY != 1). */ + return od_gain_compand(*g, q0, beta); +} + +/** Compute theta quantization range from quantized/companded gain + * + * @param [in] qcg quantized companded gain value + * @param [in] beta activity masking beta param + * @return max theta value + */ +int od_pvq_compute_max_theta(od_val32 qcg, od_val16 beta){ + /* Set angular resolution (in ra) to match the encoded gain */ +#if defined(OD_FLOAT_PVQ) + int ts = (int)floor(.5 + qcg*OD_CGAIN_SCALE_1*M_PI/(2*beta)); +#else + int ts = OD_SHR_ROUND(qcg*OD_MULT16_16_QBETA(OD_QCONST32(M_PI/2, + OD_CGAIN_SHIFT), od_beta_rcp(beta)), OD_CGAIN_SHIFT*2); +#endif + /* Special case for low gains -- will need to be tuned anyway */ + if (qcg < OD_QCONST32(1.4, OD_CGAIN_SHIFT)) ts = 1; + return ts; +} + +/** Decode quantized theta value from coded value + * + * @param [in] t quantized companded gain value + * @param [in] max_theta maximum theta value + * @return decoded theta value + */ +od_val32 od_pvq_compute_theta(int t, int max_theta) { + if (max_theta != 0) { +#if defined(OD_FLOAT_PVQ) + return OD_MINI(t, max_theta - 1)*.5*M_PI/max_theta; +#else + return (OD_MAX_THETA_SCALE*OD_MINI(t, max_theta - 1) + + (max_theta >> 1))/max_theta; +#endif + } + else return 0; +} + +#define OD_SQRT_TBL_SHIFT (10) + +#define OD_ITHETA_SHIFT 15 +/** Compute the number of pulses used for PVQ encoding a vector from + * available metrics (encode and decode side) + * + * @param [in] qcg quantized companded gain value + * @param [in] itheta quantized PVQ error angle theta + * @param [in] noref indicates present or lack of reference + * (prediction) + * @param [in] n number of elements to be coded + * @param [in] beta activity masking beta param + * @return number of pulses to use for coding + */ +int od_pvq_compute_k(od_val32 qcg, int itheta, int noref, int n, + od_val16 beta) { +#if !defined(OD_FLOAT_PVQ) + /*Lookup table for sqrt(n+3/2) and sqrt(n+2/2) in Q10. + Real max values are 32792 and 32784, but clamped to stay within 16 bits. + Update with tools/gen_sqrt_tbl if needed.*/ + static const od_val16 od_sqrt_table[2][13] = { + {0, 0, 0, 0, 2290, 2985, 4222, 0, 8256, 0, 16416, 0, 32767}, + {0, 0, 0, 0, 2401, 3072, 4284, 0, 8287, 0, 16432, 0, 32767}}; +#endif + if (noref) { + if (qcg == 0) return 0; + if (n == 15 && qcg == OD_CGAIN_SCALE && beta > OD_BETA(1.25)) { + return 1; + } + else { +#if defined(OD_FLOAT_PVQ) + return OD_MAXI(1, (int)floor(.5 + (qcg*OD_CGAIN_SCALE_1 - .2)* + sqrt((n + 3)/2)/beta)); +#else + od_val16 rt; + OD_ASSERT(OD_ILOG(n + 1) < 13); + rt = od_sqrt_table[1][OD_ILOG(n + 1)]; + /*FIXME: get rid of 64-bit mul.*/ + return OD_MAXI(1, OD_SHR_ROUND((int64_t)((qcg + - (int64_t)OD_QCONST32(.2, OD_CGAIN_SHIFT))* + OD_MULT16_16_QBETA(od_beta_rcp(beta), rt)), OD_CGAIN_SHIFT + + OD_SQRT_TBL_SHIFT)); +#endif + } + } + else { + if (itheta == 0) return 0; + /* Sets K according to gain and theta, based on the high-rate + PVQ distortion curves (see PVQ document). Low-rate will have to be + perceptually tuned anyway. We subtract 0.2 from the radius as an + approximation for the fact that the coefficients aren't identically + distributed within a band so at low gain the number of dimensions that + are likely to have a pulse is less than n. */ +#if defined(OD_FLOAT_PVQ) + return OD_MAXI(1, (int)floor(.5 + (itheta - .2)*sqrt((n + 2)/2))); +#else + od_val16 rt; + OD_ASSERT(OD_ILOG(n + 1) < 13); + rt = od_sqrt_table[0][OD_ILOG(n + 1)]; + /*FIXME: get rid of 64-bit mul.*/ + return OD_MAXI(1, OD_VSHR_ROUND(((OD_SHL(itheta, OD_ITHETA_SHIFT) + - OD_QCONST32(.2, OD_ITHETA_SHIFT)))*(int64_t)rt, + OD_SQRT_TBL_SHIFT + OD_ITHETA_SHIFT)); +#endif + } +} + +#if !defined(OD_FLOAT_PVQ) +#define OD_RSQRT_INSHIFT 16 +#define OD_RSQRT_OUTSHIFT 14 +/** Reciprocal sqrt approximation where the input is in the range [0.25,1) in + Q16 and the output is in the range (1.0, 2.0] in Q14). + Error is always within +/1 of round(1/sqrt(t))*/ +static int16_t od_rsqrt_norm(int16_t t) +{ + int16_t n; + int32_t r; + int32_t r2; + int32_t ry; + int32_t y; + int32_t ret; + /* Range of n is [-16384,32767] ([-0.5,1) in Q15).*/ + n = t - 32768; + OD_ASSERT(n >= -16384); + /*Get a rough initial guess for the root. + The optimal minimax quadratic approximation (using relative error) is + r = 1.437799046117536+n*(-0.823394375837328+n*0.4096419668459485). + Coefficients here, and the final result r, are Q14.*/ + r = (23565 + OD_MULT16_16_Q15(n, (-13481 + OD_MULT16_16_Q15(n, 6711)))); + /*We want y = t*r*r-1 in Q15, but t is 32-bit Q16 and r is Q14. + We can compute the result from n and r using Q15 multiplies with some + adjustment, carefully done to avoid overflow.*/ + r2 = r*r; + y = (((r2 >> 15)*n + r2) >> 12) - 131077; + ry = r*y; + /*Apply a 2nd-order Householder iteration: r += r*y*(y*0.375-0.5). + This yields the Q14 reciprocal square root of the Q16 t, with a maximum + relative error of 1.04956E-4, a (relative) RMSE of 2.80979E-5, and a peak + absolute error of 2.26591/16384.*/ + ret = r + ((((ry >> 16)*(3*y) >> 3) - ry) >> 18); + OD_ASSERT(ret >= 16384 && ret < 32768); + return (int16_t)ret; +} + +static int16_t od_rsqrt(int32_t x, int *rsqrt_shift) +{ + int k; + int s; + int16_t t; + k = (OD_ILOG(x) - 1) >> 1; + /*t is x in the range [0.25, 1) in QINSHIFT, or x*2^(-s). + Shift by log2(x) - log2(0.25*(1 << INSHIFT)) to ensure 0.25 lower bound.*/ + s = 2*k - (OD_RSQRT_INSHIFT - 2); + t = OD_VSHR(x, s); + /*We want to express od_rsqrt() in terms of od_rsqrt_norm(), which is + defined as (2^OUTSHIFT)/sqrt(t*(2^-INSHIFT)) with t=x*(2^-s). + This simplifies to 2^(OUTSHIFT+(INSHIFT/2)+(s/2))/sqrt(x), so the caller + needs to shift right by OUTSHIFT + INSHIFT/2 + s/2.*/ + *rsqrt_shift = OD_RSQRT_OUTSHIFT + ((s + OD_RSQRT_INSHIFT) >> 1); + return od_rsqrt_norm(t); +} +#endif + +/** Synthesizes one parition of coefficient values from a PVQ-encoded + * vector. This 'partial' version is called by the encode loop where + * the Householder reflection has already been computed and there's no + * need to recompute it. + * + * @param [out] xcoeff output coefficient partition (x in math doc) + * @param [in] ypulse PVQ-encoded values (y in the math doc); in + * the noref case, this vector has n entries, + * in the reference case it contains n-1 entries + * (the m-th entry is not included) + * @param [in] r reference vector (prediction) + * @param [in] n number of elements in this partition + * @param [in] noref indicates presence or lack of prediction + * @param [in] g decoded quantized vector gain + * @param [in] theta decoded theta (prediction error) + * @param [in] m alignment dimension of Householder reflection + * @param [in] s sign of Householder reflection + * @param [in] qm_inv inverse of the QM with magnitude compensation + */ +void od_pvq_synthesis_partial(od_coeff *xcoeff, const od_coeff *ypulse, + const od_val16 *r16, int n, int noref, od_val32 g, od_val32 theta, int m, int s, + const int16_t *qm_inv) { + int i; + int yy; + od_val32 scale; + int nn; +#if !defined(OD_FLOAT_PVQ) + int gshift; + int qshift; +#endif + OD_ASSERT(g != 0); + nn = n-(!noref); /* when noref==0, vector in is sized n-1 */ + yy = 0; + for (i = 0; i < nn; i++) + yy += ypulse[i]*(int32_t)ypulse[i]; +#if !defined(OD_FLOAT_PVQ) + /* Shift required for the magnitude of the pre-qm synthesis to be guaranteed + to fit in 16 bits. In practice, the range will be 8192-16384 after scaling + most of the time. */ + gshift = OD_MAXI(0, OD_ILOG(g) - 14); +#endif + /*scale is g/sqrt(yy) in Q(16-gshift) so that x[]*scale has a norm that fits + in 16 bits.*/ + if (yy == 0) scale = 0; +#if defined(OD_FLOAT_PVQ) + else { + scale = g/sqrt(yy); + } +#else + else { + int rsqrt_shift; + int16_t rsqrt; + /*FIXME: should be < int64_t*/ + int64_t tmp; + rsqrt = od_rsqrt(yy, &rsqrt_shift); + tmp = rsqrt*(int64_t)g; + scale = OD_VSHR_ROUND(tmp, rsqrt_shift + gshift - 16); + } + /* Shift to apply after multiplying by the inverse QM, taking into account + gshift. */ + qshift = OD_QM_INV_SHIFT - gshift; +#endif + if (noref) { + for (i = 0; i < n; i++) { + od_val32 x; + /* This multiply doesn't round, so it introduces some bias. + It would be nice (but not critical) to fix this. */ + x = OD_MULT16_32_Q16(ypulse[i], scale); +#if defined(OD_FLOAT_PVQ) + xcoeff[i] = (od_coeff)floor(.5 + + x*(qm_inv[i]*OD_QM_INV_SCALE_1)); +#else + xcoeff[i] = OD_SHR_ROUND(x*qm_inv[i], qshift); +#endif + } + } + else{ + od_val16 x[MAXN]; + scale = OD_ROUND32(scale*OD_TRIG_SCALE_1*od_pvq_sin(theta)); + /* The following multiply doesn't round, but it's probably OK since + the Householder reflection is likely to undo most of the resulting + bias. */ + for (i = 0; i < m; i++) + x[i] = OD_MULT16_32_Q16(ypulse[i], scale); + x[m] = OD_ROUND16(-s*(OD_SHR_ROUND(g, gshift))*OD_TRIG_SCALE_1* + od_pvq_cos(theta)); + for (i = m; i < nn; i++) + x[i+1] = OD_MULT16_32_Q16(ypulse[i], scale); + od_apply_householder(x, x, r16, n); + for (i = 0; i < n; i++) { +#if defined(OD_FLOAT_PVQ) + xcoeff[i] = (od_coeff)floor(.5 + (x[i]*(qm_inv[i]*OD_QM_INV_SCALE_1))); +#else + xcoeff[i] = OD_SHR_ROUND(x[i]*qm_inv[i], qshift); +#endif + } + } +} |