/* * 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 #include #include #include /* 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_val32)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_val32)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 } } }