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/*
* Copyright (c) 2011 The WebRTC project authors. All Rights Reserved.
*
* Use of this source code is governed by a BSD-style license
* that can be found in the LICENSE file in the root of the source
* tree. An additional intellectual property rights grant can be found
* in the file PATENTS. All contributing project authors may
* be found in the AUTHORS file in the root of the source tree.
*/
/*
* This file contains the function WebRtcSpl_LevinsonDurbin().
* The description header can be found in signal_processing_library.h
*
*/
#include "common_audio/signal_processing/include/signal_processing_library.h"
#include "rtc_base/sanitizer.h"
#define SPL_LEVINSON_MAXORDER 20
int16_t RTC_NO_SANITIZE("signed-integer-overflow") // bugs.webrtc.org/5486
WebRtcSpl_LevinsonDurbin(const int32_t* R, int16_t* A, int16_t* K,
size_t order)
{
size_t i, j;
// Auto-correlation coefficients in high precision
int16_t R_hi[SPL_LEVINSON_MAXORDER + 1], R_low[SPL_LEVINSON_MAXORDER + 1];
// LPC coefficients in high precision
int16_t A_hi[SPL_LEVINSON_MAXORDER + 1], A_low[SPL_LEVINSON_MAXORDER + 1];
// LPC coefficients for next iteration
int16_t A_upd_hi[SPL_LEVINSON_MAXORDER + 1], A_upd_low[SPL_LEVINSON_MAXORDER + 1];
// Reflection coefficient in high precision
int16_t K_hi, K_low;
// Prediction gain Alpha in high precision and with scale factor
int16_t Alpha_hi, Alpha_low, Alpha_exp;
int16_t tmp_hi, tmp_low;
int32_t temp1W32, temp2W32, temp3W32;
int16_t norm;
// Normalize the autocorrelation R[0]...R[order+1]
norm = WebRtcSpl_NormW32(R[0]);
for (i = 0; i <= order; ++i)
{
temp1W32 = R[i] * (1 << norm);
// UBSan: 12 * 268435456 cannot be represented in type 'int'
// Put R in hi and low format
R_hi[i] = (int16_t)(temp1W32 >> 16);
R_low[i] = (int16_t)((temp1W32 - ((int32_t)R_hi[i] * 65536)) >> 1);
}
// K = A[1] = -R[1] / R[0]
temp2W32 = R[1] * (1 << norm); // R[1] in Q31
temp3W32 = WEBRTC_SPL_ABS_W32(temp2W32); // abs R[1]
temp1W32 = WebRtcSpl_DivW32HiLow(temp3W32, R_hi[0], R_low[0]); // abs(R[1])/R[0] in Q31
// Put back the sign on R[1]
if (temp2W32 > 0)
{
temp1W32 = -temp1W32;
}
// Put K in hi and low format
K_hi = (int16_t)(temp1W32 >> 16);
K_low = (int16_t)((temp1W32 - ((int32_t)K_hi * 65536)) >> 1);
// Store first reflection coefficient
K[0] = K_hi;
temp1W32 >>= 4; // A[1] in Q27.
// Put A[1] in hi and low format
A_hi[1] = (int16_t)(temp1W32 >> 16);
A_low[1] = (int16_t)((temp1W32 - ((int32_t)A_hi[1] * 65536)) >> 1);
// Alpha = R[0] * (1-K^2)
temp1W32 = ((K_hi * K_low >> 14) + K_hi * K_hi) * 2; // = k^2 in Q31
temp1W32 = WEBRTC_SPL_ABS_W32(temp1W32); // Guard against <0
temp1W32 = (int32_t)0x7fffffffL - temp1W32; // temp1W32 = (1 - K[0]*K[0]) in Q31
// Store temp1W32 = 1 - K[0]*K[0] on hi and low format
tmp_hi = (int16_t)(temp1W32 >> 16);
tmp_low = (int16_t)((temp1W32 - ((int32_t)tmp_hi << 16)) >> 1);
// Calculate Alpha in Q31
temp1W32 = (R_hi[0] * tmp_hi + (R_hi[0] * tmp_low >> 15) +
(R_low[0] * tmp_hi >> 15)) << 1;
// Normalize Alpha and put it in hi and low format
Alpha_exp = WebRtcSpl_NormW32(temp1W32);
temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, Alpha_exp);
Alpha_hi = (int16_t)(temp1W32 >> 16);
Alpha_low = (int16_t)((temp1W32 - ((int32_t)Alpha_hi << 16)) >> 1);
// Perform the iterative calculations in the Levinson-Durbin algorithm
for (i = 2; i <= order; i++)
{
/* ----
temp1W32 = R[i] + > R[j]*A[i-j]
/
----
j=1..i-1
*/
temp1W32 = 0;
for (j = 1; j < i; j++)
{
// temp1W32 is in Q31
temp1W32 += (R_hi[j] * A_hi[i - j] * 2) +
(((R_hi[j] * A_low[i - j] >> 15) +
(R_low[j] * A_hi[i - j] >> 15)) * 2);
}
temp1W32 = temp1W32 * 16;
temp1W32 += ((int32_t)R_hi[i] * 65536)
+ WEBRTC_SPL_LSHIFT_W32((int32_t)R_low[i], 1);
// K = -temp1W32 / Alpha
temp2W32 = WEBRTC_SPL_ABS_W32(temp1W32); // abs(temp1W32)
temp3W32 = WebRtcSpl_DivW32HiLow(temp2W32, Alpha_hi, Alpha_low); // abs(temp1W32)/Alpha
// Put the sign of temp1W32 back again
if (temp1W32 > 0)
{
temp3W32 = -temp3W32;
}
// Use the Alpha shifts from earlier to de-normalize
norm = WebRtcSpl_NormW32(temp3W32);
if ((Alpha_exp <= norm) || (temp3W32 == 0))
{
temp3W32 = temp3W32 * (1 << Alpha_exp);
} else
{
if (temp3W32 > 0)
{
temp3W32 = (int32_t)0x7fffffffL;
} else
{
temp3W32 = (int32_t)0x80000000L;
}
}
// Put K on hi and low format
K_hi = (int16_t)(temp3W32 >> 16);
K_low = (int16_t)((temp3W32 - ((int32_t)K_hi * 65536)) >> 1);
// Store Reflection coefficient in Q15
K[i - 1] = K_hi;
// Test for unstable filter.
// If unstable return 0 and let the user decide what to do in that case
if ((int32_t)WEBRTC_SPL_ABS_W16(K_hi) > (int32_t)32750)
{
return 0; // Unstable filter
}
/*
Compute updated LPC coefficient: Anew[i]
Anew[j]= A[j] + K*A[i-j] for j=1..i-1
Anew[i]= K
*/
for (j = 1; j < i; j++)
{
// temp1W32 = A[j] in Q27
temp1W32 = (int32_t)A_hi[j] * 65536
+ WEBRTC_SPL_LSHIFT_W32((int32_t)A_low[j],1);
// temp1W32 += K*A[i-j] in Q27
temp1W32 += (K_hi * A_hi[i - j] + (K_hi * A_low[i - j] >> 15) +
(K_low * A_hi[i - j] >> 15)) * 2;
// Put Anew in hi and low format
A_upd_hi[j] = (int16_t)(temp1W32 >> 16);
A_upd_low[j] = (int16_t)(
(temp1W32 - ((int32_t)A_upd_hi[j] * 65536)) >> 1);
}
// temp3W32 = K in Q27 (Convert from Q31 to Q27)
temp3W32 >>= 4;
// Store Anew in hi and low format
A_upd_hi[i] = (int16_t)(temp3W32 >> 16);
A_upd_low[i] = (int16_t)(
(temp3W32 - ((int32_t)A_upd_hi[i] * 65536)) >> 1);
// Alpha = Alpha * (1-K^2)
temp1W32 = ((K_hi * K_low >> 14) + K_hi * K_hi) * 2; // K*K in Q31
temp1W32 = WEBRTC_SPL_ABS_W32(temp1W32); // Guard against <0
temp1W32 = (int32_t)0x7fffffffL - temp1W32; // 1 - K*K in Q31
// Convert 1- K^2 in hi and low format
tmp_hi = (int16_t)(temp1W32 >> 16);
tmp_low = (int16_t)((temp1W32 - ((int32_t)tmp_hi << 16)) >> 1);
// Calculate Alpha = Alpha * (1-K^2) in Q31
temp1W32 = (Alpha_hi * tmp_hi + (Alpha_hi * tmp_low >> 15) +
(Alpha_low * tmp_hi >> 15)) << 1;
// Normalize Alpha and store it on hi and low format
norm = WebRtcSpl_NormW32(temp1W32);
temp1W32 = WEBRTC_SPL_LSHIFT_W32(temp1W32, norm);
Alpha_hi = (int16_t)(temp1W32 >> 16);
Alpha_low = (int16_t)((temp1W32 - ((int32_t)Alpha_hi << 16)) >> 1);
// Update the total normalization of Alpha
Alpha_exp = Alpha_exp + norm;
// Update A[]
for (j = 1; j <= i; j++)
{
A_hi[j] = A_upd_hi[j];
A_low[j] = A_upd_low[j];
}
}
/*
Set A[0] to 1.0 and store the A[i] i=1...order in Q12
(Convert from Q27 and use rounding)
*/
A[0] = 4096;
for (i = 1; i <= order; i++)
{
// temp1W32 in Q27
temp1W32 = (int32_t)A_hi[i] * 65536
+ WEBRTC_SPL_LSHIFT_W32((int32_t)A_low[i], 1);
// Round and store upper word
A[i] = (int16_t)(((temp1W32 * 2) + 32768) >> 16);
}
return 1; // Stable filters
}