fixed.c
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/* libFLAC - Free Lossless Audio Codec library
* Copyright (C) 2000-2009 Josh Coalson
* Copyright (C) 2011-2016 Xiph.Org Foundation
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* - Neither the name of the Xiph.org Foundation nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifdef HAVE_CONFIG_H
# include <config.h>
#endif
#include <math.h>
#include <string.h>
#include "share/compat.h"
#include "private/bitmath.h"
#include "private/fixed.h"
#include "private/macros.h"
#include "FLAC/assert.h"
#ifdef local_abs
#undef local_abs
#endif
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#define local_abs(x) ((uint32_t)((x)<0? -(x) : (x)))
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#ifdef FLAC__INTEGER_ONLY_LIBRARY
/* rbps stands for residual bits per sample
*
* (ln(2) * err)
* rbps = log (-----------)
* 2 ( n )
*/
static FLAC__fixedpoint local__compute_rbps_integerized(FLAC__uint32 err, FLAC__uint32 n)
{
FLAC__uint32 rbps;
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uint32_t bits; /* the number of bits required to represent a number */
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int fracbits; /* the number of bits of rbps that comprise the fractional part */
FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
FLAC__ASSERT(err > 0);
FLAC__ASSERT(n > 0);
FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
if(err <= n)
return 0;
/*
* The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
* These allow us later to know we won't lose too much precision in the
* fixed-point division (err<<fracbits)/n.
*/
fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2(err)+1);
err <<= fracbits;
err /= n;
/* err now holds err/n with fracbits fractional bits */
/*
* Whittle err down to 16 bits max. 16 significant bits is enough for
* our purposes.
*/
FLAC__ASSERT(err > 0);
bits = FLAC__bitmath_ilog2(err)+1;
if(bits > 16) {
err >>= (bits-16);
fracbits -= (bits-16);
}
rbps = (FLAC__uint32)err;
/* Multiply by fixed-point version of ln(2), with 16 fractional bits */
rbps *= FLAC__FP_LN2;
fracbits += 16;
FLAC__ASSERT(fracbits >= 0);
/* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
{
const int f = fracbits & 3;
if(f) {
rbps >>= f;
fracbits -= f;
}
}
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rbps = FLAC__fixedpoint_log2(rbps, fracbits, (uint32_t)(-1));
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if(rbps == 0)
return 0;
/*
* The return value must have 16 fractional bits. Since the whole part
* of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
* must be >= -3, these assertion allows us to be able to shift rbps
* left if necessary to get 16 fracbits without losing any bits of the
* whole part of rbps.
*
* There is a slight chance due to accumulated error that the whole part
* will require 6 bits, so we use 6 in the assertion. Really though as
* long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
*/
FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
FLAC__ASSERT(fracbits >= -3);
/* now shift the decimal point into place */
if(fracbits < 16)
return rbps << (16-fracbits);
else if(fracbits > 16)
return rbps >> (fracbits-16);
else
return rbps;
}
static FLAC__fixedpoint local__compute_rbps_wide_integerized(FLAC__uint64 err, FLAC__uint32 n)
{
FLAC__uint32 rbps;
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uint32_t bits; /* the number of bits required to represent a number */
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int fracbits; /* the number of bits of rbps that comprise the fractional part */
FLAC__ASSERT(sizeof(rbps) == sizeof(FLAC__fixedpoint));
FLAC__ASSERT(err > 0);
FLAC__ASSERT(n > 0);
FLAC__ASSERT(n <= FLAC__MAX_BLOCK_SIZE);
if(err <= n)
return 0;
/*
* The above two things tell us 1) n fits in 16 bits; 2) err/n > 1.
* These allow us later to know we won't lose too much precision in the
* fixed-point division (err<<fracbits)/n.
*/
fracbits = (8*sizeof(err)) - (FLAC__bitmath_ilog2_wide(err)+1);
err <<= fracbits;
err /= n;
/* err now holds err/n with fracbits fractional bits */
/*
* Whittle err down to 16 bits max. 16 significant bits is enough for
* our purposes.
*/
FLAC__ASSERT(err > 0);
bits = FLAC__bitmath_ilog2_wide(err)+1;
if(bits > 16) {
err >>= (bits-16);
fracbits -= (bits-16);
}
rbps = (FLAC__uint32)err;
/* Multiply by fixed-point version of ln(2), with 16 fractional bits */
rbps *= FLAC__FP_LN2;
fracbits += 16;
FLAC__ASSERT(fracbits >= 0);
/* FLAC__fixedpoint_log2 requires fracbits%4 to be 0 */
{
const int f = fracbits & 3;
if(f) {
rbps >>= f;
fracbits -= f;
}
}
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rbps = FLAC__fixedpoint_log2(rbps, fracbits, (uint32_t)(-1));
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if(rbps == 0)
return 0;
/*
* The return value must have 16 fractional bits. Since the whole part
* of the base-2 log of a 32 bit number must fit in 5 bits, and fracbits
* must be >= -3, these assertion allows us to be able to shift rbps
* left if necessary to get 16 fracbits without losing any bits of the
* whole part of rbps.
*
* There is a slight chance due to accumulated error that the whole part
* will require 6 bits, so we use 6 in the assertion. Really though as
* long as it fits in 13 bits (32 - (16 - (-3))) we are fine.
*/
FLAC__ASSERT((int)FLAC__bitmath_ilog2(rbps)+1 <= fracbits + 6);
FLAC__ASSERT(fracbits >= -3);
/* now shift the decimal point into place */
if(fracbits < 16)
return rbps << (16-fracbits);
else if(fracbits > 16)
return rbps >> (fracbits-16);
else
return rbps;
}
#endif
#ifndef FLAC__INTEGER_ONLY_LIBRARY
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uint32_t FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], uint32_t data_len, float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
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uint32_t FLAC__fixed_compute_best_predictor(const FLAC__int32 data[], uint32_t data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
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#endif
{
FLAC__int32 last_error_0 = data[-1];
FLAC__int32 last_error_1 = data[-1] - data[-2];
FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
FLAC__int32 error, save;
FLAC__uint32 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
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uint32_t i, order;
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for(i = 0; i < data_len; i++) {
error = data[i] ; total_error_0 += local_abs(error); save = error;
error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
}
if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
order = 0;
else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
order = 1;
else if(total_error_2 < flac_min(total_error_3, total_error_4))
order = 2;
else if(total_error_3 < total_error_4)
order = 3;
else
order = 4;
/* Estimate the expected number of bits per residual signal sample. */
/* 'total_error*' is linearly related to the variance of the residual */
/* signal, so we use it directly to compute E(|x|) */
FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
#ifndef FLAC__INTEGER_ONLY_LIBRARY
residual_bits_per_sample[0] = (float)((total_error_0 > 0) ? log(M_LN2 * (double)total_error_0 / (double)data_len) / M_LN2 : 0.0);
residual_bits_per_sample[1] = (float)((total_error_1 > 0) ? log(M_LN2 * (double)total_error_1 / (double)data_len) / M_LN2 : 0.0);
residual_bits_per_sample[2] = (float)((total_error_2 > 0) ? log(M_LN2 * (double)total_error_2 / (double)data_len) / M_LN2 : 0.0);
residual_bits_per_sample[3] = (float)((total_error_3 > 0) ? log(M_LN2 * (double)total_error_3 / (double)data_len) / M_LN2 : 0.0);
residual_bits_per_sample[4] = (float)((total_error_4 > 0) ? log(M_LN2 * (double)total_error_4 / (double)data_len) / M_LN2 : 0.0);
#else
residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_integerized(total_error_0, data_len) : 0;
residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_integerized(total_error_1, data_len) : 0;
residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_integerized(total_error_2, data_len) : 0;
residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_integerized(total_error_3, data_len) : 0;
residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_integerized(total_error_4, data_len) : 0;
#endif
return order;
}
#ifndef FLAC__INTEGER_ONLY_LIBRARY
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uint32_t FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[], uint32_t data_len, float residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
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uint32_t FLAC__fixed_compute_best_predictor_wide(const FLAC__int32 data[], uint32_t data_len, FLAC__fixedpoint residual_bits_per_sample[FLAC__MAX_FIXED_ORDER+1])
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#endif
{
FLAC__int32 last_error_0 = data[-1];
FLAC__int32 last_error_1 = data[-1] - data[-2];
FLAC__int32 last_error_2 = last_error_1 - (data[-2] - data[-3]);
FLAC__int32 last_error_3 = last_error_2 - (data[-2] - 2*data[-3] + data[-4]);
FLAC__int32 error, save;
/* total_error_* are 64-bits to avoid overflow when encoding
* erratic signals when the bits-per-sample and blocksize are
* large.
*/
FLAC__uint64 total_error_0 = 0, total_error_1 = 0, total_error_2 = 0, total_error_3 = 0, total_error_4 = 0;
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uint32_t i, order;
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for(i = 0; i < data_len; i++) {
error = data[i] ; total_error_0 += local_abs(error); save = error;
error -= last_error_0; total_error_1 += local_abs(error); last_error_0 = save; save = error;
error -= last_error_1; total_error_2 += local_abs(error); last_error_1 = save; save = error;
error -= last_error_2; total_error_3 += local_abs(error); last_error_2 = save; save = error;
error -= last_error_3; total_error_4 += local_abs(error); last_error_3 = save;
}
if(total_error_0 < flac_min(flac_min(flac_min(total_error_1, total_error_2), total_error_3), total_error_4))
order = 0;
else if(total_error_1 < flac_min(flac_min(total_error_2, total_error_3), total_error_4))
order = 1;
else if(total_error_2 < flac_min(total_error_3, total_error_4))
order = 2;
else if(total_error_3 < total_error_4)
order = 3;
else
order = 4;
/* Estimate the expected number of bits per residual signal sample. */
/* 'total_error*' is linearly related to the variance of the residual */
/* signal, so we use it directly to compute E(|x|) */
FLAC__ASSERT(data_len > 0 || total_error_0 == 0);
FLAC__ASSERT(data_len > 0 || total_error_1 == 0);
FLAC__ASSERT(data_len > 0 || total_error_2 == 0);
FLAC__ASSERT(data_len > 0 || total_error_3 == 0);
FLAC__ASSERT(data_len > 0 || total_error_4 == 0);
#ifndef FLAC__INTEGER_ONLY_LIBRARY
residual_bits_per_sample[0] = (float)((total_error_0 > 0) ? log(M_LN2 * (double)total_error_0 / (double)data_len) / M_LN2 : 0.0);
residual_bits_per_sample[1] = (float)((total_error_1 > 0) ? log(M_LN2 * (double)total_error_1 / (double)data_len) / M_LN2 : 0.0);
residual_bits_per_sample[2] = (float)((total_error_2 > 0) ? log(M_LN2 * (double)total_error_2 / (double)data_len) / M_LN2 : 0.0);
residual_bits_per_sample[3] = (float)((total_error_3 > 0) ? log(M_LN2 * (double)total_error_3 / (double)data_len) / M_LN2 : 0.0);
residual_bits_per_sample[4] = (float)((total_error_4 > 0) ? log(M_LN2 * (double)total_error_4 / (double)data_len) / M_LN2 : 0.0);
#else
residual_bits_per_sample[0] = (total_error_0 > 0) ? local__compute_rbps_wide_integerized(total_error_0, data_len) : 0;
residual_bits_per_sample[1] = (total_error_1 > 0) ? local__compute_rbps_wide_integerized(total_error_1, data_len) : 0;
residual_bits_per_sample[2] = (total_error_2 > 0) ? local__compute_rbps_wide_integerized(total_error_2, data_len) : 0;
residual_bits_per_sample[3] = (total_error_3 > 0) ? local__compute_rbps_wide_integerized(total_error_3, data_len) : 0;
residual_bits_per_sample[4] = (total_error_4 > 0) ? local__compute_rbps_wide_integerized(total_error_4, data_len) : 0;
#endif
return order;
}
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void FLAC__fixed_compute_residual(const FLAC__int32 data[], uint32_t data_len, uint32_t order, FLAC__int32 residual[])
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{
const int idata_len = (int)data_len;
int i;
switch(order) {
case 0:
FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
memcpy(residual, data, sizeof(residual[0])*data_len);
break;
case 1:
for(i = 0; i < idata_len; i++)
residual[i] = data[i] - data[i-1];
break;
case 2:
for(i = 0; i < idata_len; i++)
residual[i] = data[i] - 2*data[i-1] + data[i-2];
break;
case 3:
for(i = 0; i < idata_len; i++)
residual[i] = data[i] - 3*data[i-1] + 3*data[i-2] - data[i-3];
break;
case 4:
for(i = 0; i < idata_len; i++)
residual[i] = data[i] - 4*data[i-1] + 6*data[i-2] - 4*data[i-3] + data[i-4];
break;
default:
FLAC__ASSERT(0);
}
}
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void FLAC__fixed_restore_signal(const FLAC__int32 residual[], uint32_t data_len, uint32_t order, FLAC__int32 data[])
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{
int i, idata_len = (int)data_len;
switch(order) {
case 0:
FLAC__ASSERT(sizeof(residual[0]) == sizeof(data[0]));
memcpy(data, residual, sizeof(residual[0])*data_len);
break;
case 1:
for(i = 0; i < idata_len; i++)
data[i] = residual[i] + data[i-1];
break;
case 2:
for(i = 0; i < idata_len; i++)
data[i] = residual[i] + 2*data[i-1] - data[i-2];
break;
case 3:
for(i = 0; i < idata_len; i++)
data[i] = residual[i] + 3*data[i-1] - 3*data[i-2] + data[i-3];
break;
case 4:
for(i = 0; i < idata_len; i++)
data[i] = residual[i] + 4*data[i-1] - 6*data[i-2] + 4*data[i-3] - data[i-4];
break;
default:
FLAC__ASSERT(0);
}
}