📄 fixed.c
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/* libFLAC - Free Lossless Audio Codec library
* Copyright (C) 2000,2001,2002,2003,2004,2005 Josh Coalson
*
* 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.
*/
#include <math.h>
#include "private/bitmath.h"
#include "private/fixed.h"
#include "FLAC/assert.h"
#ifndef M_LN2
/* math.h in VC++ doesn't seem to have this (how Microsoft is that?) */
#define M_LN2 0.69314718055994530942
#endif
#ifdef min
#undef min
#endif
#define min(x,y) ((x) < (y)? (x) : (y))
#ifdef local_abs
#undef local_abs
#endif
#define local_abs(x) ((unsigned)((x)<0? -(x) : (x)))
#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;
unsigned bits; /* the number of bits required to represent a number */
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;
}
}
rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
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;
unsigned bits; /* the number of bits required to represent a number */
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;
}
}
rbps = FLAC__fixedpoint_log2(rbps, fracbits, (unsigned)(-1));
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);
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