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jrevdct.cpp 35.90 KiB
/*
* jrevdct.c
*
* Copyright (C) 1991, 1992, Thomas G. Lane.
* This file is part of the Independent JPEG Group's software.
* For conditions of distribution and use, see the accompanying README file.
*
* This file contains the basic inverse-DCT transformation subroutine.
*
* This implementation is based on an algorithm described in
* C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
* Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
* Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
* The primary algorithm described there uses 11 multiplies and 29 adds.
* We use their alternate method with 12 multiplies and 32 adds.
* The advantage of this method is that no data path contains more than one
* multiplication; this allows a very simple and accurate implementation in
* scaled fixed-point arithmetic, with a minimal number of shifts.
*
* I've made lots of modifications to attempt to take advantage of the
* sparse nature of the DCT matrices we're getting. Although the logic
* is cumbersome, it's straightforward and the resulting code is much
* faster.
*
* A better way to do this would be to pass in the DCT block as a sparse
* matrix, perhaps with the difference cases encoded.
*/
#include <memory.h>
#include "all.h"
#include "ansi.h"
#include "dct.h"
#define CONST_BITS 13
/*
* This routine is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif
/*
* A 2-D IDCT can be done by 1-D IDCT on each row followed by 1-D IDCT
* on each column. Direct algorithms are also available, but they are
* much more complex and seem not to be any faster when reduced to code.
*
* The poop on this scaling stuff is as follows:
*
* Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
* larger than the true IDCT outputs. The final outputs are therefore
* a factor of N larger than desired; since N=8 this can be cured by
* a simple right shift at the end of the algorithm. The advantage of
* this arrangement is that we save two multiplications per 1-D IDCT,
* because the y0 and y4 inputs need not be divided by sqrt(N).
*
* We have to do addition and subtraction of the integer inputs, which
* is no problem, and multiplication by fractional constants, which is
* a problem to do in integer arithmetic. We multiply all the constants
* by CONST_SCALE and convert them to integer constants (thus retaining
* CONST_BITS bits of precision in the constants). After doing a
* multiplication we have to divide the product by CONST_SCALE, with proper
* rounding, to produce the correct output. This division can be done
* cheaply as a right shift of CONST_BITS bits. We postpone shifting
* as long as possible so that partial sums can be added together with
* full fractional precision.
*