📄 jidctint.c
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////////////////////////////////////////////////////////////////////////
//
// Note : this file is included as part of the Smaller Animals Software
// JpegFile package. Though this file has not been modified from it's
// original IJG 6a form, it is not the responsibility on the Independent
// JPEG Group to answer questions regarding this code.
//
// Any questions you have about this code should be addressed to :
//
// CHRISDL@PAGESZ.NET - the distributor of this package.
//
// Remember, by including this code in the JpegFile package, Smaller
// Animals Software assumes all responsibilities for answering questions
// about it. If we (SA Software) can't answer your questions ourselves, we
// will direct you to people who can.
//
// Thanks, CDL.
//
////////////////////////////////////////////////////////////////////////
/*
* jidctint.c
*
* Copyright (C) 1991-1996, 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 a slow-but-accurate integer implementation of the
* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
* must also perform dequantization of the input coefficients.
*
* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
* on each row (or vice versa, but it's more convenient to emit a row at
* a time). Direct algorithms are also available, but they are much more
* complex and seem not to be any faster when reduced to code.
*
* 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.
*/
#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h" /* Private declarations for DCT subsystem */
#ifdef DCT_ISLOW_SUPPORTED
/*
* This module is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif
/*
* 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.
*
* The outputs of the first pass are scaled up by PASS1_BITS bits so that
* they are represented to better-than-integral precision. These outputs
* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
* with the recommended scaling. (To scale up 12-bit sample data further, an
* intermediate long array would be needed.)
*
* To avoid overflow of the 32-bit intermediate results in pass 2, we must
* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
* shows that the values given below are the most effective.
*/
#if BITS_IN_JSAMPLE == 8
#define CONST_BITS 13
#define PASS1_BITS 2
#else
#define CONST_BITS 13
#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
#endif
/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
* causing a lot of useless floating-point operations at run time.
* To get around this we use the following pre-calculated constants.
* If you change CONST_BITS you may want to add appropriate values.
* (With a reasonable C compiler, you can just rely on the FIX() macro...)
*/
#if CONST_BITS == 13
#define FIX_0_298631336 ((long) 2446) /* FIX(0.298631336) */
#define FIX_0_390180644 ((long) 3196) /* FIX(0.390180644) */
#define FIX_0_541196100 ((long) 4433) /* FIX(0.541196100) */
#define FIX_0_765366865 ((long) 6270) /* FIX(0.765366865) */
#define FIX_0_899976223 ((long) 7373) /* FIX(0.899976223) */
#define FIX_1_175875602 ((long) 9633) /* FIX(1.175875602) */
#define FIX_1_501321110 ((long) 12299) /* FIX(1.501321110) */
#define FIX_1_847759065 ((long) 15137) /* FIX(1.847759065) */
#define FIX_1_961570560 ((long) 16069) /* FIX(1.961570560) */
#define FIX_2_053119869 ((long) 16819) /* FIX(2.053119869) */
#define FIX_2_562915447 ((long) 20995) /* FIX(2.562915447) */
#define FIX_3_072711026 ((long) 25172) /* FIX(3.072711026) */
#else
#define FIX_0_298631336 FIX(0.298631336)
#define FIX_0_390180644 FIX(0.390180644)
#define FIX_0_541196100 FIX(0.541196100)
#define FIX_0_765366865 FIX(0.765366865)
#define FIX_0_899976223 FIX(0.899976223)
#define FIX_1_175875602 FIX(1.175875602)
#define FIX_1_501321110 FIX(1.501321110)
#define FIX_1_847759065 FIX(1.847759065)
#define FIX_1_961570560 FIX(1.961570560)
#define FIX_2_053119869 FIX(2.053119869)
#define FIX_2_562915447 FIX(2.562915447)
#define FIX_3_072711026 FIX(3.072711026)
#endif
/* Multiply an long variable by an long constant to yield an long result.
* For 8-bit samples with the recommended scaling, all the variable
* and constant values involved are no more than 16 bits wide, so a
* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
* For 12-bit samples, a full 32-bit multiplication will be needed.
*/
#if BITS_IN_JSAMPLE == 8
#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
#else
#define MULTIPLY(var,const) ((var) * (const))
#endif
/* Dequantize a coefficient by multiplying it by the multiplier-table
* entry; produce an int result. In this module, both inputs and result
* are 16 bits or less, so either int or short multiply will work.
*/
#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))
/*
* Perform dequantization and inverse DCT on one block of coefficients.
*/
GLOBAL(void)
jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
JCOEFPTR coef_block,
JSAMPARRAY output_buf, JDIMENSION output_col)
{
long tmp0, tmp1, tmp2, tmp3;
long tmp10, tmp11, tmp12, tmp13;
long z1, z2, z3, z4, z5;
JCOEFPTR inptr;
ISLOW_MULT_TYPE * quantptr;
int * wsptr;
JSAMPROW outptr;
JSAMPLE *range_limit = IDCT_range_limit(cinfo);
int ctr;
int workspace[DCTSIZE2]; /* buffers data between passes */
SHIFT_TEMPS
/* Pass 1: process columns from input, store into work array. */
/* Note results are scaled up by sqrt(8) compared to a true IDCT; */
/* furthermore, we scale the results by 2**PASS1_BITS. */
inptr = coef_block;
quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
wsptr = workspace;
for (ctr = DCTSIZE; ctr > 0; ctr--) {
/* Due to quantization, we will usually find that many of the input
* coefficients are zero, especially the AC terms. We can exploit this
* by short-circuiting the IDCT calculation for any column in which all
* the AC terms are zero. In that case each output is equal to the
* DC coefficient (with scale factor as needed).
* With typical images and quantization tables, half or more of the
* column DCT calculations can be simplified this way.
*/
if ((inptr[DCTSIZE*1] | inptr[DCTSIZE*2] | inptr[DCTSIZE*3] |
inptr[DCTSIZE*4] | inptr[DCTSIZE*5] | inptr[DCTSIZE*6] |
inptr[DCTSIZE*7]) == 0) {
/* AC terms all zero */
int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;
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