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* IDCT implementation using the MIPS DSP ASE (little endian version)
* jidctfst.c
* Copyright (C) 1994-1998, 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 fast, not so 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 Arai, Agui, and Nakajima's algorithm for
* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
* Japanese, but the algorithm is described in the Pennebaker & Mitchell
* JPEG textbook (see REFERENCES section in file README). The following code
* is based directly on figure 4-8 in P&M.
* While an 8-point DCT cannot be done in less than 11 multiplies, it is
* possible to arrange the computation so that many of the multiplies are
* simple scalings of the final outputs. These multiplies can then be
* folded into the multiplications or divisions by the JPEG quantization
* table entries. The AA&N method leaves only 5 multiplies and 29 adds
* to be done in the DCT itself.
* The primary disadvantage of this method is that with fixed-point math,
* accuracy is lost due to imprecise representation of the scaled
* quantization values. The smaller the quantization table entry, the less
* precise the scaled value, so this implementation does worse with high-
* quality-setting files than with low-quality ones.
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h" /* Private declarations for DCT subsystem */
* This module is specialized to the case DCTSIZE = 8.
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
/* Scaling decisions are generally the same as in the LL&M algorithm;
* see jidctint.c for more details. However, we choose to descale
* (right shift) multiplication products as soon as they are formed,
* rather than carrying additional fractional bits into subsequent additions.
* This compromises accuracy slightly, but it lets us save a few shifts.
* More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
* everywhere except in the multiplications proper; this saves a good deal
* of work on 16-bit-int machines.
* The dequantized coefficients are not integers because the AA&N scaling
* factors have been incorporated. We represent them scaled up by PASS1_BITS,
* so that the first and second IDCT rounds have the same input scaling.
* For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to
* avoid a descaling shift; this compromises accuracy rather drastically
* for small quantization table entries, but it saves a lot of shifts.
* For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway,
* so we use a much larger scaling factor to preserve accuracy.
* A final compromise is to represent the multiplicative constants to only
* 8 fractional bits, rather than 13. This saves some shifting work on some
* machines, and may also reduce the cost of multiplication (since there
* are fewer one-bits in the constants).
#define CONST_BITS 8
#define PASS1_BITS 2
#define CONST_BITS 8
#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
/* 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 == 8
#define FIX_1_082392200 ((INT32) 277) /* FIX(1.082392200) */
#define FIX_1_414213562 ((INT32) 362) /* FIX(1.414213562) */
#define FIX_1_847759065 ((INT32) 473) /* FIX(1.847759065) */
#define FIX_2_613125930 ((INT32) 669) /* FIX(2.613125930) */
#define FIX_1_082392200 FIX(1.082392200)
#define FIX_1_414213562 FIX(1.414213562)
#define FIX_1_847759065 FIX(1.847759065)
#define FIX_2_613125930 FIX(2.613125930)
/* We can gain a little more speed, with a further compromise in accuracy,
* by omitting the addition in a descaling shift. This yields an incorrectly
* rounded result half the time...
#undef DESCALE
#define DESCALE(x,n) RIGHT_SHIFT(x, n)
/* Multiply a DCTELEM variable by an INT32 constant, and immediately
* descale to yield a DCTELEM result.
#define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
/* Dequantize a coefficient by multiplying it by the multiplier-table
* entry; produce a DCTELEM result. For 8-bit data a 16x16->16
* multiplication will do. For 12-bit data, the multiplier table is
* declared INT32, so a 32-bit multiply will be used.
#define DEQUANTIZE(coef,quantval) (((IFAST_MULT_TYPE) (coef)) * (quantval))
#define DEQUANTIZE(coef,quantval) \
/* Like DESCALE, but applies to a DCTELEM and produces an int.
* We assume that int right shift is unsigned if INT32 right shift is.
#define ISHIFT_TEMPS DCTELEM ishift_temp;
#define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */
#define DCTELEMBITS 32 /* DCTELEM must be 32 bits */
#define IRIGHT_SHIFT(x,shft) \
((ishift_temp = (x)) < 0 ? \
(ishift_temp >> (shft)) | ((~((DCTELEM) 0)) << (DCTELEMBITS-(shft))) : \
(ishift_temp >> (shft)))
#define IRIGHT_SHIFT(x,shft) ((x) >> (shft))
#define IDESCALE(x,n) ((int) IRIGHT_SHIFT((x) + (1 << ((n)-1)), n))
#define IDESCALE(x,n) ((int) IRIGHT_SHIFT(x, n))
// this table of constants has been moved from mips_idct_le/_be.s to
// avoid having to make the assembler code position independent
static const int mips_idct_coefs[4] = {
0x45464546, // FIX( 1.082392200 / 2) = 17734 = 0x4546
0x5A825A82, // FIX( 1.414213562 / 2) = 23170 = 0x5A82
0x76427642, // FIX( 1.847759065 / 2) = 30274 = 0x7642
0xAC61AC61 // FIX(-2.613125930 / 4) = -21407 = 0xAC61
void mips_idct_columns(JCOEF * inptr, IFAST_MULT_TYPE * quantptr,
DCTELEM * wsptr, const int * mips_idct_coefs);
void mips_idct_rows(DCTELEM * wsptr, JSAMPARRAY output_buf,
JDIMENSION output_col, const int * mips_idct_coefs);
* Perform dequantization and inverse DCT on one block of coefficients.
jpeg_idct_mips (j_decompress_ptr cinfo, jpeg_component_info * compptr,
JCOEFPTR coef_block,
JSAMPARRAY output_buf, JDIMENSION output_col)
IFAST_MULT_TYPE * quantptr;
DCTELEM workspace[DCTSIZE2]; /* buffers data between passes */
/* Pass 1: process columns from input, store into work array. */
inptr = coef_block;
quantptr = (IFAST_MULT_TYPE *) compptr->dct_table;
mips_idct_columns(inptr, quantptr, workspace, mips_idct_coefs);
/* Pass 2: process rows from work array, store into output array. */
/* Note that we must descale the results by a factor of 8 == 2**3, */
/* and also undo the PASS1_BITS scaling. */
mips_idct_rows(workspace, output_buf, output_col, mips_idct_coefs);