/*
* mfwddct.c (derived from jfwddct.c, which carries the following info)
*
* 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 DCT (Discrete Cosine Transform) transformation
* subroutine.
*
* This implementation is based on Appendix A.2 of the book "Discrete Cosine
* Transform---Algorithms, Advantages, Applications" by K.R. Rao and P. Yip
* (Academic Press, Inc, London, 1990). It uses scaled fixed-point arithmetic
* instead of floating point.
*/
#include "all.h"
#include "dct.h"
#include "mtypes.h"
#include "opts.h"
/*
* The poop on this scaling stuff is as follows:
*
* 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 DCT_SCALE and
* convert them to integer constants (thus retaining LG2_DCT_SCALE bits of
* precision in the constants). After doing a multiplication we have to
* divide the product by DCT_SCALE, with proper rounding, to produce the
* correct output. The division can be implemented cheaply as a right shift
* of LG2_DCT_SCALE bits. The DCT equations also specify an additional
* division by 2 on the final outputs; this can be folded into the
* right-shift by shifting one more bit (see UNFIXH).
*
* If you are planning to recode this in assembler, you might want to set
* LG2_DCT_SCALE to 15. This loses a bit of precision, but then all the
* multiplications are between 16-bit quantities (given 8-bit JSAMPLEs!) so
* you could use a signed 16x16=>32 bit multiply instruction instead of full
* 32x32 multiply. Unfortunately there's no way to describe such a multiply
* portably in C, so we've gone for the extra bit of accuracy here.
*/
#define EIGHT_BIT_SAMPLES
#ifdef EIGHT_BIT_SAMPLES
#define LG2_DCT_SCALE 16
#else
#define LG2_DCT_SCALE 15 /* lose a little precision to avoid overflow */
#endif
#define ONE ((int32) 1)
#define DCT_SCALE (ONE << LG2_DCT_SCALE)
/* In some places we shift the inputs left by a couple more bits, */
/* so that they can be added to fractional results without too much */
/* loss of precision. */
#define LG2_OVERSCALE 2
#define OVERSCALE (ONE << LG2_OVERSCALE)
#define OVERSHIFT(x) ((x) <<= LG2_OVERSCALE)
/* Scale a fractional constant by DCT_SCALE */
#define FIX(x) ((int32) ((x) * DCT_SCALE + 0.5))
/* Scale a fractional constant by DCT_SCALE/OVERSCALE */
/* Such a constant can be multiplied with an overscaled input */
/* to produce something that's scaled by DCT_SCALE */
#define FIXO(x) ((int32) ((x) * DCT_SCALE / OVERSCALE + 0.5))
/* Descale and correctly round a value that's scaled by DCT_SCALE */
#define UNFIX(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1)), LG2_DCT_SCALE)
/* Same with an additional division by 2, ie, correctly rounded UNFIX(x/2) */
#define UNFIXH(x) RIGHT_SHIFT((x) + (ONE << LG2_DCT_SCALE), LG2_DCT_SCALE+1)
/* Take a value scaled by DCT_SCALE and round to integer scaled by OVERSCALE */
#define UNFIXO(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1-LG2_OVERSCALE)),\
LG2_DCT_SCALE-LG2_OVERSCALE)
/* Here are the constants we need */
/* SIN_i_j is sine of i*pi/j, scaled by DCT_SCALE */
/* COS_i_j is cosine of i*pi/j, scaled by DCT_SCALE */
#define SIN_1_4 FIX(0.707106781)
#define COS_1_4 SIN_1_4
#define SIN_1_8 FIX(0.382683432)
#define COS_1_8 FIX(0.923879533)
#define SIN_3_8 COS_1_8
#define COS_3_8 SIN_1_8
#define SIN_1_16 FIX(0.195090322)
#define COS_1_16 FIX(0.980785280)
#define SIN_7_16 COS_1_16
#define COS_7_16 SIN_1_16
#define SIN_3_16 FIX(0.555570233)
#define COS_3_16 FIX(0.831469612)
#define SIN_5_16 COS_3_16
#define COS_5_16 SIN_3_16
/* OSIN_i_j is sine of i*pi/j, scaled by DCT_SCALE/OVERSCALE */
/* OCOS_i_j is cosine of i*pi/j, scaled by DCT_SCALE/OVERSCALE */
#define OSIN_1_4 FIXO(0.707106781)
#define OCOS_1_4 OSIN_1_4
#define OSIN_1_8 FIXO(0.382683432)
#define OCOS_1_8 FIXO(0.923879533)
#define OSIN_3_8 OCOS_1_8
#define OCOS_3_8 OSIN_1_8
#define OSIN_1_16 FIXO(0.195090322)
#define OCOS_1_16 FIXO(0.980785280)
#define OSIN_7_16 OCOS_1_16
#define OCOS_7_16 OSIN_1_16
#define OSIN_3_16 FIXO(0.555570233)
#define OCOS_3_16 FIXO(0.831469612)
#define OSIN_5_16 OCOS_3_16
#define OCOS_5_16 OSIN_3_16
/* Prototypes */
void reference_fwd_dct _ANSI_ARGS_((Block block, Block dest));
void mp_fwd_dct_fast _ANSI_ARGS_((Block data2d, Block dest2d));
void init_fdct _ANSI_ARGS_((void));
/*
* --------------------------------------------------------------
*
* mp_fwd_dct_block2 --
*
* Select the appropriate mp_fwd_dct routine
*
* Results: None
*
* Side effects: None
*
* --------------------------------------------------------------
*/
extern boolean pureDCT;
void
mp_fwd_dct_block2(data, dest)
Block data, dest;
{
if (pureDCT) reference_fwd_dct(data, dest);
else mp_fwd_dct_fast(data, dest);
}
/*
* --------------------------------------------------------------
*
* mp_fwd_dct_fast --
*
* Perform the forward DCT on one block of samples.
*
* A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT on each
* column.
*
* Results: None
*
* Side effects: Overwrites the input data
*
* --------------------------------------------------------------
*/
void
mp_fwd_dct_fast(data2d, dest2d)
Block data2d, dest2d;
{
int16 *data = (int16 *) data2d; /* this algorithm wants
* a 1-d array */
int16 *dest = (int16 *) dest2d;
int pass, rowctr;
register int16 *inptr, *outptr;
int16 workspace[DCTSIZE_SQ];
SHIFT_TEMPS
#ifdef ndef
{
int y;
printf("fwd_dct (beforehand):\n");
for (y = 0; y < 8; y++)
printf("%4d %4d %4d %4d %4d %4d %4d %4d\n",
data2d[y][0], data2d[y][1],
data2d[y][2], data2d[y][3],
data2d[y][4], data2d[y][5],
data2d[y][6], data2d[y][7]);
}
#endif
/*
* Each iteration of the inner loop performs one 8-point 1-D DCT. It
* reads from a *row* of the input matrix and stores into a *column*
* of the output matrix. In the first pass, we read from the data[]
* array and store into the local workspace[]. In the second pass,
* we read from the workspace[] array and store into data[], thus
* performing the equivalent of a columnar DCT pass with no variable
* array indexing.
*/
inptr = data; /* initialize pointers for first pass */
outptr = workspace;
for (pass = 1; pass >= 0; pass--) {
for (rowctr = DCTSIZE - 1; rowctr >= 0; rowctr--) {
/*
* many tmps have nonoverlapping lifetime -- flashy
* register colourers should be able to do this lot
* very well
*/
int32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
int32 tmp10, tmp11, tmp12, tmp13;
int32 tmp14, tmp15, tmp16, tmp17;
int32 tmp25, tmp26;
/* SHIFT_TEMPS */
/* temp0 through tmp7: -512 to +512 */
/* if I-block, then -256 to +256 */
tmp0 = inptr[7] + inptr[0];
tmp1 = inptr[6] + inptr[1];
tmp2 = inptr[5] + inptr[2];
tmp3 = inptr[4] + inptr[3];
tmp4 = inptr[3] - inptr[4];
tmp5 = inptr[2] - inptr[5];
tmp6 = inptr[1] - inptr[6];
tmp7 = inptr[0] - inptr[7];
/* tmp10 through tmp13: -1024 to +1024 */
/* if I-block, then -512 to +512 */
tmp10 = tmp3 + tmp0;
tmp11 = tmp2 + tmp1;
tmp12 = tmp1 - tmp2;
tmp13 = tmp0 - tmp3;
outptr[0] = (int16) UNFIXH((tmp10 + tmp11) * SIN_1_4);
outptr[DCTSIZE * 4] = (int16) UNFIXH((tmp10 - tmp11) * COS_1_4);
outptr[DCTSIZE * 2] = (int16) UNFIXH(tmp13 * COS_1_8 + tmp12 * SIN_1_8);
outptr[DCTSIZE * 6] = (int16) UNFIXH(tmp13 * SIN_1_8 - tmp12 * COS_1_8);
tmp16 = UNFIXO((tmp6 + tmp5) * SIN_1_4);
tmp15 = UNFIXO((tmp6 - tmp5) * COS_1_4);
OVERSHIFT(tmp4);
OVERSHIFT(tmp7);
/*
* tmp4, tmp7, tmp15, tmp16 are overscaled by
* OVERSCALE
*/
tmp14 = tmp4 + tmp15;
tmp25 = tmp4 - tmp15;
tmp26 = tmp7 - tmp16;
tmp17 = tmp7 + tmp16;
outptr[DCTSIZE] = (int16) UNFIXH(tmp17 * OCOS_1_16 + tmp14 * OSIN_1_16);
outptr[DCTSIZE * 7] = (int16) UNFIXH(tmp17 * OCOS_7_16 - tmp14 * OSIN_7_16);
outptr[DCTSIZE * 5] = (int16) UNFIXH(tmp26 * OCOS_5_16 + tmp25 * OSIN_5_16);
outptr[DCTSIZE * 3] = (int16) UNFIXH(tmp26 * OCOS_3_16 - tmp25 * OSIN_3_16);
inptr += DCTSIZE; /* advance inptr to next row */
outptr++; /* advance outptr to next column */
}
/* end of pass; in case it was pass 1, set up for pass 2 */
inptr = workspace;
outptr = dest;
}
#ifdef ndef
{
int y;
printf("fwd_dct (afterward):\n");
for (y = 0; y < 8; y++)
printf("%4d %4d %4d %4d %4d %4d %4d %4d\n",
dest2d[y][0], dest2d[y][1],
dest2d[y][2], dest2d[y][3],
dest2d[y][4], dest2d[y][5],
dest2d[y][6], dest2d[y][7]);
}
#endif
}
/* Modifies from the MPEG2 verification coder */
/* fdctref.c, forward discrete cosine transform, double precision */
/* Copyright (C) 1994, MPEG Software Simulation Group. All Rights Reserved. */
/*
* Disclaimer of Warranty
*
* These software programs are available to the user without any license fee or
* royalty on an "as is" basis. The MPEG Software Simulation Group disclaims
* any and all warranties, whether express, implied, or statuary, including any
* implied warranties or merchantability or of fitness for a particular
* purpose. In no event shall the copyright-holder be liable for any
* incidental, punitive, or consequential damages of any kind whatsoever
* arising from the use of these programs.
*
* This disclaimer of warranty extends to the user of these programs and user's
* customers, employees, agents, transferees, successors, and assigns.
*
* The MPEG Software Simulation Group does not represent or warrant that the
* programs furnished hereunder are free of infringement of any third-party
* patents.
*
* Commercial implementations of MPEG-1 and MPEG-2 video, including shareware,
* are subject to royalty fees to patent holders. Many of these patents are
* general enough such that they are unavoidable regardless of implementation
* design.
*
*/
#ifndef PI
#ifdef M_PI
#define PI M_PI
#else
#define PI 3.14159265358979323846
#endif
#endif
/* private data */
static double trans_coef[8][8]; /* transform coefficients */
void init_fdct()
{
int i, j;
double s;
for (i=0; i<8; i++)
{
s = (i==0) ? sqrt(0.125) : 0.5;
for (j=0; j<8; j++)
trans_coef[i][j] = s * cos((PI/8.0)*i*(j+0.5));
}
}
void reference_fwd_dct(block, dest)
Block block, dest;
{
int i, j, k;
double s;
double tmp[64];
if (DoLaplace) {
LaplaceNum++;
}
for (i=0; i<8; i++)
for (j=0; j<8; j++)
{
s = 0.0;
for (k=0; k<8; k++)
s += trans_coef[j][k] * block[i][k];
tmp[8*i+j] = s;
}
for (i=0; i<8; i++)
for (j=0; j<8; j++)
{
s = 0.0;
for (k=0; k<8; k++)
s += trans_coef[i][k] * tmp[8*k+j];
if (collect_quant) {
fprintf(collect_quant_fp, "%d %f\n", 8*i+j, s);
}
if (DoLaplace) {
L1[LaplaceCnum][i*8+j] += s*s;
L2[LaplaceCnum][i*8+j] += s;
}
dest[i][j] = (int)floor(s+0.499999);
/*
* reason for adding 0.499999 instead of 0.5:
* s is quite often x.5 (at least for i and/or j = 0 or 4)
* and setting the rounding threshold exactly to 0.5 leads to an
* extremely high arithmetic implementation dependency of the result;
* s being between x.5 and x.500001 (which is now incorrectly rounded
* downwards instead of upwards) is assumed to occur less often
* (if at all)
*/
}
}