/*
* jfwddct.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 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 "jinclude.h"
/*
* This routine 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:
*
* 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.
*/
#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
/*
* 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.
*/
GLOBAL void
j_fwd_dct (DCTBLOCK data)
{
int pass, rowctr;
register DCTELEM *inptr, *outptr;
DCTBLOCK workspace;
/* 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
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 = tmp3 + tmp0;
tmp11 = tmp2 + tmp1;
tmp12 = tmp1 - tmp2;
tmp13 = tmp0 - tmp3;
outptr[ 0] = (DCTELEM) UNFIXH((tmp10 + tmp11) * SIN_1_4);
outptr[DCTSIZE*4] = (DCTELEM) UNFIXH((tmp10 - tmp11) * COS_1_4);
outptr[DCTSIZE*2] = (DCTELEM) UNFIXH(tmp13*COS_1_8 + tmp12*SIN_1_8);
outptr[DCTSIZE*6] = (DCTELEM) 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 ] = (DCTELEM) UNFIXH(tmp17*OCOS_1_16 + tmp14*OSIN_1_16);
outptr[DCTSIZE*7] = (DCTELEM) UNFIXH(tmp17*OCOS_7_16 - tmp14*OSIN_7_16);
outptr[DCTSIZE*5] = (DCTELEM) UNFIXH(tmp26*OCOS_5_16 + tmp25*OSIN_5_16);
outptr[DCTSIZE*3] = (DCTELEM) 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 = data;
}
}