/*
* jfwddct.c
*
* Copyright (C) 1991, 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"
/* We assume that right shift corresponds to signed division by 2 with
* rounding towards minus infinity. This is correct for typical "arithmetic
* shift" instructions that shift in copies of the sign bit. But some
* C compilers implement >> with an unsigned shift. For these machines you
* must define RIGHT_SHIFT_IS_UNSIGNED.
* RIGHT_SHIFT provides a signed right shift of an INT32 quantity.
* It is only applied with constant shift counts.
*/
#ifdef RIGHT_SHIFT_IS_UNSIGNED
#define SHIFT_TEMPS INT32 shift_temp;
#define RIGHT_SHIFT(x,shft) \
((shift_temp = (x)) < 0 ? \
(shift_temp >> (shft)) | ((~0) << (32-(shft))) : \
(shift_temp >> (shft)))
#else
#define SHIFT_TEMPS
#define RIGHT_SHIFT(x,shft) ((x) >> (shft))
#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 a 1-dimensional DCT.
* Note that this code is specialized to the case DCTSIZE = 8.
*/
INLINE
LOCAL void
fast_dct_8 (DCTELEM *in, int stride)
{
/* many tmps have nonoverlapping lifetime -- flashy register colourers
* should be able to do this lot very well
*/
INT32 in0, in1, in2, in3, in4, in5, in6, in7;
INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
INT32 tmp10, tmp11, tmp12, tmp13;
INT32 tmp14, tmp15, tmp16, tmp17;
INT32 tmp25, tmp26;
SHIFT_TEMPS
in0 = in[ 0];
in1 = in[stride ];
in2 = in[stride*2];
in3 = in[stride*3];
in4 = in[stride*4];
in5 = in[stride*5];
in6 = in[stride*6];
in7 = in[stride*7];
tmp0 = in7 + in0;
tmp1 = in6 + in1;
tmp2 = in5 + in2;
tmp3 = in4 + in3;
tmp4 = in3 - in4;
tmp5 = in2 - in5;
tmp6 = in1 - in6;
tmp7 = in0 - in7;
tmp10 = tmp3 + tmp0;
tmp11 = tmp2 + tmp1;
tmp12 = tmp1 - tmp2;
tmp13 = tmp0 - tmp3;
in[ 0] = (DCTELEM) UNFIXH((tmp10 + tmp11) * SIN_1_4);
in[stride*4] = (DCTELEM) UNFIXH((tmp10 - tmp11) * COS_1_4);
in[stride*2] = (DCTELEM) UNFIXH(tmp13*COS_1_8 + tmp12*SIN_1_8);
in[stride*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;
in[stride ] = (DCTELEM) UNFIXH(tmp17*OCOS_1_16 + tmp14*OSIN_1_16);
in[stride*7] = (DCTELEM) UNFIXH(tmp17*OCOS_7_16 - tmp14*OSIN_7_16);
in[stride*5] = (DCTELEM) UNFIXH(tmp26*OCOS_5_16 + tmp25*OSIN_5_16);
in[stride*3] = (DCTELEM) UNFIXH(tmp26*OCOS_3_16 - tmp25*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 i;
for (i = 0; i < DCTSIZE; i++)
fast_dct_8(data+i*DCTSIZE, 1);
for (i = 0; i < DCTSIZE; i++)
fast_dct_8(data+i, DCTSIZE);
}