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/*
* 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"
/* The poop on this scaling stuff is as follows:
*
* Most of the numbers (after multiplication by the constants) are
* (logically) shifted left by LG2_DCT_SCALE. This is undone by UNFIXH
* before assignment to the output array. Note that we want an additional
* division by 2 on the output (required by the equations).
*
* If right shifts are unsigned, then there is a potential problem.
* However, shifting right by 16 and then assigning to a short
* (assuming short = 16 bits) will keep the sign right!!
*
* For other shifts,
*
* ((x + (1 << 30)) >> shft) - (1 << (30 - shft))
*
* gives a nice right shift with sign (assuming no overflow). However, all the
* scaling is such that this isn't a problem. (Is this true?)
*/
#define ONE 1L /* remove L if long > 32 bits */
#ifdef RIGHT_SHIFT_IS_UNSIGNED
#define LG2_DCT_SCALE 15
#define RIGHT_SHIFT(_x,_shft) ((((_x) + (ONE << 30)) >> (_shft)) - (ONE << (30 - (_shft))))
#else
#define LG2_DCT_SCALE 16
#define RIGHT_SHIFT(_x,_shft) ((_x) >> (_shft))
#endif
#define DCT_SCALE (ONE << LG2_DCT_SCALE)
#define LG2_OVERSCALE 2
#define OVERSCALE (ONE << LG2_OVERSCALE)
#define FIX(x) ((INT32) ((x) * DCT_SCALE + 0.5))
#define FIXO(x) ((INT32) ((x) * DCT_SCALE / OVERSCALE + 0.5))
#define UNFIX(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1)), LG2_DCT_SCALE)
#define UNFIXH(x) RIGHT_SHIFT((x) + (ONE << LG2_DCT_SCALE), LG2_DCT_SCALE+1)
#define UNFIXO(x) RIGHT_SHIFT((x) + (ONE << (LG2_DCT_SCALE-1-LG2_OVERSCALE)), LG2_DCT_SCALE-LG2_OVERSCALE)
#define OVERSH(x) ((x) << LG2_OVERSCALE)
#define SIN_1_4 FIX(0.7071067811856476)
#define COS_1_4 SIN_1_4
#define SIN_1_8 FIX(0.3826834323650898)
#define COS_1_8 FIX(0.9238795325112870)
#define SIN_3_8 COS_1_8
#define COS_3_8 SIN_1_8
#define SIN_1_16 FIX(0.1950903220161282)
#define COS_1_16 FIX(0.9807852804032300)
#define SIN_7_16 COS_1_16
#define COS_7_16 SIN_1_16
#define SIN_3_16 FIX(0.5555702330196022)
#define COS_3_16 FIX(0.8314696123025450)
#define SIN_5_16 COS_3_16
#define COS_5_16 SIN_3_16
#define OSIN_1_4 FIXO(0.707106781185647)
#define OCOS_1_4 OSIN_1_4
#define OSIN_1_8 FIXO(0.3826834323650898)
#define OCOS_1_8 FIXO(0.9238795325112870)
#define OSIN_3_8 OCOS_1_8
#define OCOS_3_8 OSIN_1_8
#define OSIN_1_16 FIXO(0.1950903220161282)
#define OCOS_1_16 FIXO(0.9807852804032300)
#define OSIN_7_16 OCOS_1_16
#define OCOS_7_16 OSIN_1_16
#define OSIN_3_16 FIXO(0.5555702330196022)
#define OCOS_3_16 FIXO(0.8314696123025450)
#define OSIN_5_16 OCOS_3_16
#define OCOS_5_16 OSIN_3_16
INLINE
LOCAL void
fast_dct_8 (DCTELEM *in, int stride)
{
/* tmp1x are new values of tmpx -- 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, tmp14, tmp15, tmp16, tmp17;
INT32 tmp25, tmp26;
INT32 in0, in1, in2, in3, in4, in5, in6, in7;
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 ;
/* Now using tmp10, tmp11, tmp12, tmp13 */
in[ 0] = UNFIXH((tmp10 + tmp11) * SIN_1_4);
in[stride*4] = UNFIXH((tmp10 - tmp11) * COS_1_4);
in[stride*2] = UNFIXH(tmp13*COS_1_8 + tmp12*SIN_1_8);
in[stride*6] = UNFIXH(tmp13*SIN_1_8 - tmp12*COS_1_8);
tmp16 = UNFIXO((tmp6 + tmp5) * SIN_1_4);
tmp15 = UNFIXO((tmp6 - tmp5) * COS_1_4);
/* Now using tmp10, tmp11, tmp13, tmp14, tmp15, tmp16 */
tmp14 = OVERSH(tmp4) + tmp15;
tmp25 = OVERSH(tmp4) - tmp15;
tmp26 = OVERSH(tmp7) - tmp16;
tmp17 = OVERSH(tmp7) + tmp16;
/* These are now overscaled by OVERSCALE */
/* tmp10, tmp11, tmp12, tmp13, tmp14, tmp25, tmp26, tmp17 */
in[stride ] = UNFIXH(tmp17*OCOS_1_16 + tmp14*OSIN_1_16);
in[stride*7] = UNFIXH(tmp17*OCOS_7_16 - tmp14*OSIN_7_16);
in[stride*5] = UNFIXH(tmp26*OCOS_5_16 + tmp25*OSIN_5_16);
in[stride*3] = UNFIXH(tmp26*OCOS_3_16 - tmp25*OSIN_3_16);
}
/*
* Perform the forward DCT on one block of samples.
*
* Note that this code is specialized to the case DCTSIZE = 8.
*/
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);
}
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