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/*
* jrevdct.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 inverse-DCT 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_idct_8 (DCTELEM *in, int stride)
{
/* tmp1x are new values of tmpx -- flashy register colourers
* should be able to do this lot very well
*/
INT32 tmp10, tmp11, tmp12, tmp13;
INT32 tmp20, tmp21, tmp22, tmp23;
INT32 tmp30, tmp31;
INT32 tmp40, tmp41, tmp42, tmp43;
INT32 tmp50, tmp51, tmp52, tmp53;
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];
tmp10 = (in0 + in4) * COS_1_4;
tmp11 = (in0 - in4) * COS_1_4;
tmp12 = in2 * SIN_1_8 - in6 * COS_1_8;
tmp13 = in6 * SIN_1_8 + in2 * COS_1_8;
tmp20 = tmp10 + tmp13;
tmp21 = tmp11 + tmp12;
tmp22 = tmp11 - tmp12;
tmp23 = tmp10 - tmp13;
tmp30 = UNFIXO((in3 + in5) * COS_1_4);
tmp31 = UNFIXO((in3 - in5) * COS_1_4);
tmp40 = OVERSH(in1) + tmp30;
tmp41 = OVERSH(in7) + tmp31;
tmp42 = OVERSH(in1) - tmp30;
tmp43 = OVERSH(in7) - tmp31;
tmp50 = tmp40 * OCOS_1_16 + tmp41 * OSIN_1_16;
tmp51 = tmp40 * OSIN_1_16 - tmp41 * OCOS_1_16;
tmp52 = tmp42 * OCOS_5_16 + tmp43 * OSIN_5_16;
tmp53 = tmp42 * OSIN_5_16 - tmp43 * OCOS_5_16;
in[ 0] = UNFIXH(tmp20 + tmp50);
in[stride ] = UNFIXH(tmp21 + tmp53);
in[stride*2] = UNFIXH(tmp22 + tmp52);
in[stride*3] = UNFIXH(tmp23 + tmp51);
in[stride*4] = UNFIXH(tmp23 - tmp51);
in[stride*5] = UNFIXH(tmp22 - tmp52);
in[stride*6] = UNFIXH(tmp21 - tmp53);
in[stride*7] = UNFIXH(tmp20 - tmp50);
}
/*
* Perform the inverse DCT on one block of coefficients.
*
* Note that this code is specialized to the case DCTSIZE = 8.
*/
GLOBAL void
j_rev_dct (DCTBLOCK data)
{
int i;
for (i = 0; i < DCTSIZE; i++)
fast_idct_8(data+i*DCTSIZE, 1);
for (i = 0; i < DCTSIZE; i++)
fast_idct_8(data+i, DCTSIZE);
}
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