jrevdct.c

/*
 * 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"


/* 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 inverse DCT.
 * Note that this code is specialized to the case DCTSIZE = 8.
 */

INLINE
LOCAL void
fast_idct_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 tmp10, tmp11, tmp12, tmp13;
  INT32 tmp20, tmp21, tmp22, tmp23;
  INT32 tmp30, tmp31;
  INT32 tmp40, tmp41, tmp42, tmp43;
  INT32 tmp50, tmp51, tmp52, tmp53;
  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];

  /* These values are scaled by DCT_SCALE */

  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;

  /* These values are scaled by OVERSCALE */

  tmp30 = UNFIXO((in3 + in5) * COS_1_4);
  tmp31 = UNFIXO((in3 - in5) * COS_1_4);

  OVERSHIFT(in1);
  OVERSHIFT(in7);

  tmp40 = in1 + tmp30;
  tmp41 = in7 + tmp31;
  tmp42 = in1 - tmp30;
  tmp43 = in7 - tmp31;

  /* And these are scaled by DCT_SCALE */

  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] = (DCTELEM) UNFIXH(tmp20 + tmp50);
  in[stride  ] = (DCTELEM) UNFIXH(tmp21 + tmp53);
  in[stride*2] = (DCTELEM) UNFIXH(tmp22 + tmp52);
  in[stride*3] = (DCTELEM) UNFIXH(tmp23 + tmp51);
  in[stride*4] = (DCTELEM) UNFIXH(tmp23 - tmp51);
  in[stride*5] = (DCTELEM) UNFIXH(tmp22 - tmp52);
  in[stride*6] = (DCTELEM) UNFIXH(tmp21 - tmp53);
  in[stride*7] = (DCTELEM) UNFIXH(tmp20 - tmp50);
}


/*
 * Perform the inverse DCT on one block of coefficients.
 *
 * A 2-D IDCT can be done by 1-D IDCT on each row
 * followed by 1-D IDCT on each column.
 */

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);
}