src/jpeg/jidctint.c

/*
 * jidctint.c
 *
 * Copyright (C) 1991-1998, 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 a slow-but-accurate integer implementation of the
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
 * must also perform dequantization of the input coefficients.
 *
 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
 * on each row (or vice versa, but it's more convenient to emit a row at
 * a time).  Direct algorithms are also available, but they are much more
 * complex and seem not to be any faster when reduced to code.
 *
 * This implementation is based on an algorithm described in
 *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
 *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
 *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
 * The primary algorithm described there uses 11 multiplies and 29 adds.
 * We use their alternate method with 12 multiplies and 32 adds.
 * The advantage of this method is that no data path contains more than one
 * multiplication; this allows a very simple and accurate implementation in
 * scaled fixed-point arithmetic, with a minimal number of shifts.
 */

#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h"		/* Private declarations for DCT subsystem */

#ifdef DCT_ISLOW_SUPPORTED


/*
 * This module 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:
 *
 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
 * larger than the true IDCT outputs.  The final outputs are therefore
 * a factor of N larger than desired; since N=8 this can be cured by
 * a simple right shift at the end of the algorithm.  The advantage of
 * this arrangement is that we save two multiplications per 1-D IDCT,
 * because the y0 and y4 inputs need not be divided by sqrt(N).
 *
 * 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 CONST_SCALE and convert them to integer constants (thus retaining
 * CONST_BITS bits of precision in the constants).  After doing a
 * multiplication we have to divide the product by CONST_SCALE, with proper
 * rounding, to produce the correct output.  This division can be done
 * cheaply as a right shift of CONST_BITS bits.  We postpone shifting
 * as long as possible so that partial sums can be added together with
 * full fractional precision.
 *
 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
 * they are represented to better-than-integral precision.  These outputs
 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
 * with the recommended scaling.  (To scale up 12-bit sample data further, an
 * intermediate INT32 array would be needed.)
 *
 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
 * shows that the values given below are the most effective.
 */

#if BITS_IN_JSAMPLE == 8
#define CONST_BITS  13
#define PASS1_BITS  2
#else
#define CONST_BITS  13
#define PASS1_BITS  1		/* lose a little precision to avoid overflow */
#endif

/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
 * causing a lot of useless floating-point operations at run time.
 * To get around this we use the following pre-calculated constants.
 * If you change CONST_BITS you may want to add appropriate values.
 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
 */

#if CONST_BITS == 13
#define FIX_0_298631336  ((INT32)  2446)	/* FIX(0.298631336) */
#define FIX_0_390180644  ((INT32)  3196)	/* FIX(0.390180644) */
#define FIX_0_541196100  ((INT32)  4433)	/* FIX(0.541196100) */
#define FIX_0_765366865  ((INT32)  6270)	/* FIX(0.765366865) */
#define FIX_0_899976223  ((INT32)  7373)	/* FIX(0.899976223) */
#define FIX_1_175875602  ((INT32)  9633)	/* FIX(1.175875602) */
#define FIX_1_501321110  ((INT32)  12299)	/* FIX(1.501321110) */
#define FIX_1_847759065  ((INT32)  15137)	/* FIX(1.847759065) */
#define FIX_1_961570560  ((INT32)  16069)	/* FIX(1.961570560) */
#define FIX_2_053119869  ((INT32)  16819)	/* FIX(2.053119869) */
#define FIX_2_562915447  ((INT32)  20995)	/* FIX(2.562915447) */
#define FIX_3_072711026  ((INT32)  25172)	/* FIX(3.072711026) */
#else
#define FIX_0_298631336  FIX(0.298631336)
#define FIX_0_390180644  FIX(0.390180644)
#define FIX_0_541196100  FIX(0.541196100)
#define FIX_0_765366865  FIX(0.765366865)
#define FIX_0_899976223  FIX(0.899976223)
#define FIX_1_175875602  FIX(1.175875602)
#define FIX_1_501321110  FIX(1.501321110)
#define FIX_1_847759065  FIX(1.847759065)
#define FIX_1_961570560  FIX(1.961570560)
#define FIX_2_053119869  FIX(2.053119869)
#define FIX_2_562915447  FIX(2.562915447)
#define FIX_3_072711026  FIX(3.072711026)
#endif


/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
 * For 8-bit samples with the recommended scaling, all the variable
 * and constant values involved are no more than 16 bits wide, so a
 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
 * For 12-bit samples, a full 32-bit multiplication will be needed.
 */

#if BITS_IN_JSAMPLE == 8
#define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
#else
#define MULTIPLY(var,const)  ((var) * (const))
#endif


/* Dequantize a coefficient by multiplying it by the multiplier-table
 * entry; produce an int result.  In this module, both inputs and result
 * are 16 bits or less, so either int or short multiply will work.
 */

#define DEQUANTIZE(coef,quantval)  (((ISLOW_MULT_TYPE) (coef)) * (quantval))


/*
 * Perform dequantization and inverse DCT on one block of coefficients.
 */

GLOBAL(void)
jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
		 JCOEFPTR coef_block,
		 JSAMPARRAY output_buf, JDIMENSION output_col)
{
  INT32 tmp0, tmp1, tmp2, tmp3;
  INT32 tmp10, tmp11, tmp12, tmp13;
  INT32 z1, z2, z3, z4, z5;
  JCOEFPTR inptr;
  ISLOW_MULT_TYPE * quantptr;
  int * wsptr;
  JSAMPROW outptr;
  JSAMPLE *range_limit = IDCT_range_limit(cinfo);
  int ctr;
  int workspace[DCTSIZE2];	/* buffers data between passes */
  SHIFT_TEMPS

  /* Pass 1: process columns from input, store into work array. */
  /* Note results are scaled up by sqrt(8) compared to a true IDCT; */
  /* furthermore, we scale the results by 2**PASS1_BITS. */

  inptr = coef_block;
  quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
  wsptr = workspace;
  for (ctr = DCTSIZE; ctr > 0; ctr--) {
    /* Due to quantization, we will usually find that many of the input
     * coefficients are zero, especially the AC terms.  We can exploit this
     * by short-circuiting the IDCT calculation for any column in which all
     * the AC terms are zero.  In that case each output is equal to the
     * DC coefficient (with scale factor as needed).
     * With typical images and quantization tables, half or more of the
     * column DCT calculations can be simplified this way.
     */

    if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
	inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
	inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
	inptr[DCTSIZE*7] == 0) {
      /* AC terms all zero */
      int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;

      wsptr[DCTSIZE*0] = dcval;
      wsptr[DCTSIZE*1] = dcval;
      wsptr[DCTSIZE*2] = dcval;
      wsptr[DCTSIZE*3] = dcval;
      wsptr[DCTSIZE*4] = dcval;
      wsptr[DCTSIZE*5] = dcval;
      wsptr[DCTSIZE*6] = dcval;
      wsptr[DCTSIZE*7] = dcval;

      inptr++;			/* advance pointers to next column */
      quantptr++;
      wsptr++;
      continue;
    }

    /* Even part: reverse the even part of the forward DCT. */
    /* The rotator is sqrt(2)*c(-6). */

    z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
    z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);

    z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
    tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
    tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);

    z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
    z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);

    tmp0 = (z2 + z3) << CONST_BITS;
    tmp1 = (z2 - z3) << CONST_BITS;

    tmp10 = tmp0 + tmp3;
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;

    /* Odd part per figure 8; the matrix is unitary and hence its
     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
     */

    tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
    tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
    tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
    tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

    z1 = tmp0 + tmp3;
    z2 = tmp1 + tmp2;
    z3 = tmp0 + tmp2;
    z4 = tmp1 + tmp3;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

    tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */

    z3 += z5;
    z4 += z5;

    tmp0 += z1 + z3;
    tmp1 += z2 + z4;
    tmp2 += z2 + z3;
    tmp3 += z1 + z4;

    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

    wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
    wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
    wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
    wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
    wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
    wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
    wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
    wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);

    inptr++;			/* advance pointers to next column */
    quantptr++;
    wsptr++;
  }

  /* Pass 2: process rows from work array, store into output array. */
  /* Note that we must descale the results by a factor of 8 == 2**3, */
  /* and also undo the PASS1_BITS scaling. */

  wsptr = workspace;
  for (ctr = 0; ctr < DCTSIZE; ctr++) {
    outptr = output_buf[ctr] + output_col;
    /* Rows of zeroes can be exploited in the same way as we did with columns.
     * However, the column calculation has created many nonzero AC terms, so
     * the simplification applies less often (typically 5% to 10% of the time).
     * On machines with very fast multiplication, it's possible that the
     * test takes more time than it's worth.  In that case this section
     * may be commented out.
     */

#ifndef NO_ZERO_ROW_TEST
    if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
	wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
      /* AC terms all zero */
      JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
				  & RANGE_MASK];

      outptr[0] = dcval;
      outptr[1] = dcval;
      outptr[2] = dcval;
      outptr[3] = dcval;
      outptr[4] = dcval;
      outptr[5] = dcval;
      outptr[6] = dcval;
      outptr[7] = dcval;

      wsptr += DCTSIZE;		/* advance pointer to next row */
      continue;
    }
#endif

    /* Even part: reverse the even part of the forward DCT. */
    /* The rotator is sqrt(2)*c(-6). */

    z2 = (INT32) wsptr[2];
    z3 = (INT32) wsptr[6];

    z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
    tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
    tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);

    tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
    tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;

    tmp10 = tmp0 + tmp3;
    tmp13 = tmp0 - tmp3;
    tmp11 = tmp1 + tmp2;
    tmp12 = tmp1 - tmp2;

    /* Odd part per figure 8; the matrix is unitary and hence its
     * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
     */

    tmp0 = (INT32) wsptr[7];
    tmp1 = (INT32) wsptr[5];
    tmp2 = (INT32) wsptr[3];
    tmp3 = (INT32) wsptr[1];

    z1 = tmp0 + tmp3;
    z2 = tmp1 + tmp2;
    z3 = tmp0 + tmp2;
    z4 = tmp1 + tmp3;
    z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

    tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
    tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
    tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
    tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
    z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
    z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
    z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
    z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */

    z3 += z5;
    z4 += z5;

    tmp0 += z1 + z3;
    tmp1 += z2 + z4;
    tmp2 += z2 + z3;
    tmp3 += z1 + z4;

    /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

    outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
					  CONST_BITS+PASS1_BITS+3)
			    & RANGE_MASK];
    outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
					  CONST_BITS+PASS1_BITS+3)
			    & RANGE_MASK];
    outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
					  CONST_BITS+PASS1_BITS+3)
			    & RANGE_MASK];
    outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
					  CONST_BITS+PASS1_BITS+3)
			    & RANGE_MASK];
    outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
					  CONST_BITS+PASS1_BITS+3)
			    & RANGE_MASK];
    outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
					  CONST_BITS+PASS1_BITS+3)
			    & RANGE_MASK];
    outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
					  CONST_BITS+PASS1_BITS+3)
			    & RANGE_MASK];
    outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
					  CONST_BITS+PASS1_BITS+3)
			    & RANGE_MASK];

    wsptr += DCTSIZE;		/* advance pointer to next row */
  }
}

#endif /* DCT_ISLOW_SUPPORTED */
Commit	Line	Data
	1	/*
	2	* jidctint.c
	3	*
	4	* Copyright (C) 1991-1998, Thomas G. Lane.
	5	* This file is part of the Independent JPEG Group's software.
	6	* For conditions of distribution and use, see the accompanying README file.
	7	*
	8	* This file contains a slow-but-accurate integer implementation of the
	9	* inverse DCT (Discrete Cosine Transform). In the IJG code, this routine
	10	* must also perform dequantization of the input coefficients.
	11	*
	12	* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
	13	* on each row (or vice versa, but it's more convenient to emit a row at
	14	* a time). Direct algorithms are also available, but they are much more
	15	* complex and seem not to be any faster when reduced to code.
	16	*
	17	* This implementation is based on an algorithm described in
	18	* C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
	19	* Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
	20	* Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
	21	* The primary algorithm described there uses 11 multiplies and 29 adds.
	22	* We use their alternate method with 12 multiplies and 32 adds.
	23	* The advantage of this method is that no data path contains more than one
	24	* multiplication; this allows a very simple and accurate implementation in
	25	* scaled fixed-point arithmetic, with a minimal number of shifts.
	26	*/
	27
	28	#define JPEG_INTERNALS
	29	#include "jinclude.h"
	30	#include "jpeglib.h"
	31	#include "jdct.h" /* Private declarations for DCT subsystem */
	32
	33	#ifdef DCT_ISLOW_SUPPORTED
	34
	35
	36	/*
	37	* This module is specialized to the case DCTSIZE = 8.
	38	*/
	39
	40	#if DCTSIZE != 8
	41	Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
	42	#endif
	43
	44
	45	/*
	46	* The poop on this scaling stuff is as follows:
	47	*
	48	* Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
	49	* larger than the true IDCT outputs. The final outputs are therefore
	50	* a factor of N larger than desired; since N=8 this can be cured by
	51	* a simple right shift at the end of the algorithm. The advantage of
	52	* this arrangement is that we save two multiplications per 1-D IDCT,
	53	* because the y0 and y4 inputs need not be divided by sqrt(N).
	54	*
	55	* We have to do addition and subtraction of the integer inputs, which
	56	* is no problem, and multiplication by fractional constants, which is
	57	* a problem to do in integer arithmetic. We multiply all the constants
	58	* by CONST_SCALE and convert them to integer constants (thus retaining
	59	* CONST_BITS bits of precision in the constants). After doing a
	60	* multiplication we have to divide the product by CONST_SCALE, with proper
	61	* rounding, to produce the correct output. This division can be done
	62	* cheaply as a right shift of CONST_BITS bits. We postpone shifting
	63	* as long as possible so that partial sums can be added together with
	64	* full fractional precision.
	65	*
	66	* The outputs of the first pass are scaled up by PASS1_BITS bits so that
	67	* they are represented to better-than-integral precision. These outputs
	68	* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
	69	* with the recommended scaling. (To scale up 12-bit sample data further, an
	70	* intermediate INT32 array would be needed.)
	71	*
	72	* To avoid overflow of the 32-bit intermediate results in pass 2, we must
	73	* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
	74	* shows that the values given below are the most effective.
	75	*/
	76
	77	#if BITS_IN_JSAMPLE == 8
	78	#define CONST_BITS 13
	79	#define PASS1_BITS 2
	80	#else
	81	#define CONST_BITS 13
	82	#define PASS1_BITS 1 /* lose a little precision to avoid overflow */
	83	#endif
	84
	85	/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
	86	* causing a lot of useless floating-point operations at run time.
	87	* To get around this we use the following pre-calculated constants.
	88	* If you change CONST_BITS you may want to add appropriate values.
	89	* (With a reasonable C compiler, you can just rely on the FIX() macro...)
	90	*/
	91
	92	#if CONST_BITS == 13
	93	#define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
	94	#define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
	95	#define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
	96	#define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
	97	#define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
	98	#define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
	99	#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
	100	#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
	101	#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
	102	#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
	103	#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
	104	#define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
	105	#else
	106	#define FIX_0_298631336 FIX(0.298631336)
	107	#define FIX_0_390180644 FIX(0.390180644)
	108	#define FIX_0_541196100 FIX(0.541196100)
	109	#define FIX_0_765366865 FIX(0.765366865)
	110	#define FIX_0_899976223 FIX(0.899976223)
	111	#define FIX_1_175875602 FIX(1.175875602)
	112	#define FIX_1_501321110 FIX(1.501321110)
	113	#define FIX_1_847759065 FIX(1.847759065)
	114	#define FIX_1_961570560 FIX(1.961570560)
	115	#define FIX_2_053119869 FIX(2.053119869)
	116	#define FIX_2_562915447 FIX(2.562915447)
	117	#define FIX_3_072711026 FIX(3.072711026)
	118	#endif
	119
	120
	121	/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
	122	* For 8-bit samples with the recommended scaling, all the variable
	123	* and constant values involved are no more than 16 bits wide, so a
	124	* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
	125	* For 12-bit samples, a full 32-bit multiplication will be needed.
	126	*/
	127
	128	#if BITS_IN_JSAMPLE == 8
	129	#define MULTIPLY(var,const) MULTIPLY16C16(var,const)
	130	#else
	131	#define MULTIPLY(var,const) ((var) * (const))
	132	#endif
	133
	134
	135	/* Dequantize a coefficient by multiplying it by the multiplier-table
	136	* entry; produce an int result. In this module, both inputs and result
	137	* are 16 bits or less, so either int or short multiply will work.
	138	*/
	139
	140	#define DEQUANTIZE(coef,quantval) (((ISLOW_MULT_TYPE) (coef)) * (quantval))
	141
	142
	143	/*
	144	* Perform dequantization and inverse DCT on one block of coefficients.
	145	*/
	146
	147	GLOBAL(void)
	148	jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
	149	JCOEFPTR coef_block,
	150	JSAMPARRAY output_buf, JDIMENSION output_col)
	151	{
	152	INT32 tmp0, tmp1, tmp2, tmp3;
	153	INT32 tmp10, tmp11, tmp12, tmp13;
	154	INT32 z1, z2, z3, z4, z5;
	155	JCOEFPTR inptr;
	156	ISLOW_MULT_TYPE * quantptr;
	157	int * wsptr;
	158	JSAMPROW outptr;
	159	JSAMPLE *range_limit = IDCT_range_limit(cinfo);
	160	int ctr;
	161	int workspace[DCTSIZE2]; /* buffers data between passes */
	162	SHIFT_TEMPS
	163
	164	/* Pass 1: process columns from input, store into work array. */
	165	/* Note results are scaled up by sqrt(8) compared to a true IDCT; */
	166	/* furthermore, we scale the results by 2*PASS1_BITS. /
	167
	168	inptr = coef_block;
	169	quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
	170	wsptr = workspace;
	171	for (ctr = DCTSIZE; ctr > 0; ctr--) {
	172	/* Due to quantization, we will usually find that many of the input
	173	* coefficients are zero, especially the AC terms. We can exploit this
	174	* by short-circuiting the IDCT calculation for any column in which all
	175	* the AC terms are zero. In that case each output is equal to the
	176	* DC coefficient (with scale factor as needed).
	177	* With typical images and quantization tables, half or more of the
	178	* column DCT calculations can be simplified this way.
	179	*/
	180
	181	if (inptr[DCTSIZE1] == 0 && inptr[DCTSIZE2] == 0 &&
	182	inptr[DCTSIZE3] == 0 && inptr[DCTSIZE4] == 0 &&
	183	inptr[DCTSIZE5] == 0 && inptr[DCTSIZE6] == 0 &&
	184	inptr[DCTSIZE*7] == 0) {
	185	/* AC terms all zero */
	186	int dcval = DEQUANTIZE(inptr[DCTSIZE0], quantptr[DCTSIZE0]) << PASS1_BITS;
	187
	188	wsptr[DCTSIZE*0] = dcval;
	189	wsptr[DCTSIZE*1] = dcval;
	190	wsptr[DCTSIZE*2] = dcval;
	191	wsptr[DCTSIZE*3] = dcval;
	192	wsptr[DCTSIZE*4] = dcval;
	193	wsptr[DCTSIZE*5] = dcval;
	194	wsptr[DCTSIZE*6] = dcval;
	195	wsptr[DCTSIZE*7] = dcval;
	196
	197	inptr++; /* advance pointers to next column */
	198	quantptr++;
	199	wsptr++;
	200	continue;
	201	}
	202
	203	/* Even part: reverse the even part of the forward DCT. */
	204	/* The rotator is sqrt(2)c(-6). /
	205
	206	z2 = DEQUANTIZE(inptr[DCTSIZE2], quantptr[DCTSIZE2]);
	207	z3 = DEQUANTIZE(inptr[DCTSIZE6], quantptr[DCTSIZE6]);
	208
	209	z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
	210	tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
	211	tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
	212
	213	z2 = DEQUANTIZE(inptr[DCTSIZE0], quantptr[DCTSIZE0]);
	214	z3 = DEQUANTIZE(inptr[DCTSIZE4], quantptr[DCTSIZE4]);
	215
	216	tmp0 = (z2 + z3) << CONST_BITS;
	217	tmp1 = (z2 - z3) << CONST_BITS;
	218
	219	tmp10 = tmp0 + tmp3;
	220	tmp13 = tmp0 - tmp3;
	221	tmp11 = tmp1 + tmp2;
	222	tmp12 = tmp1 - tmp2;
	223
	224	/* Odd part per figure 8; the matrix is unitary and hence its
	225	* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
	226	*/
	227
	228	tmp0 = DEQUANTIZE(inptr[DCTSIZE7], quantptr[DCTSIZE7]);
	229	tmp1 = DEQUANTIZE(inptr[DCTSIZE5], quantptr[DCTSIZE5]);
	230	tmp2 = DEQUANTIZE(inptr[DCTSIZE3], quantptr[DCTSIZE3]);
	231	tmp3 = DEQUANTIZE(inptr[DCTSIZE1], quantptr[DCTSIZE1]);
	232
	233	z1 = tmp0 + tmp3;
	234	z2 = tmp1 + tmp2;
	235	z3 = tmp0 + tmp2;
	236	z4 = tmp1 + tmp3;
	237	z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
	238
	239	tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
	240	tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
	241	tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
	242	tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
	243	z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
	244	z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
	245	z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
	246	z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
	247
	248	z3 += z5;
	249	z4 += z5;
	250
	251	tmp0 += z1 + z3;
	252	tmp1 += z2 + z4;
	253	tmp2 += z2 + z3;
	254	tmp3 += z1 + z4;
	255
	256	/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
	257
	258	wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
	259	wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
	260	wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
	261	wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
	262	wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
	263	wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
	264	wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
	265	wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);
	266
	267	inptr++; /* advance pointers to next column */
	268	quantptr++;
	269	wsptr++;
	270	}
	271
	272	/* Pass 2: process rows from work array, store into output array. */
	273	/* Note that we must descale the results by a factor of 8 == 2*3, /
	274	/* and also undo the PASS1_BITS scaling. */
	275
	276	wsptr = workspace;
	277	for (ctr = 0; ctr < DCTSIZE; ctr++) {
	278	outptr = output_buf[ctr] + output_col;
	279	/* Rows of zeroes can be exploited in the same way as we did with columns.
	280	* However, the column calculation has created many nonzero AC terms, so
	281	* the simplification applies less often (typically 5% to 10% of the time).
	282	* On machines with very fast multiplication, it's possible that the
	283	* test takes more time than it's worth. In that case this section
	284	* may be commented out.
	285	*/
	286
	287	#ifndef NO_ZERO_ROW_TEST
	288	if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
	289	wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
	290	/* AC terms all zero */
	291	JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
	292	& RANGE_MASK];
	293
	294	outptr[0] = dcval;
	295	outptr[1] = dcval;
	296	outptr[2] = dcval;
	297	outptr[3] = dcval;
	298	outptr[4] = dcval;
	299	outptr[5] = dcval;
	300	outptr[6] = dcval;
	301	outptr[7] = dcval;
	302
	303	wsptr += DCTSIZE; /* advance pointer to next row */
	304	continue;
	305	}
	306	#endif
	307
	308	/* Even part: reverse the even part of the forward DCT. */
	309	/* The rotator is sqrt(2)c(-6). /
	310
	311	z2 = (INT32) wsptr[2];
	312	z3 = (INT32) wsptr[6];
	313
	314	z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
	315	tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
	316	tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);
	317
	318	tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
	319	tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;
	320
	321	tmp10 = tmp0 + tmp3;
	322	tmp13 = tmp0 - tmp3;
	323	tmp11 = tmp1 + tmp2;
	324	tmp12 = tmp1 - tmp2;
	325
	326	/* Odd part per figure 8; the matrix is unitary and hence its
	327	* transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively.
	328	*/
	329
	330	tmp0 = (INT32) wsptr[7];
	331	tmp1 = (INT32) wsptr[5];
	332	tmp2 = (INT32) wsptr[3];
	333	tmp3 = (INT32) wsptr[1];
	334
	335	z1 = tmp0 + tmp3;
	336	z2 = tmp1 + tmp2;
	337	z3 = tmp0 + tmp2;
	338	z4 = tmp1 + tmp3;
	339	z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
	340
	341	tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
	342	tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
	343	tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
	344	tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
	345	z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
	346	z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
	347	z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
	348	z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
	349
	350	z3 += z5;
	351	z4 += z5;
	352
	353	tmp0 += z1 + z3;
	354	tmp1 += z2 + z4;
	355	tmp2 += z2 + z3;
	356	tmp3 += z1 + z4;
	357
	358	/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */
	359
	360	outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
	361	CONST_BITS+PASS1_BITS+3)
	362	& RANGE_MASK];
	363	outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
	364	CONST_BITS+PASS1_BITS+3)
	365	& RANGE_MASK];
	366	outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
	367	CONST_BITS+PASS1_BITS+3)
	368	& RANGE_MASK];
	369	outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
	370	CONST_BITS+PASS1_BITS+3)
	371	& RANGE_MASK];
	372	outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
	373	CONST_BITS+PASS1_BITS+3)
	374	& RANGE_MASK];
	375	outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
	376	CONST_BITS+PASS1_BITS+3)
	377	& RANGE_MASK];
	378	outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
	379	CONST_BITS+PASS1_BITS+3)
	380	& RANGE_MASK];
	381	outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
	382	CONST_BITS+PASS1_BITS+3)
	383	& RANGE_MASK];
	384
	385	wsptr += DCTSIZE; /* advance pointer to next row */
	386	}
	387	}
	388
	389	#endif /* DCT_ISLOW_SUPPORTED */