src/jpeg/jidctflt.c

/*
 * jidctflt.c
 *
 * Copyright (C) 1994-1998, 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 floating-point implementation of the
 * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
 * must also perform dequantization of the input coefficients.
 *
 * This implementation should be more accurate than either of the integer
 * IDCT implementations.  However, it may not give the same results on all
 * machines because of differences in roundoff behavior.  Speed will depend
 * on the hardware's floating point capacity.
 *
 * 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 Arai, Agui, and Nakajima's algorithm for
 * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
 * JPEG textbook (see REFERENCES section in file README).  The following code
 * is based directly on figure 4-8 in P&M.
 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
 * possible to arrange the computation so that many of the multiplies are
 * simple scalings of the final outputs.  These multiplies can then be
 * folded into the multiplications or divisions by the JPEG quantization
 * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
 * to be done in the DCT itself.
 * The primary disadvantage of this method is that with a fixed-point
 * implementation, accuracy is lost due to imprecise representation of the
 * scaled quantization values.  However, that problem does not arise if
 * we use floating point arithmetic.
 */

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

#ifdef DCT_FLOAT_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


/* Dequantize a coefficient by multiplying it by the multiplier-table
 * entry; produce a float result.
 */

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


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

GLOBAL(void)
jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
		 JCOEFPTR coef_block,
		 JSAMPARRAY output_buf, JDIMENSION output_col)
{
  FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
  FAST_FLOAT z5, z10, z11, z12, z13;
  JCOEFPTR inptr;
  FLOAT_MULT_TYPE * quantptr;
  FAST_FLOAT * wsptr;
  JSAMPROW outptr;
  JSAMPLE *range_limit = IDCT_range_limit(cinfo);
  int ctr;
  FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
  SHIFT_TEMPS

  /* Pass 1: process columns from input, store into work array. */

  inptr = coef_block;
  quantptr = (FLOAT_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 */
      FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);

      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 */

    tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
    tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
    tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
    tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);

    tmp10 = tmp0 + tmp2;	/* phase 3 */
    tmp11 = tmp0 - tmp2;

    tmp13 = tmp1 + tmp3;	/* phases 5-3 */
    tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */

    tmp0 = tmp10 + tmp13;	/* phase 2 */
    tmp3 = tmp10 - tmp13;
    tmp1 = tmp11 + tmp12;
    tmp2 = tmp11 - tmp12;

    /* Odd part */

    tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
    tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
    tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
    tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);

    z13 = tmp6 + tmp5;		/* phase 6 */
    z10 = tmp6 - tmp5;
    z11 = tmp4 + tmp7;
    z12 = tmp4 - tmp7;

    tmp7 = z11 + z13;		/* phase 5 */
    tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */

    z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
    tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
    tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */

    tmp6 = tmp12 - tmp7;	/* phase 2 */
    tmp5 = tmp11 - tmp6;
    tmp4 = tmp10 + tmp5;

    wsptr[DCTSIZE*0] = tmp0 + tmp7;
    wsptr[DCTSIZE*7] = tmp0 - tmp7;
    wsptr[DCTSIZE*1] = tmp1 + tmp6;
    wsptr[DCTSIZE*6] = tmp1 - tmp6;
    wsptr[DCTSIZE*2] = tmp2 + tmp5;
    wsptr[DCTSIZE*5] = tmp2 - tmp5;
    wsptr[DCTSIZE*4] = tmp3 + tmp4;
    wsptr[DCTSIZE*3] = tmp3 - tmp4;

    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. */

  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).
     * And testing floats for zero is relatively expensive, so we don't bother.
     */

    /* Even part */

    tmp10 = wsptr[0] + wsptr[4];
    tmp11 = wsptr[0] - wsptr[4];

    tmp13 = wsptr[2] + wsptr[6];
    tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;

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

    /* Odd part */

    z13 = wsptr[5] + wsptr[3];
    z10 = wsptr[5] - wsptr[3];
    z11 = wsptr[1] + wsptr[7];
    z12 = wsptr[1] - wsptr[7];

    tmp7 = z11 + z13;
    tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);

    z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
    tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
    tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */

    tmp6 = tmp12 - tmp7;
    tmp5 = tmp11 - tmp6;
    tmp4 = tmp10 + tmp5;

    /* Final output stage: scale down by a factor of 8 and range-limit */

    outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3)
			    & RANGE_MASK];
    outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)
			    & RANGE_MASK];
    outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)
			    & RANGE_MASK];
    outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)
			    & RANGE_MASK];
    outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)
			    & RANGE_MASK];
    outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)
			    & RANGE_MASK];
    outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)
			    & RANGE_MASK];
    outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)
			    & RANGE_MASK];

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

#endif /* DCT_FLOAT_SUPPORTED */
Commit	Line	Data
	1	/*
	2	* jidctflt.c
	3	*
	4	* Copyright (C) 1994-1998, 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 floating-point 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	* This implementation should be more accurate than either of the integer
	13	* IDCT implementations. However, it may not give the same results on all
	14	* machines because of differences in roundoff behavior. Speed will depend
	15	* on the hardware's floating point capacity.
	16	*
	17	* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
	18	* on each row (or vice versa, but it's more convenient to emit a row at
	19	* a time). Direct algorithms are also available, but they are much more
	20	* complex and seem not to be any faster when reduced to code.
	21	*
	22	* This implementation is based on Arai, Agui, and Nakajima's algorithm for
	23	* scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
	24	* Japanese, but the algorithm is described in the Pennebaker & Mitchell
	25	* JPEG textbook (see REFERENCES section in file README). The following code
	26	* is based directly on figure 4-8 in P&M.
	27	* While an 8-point DCT cannot be done in less than 11 multiplies, it is
	28	* possible to arrange the computation so that many of the multiplies are
	29	* simple scalings of the final outputs. These multiplies can then be
	30	* folded into the multiplications or divisions by the JPEG quantization
	31	* table entries. The AA&N method leaves only 5 multiplies and 29 adds
	32	* to be done in the DCT itself.
	33	* The primary disadvantage of this method is that with a fixed-point
	34	* implementation, accuracy is lost due to imprecise representation of the
	35	* scaled quantization values. However, that problem does not arise if
	36	* we use floating point arithmetic.
	37	*/
	38
	39	#define JPEG_INTERNALS
	40	#include "jinclude.h"
	41	#include "jpeglib.h"
	42	#include "jdct.h" /* Private declarations for DCT subsystem */
	43
	44	#ifdef DCT_FLOAT_SUPPORTED
	45
	46
	47	/*
	48	* This module is specialized to the case DCTSIZE = 8.
	49	*/
	50
	51	#if DCTSIZE != 8
	52	Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
	53	#endif
	54
	55
	56	/* Dequantize a coefficient by multiplying it by the multiplier-table
	57	* entry; produce a float result.
	58	*/
	59
	60	#define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval))
	61
	62
	63	/*
	64	* Perform dequantization and inverse DCT on one block of coefficients.
	65	*/
	66
	67	GLOBAL(void)
	68	jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
	69	JCOEFPTR coef_block,
	70	JSAMPARRAY output_buf, JDIMENSION output_col)
	71	{
	72	FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
	73	FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
	74	FAST_FLOAT z5, z10, z11, z12, z13;
	75	JCOEFPTR inptr;
	76	FLOAT_MULT_TYPE * quantptr;
	77	FAST_FLOAT * wsptr;
	78	JSAMPROW outptr;
	79	JSAMPLE *range_limit = IDCT_range_limit(cinfo);
	80	int ctr;
	81	FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
	82	SHIFT_TEMPS
	83
	84	/* Pass 1: process columns from input, store into work array. */
	85
	86	inptr = coef_block;
	87	quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
	88	wsptr = workspace;
	89	for (ctr = DCTSIZE; ctr > 0; ctr--) {
	90	/* Due to quantization, we will usually find that many of the input
	91	* coefficients are zero, especially the AC terms. We can exploit this
	92	* by short-circuiting the IDCT calculation for any column in which all
	93	* the AC terms are zero. In that case each output is equal to the
	94	* DC coefficient (with scale factor as needed).
	95	* With typical images and quantization tables, half or more of the
	96	* column DCT calculations can be simplified this way.
	97	*/
	98
	99	if (inptr[DCTSIZE1] == 0 && inptr[DCTSIZE2] == 0 &&
	100	inptr[DCTSIZE3] == 0 && inptr[DCTSIZE4] == 0 &&
	101	inptr[DCTSIZE5] == 0 && inptr[DCTSIZE6] == 0 &&
	102	inptr[DCTSIZE*7] == 0) {
	103	/* AC terms all zero */
	104	FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE0], quantptr[DCTSIZE0]);
	105
	106	wsptr[DCTSIZE*0] = dcval;
	107	wsptr[DCTSIZE*1] = dcval;
	108	wsptr[DCTSIZE*2] = dcval;
	109	wsptr[DCTSIZE*3] = dcval;
	110	wsptr[DCTSIZE*4] = dcval;
	111	wsptr[DCTSIZE*5] = dcval;
	112	wsptr[DCTSIZE*6] = dcval;
	113	wsptr[DCTSIZE*7] = dcval;
	114
	115	inptr++; /* advance pointers to next column */
	116	quantptr++;
	117	wsptr++;
	118	continue;
	119	}
	120
	121	/* Even part */
	122
	123	tmp0 = DEQUANTIZE(inptr[DCTSIZE0], quantptr[DCTSIZE0]);
	124	tmp1 = DEQUANTIZE(inptr[DCTSIZE2], quantptr[DCTSIZE2]);
	125	tmp2 = DEQUANTIZE(inptr[DCTSIZE4], quantptr[DCTSIZE4]);
	126	tmp3 = DEQUANTIZE(inptr[DCTSIZE6], quantptr[DCTSIZE6]);
	127
	128	tmp10 = tmp0 + tmp2; /* phase 3 */
	129	tmp11 = tmp0 - tmp2;
	130
	131	tmp13 = tmp1 + tmp3; /* phases 5-3 */
	132	tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2c4 /
	133
	134	tmp0 = tmp10 + tmp13; /* phase 2 */
	135	tmp3 = tmp10 - tmp13;
	136	tmp1 = tmp11 + tmp12;
	137	tmp2 = tmp11 - tmp12;
	138
	139	/* Odd part */
	140
	141	tmp4 = DEQUANTIZE(inptr[DCTSIZE1], quantptr[DCTSIZE1]);
	142	tmp5 = DEQUANTIZE(inptr[DCTSIZE3], quantptr[DCTSIZE3]);
	143	tmp6 = DEQUANTIZE(inptr[DCTSIZE5], quantptr[DCTSIZE5]);
	144	tmp7 = DEQUANTIZE(inptr[DCTSIZE7], quantptr[DCTSIZE7]);
	145
	146	z13 = tmp6 + tmp5; /* phase 6 */
	147	z10 = tmp6 - tmp5;
	148	z11 = tmp4 + tmp7;
	149	z12 = tmp4 - tmp7;
	150
	151	tmp7 = z11 + z13; /* phase 5 */
	152	tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2c4 /
	153
	154	z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2c2 /
	155	tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2(c2-c6) /
	156	tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2(c2+c6) /
	157
	158	tmp6 = tmp12 - tmp7; /* phase 2 */
	159	tmp5 = tmp11 - tmp6;
	160	tmp4 = tmp10 + tmp5;
	161
	162	wsptr[DCTSIZE*0] = tmp0 + tmp7;
	163	wsptr[DCTSIZE*7] = tmp0 - tmp7;
	164	wsptr[DCTSIZE*1] = tmp1 + tmp6;
	165	wsptr[DCTSIZE*6] = tmp1 - tmp6;
	166	wsptr[DCTSIZE*2] = tmp2 + tmp5;
	167	wsptr[DCTSIZE*5] = tmp2 - tmp5;
	168	wsptr[DCTSIZE*4] = tmp3 + tmp4;
	169	wsptr[DCTSIZE*3] = tmp3 - tmp4;
	170
	171	inptr++; /* advance pointers to next column */
	172	quantptr++;
	173	wsptr++;
	174	}
	175
	176	/* Pass 2: process rows from work array, store into output array. */
	177	/* Note that we must descale the results by a factor of 8 == 2*3. /
	178
	179	wsptr = workspace;
	180	for (ctr = 0; ctr < DCTSIZE; ctr++) {
	181	outptr = output_buf[ctr] + output_col;
	182	/* Rows of zeroes can be exploited in the same way as we did with columns.
	183	* However, the column calculation has created many nonzero AC terms, so
	184	* the simplification applies less often (typically 5% to 10% of the time).
	185	* And testing floats for zero is relatively expensive, so we don't bother.
	186	*/
	187
	188	/* Even part */
	189
	190	tmp10 = wsptr[0] + wsptr[4];
	191	tmp11 = wsptr[0] - wsptr[4];
	192
	193	tmp13 = wsptr[2] + wsptr[6];
	194	tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
	195
	196	tmp0 = tmp10 + tmp13;
	197	tmp3 = tmp10 - tmp13;
	198	tmp1 = tmp11 + tmp12;
	199	tmp2 = tmp11 - tmp12;
	200
	201	/* Odd part */
	202
	203	z13 = wsptr[5] + wsptr[3];
	204	z10 = wsptr[5] - wsptr[3];
	205	z11 = wsptr[1] + wsptr[7];
	206	z12 = wsptr[1] - wsptr[7];
	207
	208	tmp7 = z11 + z13;
	209	tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
	210
	211	z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2c2 /
	212	tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2(c2-c6) /
	213	tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2(c2+c6) /
	214
	215	tmp6 = tmp12 - tmp7;
	216	tmp5 = tmp11 - tmp6;
	217	tmp4 = tmp10 + tmp5;
	218
	219	/* Final output stage: scale down by a factor of 8 and range-limit */
	220
	221	outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3)
	222	& RANGE_MASK];
	223	outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)
	224	& RANGE_MASK];
	225	outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)
	226	& RANGE_MASK];
	227	outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)
	228	& RANGE_MASK];
	229	outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)
	230	& RANGE_MASK];
	231	outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)
	232	& RANGE_MASK];
	233	outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)
	234	& RANGE_MASK];
	235	outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)
	236	& RANGE_MASK];
	237
	238	wsptr += DCTSIZE; /* advance pointer to next row */
	239	}
	240	}
	241
	242	#endif /* DCT_FLOAT_SUPPORTED */