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							- /*
 -  * 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 */
 
 
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