michael@0: /*
michael@0:  * jidctflt.c
michael@0:  *
michael@0:  * Copyright (C) 1994-1998, Thomas G. Lane.
michael@0:  * This file is part of the Independent JPEG Group's software.
michael@0:  * For conditions of distribution and use, see the accompanying README file.
michael@0:  *
michael@0:  * This file contains a floating-point implementation of the
michael@0:  * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
michael@0:  * must also perform dequantization of the input coefficients.
michael@0:  *
michael@0:  * This implementation should be more accurate than either of the integer
michael@0:  * IDCT implementations.  However, it may not give the same results on all
michael@0:  * machines because of differences in roundoff behavior.  Speed will depend
michael@0:  * on the hardware's floating point capacity.
michael@0:  *
michael@0:  * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
michael@0:  * on each row (or vice versa, but it's more convenient to emit a row at
michael@0:  * a time).  Direct algorithms are also available, but they are much more
michael@0:  * complex and seem not to be any faster when reduced to code.
michael@0:  *
michael@0:  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
michael@0:  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
michael@0:  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
michael@0:  * JPEG textbook (see REFERENCES section in file README).  The following code
michael@0:  * is based directly on figure 4-8 in P&M.
michael@0:  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
michael@0:  * possible to arrange the computation so that many of the multiplies are
michael@0:  * simple scalings of the final outputs.  These multiplies can then be
michael@0:  * folded into the multiplications or divisions by the JPEG quantization
michael@0:  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
michael@0:  * to be done in the DCT itself.
michael@0:  * The primary disadvantage of this method is that with a fixed-point
michael@0:  * implementation, accuracy is lost due to imprecise representation of the
michael@0:  * scaled quantization values.  However, that problem does not arise if
michael@0:  * we use floating point arithmetic.
michael@0:  */
michael@0: 
michael@0: #define JPEG_INTERNALS
michael@0: #include "jinclude.h"
michael@0: #include "jpeglib.h"
michael@0: #include "jdct.h"		/* Private declarations for DCT subsystem */
michael@0: 
michael@0: #ifdef DCT_FLOAT_SUPPORTED
michael@0: 
michael@0: 
michael@0: /*
michael@0:  * This module is specialized to the case DCTSIZE = 8.
michael@0:  */
michael@0: 
michael@0: #if DCTSIZE != 8
michael@0:   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
michael@0: #endif
michael@0: 
michael@0: 
michael@0: /* Dequantize a coefficient by multiplying it by the multiplier-table
michael@0:  * entry; produce a float result.
michael@0:  */
michael@0: 
michael@0: #define DEQUANTIZE(coef,quantval)  (((FAST_FLOAT) (coef)) * (quantval))
michael@0: 
michael@0: 
michael@0: /*
michael@0:  * Perform dequantization and inverse DCT on one block of coefficients.
michael@0:  */
michael@0: 
michael@0: GLOBAL(void)
michael@0: jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr,
michael@0: 		 JCOEFPTR coef_block,
michael@0: 		 JSAMPARRAY output_buf, JDIMENSION output_col)
michael@0: {
michael@0:   FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
michael@0:   FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
michael@0:   FAST_FLOAT z5, z10, z11, z12, z13;
michael@0:   JCOEFPTR inptr;
michael@0:   FLOAT_MULT_TYPE * quantptr;
michael@0:   FAST_FLOAT * wsptr;
michael@0:   JSAMPROW outptr;
michael@0:   JSAMPLE *range_limit = IDCT_range_limit(cinfo);
michael@0:   int ctr;
michael@0:   FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
michael@0:   SHIFT_TEMPS
michael@0: 
michael@0:   /* Pass 1: process columns from input, store into work array. */
michael@0: 
michael@0:   inptr = coef_block;
michael@0:   quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table;
michael@0:   wsptr = workspace;
michael@0:   for (ctr = DCTSIZE; ctr > 0; ctr--) {
michael@0:     /* Due to quantization, we will usually find that many of the input
michael@0:      * coefficients are zero, especially the AC terms.  We can exploit this
michael@0:      * by short-circuiting the IDCT calculation for any column in which all
michael@0:      * the AC terms are zero.  In that case each output is equal to the
michael@0:      * DC coefficient (with scale factor as needed).
michael@0:      * With typical images and quantization tables, half or more of the
michael@0:      * column DCT calculations can be simplified this way.
michael@0:      */
michael@0:     
michael@0:     if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
michael@0: 	inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
michael@0: 	inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
michael@0: 	inptr[DCTSIZE*7] == 0) {
michael@0:       /* AC terms all zero */
michael@0:       FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
michael@0:       
michael@0:       wsptr[DCTSIZE*0] = dcval;
michael@0:       wsptr[DCTSIZE*1] = dcval;
michael@0:       wsptr[DCTSIZE*2] = dcval;
michael@0:       wsptr[DCTSIZE*3] = dcval;
michael@0:       wsptr[DCTSIZE*4] = dcval;
michael@0:       wsptr[DCTSIZE*5] = dcval;
michael@0:       wsptr[DCTSIZE*6] = dcval;
michael@0:       wsptr[DCTSIZE*7] = dcval;
michael@0:       
michael@0:       inptr++;			/* advance pointers to next column */
michael@0:       quantptr++;
michael@0:       wsptr++;
michael@0:       continue;
michael@0:     }
michael@0:     
michael@0:     /* Even part */
michael@0: 
michael@0:     tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
michael@0:     tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
michael@0:     tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
michael@0:     tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
michael@0: 
michael@0:     tmp10 = tmp0 + tmp2;	/* phase 3 */
michael@0:     tmp11 = tmp0 - tmp2;
michael@0: 
michael@0:     tmp13 = tmp1 + tmp3;	/* phases 5-3 */
michael@0:     tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
michael@0: 
michael@0:     tmp0 = tmp10 + tmp13;	/* phase 2 */
michael@0:     tmp3 = tmp10 - tmp13;
michael@0:     tmp1 = tmp11 + tmp12;
michael@0:     tmp2 = tmp11 - tmp12;
michael@0:     
michael@0:     /* Odd part */
michael@0: 
michael@0:     tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
michael@0:     tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
michael@0:     tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
michael@0:     tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
michael@0: 
michael@0:     z13 = tmp6 + tmp5;		/* phase 6 */
michael@0:     z10 = tmp6 - tmp5;
michael@0:     z11 = tmp4 + tmp7;
michael@0:     z12 = tmp4 - tmp7;
michael@0: 
michael@0:     tmp7 = z11 + z13;		/* phase 5 */
michael@0:     tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
michael@0: 
michael@0:     z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
michael@0:     tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
michael@0:     tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
michael@0: 
michael@0:     tmp6 = tmp12 - tmp7;	/* phase 2 */
michael@0:     tmp5 = tmp11 - tmp6;
michael@0:     tmp4 = tmp10 + tmp5;
michael@0: 
michael@0:     wsptr[DCTSIZE*0] = tmp0 + tmp7;
michael@0:     wsptr[DCTSIZE*7] = tmp0 - tmp7;
michael@0:     wsptr[DCTSIZE*1] = tmp1 + tmp6;
michael@0:     wsptr[DCTSIZE*6] = tmp1 - tmp6;
michael@0:     wsptr[DCTSIZE*2] = tmp2 + tmp5;
michael@0:     wsptr[DCTSIZE*5] = tmp2 - tmp5;
michael@0:     wsptr[DCTSIZE*4] = tmp3 + tmp4;
michael@0:     wsptr[DCTSIZE*3] = tmp3 - tmp4;
michael@0: 
michael@0:     inptr++;			/* advance pointers to next column */
michael@0:     quantptr++;
michael@0:     wsptr++;
michael@0:   }
michael@0:   
michael@0:   /* Pass 2: process rows from work array, store into output array. */
michael@0:   /* Note that we must descale the results by a factor of 8 == 2**3. */
michael@0: 
michael@0:   wsptr = workspace;
michael@0:   for (ctr = 0; ctr < DCTSIZE; ctr++) {
michael@0:     outptr = output_buf[ctr] + output_col;
michael@0:     /* Rows of zeroes can be exploited in the same way as we did with columns.
michael@0:      * However, the column calculation has created many nonzero AC terms, so
michael@0:      * the simplification applies less often (typically 5% to 10% of the time).
michael@0:      * And testing floats for zero is relatively expensive, so we don't bother.
michael@0:      */
michael@0:     
michael@0:     /* Even part */
michael@0: 
michael@0:     tmp10 = wsptr[0] + wsptr[4];
michael@0:     tmp11 = wsptr[0] - wsptr[4];
michael@0: 
michael@0:     tmp13 = wsptr[2] + wsptr[6];
michael@0:     tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
michael@0: 
michael@0:     tmp0 = tmp10 + tmp13;
michael@0:     tmp3 = tmp10 - tmp13;
michael@0:     tmp1 = tmp11 + tmp12;
michael@0:     tmp2 = tmp11 - tmp12;
michael@0: 
michael@0:     /* Odd part */
michael@0: 
michael@0:     z13 = wsptr[5] + wsptr[3];
michael@0:     z10 = wsptr[5] - wsptr[3];
michael@0:     z11 = wsptr[1] + wsptr[7];
michael@0:     z12 = wsptr[1] - wsptr[7];
michael@0: 
michael@0:     tmp7 = z11 + z13;
michael@0:     tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
michael@0: 
michael@0:     z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
michael@0:     tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
michael@0:     tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
michael@0: 
michael@0:     tmp6 = tmp12 - tmp7;
michael@0:     tmp5 = tmp11 - tmp6;
michael@0:     tmp4 = tmp10 + tmp5;
michael@0: 
michael@0:     /* Final output stage: scale down by a factor of 8 and range-limit */
michael@0: 
michael@0:     outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3)
michael@0: 			    & RANGE_MASK];
michael@0:     outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3)
michael@0: 			    & RANGE_MASK];
michael@0:     outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3)
michael@0: 			    & RANGE_MASK];
michael@0:     outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3)
michael@0: 			    & RANGE_MASK];
michael@0:     outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3)
michael@0: 			    & RANGE_MASK];
michael@0:     outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3)
michael@0: 			    & RANGE_MASK];
michael@0:     outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3)
michael@0: 			    & RANGE_MASK];
michael@0:     outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3)
michael@0: 			    & RANGE_MASK];
michael@0:     
michael@0:     wsptr += DCTSIZE;		/* advance pointer to next row */
michael@0:   }
michael@0: }
michael@0: 
michael@0: #endif /* DCT_FLOAT_SUPPORTED */