nengel@0: /*
nengel@0:  * jidctflt.c
nengel@0:  *
nengel@0:  * Copyright (C) 1994-1998, Thomas G. Lane.
nengel@0:  * This file is part of the Independent JPEG Group's software.
nengel@0:  *
nengel@0:  * The authors make NO WARRANTY or representation, either express or implied,
nengel@0:  * with respect to this software, its quality, accuracy, merchantability, or
nengel@0:  * fitness for a particular purpose.  This software is provided "AS IS", and you,
nengel@0:  * its user, assume the entire risk as to its quality and accuracy.
nengel@0:  *
nengel@0:  * This software is copyright (C) 1991-1998, Thomas G. Lane.
nengel@0:  * All Rights Reserved except as specified below.
nengel@0:  *
nengel@0:  * Permission is hereby granted to use, copy, modify, and distribute this
nengel@0:  * software (or portions thereof) for any purpose, without fee, subject to these
nengel@0:  * conditions:
nengel@0:  * (1) If any part of the source code for this software is distributed, then this
nengel@0:  * README file must be included, with this copyright and no-warranty notice
nengel@0:  * unaltered; and any additions, deletions, or changes to the original files
nengel@0:  * must be clearly indicated in accompanying documentation.
nengel@0:  * (2) If only executable code is distributed, then the accompanying
nengel@0:  * documentation must state that "this software is based in part on the work of
nengel@0:  * the Independent JPEG Group".
nengel@0:  * (3) Permission for use of this software is granted only if the user accepts
nengel@0:  * full responsibility for any undesirable consequences; the authors accept
nengel@0:  * NO LIABILITY for damages of any kind.
nengel@0:  *
nengel@0:  * These conditions apply to any software derived from or based on the IJG code,
nengel@0:  * not just to the unmodified library.  If you use our work, you ought to
nengel@0:  * acknowledge us.
nengel@0:  *
nengel@0:  * Permission is NOT granted for the use of any IJG author's name or company name
nengel@0:  * in advertising or publicity relating to this software or products derived from
nengel@0:  * it.  This software may be referred to only as "the Independent JPEG Group's
nengel@0:  * software".
nengel@0:  *
nengel@0:  * We specifically permit and encourage the use of this software as the basis of
nengel@0:  * commercial products, provided that all warranty or liability claims are
nengel@0:  * assumed by the product vendor.
nengel@0:  *
nengel@0:  *
nengel@0:  * This file contains a floating-point implementation of the
nengel@0:  * inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
nengel@0:  * must also perform dequantization of the input coefficients.
nengel@0:  *
nengel@0:  * This implementation should be more accurate than either of the integer
nengel@0:  * IDCT implementations.  However, it may not give the same results on all
nengel@0:  * machines because of differences in roundoff behavior.  Speed will depend
nengel@0:  * on the hardware's floating point capacity.
nengel@0:  *
nengel@0:  * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
nengel@0:  * on each row (or vice versa, but it's more convenient to emit a row at
nengel@0:  * a time).  Direct algorithms are also available, but they are much more
nengel@0:  * complex and seem not to be any faster when reduced to code.
nengel@0:  *
nengel@0:  * This implementation is based on Arai, Agui, and Nakajima's algorithm for
nengel@0:  * scaled DCT.  Their original paper (Trans. IEICE E-71(11):1095) is in
nengel@0:  * Japanese, but the algorithm is described in the Pennebaker & Mitchell
nengel@0:  * JPEG textbook (see REFERENCES section in file README).  The following code
nengel@0:  * is based directly on figure 4-8 in P&M.
nengel@0:  * While an 8-point DCT cannot be done in less than 11 multiplies, it is
nengel@0:  * possible to arrange the computation so that many of the multiplies are
nengel@0:  * simple scalings of the final outputs.  These multiplies can then be
nengel@0:  * folded into the multiplications or divisions by the JPEG quantization
nengel@0:  * table entries.  The AA&N method leaves only 5 multiplies and 29 adds
nengel@0:  * to be done in the DCT itself.
nengel@0:  * The primary disadvantage of this method is that with a fixed-point
nengel@0:  * implementation, accuracy is lost due to imprecise representation of the
nengel@0:  * scaled quantization values.  However, that problem does not arise if
nengel@0:  * we use floating point arithmetic.
nengel@0:  */
nengel@0: 
nengel@0: #include <stdint.h>
nengel@0: #include "tinyjpeg-internal.h"
nengel@0: 
nengel@0: #define FAST_FLOAT float
nengel@0: #define DCTSIZE	   8
nengel@0: #define DCTSIZE2   (DCTSIZE*DCTSIZE)
nengel@0: 
nengel@0: #define DEQUANTIZE(coef,quantval)  (((FAST_FLOAT) (coef)) * (quantval))
nengel@0: 
nengel@0: static inline unsigned char descale_and_clamp(int x, int shift)
nengel@0: {
nengel@0: 	x += (1UL<<(shift-1));
nengel@0: 	if (x<0)
nengel@0: 		x = (x >> shift) | ((~(0UL)) << (32-(shift)));
nengel@0: 	else
nengel@0: 		x >>= shift;
nengel@0: 	x += 128;
nengel@0: 	if (x>255)
nengel@0: 		return 255;
nengel@0: 	else if (x<0)
nengel@0: 		return 0;
nengel@0: 	else
nengel@0: 		return x;
nengel@0: }
nengel@0: 
nengel@0: /*
nengel@0:  * Perform dequantization and inverse DCT on one block of coefficients.
nengel@0:  */
nengel@0: void tinyjpeg_idct_float (struct component *compptr, uint8_t *output_buf, int stride)
nengel@0: {
nengel@0: 	FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
nengel@0: 	FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
nengel@0: 	FAST_FLOAT z5, z10, z11, z12, z13;
nengel@0: 	int16_t *inptr;
nengel@0: 	FAST_FLOAT *quantptr;
nengel@0: 	FAST_FLOAT *wsptr;
nengel@0: 	uint8_t *outptr;
nengel@0: 	int ctr;
nengel@0: 	FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */
nengel@0: 
nengel@0: 	/* Pass 1: process columns from input, store into work array. */
nengel@0: 
nengel@0: 	inptr = compptr->DCT;
nengel@0: 	quantptr = compptr->Q_table;
nengel@0: 	wsptr = workspace;
nengel@0: 	for (ctr = DCTSIZE; ctr > 0; ctr--) {
nengel@0: 		/* Due to quantization, we will usually find that many of the input
nengel@0: 		 * coefficients are zero, especially the AC terms.  We can exploit this
nengel@0: 		 * by short-circuiting the IDCT calculation for any column in which all
nengel@0: 		 * the AC terms are zero.  In that case each output is equal to the
nengel@0: 		 * DC coefficient (with scale factor as needed).
nengel@0: 		 * With typical images and quantization tables, half or more of the
nengel@0: 		 * column DCT calculations can be simplified this way.
nengel@0: 		 */
nengel@0: 
nengel@0: 		if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
nengel@0: 			inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
nengel@0: 			inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
nengel@0: 			inptr[DCTSIZE*7] == 0) {
nengel@0: 			/* AC terms all zero */
nengel@0: 			FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
nengel@0: 
nengel@0: 		wsptr[DCTSIZE*0] = dcval;
nengel@0: 		wsptr[DCTSIZE*1] = dcval;
nengel@0: 		wsptr[DCTSIZE*2] = dcval;
nengel@0: 		wsptr[DCTSIZE*3] = dcval;
nengel@0: 		wsptr[DCTSIZE*4] = dcval;
nengel@0: 		wsptr[DCTSIZE*5] = dcval;
nengel@0: 		wsptr[DCTSIZE*6] = dcval;
nengel@0: 		wsptr[DCTSIZE*7] = dcval;
nengel@0: 
nengel@0: 		inptr++;			/* advance pointers to next column */
nengel@0: 		quantptr++;
nengel@0: 		wsptr++;
nengel@0: 		continue;
nengel@0: 			}
nengel@0: 
nengel@0: 			/* Even part */
nengel@0: 
nengel@0: 			tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
nengel@0: 			tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
nengel@0: 			tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);
nengel@0: 			tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);
nengel@0: 
nengel@0: 			tmp10 = tmp0 + tmp2;	/* phase 3 */
nengel@0: 			tmp11 = tmp0 - tmp2;
nengel@0: 
nengel@0: 			tmp13 = tmp1 + tmp3;	/* phases 5-3 */
nengel@0: 			tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */
nengel@0: 
nengel@0: 			tmp0 = tmp10 + tmp13;	/* phase 2 */
nengel@0: 			tmp3 = tmp10 - tmp13;
nengel@0: 			tmp1 = tmp11 + tmp12;
nengel@0: 			tmp2 = tmp11 - tmp12;
nengel@0: 
nengel@0: 			/* Odd part */
nengel@0: 
nengel@0: 			tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);
nengel@0: 			tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
nengel@0: 			tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
nengel@0: 			tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
nengel@0: 
nengel@0: 			z13 = tmp6 + tmp5;		/* phase 6 */
nengel@0: 			z10 = tmp6 - tmp5;
nengel@0: 			z11 = tmp4 + tmp7;
nengel@0: 			z12 = tmp4 - tmp7;
nengel@0: 
nengel@0: 			tmp7 = z11 + z13;		/* phase 5 */
nengel@0: 			tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */
nengel@0: 
nengel@0: 			z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
nengel@0: 			tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
nengel@0: 			tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
nengel@0: 
nengel@0: 			tmp6 = tmp12 - tmp7;	/* phase 2 */
nengel@0: 			tmp5 = tmp11 - tmp6;
nengel@0: 			tmp4 = tmp10 + tmp5;
nengel@0: 
nengel@0: 			wsptr[DCTSIZE*0] = tmp0 + tmp7;
nengel@0: 			wsptr[DCTSIZE*7] = tmp0 - tmp7;
nengel@0: 			wsptr[DCTSIZE*1] = tmp1 + tmp6;
nengel@0: 			wsptr[DCTSIZE*6] = tmp1 - tmp6;
nengel@0: 			wsptr[DCTSIZE*2] = tmp2 + tmp5;
nengel@0: 			wsptr[DCTSIZE*5] = tmp2 - tmp5;
nengel@0: 			wsptr[DCTSIZE*4] = tmp3 + tmp4;
nengel@0: 			wsptr[DCTSIZE*3] = tmp3 - tmp4;
nengel@0: 
nengel@0: 			inptr++;			/* advance pointers to next column */
nengel@0: 			quantptr++;
nengel@0: 			wsptr++;
nengel@0: 	}
nengel@0: 
nengel@0: 	/* Pass 2: process rows from work array, store into output array. */
nengel@0: 	/* Note that we must descale the results by a factor of 8 == 2**3. */
nengel@0: 
nengel@0: 	wsptr = workspace;
nengel@0: 	outptr = output_buf;
nengel@0: 	for (ctr = 0; ctr < DCTSIZE; ctr++) {
nengel@0: 		/* Rows of zeroes can be exploited in the same way as we did with columns.
nengel@0: 		 * However, the column calculation has created many nonzero AC terms, so
nengel@0: 		 * the simplification applies less often (typically 5% to 10% of the time).
nengel@0: 		 * And testing floats for zero is relatively expensive, so we don't bother.
nengel@0: 		 */
nengel@0: 
nengel@0: 		/* Even part */
nengel@0: 
nengel@0: 		tmp10 = wsptr[0] + wsptr[4];
nengel@0: 		tmp11 = wsptr[0] - wsptr[4];
nengel@0: 
nengel@0: 		tmp13 = wsptr[2] + wsptr[6];
nengel@0: 		tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13;
nengel@0: 
nengel@0: 		tmp0 = tmp10 + tmp13;
nengel@0: 		tmp3 = tmp10 - tmp13;
nengel@0: 		tmp1 = tmp11 + tmp12;
nengel@0: 		tmp2 = tmp11 - tmp12;
nengel@0: 
nengel@0: 		/* Odd part */
nengel@0: 
nengel@0: 		z13 = wsptr[5] + wsptr[3];
nengel@0: 		z10 = wsptr[5] - wsptr[3];
nengel@0: 		z11 = wsptr[1] + wsptr[7];
nengel@0: 		z12 = wsptr[1] - wsptr[7];
nengel@0: 
nengel@0: 		tmp7 = z11 + z13;
nengel@0: 		tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562);
nengel@0: 
nengel@0: 		z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */
nengel@0: 		tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */
nengel@0: 		tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */
nengel@0: 
nengel@0: 		tmp6 = tmp12 - tmp7;
nengel@0: 		tmp5 = tmp11 - tmp6;
nengel@0: 		tmp4 = tmp10 + tmp5;
nengel@0: 
nengel@0: 		/* Final output stage: scale down by a factor of 8 and range-limit */
nengel@0: 
nengel@0: 		outptr[0] = descale_and_clamp((int)(tmp0 + tmp7), 3);
nengel@0: 		outptr[7] = descale_and_clamp((int)(tmp0 - tmp7), 3);
nengel@0: 		outptr[1] = descale_and_clamp((int)(tmp1 + tmp6), 3);
nengel@0: 		outptr[6] = descale_and_clamp((int)(tmp1 - tmp6), 3);
nengel@0: 		outptr[2] = descale_and_clamp((int)(tmp2 + tmp5), 3);
nengel@0: 		outptr[5] = descale_and_clamp((int)(tmp2 - tmp5), 3);
nengel@0: 		outptr[4] = descale_and_clamp((int)(tmp3 + tmp4), 3);
nengel@0: 		outptr[3] = descale_and_clamp((int)(tmp3 - tmp4), 3);
nengel@0: 
nengel@0: 
nengel@0: 		wsptr += DCTSIZE;		/* advance pointer to next row */
nengel@0: 		outptr += stride;
nengel@0: 	}
nengel@0: }
nengel@0: