/* * This file is part of the Independent JPEG Group's software. * * The authors make NO WARRANTY or representation, either express or implied, * with respect to this software, its quality, accuracy, merchantability, or * fitness for a particular purpose. This software is provided "AS IS", and * you, its user, assume the entire risk as to its quality and accuracy. * * This software is copyright (C) 1991, 1992, Thomas G. Lane. * All Rights Reserved except as specified below. * * Permission is hereby granted to use, copy, modify, and distribute this * software (or portions thereof) for any purpose, without fee, subject to * these conditions: * (1) If any part of the source code for this software is distributed, then * this README file must be included, with this copyright and no-warranty * notice unaltered; and any additions, deletions, or changes to the original * files must be clearly indicated in accompanying documentation. * (2) If only executable code is distributed, then the accompanying * documentation must state that "this software is based in part on the work * of the Independent JPEG Group". * (3) Permission for use of this software is granted only if the user accepts * full responsibility for any undesirable consequences; the authors accept * NO LIABILITY for damages of any kind. * * These conditions apply to any software derived from or based on the IJG * code, not just to the unmodified library. If you use our work, you ought * to acknowledge us. * * Permission is NOT granted for the use of any IJG author's name or company * name in advertising or publicity relating to this software or products * derived from it. This software may be referred to only as "the Independent * JPEG Group's software". * * We specifically permit and encourage the use of this software as the basis * of commercial products, provided that all warranty or liability claims are * assumed by the product vendor. * * This file contains the basic inverse-DCT transformation subroutine. * * 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. * * I've made lots of modifications to attempt to take advantage of the * sparse nature of the DCT matrices we're getting. Although the logic * is cumbersome, it's straightforward and the resulting code is much * faster. * * A better way to do this would be to pass in the DCT block as a sparse * matrix, perhaps with the difference cases encoded.
*/
/* * This routine is specialized to the case DCTSIZE = 8.
*/
#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ #endif
/* * A 2-D IDCT can be done by 1-D IDCT on each row followed by 1-D IDCT * on each column. Direct algorithms are also available, but they are * much more complex and seem not to be any faster when reduced to code. * * 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.
*/
#ifdef EIGHT_BIT_SAMPLES #define PASS1_BITS 2 #else #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ #endif
#define ONE ((int32_t) 1)
#define CONST_SCALE (ONE << CONST_BITS)
/* Convert a positive real constant to an integer scaled by CONST_SCALE. * IMPORTANT: if your compiler doesn't do this arithmetic at compile time, * you will pay a significant penalty in run time. In that case, figure * the correct integer constant values and insert them by hand.
*/
/* Actually FIX is no longer used, we precomputed them all */ #define FIX(x) ((int32_t) ((x) * CONST_SCALE + 0.5))
/* Descale and correctly round an int32_t value that's scaled by N bits. * We assume RIGHT_SHIFT rounds towards minus infinity, so adding * the fudge factor is correct for either sign of X.
*/
/* Multiply an int32_t variable by an int32_t constant to yield an int32_t 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; * this provides a useful speedup on many machines. * There is no way to specify a 16x16->32 multiply in portable C, but * some C compilers will do the right thing if you provide the correct * combination of casts. * NB: for 12-bit samples, a full 32-bit multiplication will be needed.
*/
#ifdef EIGHT_BIT_SAMPLES #ifdef SHORTxSHORT_32 /* may work if 'int' is 32 bits */ #define MULTIPLY(var,const) (((int16_t) (var)) * ((int16_t) (const))) #endif #ifdef SHORTxLCONST_32 /* known to work with Microsoft C 6.0 */ #define MULTIPLY(var,const) (((int16_t) (var)) * ((int32_t) (const))) #endif #endif
/* Pass 1: process rows. */ /* Note results are scaled up by sqrt(8) compared to a true IDCT; */ /* furthermore, we scale the results by 2**PASS1_BITS. */
dataptr = data;
for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) { /* 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 row 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 * row DCT calculations can be simplified this way.
*/
register uint8_t *idataptr = (uint8_t*)dataptr;
/* WARNING: we do the same permutation as MMX idct to simplify the
video core */
d0 = dataptr[0];
d2 = dataptr[1];
d4 = dataptr[2];
d6 = dataptr[3];
d1 = dataptr[4];
d3 = dataptr[5];
d5 = dataptr[6];
d7 = dataptr[7];
if ((d1 | d2 | d3 | d4 | d5 | d6 | d7) == 0) { /* AC terms all zero */ if (d0) { /* Compute a 32 bit value to assign. */
int16_t dcval = (int16_t) (d0 * (1 << PASS1_BITS)); registerunsigned v = (dcval & 0xffff) | ((uint32_t)dcval << 16);
dataptr += DCTSIZE; /* advance pointer to next row */
}
/* Pass 2: process columns. */ /* Note that we must descale the results by a factor of 8 == 2**3, */ /* and also undo the PASS1_BITS scaling. */
dataptr = data; for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) { /* Columns of zeroes can be exploited in the same way as we did with rows. * However, the row 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.
*/
/* Pass 1: process rows. */ /* Note results are scaled up by sqrt(8) compared to a true IDCT; */ /* furthermore, we scale the results by 2**PASS1_BITS. */
data[0] += 4;
dataptr = data;
for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) { /* 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 row 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 * row DCT calculations can be simplified this way.
*/
if ((d2 | d4 | d6) == 0) { /* AC terms all zero */ if (d0) { /* Compute a 32 bit value to assign. */
int16_t dcval = (int16_t) (d0 * (1 << PASS1_BITS)); registerunsigned v = (dcval & 0xffff) | ((uint32_t)dcval << 16);
dataptr += DCTSTRIDE; /* advance pointer to next row */
}
/* Pass 2: process columns. */ /* Note that we must descale the results by a factor of 8 == 2**3, */ /* and also undo the PASS1_BITS scaling. */
dataptr = data; for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) { /* Columns of zeroes can be exploited in the same way as we did with rows. * However, the row 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.
*/
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