/* * jrevdct.c * * This file is part of the Independent JPEG Group's software. * The IJG code is distributed under the terms reproduced here: * * LEGAL ISSUES * ============ * * In plain English: * * 1. We don't promise that this software works. (But if you find any bugs, * please let us know!) * 2. You can use this software for whatever you want. You don't have to * pay us. * 3. You may not pretend that you wrote this software. If you use it in a * program, you must acknowledge somewhere in your documentation that * you've used the IJG code. * * In legalese: * * 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 copyright and no-warranty notice must be included 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. * * * ARCHIVE LOCATIONS * ================= * * The "official" archive site for this software is ftp.uu.net (Internet * address 192.48.96.9). The most recent released version can always be * found there in directory graphics/jpeg. This particular version will * be archived as graphics/jpeg/jpegsrc.v6a.tar.gz. If you are on the * Internet, you can retrieve files from ftp.uu.net by standard anonymous * FTP. If you don't have FTP access, UUNET's archives are also available * via UUCP; contact help@uunet.uu.net for information on retrieving files * that way. * * Numerous Internet sites maintain copies of the UUNET files. However, * only ftp.uu.net is guaranteed to have the latest official version. * * You can also obtain this software in DOS-compatible "zip" archive * format from the SimTel archives (ftp.coast.net:/SimTel/msdos/graphics/), * or on CompuServe in the Graphics Support forum (GO CIS:GRAPHSUP), * library 12 "JPEG Tools". Again, these versions may sometimes lag behind * the ftp.uu.net release. * * The JPEG FAQ (Frequently Asked Questions) article is a useful source of * general information about JPEG. It is updated constantly and therefore * is not included in this distribution. The FAQ is posted every two weeks * to Usenet newsgroups comp.graphics.misc, news.answers, and other groups. * You can always obtain the latest version from the news.answers archive * at rtfm.mit.edu. By FTP, fetch /pub/usenet/news.answers/jpeg-faq/part1 * and .../part2. If you don't have FTP, send e-mail to * mail-server@rtfm.mit.edu with body * send usenet/news.answers/jpeg-faq/part1 * send usenet/news.answers/jpeg-faq/part2 * * ============== * * * 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. * * * CHANGES FOR BERKELEY MPEG * ========================= * * This file has been altered to use the Berkeley MPEG header files, * to add the capability to handle sparse DCT matrices efficiently, * and to relabel the inverse DCT function as well as the file * (formerly jidctint.c). * * 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. */ #include "jrevdct.h" /* We assume that right shift corresponds to signed division by 2 with * rounding towards minus infinity. This is correct for typical "arithmetic * shift" instructions that shift in copies of the sign bit. But some * C compilers implement >> with an unsigned shift. For these machines you * must define RIGHT_SHIFT_IS_UNSIGNED. * RIGHT_SHIFT provides a proper signed right shift of an INT32 quantity. * It is only applied with constant shift counts. SHIFT_TEMPS must be * included in the variables of any routine using RIGHT_SHIFT. */ #ifdef RIGHT_SHIFT_IS_UNSIGNED #define SHIFT_TEMPS INT32 shift_temp; #define RIGHT_SHIFT(x,shft) \ ((shift_temp = (x)) < 0 ? \ (shift_temp >> (shft)) | ((~((INT32) 0)) << (32-(shft))) : \ (shift_temp >> (shft))) #else #define SHIFT_TEMPS #define RIGHT_SHIFT(x,shft) ((x) >> (shft)) #endif /* * 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) 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. */ #define FIX(x) ((INT32) ((x) * CONST_SCALE + 0.5)) /* When adding two opposite-signed fixes, the 0.5 cancels */ #define FIX2(x) ((INT32) ((x) * CONST_SCALE)) /* Descale and correctly round an INT32 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. */ #define DESCALE(x,n) RIGHT_SHIFT((x) + (ONE << ((n)-1)), n) /* Multiply an INT32 variable by an INT32 constant to yield an INT32 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) (var)) * ((INT16) (const))) #endif #ifdef SHORTxLCONST_32 /* known to work with Microsoft C 6.0 */ #define MULTIPLY(var,const) (((INT16) (var)) * ((INT32) (const))) #endif #endif #ifndef MULTIPLY /* default definition */ #define MULTIPLY(var,const) ((var) * (const)) #endif #ifndef NO_SPARSE_DCT #define SPARSE_SCALE_FACTOR 8 #endif /* Precomputed idct value arrays. */ static DCTELEM PreIDCT[64][64]; /* *-------------------------------------------------------------- * * init_pre_idct -- * * Pre-computes singleton coefficient IDCT values. * * Results: * None. * * Side effects: * None. * *-------------------------------------------------------------- */ void init_pre_idct() { int i; for (i=0; i<64; i++) { memset((char *) PreIDCT[i], 0, 64*sizeof(DCTELEM)); PreIDCT[i][i] = 1 << SPARSE_SCALE_FACTOR; j_rev_dct(PreIDCT[i]); } int pos; int rr; DCTELEM *ndataptr; for(pos=0;pos<64;pos++) { ndataptr = PreIDCT[pos]; for(rr=0; rr<4; rr++) { for(i=0;i<16;i++) { ndataptr[i] = ndataptr[i]/256; } ndataptr += 16; } } } #ifndef NO_SPARSE_DCT /* *-------------------------------------------------------------- * * j_rev_dct_sparse -- * * Performs the inverse DCT on one block of coefficients. * * Results: * None. * * Side effects: * None. * *-------------------------------------------------------------- */ void j_rev_dct_sparse (DCTBLOCK data, int pos) { short int val; register int *dp; register int v; int quant; // cout << "j_rev_dct_sparse"<= 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 int *idataptr = (int*)dataptr; d0 = dataptr[0]; d1 = dataptr[1]; if ((d1 == 0) && (idataptr[1] + idataptr[2] + idataptr[3]) == 0) { /* AC terms all zero */ if (d0) { /* Compute a 32 bit value to assign. */ DCTELEM dcval = (DCTELEM) (d0 << PASS1_BITS); register int v = (dcval & 0xffff) + (dcval << 16); idataptr[0] = v; idataptr[1] = v; idataptr[2] = v; idataptr[3] = v; } dataptr += DCTSIZE; /* advance pointer to next row */ continue; } d2 = dataptr[2]; d3 = dataptr[3]; d4 = dataptr[4]; d5 = dataptr[5]; d6 = dataptr[6]; d7 = dataptr[7]; /* Even part: reverse the even part of the forward DCT. */ /* The rotator is sqrt(2)*c(-6). */ if (d6) { if (d4) { if (d2) { if (d0) { /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */ z1 = MULTIPLY(d2 + d6, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865)); tmp0 = (d0 + d4) << CONST_BITS; tmp1 = (d0 - d4) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; } else { /* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */ z1 = MULTIPLY(d2 + d6, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865)); tmp0 = d4 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp2 - tmp0; tmp12 = -(tmp0 + tmp2); } } else { if (d0) { /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */ tmp2 = MULTIPLY(d6, - FIX2(1.306562965)); tmp3 = MULTIPLY(d6, FIX(0.541196100)); tmp0 = (d0 + d4) << CONST_BITS; tmp1 = (d0 - d4) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; } else { /* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */ tmp2 = MULTIPLY(d6, - FIX2(1.306562965)); tmp3 = MULTIPLY(d6, FIX(0.541196100)); tmp0 = d4 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp2 - tmp0; tmp12 = -(tmp0 + tmp2); } } } else { if (d2) { if (d0) { /* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */ z1 = MULTIPLY(d2 + d6, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865)); tmp0 = d0 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp0 + tmp2; tmp12 = tmp0 - tmp2; } else { /* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */ z1 = MULTIPLY(d2 + d6, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865)); tmp10 = tmp3; tmp13 = -tmp3; tmp11 = tmp2; tmp12 = -tmp2; } } else { if (d0) { /* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */ tmp2 = MULTIPLY(d6, - FIX2(1.306562965)); tmp3 = MULTIPLY(d6, FIX(0.541196100)); tmp0 = d0 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp0 + tmp2; tmp12 = tmp0 - tmp2; } else { /* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */ tmp2 = MULTIPLY(d6, - FIX2(1.306562965)); tmp3 = MULTIPLY(d6, FIX(0.541196100)); tmp10 = tmp3; tmp13 = -tmp3; tmp11 = tmp2; tmp12 = -tmp2; } } } } else { if (d4) { if (d2) { if (d0) { /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */ tmp2 = MULTIPLY(d2, FIX(0.541196100)); tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5))); tmp0 = (d0 + d4) << CONST_BITS; tmp1 = (d0 - d4) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; } else { /* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */ tmp2 = MULTIPLY(d2, FIX(0.541196100)); tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5))); tmp0 = d4 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp2 - tmp0; tmp12 = -(tmp0 + tmp2); } } else { if (d0) { /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */ tmp10 = tmp13 = (d0 + d4) << CONST_BITS; tmp11 = tmp12 = (d0 - d4) << CONST_BITS; } else { /* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */ tmp10 = tmp13 = d4 << CONST_BITS; tmp11 = tmp12 = -tmp10; } } } else { if (d2) { if (d0) { /* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */ tmp2 = MULTIPLY(d2, FIX(0.541196100)); tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5))); tmp0 = d0 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp0 + tmp2; tmp12 = tmp0 - tmp2; } else { /* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */ tmp2 = MULTIPLY(d2, FIX(0.541196100)); tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5))); tmp10 = tmp3; tmp13 = -tmp3; tmp11 = tmp2; tmp12 = -tmp2; } } else { if (d0) { /* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */ tmp10 = tmp13 = tmp11 = tmp12 = d0 << CONST_BITS; } else { /* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */ tmp10 = tmp13 = tmp11 = tmp12 = 0; } } } } /* Odd part per figure 8; the matrix is unitary and hence its * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. */ if (d7) { if (d5) { if (d3) { if (d1) { /* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */ z1 = d7 + d1; z2 = d5 + d3; z3 = d7 + d3; z4 = d5 + d1; z5 = MULTIPLY(z3 + z4, FIX(1.175875602)); tmp0 = MULTIPLY(d7, FIX(0.298631336)); tmp1 = MULTIPLY(d5, FIX(2.053119869)); tmp2 = MULTIPLY(d3, FIX(3.072711026)); tmp3 = MULTIPLY(d1, FIX(1.501321110)); z1 = MULTIPLY(z1, - FIX(0.899976223)); z2 = MULTIPLY(z2, - FIX(2.562915447)); z3 = MULTIPLY(z3, - FIX(1.961570560)); z4 = MULTIPLY(z4, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; } else { /* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */ z2 = d5 + d3; z3 = d7 + d3; z5 = MULTIPLY(z3 + d5, FIX(1.175875602)); tmp0 = MULTIPLY(d7, FIX(0.298631336)); tmp1 = MULTIPLY(d5, FIX(2.053119869)); tmp2 = MULTIPLY(d3, FIX(3.072711026)); z1 = MULTIPLY(d7, - FIX(0.899976223)); z2 = MULTIPLY(z2, - FIX(2.562915447)); z3 = MULTIPLY(z3, - FIX(1.961570560)); z4 = MULTIPLY(d5, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 = z1 + z4; } } else { if (d1) { /* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */ z1 = d7 + d1; z4 = d5 + d1; z5 = MULTIPLY(d7 + z4, FIX(1.175875602)); tmp0 = MULTIPLY(d7, FIX(0.298631336)); tmp1 = MULTIPLY(d5, FIX(2.053119869)); tmp3 = MULTIPLY(d1, FIX(1.501321110)); z1 = MULTIPLY(z1, - FIX(0.899976223)); z2 = MULTIPLY(d5, - FIX(2.562915447)); z3 = MULTIPLY(d7, - FIX(1.961570560)); z4 = MULTIPLY(z4, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 = z2 + z3; tmp3 += z1 + z4; } else { /* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */ z5 = MULTIPLY(d7 + d5, FIX(1.175875602)); tmp0 = MULTIPLY(d7, - FIX2(0.601344887)); tmp1 = MULTIPLY(d5, - FIX2(0.509795578)); z1 = MULTIPLY(d7, - FIX(0.899976223)); z3 = MULTIPLY(d7, - FIX(1.961570560)); z2 = MULTIPLY(d5, - FIX(2.562915447)); z4 = MULTIPLY(d5, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z3; tmp1 += z4; tmp2 = z2 + z3; tmp3 = z1 + z4; } } } else { if (d3) { if (d1) { /* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */ z1 = d7 + d1; z3 = d7 + d3; z5 = MULTIPLY(z3 + d1, FIX(1.175875602)); tmp0 = MULTIPLY(d7, FIX(0.298631336)); tmp2 = MULTIPLY(d3, FIX(3.072711026)); tmp3 = MULTIPLY(d1, FIX(1.501321110)); z1 = MULTIPLY(z1, - FIX(0.899976223)); z2 = MULTIPLY(d3, - FIX(2.562915447)); z3 = MULTIPLY(z3, - FIX(1.961570560)); z4 = MULTIPLY(d1, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 = z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; } else { /* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */ z3 = d7 + d3; z5 = MULTIPLY(z3, FIX(1.175875602)); tmp0 = MULTIPLY(d7, - FIX2(0.601344887)); tmp2 = MULTIPLY(d3, FIX(0.509795579)); z1 = MULTIPLY(d7, - FIX(0.899976223)); z2 = MULTIPLY(d3, - FIX(2.562915447)); z3 = MULTIPLY(z3, - FIX2(0.785694958)); tmp0 += z3; tmp1 = z2 + z5; tmp2 += z3; tmp3 = z1 + z5; } } else { if (d1) { /* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */ z1 = d7 + d1; z5 = MULTIPLY(z1, FIX(1.175875602)); tmp0 = MULTIPLY(d7, - FIX2(1.662939224)); tmp3 = MULTIPLY(d1, FIX2(1.111140466)); z1 = MULTIPLY(z1, FIX2(0.275899379)); z3 = MULTIPLY(d7, - FIX(1.961570560)); z4 = MULTIPLY(d1, - FIX(0.390180644)); tmp0 += z1; tmp1 = z4 + z5; tmp2 = z3 + z5; tmp3 += z1; } else { /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */ tmp0 = MULTIPLY(d7, - FIX2(1.387039845)); tmp1 = MULTIPLY(d7, FIX(1.175875602)); tmp2 = MULTIPLY(d7, - FIX2(0.785694958)); tmp3 = MULTIPLY(d7, FIX2(0.275899379)); } } } } else { if (d5) { if (d3) { if (d1) { /* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */ z2 = d5 + d3; z4 = d5 + d1; z5 = MULTIPLY(d3 + z4, FIX(1.175875602)); tmp1 = MULTIPLY(d5, FIX(2.053119869)); tmp2 = MULTIPLY(d3, FIX(3.072711026)); tmp3 = MULTIPLY(d1, FIX(1.501321110)); z1 = MULTIPLY(d1, - FIX(0.899976223)); z2 = MULTIPLY(z2, - FIX(2.562915447)); z3 = MULTIPLY(d3, - FIX(1.961570560)); z4 = MULTIPLY(z4, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 = z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; } else { /* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */ z2 = d5 + d3; z5 = MULTIPLY(z2, FIX(1.175875602)); tmp1 = MULTIPLY(d5, FIX2(1.662939225)); tmp2 = MULTIPLY(d3, FIX2(1.111140466)); z2 = MULTIPLY(z2, - FIX2(1.387039845)); z3 = MULTIPLY(d3, - FIX(1.961570560)); z4 = MULTIPLY(d5, - FIX(0.390180644)); tmp0 = z3 + z5; tmp1 += z2; tmp2 += z2; tmp3 = z4 + z5; } } else { if (d1) { /* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */ z4 = d5 + d1; z5 = MULTIPLY(z4, FIX(1.175875602)); tmp1 = MULTIPLY(d5, - FIX2(0.509795578)); tmp3 = MULTIPLY(d1, FIX2(0.601344887)); z1 = MULTIPLY(d1, - FIX(0.899976223)); z2 = MULTIPLY(d5, - FIX(2.562915447)); z4 = MULTIPLY(z4, FIX2(0.785694958)); tmp0 = z1 + z5; tmp2 = z2 + z5; tmp1 += z4; tmp3 += z4; } else { /* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */ tmp0 = MULTIPLY(d5, FIX(1.175875602)); tmp1 = MULTIPLY(d5, FIX2(0.275899380)); tmp2 = MULTIPLY(d5, - FIX2(1.387039845)); tmp3 = MULTIPLY(d5, FIX2(0.785694958)); } } } else { if (d3) { if (d1) { /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */ z5 = d3 + d1; tmp2 = MULTIPLY(d3, - FIX(1.451774981)); tmp3 = MULTIPLY(d1, (FIX(0.211164243) - 1)); z1 = MULTIPLY(d1, FIX(1.061594337)); z2 = MULTIPLY(d3, - FIX(2.172734803)); z4 = MULTIPLY(z5, FIX(0.785694958)); z5 = MULTIPLY(z5, FIX(1.175875602)); tmp0 = z1 - z4; tmp1 = z2 + z4; tmp2 += z5; tmp3 += z5; } else { /* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */ tmp0 = MULTIPLY(d3, - FIX2(0.785694958)); tmp1 = MULTIPLY(d3, - FIX2(1.387039845)); tmp2 = MULTIPLY(d3, - FIX2(0.275899379)); tmp3 = MULTIPLY(d3, FIX(1.175875602)); } } else { if (d1) { /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */ tmp0 = MULTIPLY(d1, FIX2(0.275899379)); tmp1 = MULTIPLY(d1, FIX2(0.785694958)); tmp2 = MULTIPLY(d1, FIX(1.175875602)); tmp3 = MULTIPLY(d1, FIX2(1.387039845)); } else { /* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */ tmp0 = tmp1 = tmp2 = tmp3 = 0; } } } } /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ dataptr[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS); dataptr[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS); dataptr[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS); dataptr[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS); dataptr[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS); dataptr[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS); dataptr[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS); dataptr[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS); 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. */ d0 = dataptr[DCTSIZE*0]; d1 = dataptr[DCTSIZE*1]; d2 = dataptr[DCTSIZE*2]; d3 = dataptr[DCTSIZE*3]; d4 = dataptr[DCTSIZE*4]; d5 = dataptr[DCTSIZE*5]; d6 = dataptr[DCTSIZE*6]; d7 = dataptr[DCTSIZE*7]; /* Even part: reverse the even part of the forward DCT. */ /* The rotator is sqrt(2)*c(-6). */ if (d6) { if (d4) { if (d2) { if (d0) { /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */ z1 = MULTIPLY(d2 + d6, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865)); tmp0 = (d0 + d4) << CONST_BITS; tmp1 = (d0 - d4) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; } else { /* d0 == 0, d2 != 0, d4 != 0, d6 != 0 */ z1 = MULTIPLY(d2 + d6, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865)); tmp0 = d4 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp2 - tmp0; tmp12 = -(tmp0 + tmp2); } } else { if (d0) { /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */ tmp2 = MULTIPLY(d6, - FIX2(1.306562965)); tmp3 = MULTIPLY(d6, FIX(0.541196100)); tmp0 = (d0 + d4) << CONST_BITS; tmp1 = (d0 - d4) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; } else { /* d0 == 0, d2 == 0, d4 != 0, d6 != 0 */ tmp2 = MULTIPLY(d6, -FIX2(1.306562965)); tmp3 = MULTIPLY(d6, FIX(0.541196100)); tmp0 = d4 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp2 - tmp0; tmp12 = -(tmp0 + tmp2); } } } else { if (d2) { if (d0) { /* d0 != 0, d2 != 0, d4 == 0, d6 != 0 */ z1 = MULTIPLY(d2 + d6, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865)); tmp0 = d0 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp0 + tmp2; tmp12 = tmp0 - tmp2; } else { /* d0 == 0, d2 != 0, d4 == 0, d6 != 0 */ z1 = MULTIPLY(d2 + d6, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(d6, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(d2, FIX(0.765366865)); tmp10 = tmp3; tmp13 = -tmp3; tmp11 = tmp2; tmp12 = -tmp2; } } else { if (d0) { /* d0 != 0, d2 == 0, d4 == 0, d6 != 0 */ tmp2 = MULTIPLY(d6, - FIX2(1.306562965)); tmp3 = MULTIPLY(d6, FIX(0.541196100)); tmp0 = d0 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp0 + tmp2; tmp12 = tmp0 - tmp2; } else { /* d0 == 0, d2 == 0, d4 == 0, d6 != 0 */ tmp2 = MULTIPLY(d6, - FIX2(1.306562965)); tmp3 = MULTIPLY(d6, FIX(0.541196100)); tmp10 = tmp3; tmp13 = -tmp3; tmp11 = tmp2; tmp12 = -tmp2; } } } } else { if (d4) { if (d2) { if (d0) { /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */ tmp2 = MULTIPLY(d2, FIX(0.541196100)); tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5))); tmp0 = (d0 + d4) << CONST_BITS; tmp1 = (d0 - d4) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; } else { /* d0 == 0, d2 != 0, d4 != 0, d6 == 0 */ tmp2 = MULTIPLY(d2, FIX(0.541196100)); tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5))); tmp0 = d4 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp2 - tmp0; tmp12 = -(tmp0 + tmp2); } } else { if (d0) { /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */ tmp10 = tmp13 = (d0 + d4) << CONST_BITS; tmp11 = tmp12 = (d0 - d4) << CONST_BITS; } else { /* d0 == 0, d2 == 0, d4 != 0, d6 == 0 */ tmp10 = tmp13 = d4 << CONST_BITS; tmp11 = tmp12 = -tmp10; } } } else { if (d2) { if (d0) { /* d0 != 0, d2 != 0, d4 == 0, d6 == 0 */ tmp2 = MULTIPLY(d2, FIX(0.541196100)); tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5))); tmp0 = d0 << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp0 + tmp2; tmp12 = tmp0 - tmp2; } else { /* d0 == 0, d2 != 0, d4 == 0, d6 == 0 */ tmp2 = MULTIPLY(d2, FIX(0.541196100)); tmp3 = (INT32) (MULTIPLY(d2, (FIX(1.306562965) + .5))); tmp10 = tmp3; tmp13 = -tmp3; tmp11 = tmp2; tmp12 = -tmp2; } } else { if (d0) { /* d0 != 0, d2 == 0, d4 == 0, d6 == 0 */ tmp10 = tmp13 = tmp11 = tmp12 = d0 << CONST_BITS; } else { /* d0 == 0, d2 == 0, d4 == 0, d6 == 0 */ tmp10 = tmp13 = tmp11 = tmp12 = 0; } } } } /* Odd part per figure 8; the matrix is unitary and hence its * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. */ if (d7) { if (d5) { if (d3) { if (d1) { /* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */ z1 = d7 + d1; z2 = d5 + d3; z3 = d7 + d3; z4 = d5 + d1; z5 = MULTIPLY(z3 + z4, FIX(1.175875602)); tmp0 = MULTIPLY(d7, FIX(0.298631336)); tmp1 = MULTIPLY(d5, FIX(2.053119869)); tmp2 = MULTIPLY(d3, FIX(3.072711026)); tmp3 = MULTIPLY(d1, FIX(1.501321110)); z1 = MULTIPLY(z1, - FIX(0.899976223)); z2 = MULTIPLY(z2, - FIX(2.562915447)); z3 = MULTIPLY(z3, - FIX(1.961570560)); z4 = MULTIPLY(z4, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; } else { /* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */ z2 = d5 + d3; z3 = d7 + d3; z5 = MULTIPLY(z3 + d5, FIX(1.175875602)); tmp0 = MULTIPLY(d7, FIX(0.298631336)); tmp1 = MULTIPLY(d5, FIX(2.053119869)); tmp2 = MULTIPLY(d3, FIX(3.072711026)); z1 = MULTIPLY(d7, - FIX(0.899976223)); z2 = MULTIPLY(z2, - FIX(2.562915447)); z3 = MULTIPLY(z3, - FIX(1.961570560)); z4 = MULTIPLY(d5, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 = z1 + z4; } } else { if (d1) { /* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */ z1 = d7 + d1; z4 = d5 + d1; z5 = MULTIPLY(d7 + z4, FIX(1.175875602)); tmp0 = MULTIPLY(d7, FIX(0.298631336)); tmp1 = MULTIPLY(d5, FIX(2.053119869)); tmp3 = MULTIPLY(d1, FIX(1.501321110)); z1 = MULTIPLY(z1, - FIX(0.899976223)); z2 = MULTIPLY(d5, - FIX(2.562915447)); z3 = MULTIPLY(d7, - FIX(1.961570560)); z4 = MULTIPLY(z4, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 = z2 + z3; tmp3 += z1 + z4; } else { /* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */ z5 = MULTIPLY(d5 + d7, FIX(1.175875602)); tmp0 = MULTIPLY(d7, - FIX2(0.601344887)); tmp1 = MULTIPLY(d5, - FIX2(0.509795578)); z1 = MULTIPLY(d7, - FIX(0.899976223)); z3 = MULTIPLY(d7, - FIX(1.961570560)); z2 = MULTIPLY(d5, - FIX(2.562915447)); z4 = MULTIPLY(d5, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z3; tmp1 += z4; tmp2 = z2 + z3; tmp3 = z1 + z4; } } } else { if (d3) { if (d1) { /* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */ z1 = d7 + d1; z3 = d7 + d3; z5 = MULTIPLY(z3 + d1, FIX(1.175875602)); tmp0 = MULTIPLY(d7, FIX(0.298631336)); tmp2 = MULTIPLY(d3, FIX(3.072711026)); tmp3 = MULTIPLY(d1, FIX(1.501321110)); z1 = MULTIPLY(z1, - FIX(0.899976223)); z2 = MULTIPLY(d3, - FIX(2.562915447)); z3 = MULTIPLY(z3, - FIX(1.961570560)); z4 = MULTIPLY(d1, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 = z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; } else { /* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */ z3 = d7 + d3; z5 = MULTIPLY(z3, FIX(1.175875602)); tmp0 = MULTIPLY(d7, - FIX2(0.601344887)); z1 = MULTIPLY(d7, - FIX(0.899976223)); tmp2 = MULTIPLY(d3, FIX(0.509795579)); z2 = MULTIPLY(d3, - FIX(2.562915447)); z3 = MULTIPLY(z3, - FIX2(0.785694958)); tmp0 += z3; tmp1 = z2 + z5; tmp2 += z3; tmp3 = z1 + z5; } } else { if (d1) { /* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */ z1 = d7 + d1; z5 = MULTIPLY(z1, FIX(1.175875602)); tmp0 = MULTIPLY(d7, - FIX2(1.662939224)); tmp3 = MULTIPLY(d1, FIX2(1.111140466)); z1 = MULTIPLY(z1, FIX2(0.275899379)); z3 = MULTIPLY(d7, - FIX(1.961570560)); z4 = MULTIPLY(d1, - FIX(0.390180644)); tmp0 += z1; tmp1 = z4 + z5; tmp2 = z3 + z5; tmp3 += z1; } else { /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */ tmp0 = MULTIPLY(d7, - FIX2(1.387039845)); tmp1 = MULTIPLY(d7, FIX(1.175875602)); tmp2 = MULTIPLY(d7, - FIX2(0.785694958)); tmp3 = MULTIPLY(d7, FIX2(0.275899379)); } } } } else { if (d5) { if (d3) { if (d1) { /* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */ z2 = d5 + d3; z4 = d5 + d1; z5 = MULTIPLY(d3 + z4, FIX(1.175875602)); tmp1 = MULTIPLY(d5, FIX(2.053119869)); tmp2 = MULTIPLY(d3, FIX(3.072711026)); tmp3 = MULTIPLY(d1, FIX(1.501321110)); z1 = MULTIPLY(d1, - FIX(0.899976223)); z2 = MULTIPLY(z2, - FIX(2.562915447)); z3 = MULTIPLY(d3, - FIX(1.961570560)); z4 = MULTIPLY(z4, - FIX(0.390180644)); z3 += z5; z4 += z5; tmp0 = z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; } else { /* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */ z2 = d5 + d3; z5 = MULTIPLY(z2, FIX(1.175875602)); tmp1 = MULTIPLY(d5, FIX2(1.662939225)); tmp2 = MULTIPLY(d3, FIX2(1.111140466)); z2 = MULTIPLY(z2, - FIX2(1.387039845)); z3 = MULTIPLY(d3, - FIX(1.961570560)); z4 = MULTIPLY(d5, - FIX(0.390180644)); tmp0 = z3 + z5; tmp1 += z2; tmp2 += z2; tmp3 = z4 + z5; } } else { if (d1) { /* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */ z4 = d5 + d1; z5 = MULTIPLY(z4, FIX(1.175875602)); tmp1 = MULTIPLY(d5, - FIX2(0.509795578)); tmp3 = MULTIPLY(d1, FIX2(0.601344887)); z1 = MULTIPLY(d1, - FIX(0.899976223)); z2 = MULTIPLY(d5, - FIX(2.562915447)); z4 = MULTIPLY(z4, FIX2(0.785694958)); tmp0 = z1 + z5; tmp1 += z4; tmp2 = z2 + z5; tmp3 += z4; } else { /* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */ tmp0 = MULTIPLY(d5, FIX(1.175875602)); tmp1 = MULTIPLY(d5, FIX2(0.275899380)); tmp2 = MULTIPLY(d5, - FIX2(1.387039845)); tmp3 = MULTIPLY(d5, FIX2(0.785694958)); } } } else { if (d3) { if (d1) { /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */ z5 = d3 + d1; tmp2 = MULTIPLY(d3, - FIX(1.451774981)); tmp3 = MULTIPLY(d1, (FIX(0.211164243) - 1)); z1 = MULTIPLY(d1, FIX(1.061594337)); z2 = MULTIPLY(d3, - FIX(2.172734803)); z4 = MULTIPLY(z5, FIX(0.785694958)); z5 = MULTIPLY(z5, FIX(1.175875602)); tmp0 = z1 - z4; tmp1 = z2 + z4; tmp2 += z5; tmp3 += z5; } else { /* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */ tmp0 = MULTIPLY(d3, - FIX2(0.785694958)); tmp1 = MULTIPLY(d3, - FIX2(1.387039845)); tmp2 = MULTIPLY(d3, - FIX2(0.275899379)); tmp3 = MULTIPLY(d3, FIX(1.175875602)); } } else { if (d1) { /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */ tmp0 = MULTIPLY(d1, FIX2(0.275899379)); tmp1 = MULTIPLY(d1, FIX2(0.785694958)); tmp2 = MULTIPLY(d1, FIX(1.175875602)); tmp3 = MULTIPLY(d1, FIX2(1.387039845)); } else { /* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */ tmp0 = tmp1 = tmp2 = tmp3 = 0; } } } } /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS+PASS1_BITS+3); dataptr++; /* advance pointer to next column */ } } #else /* *-------------------------------------------------------------- * * j_rev_dct -- * * The original inverse DCT function. * * Results: * None. * * Side effects: * None. * *-------------------------------------------------------------- */ void j_rev_dct (DCTBLOCK data) { INT32 tmp0, tmp1, tmp2, tmp3; INT32 tmp10, tmp11, tmp12, tmp13; INT32 z1, z2, z3, z4, z5; register DCTELEM *dataptr; int rowctr; SHIFT_TEMPS /* 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. */ if ((dataptr[1] | dataptr[2] | dataptr[3] | dataptr[4] | dataptr[5] | dataptr[6] | dataptr[7]) == 0) { /* AC terms all zero */ DCTELEM dcval = (DCTELEM) (dataptr[0] << PASS1_BITS); dataptr[0] = dcval; dataptr[1] = dcval; dataptr[2] = dcval; dataptr[3] = dcval; dataptr[4] = dcval; dataptr[5] = dcval; dataptr[6] = dcval; dataptr[7] = dcval; dataptr += DCTSIZE; /* advance pointer to next row */ continue; } /* Even part: reverse the even part of the forward DCT. */ /* The rotator is sqrt(2)*c(-6). */ z2 = (INT32) dataptr[2]; z3 = (INT32) dataptr[6]; z1 = MULTIPLY(z2 + z3, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(z3, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(z2, FIX(0.765366865)); tmp0 = ((INT32) dataptr[0] + (INT32) dataptr[4]) << CONST_BITS; tmp1 = ((INT32) dataptr[0] - (INT32) dataptr[4]) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; /* Odd part per figure 8; the matrix is unitary and hence its * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. */ tmp0 = (INT32) dataptr[7]; tmp1 = (INT32) dataptr[5]; tmp2 = (INT32) dataptr[3]; tmp3 = (INT32) dataptr[1]; z1 = tmp0 + tmp3; z2 = tmp1 + tmp2; z3 = tmp0 + tmp2; z4 = tmp1 + tmp3; z5 = MULTIPLY(z3 + z4, FIX(1.175875602)); /* sqrt(2) * c3 */ tmp0 = MULTIPLY(tmp0, FIX(0.298631336)); /* sqrt(2) * (-c1+c3+c5-c7) */ tmp1 = MULTIPLY(tmp1, FIX(2.053119869)); /* sqrt(2) * ( c1+c3-c5+c7) */ tmp2 = MULTIPLY(tmp2, FIX(3.072711026)); /* sqrt(2) * ( c1+c3+c5-c7) */ tmp3 = MULTIPLY(tmp3, FIX(1.501321110)); /* sqrt(2) * ( c1+c3-c5-c7) */ z1 = MULTIPLY(z1, - FIX(0.899976223)); /* sqrt(2) * (c7-c3) */ z2 = MULTIPLY(z2, - FIX(2.562915447)); /* sqrt(2) * (-c1-c3) */ z3 = MULTIPLY(z3, - FIX(1.961570560)); /* sqrt(2) * (-c3-c5) */ z4 = MULTIPLY(z4, - FIX(0.390180644)); /* sqrt(2) * (c5-c3) */ z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ dataptr[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS); dataptr[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS); dataptr[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS); dataptr[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS); dataptr[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS); dataptr[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS); dataptr[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS); dataptr[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS); 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. */ #ifndef NO_ZERO_COLUMN_TEST if ((dataptr[DCTSIZE*1] | dataptr[DCTSIZE*2] | dataptr[DCTSIZE*3] | dataptr[DCTSIZE*4] | dataptr[DCTSIZE*5] | dataptr[DCTSIZE*6] | dataptr[DCTSIZE*7]) == 0) { /* AC terms all zero */ DCTELEM dcval = (DCTELEM) DESCALE((INT32) dataptr[0], PASS1_BITS+3); dataptr[DCTSIZE*0] = dcval; dataptr[DCTSIZE*1] = dcval; dataptr[DCTSIZE*2] = dcval; dataptr[DCTSIZE*3] = dcval; dataptr[DCTSIZE*4] = dcval; dataptr[DCTSIZE*5] = dcval; dataptr[DCTSIZE*6] = dcval; dataptr[DCTSIZE*7] = dcval; dataptr++; /* advance pointer to next column */ continue; } #endif /* Even part: reverse the even part of the forward DCT. */ /* The rotator is sqrt(2)*c(-6). */ z2 = (INT32) dataptr[DCTSIZE*2]; z3 = (INT32) dataptr[DCTSIZE*6]; z1 = MULTIPLY(z2 + z3, FIX(0.541196100)); tmp2 = z1 + MULTIPLY(z3, - FIX(1.847759065)); tmp3 = z1 + MULTIPLY(z2, FIX(0.765366865)); tmp0 = ((INT32) dataptr[DCTSIZE*0] + (INT32) dataptr[DCTSIZE*4]) << CONST_BITS; tmp1 = ((INT32) dataptr[DCTSIZE*0] - (INT32) dataptr[DCTSIZE*4]) << CONST_BITS; tmp10 = tmp0 + tmp3; tmp13 = tmp0 - tmp3; tmp11 = tmp1 + tmp2; tmp12 = tmp1 - tmp2; /* Odd part per figure 8; the matrix is unitary and hence its * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. */ tmp0 = (INT32) dataptr[DCTSIZE*7]; tmp1 = (INT32) dataptr[DCTSIZE*5]; tmp2 = (INT32) dataptr[DCTSIZE*3]; tmp3 = (INT32) dataptr[DCTSIZE*1]; z1 = tmp0 + tmp3; z2 = tmp1 + tmp2; z3 = tmp0 + tmp2; z4 = tmp1 + tmp3; z5 = MULTIPLY(z3 + z4, FIX(1.175875602)); /* sqrt(2) * c3 */ tmp0 = MULTIPLY(tmp0, FIX(0.298631336)); /* sqrt(2) * (-c1+c3+c5-c7) */ tmp1 = MULTIPLY(tmp1, FIX(2.053119869)); /* sqrt(2) * ( c1+c3-c5+c7) */ tmp2 = MULTIPLY(tmp2, FIX(3.072711026)); /* sqrt(2) * ( c1+c3+c5-c7) */ tmp3 = MULTIPLY(tmp3, FIX(1.501321110)); /* sqrt(2) * ( c1+c3-c5-c7) */ z1 = MULTIPLY(z1, - FIX(0.899976223)); /* sqrt(2) * (c7-c3) */ z2 = MULTIPLY(z2, - FIX(2.562915447)); /* sqrt(2) * (-c1-c3) */ z3 = MULTIPLY(z3, - FIX(1.961570560)); /* sqrt(2) * (-c3-c5) */ z4 = MULTIPLY(z4, - FIX(0.390180644)); /* sqrt(2) * (c5-c3) */ z3 += z5; z4 += z5; tmp0 += z1 + z3; tmp1 += z2 + z4; tmp2 += z2 + z3; tmp3 += z1 + z4; /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS+PASS1_BITS+3); dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS+PASS1_BITS+3); dataptr++; /* advance pointer to next column */ } } #endif /* ORIG_DCT */ #endif /* FIVE_DCT */