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FFmpeg/libavcodec/jrevdct.c

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  1. /*

  2.  * jrevdct.c

  3.  *

  4.  * This file is part of the Independent JPEG Group's software.

  5.  *

  6.  * The authors make NO WARRANTY or representation, either express or implied,

  7.  * with respect to this software, its quality, accuracy, merchantability, or

  8.  * fitness for a particular purpose.  This software is provided "AS IS", and

  9.  * you, its user, assume the entire risk as to its quality and accuracy.

  10.  *

  11.  * This software is copyright (C) 1991, 1992, Thomas G. Lane.

  12.  * All Rights Reserved except as specified below.

  13.  *

  14.  * Permission is hereby granted to use, copy, modify, and distribute this

  15.  * software (or portions thereof) for any purpose, without fee, subject to

  16.  * these conditions:

  17.  * (1) If any part of the source code for this software is distributed, then

  18.  * this README file must be included, with this copyright and no-warranty

  19.  * notice unaltered; and any additions, deletions, or changes to the original

  20.  * files must be clearly indicated in accompanying documentation.

  21.  * (2) If only executable code is distributed, then the accompanying

  22.  * documentation must state that "this software is based in part on the work

  23.  * of the Independent JPEG Group".

  24.  * (3) Permission for use of this software is granted only if the user accepts

  25.  * full responsibility for any undesirable consequences; the authors accept

  26.  * NO LIABILITY for damages of any kind.

  27.  *

  28.  * These conditions apply to any software derived from or based on the IJG

  29.  * code, not just to the unmodified library.  If you use our work, you ought

  30.  * to acknowledge us.

  31.  *

  32.  * Permission is NOT granted for the use of any IJG author's name or company

  33.  * name in advertising or publicity relating to this software or products

  34.  * derived from it.  This software may be referred to only as "the Independent

  35.  * JPEG Group's software".

  36.  *

  37.  * We specifically permit and encourage the use of this software as the basis

  38.  * of commercial products, provided that all warranty or liability claims are

  39.  * assumed by the product vendor.

  40.  *

  41.  * This file contains the basic inverse-DCT transformation subroutine.

  42.  *

  43.  * This implementation is based on an algorithm described in

  44.  *   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT

  45.  *   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,

  46.  *   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.

  47.  * The primary algorithm described there uses 11 multiplies and 29 adds.

  48.  * We use their alternate method with 12 multiplies and 32 adds.

  49.  * The advantage of this method is that no data path contains more than one

  50.  * multiplication; this allows a very simple and accurate implementation in

  51.  * scaled fixed-point arithmetic, with a minimal number of shifts.

  52.  *

  53.  * I've made lots of modifications to attempt to take advantage of the

  54.  * sparse nature of the DCT matrices we're getting.  Although the logic

  55.  * is cumbersome, it's straightforward and the resulting code is much

  56.  * faster.

  57.  *

  58.  * A better way to do this would be to pass in the DCT block as a sparse

  59.  * matrix, perhaps with the difference cases encoded.

  60.  */

  61. 

  62. /**

  63.  * @file libavcodec/jrevdct.c

  64.  * Independent JPEG Group's LLM idct.

  65.  */

  66. 

  67. #include "libavutil/common.h"

  68. #include "dsputil.h"

  69. 

  70. #define EIGHT_BIT_SAMPLES

  71. 

  72. #define DCTSIZE 8

  73. #define DCTSIZE2 64

  74. 

  75. #define GLOBAL

  76. 

  77. #define RIGHT_SHIFT(x, n) ((x) >> (n))

  78. 

  79. typedef DCTELEM DCTBLOCK[DCTSIZE2];

  80. 

  81. #define CONST_BITS 13

  82. 

  83. /*

  84.  * This routine is specialized to the case DCTSIZE = 8.

  85.  */

  86. 

  87. #if DCTSIZE != 8

  88.   Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */

  89. #endif

  90. 

  91. 

  92. /*

  93.  * A 2-D IDCT can be done by 1-D IDCT on each row followed by 1-D IDCT

  94.  * on each column.  Direct algorithms are also available, but they are

  95.  * much more complex and seem not to be any faster when reduced to code.

  96.  *

  97.  * The poop on this scaling stuff is as follows:

  98.  *

  99.  * Each 1-D IDCT step produces outputs which are a factor of sqrt(N)

  100.  * larger than the true IDCT outputs.  The final outputs are therefore

  101.  * a factor of N larger than desired; since N=8 this can be cured by

  102.  * a simple right shift at the end of the algorithm.  The advantage of

  103.  * this arrangement is that we save two multiplications per 1-D IDCT,

  104.  * because the y0 and y4 inputs need not be divided by sqrt(N).

  105.  *

  106.  * We have to do addition and subtraction of the integer inputs, which

  107.  * is no problem, and multiplication by fractional constants, which is

  108.  * a problem to do in integer arithmetic.  We multiply all the constants

  109.  * by CONST_SCALE and convert them to integer constants (thus retaining

  110.  * CONST_BITS bits of precision in the constants).  After doing a

  111.  * multiplication we have to divide the product by CONST_SCALE, with proper

  112.  * rounding, to produce the correct output.  This division can be done

  113.  * cheaply as a right shift of CONST_BITS bits.  We postpone shifting

  114.  * as long as possible so that partial sums can be added together with

  115.  * full fractional precision.

  116.  *

  117.  * The outputs of the first pass are scaled up by PASS1_BITS bits so that

  118.  * they are represented to better-than-integral precision.  These outputs

  119.  * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word

  120.  * with the recommended scaling.  (To scale up 12-bit sample data further, an

  121.  * intermediate int32 array would be needed.)

  122.  *

  123.  * To avoid overflow of the 32-bit intermediate results in pass 2, we must

  124.  * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis

  125.  * shows that the values given below are the most effective.

  126.  */

  127. 

  128. #ifdef EIGHT_BIT_SAMPLES

  129. #define PASS1_BITS  2

  130. #else

  131. #define PASS1_BITS  1   /* lose a little precision to avoid overflow */

  132. #endif

  133. 

  134. #define ONE         ((int32_t) 1)

  135. 

  136. #define CONST_SCALE (ONE << CONST_BITS)

  137. 

  138. /* Convert a positive real constant to an integer scaled by CONST_SCALE.

  139.  * IMPORTANT: if your compiler doesn't do this arithmetic at compile time,

  140.  * you will pay a significant penalty in run time.  In that case, figure

  141.  * the correct integer constant values and insert them by hand.

  142.  */

  143. 

  144. /* Actually FIX is no longer used, we precomputed them all */

  145. #define FIX(x)  ((int32_t) ((x) * CONST_SCALE + 0.5))

  146. 

  147. /* Descale and correctly round an int32_t value that's scaled by N bits.

  148.  * We assume RIGHT_SHIFT rounds towards minus infinity, so adding

  149.  * the fudge factor is correct for either sign of X.

  150.  */

  151. 

  152. #define DESCALE(x,n)  RIGHT_SHIFT((x) + (ONE << ((n)-1)), n)

  153. 

  154. /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.

  155.  * For 8-bit samples with the recommended scaling, all the variable

  156.  * and constant values involved are no more than 16 bits wide, so a

  157.  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply;

  158.  * this provides a useful speedup on many machines.

  159.  * There is no way to specify a 16x16->32 multiply in portable C, but

  160.  * some C compilers will do the right thing if you provide the correct

  161.  * combination of casts.

  162.  * NB: for 12-bit samples, a full 32-bit multiplication will be needed.

  163.  */

  164. 

  165. #ifdef EIGHT_BIT_SAMPLES

  166. #ifdef SHORTxSHORT_32           /* may work if 'int' is 32 bits */

  167. #define MULTIPLY(var,const)  (((int16_t) (var)) * ((int16_t) (const)))

  168. #endif

  169. #ifdef SHORTxLCONST_32          /* known to work with Microsoft C 6.0 */

  170. #define MULTIPLY(var,const)  (((int16_t) (var)) * ((int32_t) (const)))

  171. #endif

  172. #endif

  173. 

  174. #ifndef MULTIPLY                /* default definition */

  175. #define MULTIPLY(var,const)  ((var) * (const))

  176. #endif

  177. 

  178. 

  179. /*

  180.   Unlike our decoder where we approximate the FIXes, we need to use exact

  181. ones here or successive P-frames will drift too much with Reference frame coding

  182. */

  183. #define FIX_0_211164243 1730

  184. #define FIX_0_275899380 2260

  185. #define FIX_0_298631336 2446

  186. #define FIX_0_390180644 3196

  187. #define FIX_0_509795579 4176

  188. #define FIX_0_541196100 4433

  189. #define FIX_0_601344887 4926

  190. #define FIX_0_765366865 6270

  191. #define FIX_0_785694958 6436

  192. #define FIX_0_899976223 7373

  193. #define FIX_1_061594337 8697

  194. #define FIX_1_111140466 9102

  195. #define FIX_1_175875602 9633

  196. #define FIX_1_306562965 10703

  197. #define FIX_1_387039845 11363

  198. #define FIX_1_451774981 11893

  199. #define FIX_1_501321110 12299

  200. #define FIX_1_662939225 13623

  201. #define FIX_1_847759065 15137

  202. #define FIX_1_961570560 16069

  203. #define FIX_2_053119869 16819

  204. #define FIX_2_172734803 17799

  205. #define FIX_2_562915447 20995

  206. #define FIX_3_072711026 25172

  207. 

  208. /*

  209.  * Perform the inverse DCT on one block of coefficients.

  210.  */

  211. 

  212. void j_rev_dct(DCTBLOCK data)

  213. {

  214.   int32_t tmp0, tmp1, tmp2, tmp3;

  215.   int32_t tmp10, tmp11, tmp12, tmp13;

  216.   int32_t z1, z2, z3, z4, z5;

  217.   int32_t d0, d1, d2, d3, d4, d5, d6, d7;

  218.   register DCTELEM *dataptr;

  219.   int rowctr;

  220. 

  221.   /* Pass 1: process rows. */

  222.   /* Note results are scaled up by sqrt(8) compared to a true IDCT; */

  223.   /* furthermore, we scale the results by 2**PASS1_BITS. */

  224. 

  225.   dataptr = data;

  226. 

  227.   for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {

  228.     /* Due to quantization, we will usually find that many of the input

  229.      * coefficients are zero, especially the AC terms.  We can exploit this

  230.      * by short-circuiting the IDCT calculation for any row in which all

  231.      * the AC terms are zero.  In that case each output is equal to the

  232.      * DC coefficient (with scale factor as needed).

  233.      * With typical images and quantization tables, half or more of the

  234.      * row DCT calculations can be simplified this way.

  235.      */

  236. 

  237.     register int *idataptr = (int*)dataptr;

  238. 

  239.     /* WARNING: we do the same permutation as MMX idct to simplify the

  240.        video core */

  241.     d0 = dataptr[0];

  242.     d2 = dataptr[1];

  243.     d4 = dataptr[2];

  244.     d6 = dataptr[3];

  245.     d1 = dataptr[4];

  246.     d3 = dataptr[5];

  247.     d5 = dataptr[6];

  248.     d7 = dataptr[7];

  249. 

  250.     if ((d1 | d2 | d3 | d4 | d5 | d6 | d7) == 0) {

  251.       /* AC terms all zero */

  252.       if (d0) {

  253.           /* Compute a 32 bit value to assign. */

  254.           DCTELEM dcval = (DCTELEM) (d0 << PASS1_BITS);

  255.           register int v = (dcval & 0xffff) | ((dcval << 16) & 0xffff0000);

  256. 

  257.           idataptr[0] = v;

  258.           idataptr[1] = v;

  259.           idataptr[2] = v;

  260.           idataptr[3] = v;

  261.       }

  262. 

  263.       dataptr += DCTSIZE;       /* advance pointer to next row */

  264.       continue;

  265.     }

  266. 

  267.     /* Even part: reverse the even part of the forward DCT. */

  268.     /* The rotator is sqrt(2)*c(-6). */

  269. {

  270.     if (d6) {

  271.             if (d2) {

  272.                     /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */

  273.                     z1 = MULTIPLY(d2 + d6, FIX_0_541196100);

  274.                     tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);

  275.                     tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);

  276. 

  277.                     tmp0 = (d0 + d4) << CONST_BITS;

  278.                     tmp1 = (d0 - d4) << CONST_BITS;

  279. 

  280.                     tmp10 = tmp0 + tmp3;

  281.                     tmp13 = tmp0 - tmp3;

  282.                     tmp11 = tmp1 + tmp2;

  283.                     tmp12 = tmp1 - tmp2;

  284.             } else {

  285.                     /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */

  286.                     tmp2 = MULTIPLY(-d6, FIX_1_306562965);

  287.                     tmp3 = MULTIPLY(d6, FIX_0_541196100);

  288. 

  289.                     tmp0 = (d0 + d4) << CONST_BITS;

  290.                     tmp1 = (d0 - d4) << CONST_BITS;

  291. 

  292.                     tmp10 = tmp0 + tmp3;

  293.                     tmp13 = tmp0 - tmp3;

  294.                     tmp11 = tmp1 + tmp2;

  295.                     tmp12 = tmp1 - tmp2;

  296.             }

  297.     } else {

  298.             if (d2) {

  299.                     /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */

  300.                     tmp2 = MULTIPLY(d2, FIX_0_541196100);

  301.                     tmp3 = MULTIPLY(d2, FIX_1_306562965);

  302. 

  303.                     tmp0 = (d0 + d4) << CONST_BITS;

  304.                     tmp1 = (d0 - d4) << CONST_BITS;

  305. 

  306.                     tmp10 = tmp0 + tmp3;

  307.                     tmp13 = tmp0 - tmp3;

  308.                     tmp11 = tmp1 + tmp2;

  309.                     tmp12 = tmp1 - tmp2;

  310.             } else {

  311.                     /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */

  312.                     tmp10 = tmp13 = (d0 + d4) << CONST_BITS;

  313.                     tmp11 = tmp12 = (d0 - d4) << CONST_BITS;

  314.             }

  315.       }

  316. 

  317.     /* Odd part per figure 8; the matrix is unitary and hence its

  318.      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.

  319.      */

  320. 

  321.     if (d7) {

  322.         if (d5) {

  323.             if (d3) {

  324.                 if (d1) {

  325.                     /* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */

  326.                     z1 = d7 + d1;

  327.                     z2 = d5 + d3;

  328.                     z3 = d7 + d3;

  329.                     z4 = d5 + d1;

  330.                     z5 = MULTIPLY(z3 + z4, FIX_1_175875602);

  331. 

  332.                     tmp0 = MULTIPLY(d7, FIX_0_298631336);

  333.                     tmp1 = MULTIPLY(d5, FIX_2_053119869);

  334.                     tmp2 = MULTIPLY(d3, FIX_3_072711026);

  335.                     tmp3 = MULTIPLY(d1, FIX_1_501321110);

  336.                     z1 = MULTIPLY(-z1, FIX_0_899976223);

  337.                     z2 = MULTIPLY(-z2, FIX_2_562915447);

  338.                     z3 = MULTIPLY(-z3, FIX_1_961570560);

  339.                     z4 = MULTIPLY(-z4, FIX_0_390180644);

  340. 

  341.                     z3 += z5;

  342.                     z4 += z5;

  343. 

  344.                     tmp0 += z1 + z3;

  345.                     tmp1 += z2 + z4;

  346.                     tmp2 += z2 + z3;

  347.                     tmp3 += z1 + z4;

  348.                 } else {

  349.                     /* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */

  350.                     z2 = d5 + d3;

  351.                     z3 = d7 + d3;

  352.                     z5 = MULTIPLY(z3 + d5, FIX_1_175875602);

  353. 

  354.                     tmp0 = MULTIPLY(d7, FIX_0_298631336);

  355.                     tmp1 = MULTIPLY(d5, FIX_2_053119869);

  356.                     tmp2 = MULTIPLY(d3, FIX_3_072711026);

  357.                     z1 = MULTIPLY(-d7, FIX_0_899976223);

  358.                     z2 = MULTIPLY(-z2, FIX_2_562915447);

  359.                     z3 = MULTIPLY(-z3, FIX_1_961570560);

  360.                     z4 = MULTIPLY(-d5, FIX_0_390180644);

  361. 

  362.                     z3 += z5;

  363.                     z4 += z5;

  364. 

  365.                     tmp0 += z1 + z3;

  366.                     tmp1 += z2 + z4;

  367.                     tmp2 += z2 + z3;

  368.                     tmp3 = z1 + z4;

  369.                 }

  370.             } else {

  371.                 if (d1) {

  372.                     /* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */

  373.                     z1 = d7 + d1;

  374.                     z4 = d5 + d1;

  375.                     z5 = MULTIPLY(d7 + z4, FIX_1_175875602);

  376. 

  377.                     tmp0 = MULTIPLY(d7, FIX_0_298631336);

  378.                     tmp1 = MULTIPLY(d5, FIX_2_053119869);

  379.                     tmp3 = MULTIPLY(d1, FIX_1_501321110);

  380.                     z1 = MULTIPLY(-z1, FIX_0_899976223);

  381.                     z2 = MULTIPLY(-d5, FIX_2_562915447);

  382.                     z3 = MULTIPLY(-d7, FIX_1_961570560);

  383.                     z4 = MULTIPLY(-z4, FIX_0_390180644);

  384. 

  385.                     z3 += z5;

  386.                     z4 += z5;

  387. 

  388.                     tmp0 += z1 + z3;

  389.                     tmp1 += z2 + z4;

  390.                     tmp2 = z2 + z3;

  391.                     tmp3 += z1 + z4;

  392.                 } else {

  393.                     /* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */

  394.                     tmp0 = MULTIPLY(-d7, FIX_0_601344887);

  395.                     z1 = MULTIPLY(-d7, FIX_0_899976223);

  396.                     z3 = MULTIPLY(-d7, FIX_1_961570560);

  397.                     tmp1 = MULTIPLY(-d5, FIX_0_509795579);

  398.                     z2 = MULTIPLY(-d5, FIX_2_562915447);

  399.                     z4 = MULTIPLY(-d5, FIX_0_390180644);

  400.                     z5 = MULTIPLY(d5 + d7, FIX_1_175875602);

  401. 

  402.                     z3 += z5;

  403.                     z4 += z5;

  404. 

  405.                     tmp0 += z3;

  406.                     tmp1 += z4;

  407.                     tmp2 = z2 + z3;

  408.                     tmp3 = z1 + z4;

  409.                 }

  410.             }

  411.         } else {

  412.             if (d3) {

  413.                 if (d1) {

  414.                     /* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */

  415.                     z1 = d7 + d1;

  416.                     z3 = d7 + d3;

  417.                     z5 = MULTIPLY(z3 + d1, FIX_1_175875602);

  418. 

  419.                     tmp0 = MULTIPLY(d7, FIX_0_298631336);

  420.                     tmp2 = MULTIPLY(d3, FIX_3_072711026);

  421.                     tmp3 = MULTIPLY(d1, FIX_1_501321110);

  422.                     z1 = MULTIPLY(-z1, FIX_0_899976223);

  423.                     z2 = MULTIPLY(-d3, FIX_2_562915447);

  424.                     z3 = MULTIPLY(-z3, FIX_1_961570560);

  425.                     z4 = MULTIPLY(-d1, FIX_0_390180644);

  426. 

  427.                     z3 += z5;

  428.                     z4 += z5;

  429. 

  430.                     tmp0 += z1 + z3;

  431.                     tmp1 = z2 + z4;

  432.                     tmp2 += z2 + z3;

  433.                     tmp3 += z1 + z4;

  434.                 } else {

  435.                     /* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */

  436.                     z3 = d7 + d3;

  437. 

  438.                     tmp0 = MULTIPLY(-d7, FIX_0_601344887);

  439.                     z1 = MULTIPLY(-d7, FIX_0_899976223);

  440.                     tmp2 = MULTIPLY(d3, FIX_0_509795579);

  441.                     z2 = MULTIPLY(-d3, FIX_2_562915447);

  442.                     z5 = MULTIPLY(z3, FIX_1_175875602);

  443.                     z3 = MULTIPLY(-z3, FIX_0_785694958);

  444. 

  445.                     tmp0 += z3;

  446.                     tmp1 = z2 + z5;

  447.                     tmp2 += z3;

  448.                     tmp3 = z1 + z5;

  449.                 }

  450.             } else {

  451.                 if (d1) {

  452.                     /* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */

  453.                     z1 = d7 + d1;

  454.                     z5 = MULTIPLY(z1, FIX_1_175875602);

  455. 

  456.                     z1 = MULTIPLY(z1, FIX_0_275899380);

  457.                     z3 = MULTIPLY(-d7, FIX_1_961570560);

  458.                     tmp0 = MULTIPLY(-d7, FIX_1_662939225);

  459.                     z4 = MULTIPLY(-d1, FIX_0_390180644);

  460.                     tmp3 = MULTIPLY(d1, FIX_1_111140466);

  461. 

  462.                     tmp0 += z1;

  463.                     tmp1 = z4 + z5;

  464.                     tmp2 = z3 + z5;

  465.                     tmp3 += z1;

  466.                 } else {

  467.                     /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */

  468.                     tmp0 = MULTIPLY(-d7, FIX_1_387039845);

  469.                     tmp1 = MULTIPLY(d7, FIX_1_175875602);

  470.                     tmp2 = MULTIPLY(-d7, FIX_0_785694958);

  471.                     tmp3 = MULTIPLY(d7, FIX_0_275899380);

  472.                 }

  473.             }

  474.         }

  475.     } else {

  476.         if (d5) {

  477.             if (d3) {

  478.                 if (d1) {

  479.                     /* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */

  480.                     z2 = d5 + d3;

  481.                     z4 = d5 + d1;

  482.                     z5 = MULTIPLY(d3 + z4, FIX_1_175875602);

  483. 

  484.                     tmp1 = MULTIPLY(d5, FIX_2_053119869);

  485.                     tmp2 = MULTIPLY(d3, FIX_3_072711026);

  486.                     tmp3 = MULTIPLY(d1, FIX_1_501321110);

  487.                     z1 = MULTIPLY(-d1, FIX_0_899976223);

  488.                     z2 = MULTIPLY(-z2, FIX_2_562915447);

  489.                     z3 = MULTIPLY(-d3, FIX_1_961570560);

  490.                     z4 = MULTIPLY(-z4, FIX_0_390180644);

  491. 

  492.                     z3 += z5;

  493.                     z4 += z5;

  494. 

  495.                     tmp0 = z1 + z3;

  496.                     tmp1 += z2 + z4;

  497.                     tmp2 += z2 + z3;

  498.                     tmp3 += z1 + z4;

  499.                 } else {

  500.                     /* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */

  501.                     z2 = d5 + d3;

  502. 

  503.                     z5 = MULTIPLY(z2, FIX_1_175875602);

  504.                     tmp1 = MULTIPLY(d5, FIX_1_662939225);

  505.                     z4 = MULTIPLY(-d5, FIX_0_390180644);

  506.                     z2 = MULTIPLY(-z2, FIX_1_387039845);

  507.                     tmp2 = MULTIPLY(d3, FIX_1_111140466);

  508.                     z3 = MULTIPLY(-d3, FIX_1_961570560);

  509. 

  510.                     tmp0 = z3 + z5;

  511.                     tmp1 += z2;

  512.                     tmp2 += z2;

  513.                     tmp3 = z4 + z5;

  514.                 }

  515.             } else {

  516.                 if (d1) {

  517.                     /* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */

  518.                     z4 = d5 + d1;

  519. 

  520.                     z5 = MULTIPLY(z4, FIX_1_175875602);

  521.                     z1 = MULTIPLY(-d1, FIX_0_899976223);

  522.                     tmp3 = MULTIPLY(d1, FIX_0_601344887);

  523.                     tmp1 = MULTIPLY(-d5, FIX_0_509795579);

  524.                     z2 = MULTIPLY(-d5, FIX_2_562915447);

  525.                     z4 = MULTIPLY(z4, FIX_0_785694958);

  526. 

  527.                     tmp0 = z1 + z5;

  528.                     tmp1 += z4;

  529.                     tmp2 = z2 + z5;

  530.                     tmp3 += z4;

  531.                 } else {

  532.                     /* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */

  533.                     tmp0 = MULTIPLY(d5, FIX_1_175875602);

  534.                     tmp1 = MULTIPLY(d5, FIX_0_275899380);

  535.                     tmp2 = MULTIPLY(-d5, FIX_1_387039845);

  536.                     tmp3 = MULTIPLY(d5, FIX_0_785694958);

  537.                 }

  538.             }

  539.         } else {

  540.             if (d3) {

  541.                 if (d1) {

  542.                     /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */

  543.                     z5 = d1 + d3;

  544.                     tmp3 = MULTIPLY(d1, FIX_0_211164243);

  545.                     tmp2 = MULTIPLY(-d3, FIX_1_451774981);

  546.                     z1 = MULTIPLY(d1, FIX_1_061594337);

  547.                     z2 = MULTIPLY(-d3, FIX_2_172734803);

  548.                     z4 = MULTIPLY(z5, FIX_0_785694958);

  549.                     z5 = MULTIPLY(z5, FIX_1_175875602);

  550. 

  551.                     tmp0 = z1 - z4;

  552.                     tmp1 = z2 + z4;

  553.                     tmp2 += z5;

  554.                     tmp3 += z5;

  555.                 } else {

  556.                     /* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */

  557.                     tmp0 = MULTIPLY(-d3, FIX_0_785694958);

  558.                     tmp1 = MULTIPLY(-d3, FIX_1_387039845);

  559.                     tmp2 = MULTIPLY(-d3, FIX_0_275899380);

  560.                     tmp3 = MULTIPLY(d3, FIX_1_175875602);

  561.                 }

  562.             } else {

  563.                 if (d1) {

  564.                     /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */

  565.                     tmp0 = MULTIPLY(d1, FIX_0_275899380);

  566.                     tmp1 = MULTIPLY(d1, FIX_0_785694958);

  567.                     tmp2 = MULTIPLY(d1, FIX_1_175875602);

  568.                     tmp3 = MULTIPLY(d1, FIX_1_387039845);

  569.                 } else {

  570.                     /* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */

  571.                     tmp0 = tmp1 = tmp2 = tmp3 = 0;

  572.                 }

  573.             }

  574.         }

  575.     }

  576. }

  577.     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

  578. 

  579.     dataptr[0] = (DCTELEM) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);

  580.     dataptr[7] = (DCTELEM) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);

  581.     dataptr[1] = (DCTELEM) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);

  582.     dataptr[6] = (DCTELEM) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);

  583.     dataptr[2] = (DCTELEM) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);

  584.     dataptr[5] = (DCTELEM) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);

  585.     dataptr[3] = (DCTELEM) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);

  586.     dataptr[4] = (DCTELEM) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);

  587. 

  588.     dataptr += DCTSIZE;         /* advance pointer to next row */

  589.   }

  590. 

  591.   /* Pass 2: process columns. */

  592.   /* Note that we must descale the results by a factor of 8 == 2**3, */

  593.   /* and also undo the PASS1_BITS scaling. */

  594. 

  595.   dataptr = data;

  596.   for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {

  597.     /* Columns of zeroes can be exploited in the same way as we did with rows.

  598.      * However, the row calculation has created many nonzero AC terms, so the

  599.      * simplification applies less often (typically 5% to 10% of the time).

  600.      * On machines with very fast multiplication, it's possible that the

  601.      * test takes more time than it's worth.  In that case this section

  602.      * may be commented out.

  603.      */

  604. 

  605.     d0 = dataptr[DCTSIZE*0];

  606.     d1 = dataptr[DCTSIZE*1];

  607.     d2 = dataptr[DCTSIZE*2];

  608.     d3 = dataptr[DCTSIZE*3];

  609.     d4 = dataptr[DCTSIZE*4];

  610.     d5 = dataptr[DCTSIZE*5];

  611.     d6 = dataptr[DCTSIZE*6];

  612.     d7 = dataptr[DCTSIZE*7];

  613. 

  614.     /* Even part: reverse the even part of the forward DCT. */

  615.     /* The rotator is sqrt(2)*c(-6). */

  616.     if (d6) {

  617.             if (d2) {

  618.                     /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */

  619.                     z1 = MULTIPLY(d2 + d6, FIX_0_541196100);

  620.                     tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);

  621.                     tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);

  622. 

  623.                     tmp0 = (d0 + d4) << CONST_BITS;

  624.                     tmp1 = (d0 - d4) << CONST_BITS;

  625. 

  626.                     tmp10 = tmp0 + tmp3;

  627.                     tmp13 = tmp0 - tmp3;

  628.                     tmp11 = tmp1 + tmp2;

  629.                     tmp12 = tmp1 - tmp2;

  630.             } else {

  631.                     /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */

  632.                     tmp2 = MULTIPLY(-d6, FIX_1_306562965);

  633.                     tmp3 = MULTIPLY(d6, FIX_0_541196100);

  634. 

  635.                     tmp0 = (d0 + d4) << CONST_BITS;

  636.                     tmp1 = (d0 - d4) << CONST_BITS;

  637. 

  638.                     tmp10 = tmp0 + tmp3;

  639.                     tmp13 = tmp0 - tmp3;

  640.                     tmp11 = tmp1 + tmp2;

  641.                     tmp12 = tmp1 - tmp2;

  642.             }

  643.     } else {

  644.             if (d2) {

  645.                     /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */

  646.                     tmp2 = MULTIPLY(d2, FIX_0_541196100);

  647.                     tmp3 = MULTIPLY(d2, FIX_1_306562965);

  648. 

  649.                     tmp0 = (d0 + d4) << CONST_BITS;

  650.                     tmp1 = (d0 - d4) << CONST_BITS;

  651. 

  652.                     tmp10 = tmp0 + tmp3;

  653.                     tmp13 = tmp0 - tmp3;

  654.                     tmp11 = tmp1 + tmp2;

  655.                     tmp12 = tmp1 - tmp2;

  656.             } else {

  657.                     /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */

  658.                     tmp10 = tmp13 = (d0 + d4) << CONST_BITS;

  659.                     tmp11 = tmp12 = (d0 - d4) << CONST_BITS;

  660.             }

  661.     }

  662. 

  663.     /* Odd part per figure 8; the matrix is unitary and hence its

  664.      * transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.

  665.      */

  666.     if (d7) {

  667.         if (d5) {

  668.             if (d3) {

  669.                 if (d1) {

  670.                     /* d1 != 0, d3 != 0, d5 != 0, d7 != 0 */

  671.                     z1 = d7 + d1;

  672.                     z2 = d5 + d3;

  673.                     z3 = d7 + d3;

  674.                     z4 = d5 + d1;

  675.                     z5 = MULTIPLY(z3 + z4, FIX_1_175875602);

  676. 

  677.                     tmp0 = MULTIPLY(d7, FIX_0_298631336);

  678.                     tmp1 = MULTIPLY(d5, FIX_2_053119869);

  679.                     tmp2 = MULTIPLY(d3, FIX_3_072711026);

  680.                     tmp3 = MULTIPLY(d1, FIX_1_501321110);

  681.                     z1 = MULTIPLY(-z1, FIX_0_899976223);

  682.                     z2 = MULTIPLY(-z2, FIX_2_562915447);

  683.                     z3 = MULTIPLY(-z3, FIX_1_961570560);

  684.                     z4 = MULTIPLY(-z4, FIX_0_390180644);

  685. 

  686.                     z3 += z5;

  687.                     z4 += z5;

  688. 

  689.                     tmp0 += z1 + z3;

  690.                     tmp1 += z2 + z4;

  691.                     tmp2 += z2 + z3;

  692.                     tmp3 += z1 + z4;

  693.                 } else {

  694.                     /* d1 == 0, d3 != 0, d5 != 0, d7 != 0 */

  695.                     z2 = d5 + d3;

  696.                     z3 = d7 + d3;

  697.                     z5 = MULTIPLY(z3 + d5, FIX_1_175875602);

  698. 

  699.                     tmp0 = MULTIPLY(d7, FIX_0_298631336);

  700.                     tmp1 = MULTIPLY(d5, FIX_2_053119869);

  701.                     tmp2 = MULTIPLY(d3, FIX_3_072711026);

  702.                     z1 = MULTIPLY(-d7, FIX_0_899976223);

  703.                     z2 = MULTIPLY(-z2, FIX_2_562915447);

  704.                     z3 = MULTIPLY(-z3, FIX_1_961570560);

  705.                     z4 = MULTIPLY(-d5, FIX_0_390180644);

  706. 

  707.                     z3 += z5;

  708.                     z4 += z5;

  709. 

  710.                     tmp0 += z1 + z3;

  711.                     tmp1 += z2 + z4;

  712.                     tmp2 += z2 + z3;

  713.                     tmp3 = z1 + z4;

  714.                 }

  715.             } else {

  716.                 if (d1) {

  717.                     /* d1 != 0, d3 == 0, d5 != 0, d7 != 0 */

  718.                     z1 = d7 + d1;

  719.                     z3 = d7;

  720.                     z4 = d5 + d1;

  721.                     z5 = MULTIPLY(z3 + z4, FIX_1_175875602);

  722. 

  723.                     tmp0 = MULTIPLY(d7, FIX_0_298631336);

  724.                     tmp1 = MULTIPLY(d5, FIX_2_053119869);

  725.                     tmp3 = MULTIPLY(d1, FIX_1_501321110);

  726.                     z1 = MULTIPLY(-z1, FIX_0_899976223);

  727.                     z2 = MULTIPLY(-d5, FIX_2_562915447);

  728.                     z3 = MULTIPLY(-d7, FIX_1_961570560);

  729.                     z4 = MULTIPLY(-z4, FIX_0_390180644);

  730. 

  731.                     z3 += z5;

  732.                     z4 += z5;

  733. 

  734.                     tmp0 += z1 + z3;

  735.                     tmp1 += z2 + z4;

  736.                     tmp2 = z2 + z3;

  737.                     tmp3 += z1 + z4;

  738.                 } else {

  739.                     /* d1 == 0, d3 == 0, d5 != 0, d7 != 0 */

  740.                     tmp0 = MULTIPLY(-d7, FIX_0_601344887);

  741.                     z1 = MULTIPLY(-d7, FIX_0_899976223);

  742.                     z3 = MULTIPLY(-d7, FIX_1_961570560);

  743.                     tmp1 = MULTIPLY(-d5, FIX_0_509795579);

  744.                     z2 = MULTIPLY(-d5, FIX_2_562915447);

  745.                     z4 = MULTIPLY(-d5, FIX_0_390180644);

  746.                     z5 = MULTIPLY(d5 + d7, FIX_1_175875602);

  747. 

  748.                     z3 += z5;

  749.                     z4 += z5;

  750. 

  751.                     tmp0 += z3;

  752.                     tmp1 += z4;

  753.                     tmp2 = z2 + z3;

  754.                     tmp3 = z1 + z4;

  755.                 }

  756.             }

  757.         } else {

  758.             if (d3) {

  759.                 if (d1) {

  760.                     /* d1 != 0, d3 != 0, d5 == 0, d7 != 0 */

  761.                     z1 = d7 + d1;

  762.                     z3 = d7 + d3;

  763.                     z5 = MULTIPLY(z3 + d1, FIX_1_175875602);

  764. 

  765.                     tmp0 = MULTIPLY(d7, FIX_0_298631336);

  766.                     tmp2 = MULTIPLY(d3, FIX_3_072711026);

  767.                     tmp3 = MULTIPLY(d1, FIX_1_501321110);

  768.                     z1 = MULTIPLY(-z1, FIX_0_899976223);

  769.                     z2 = MULTIPLY(-d3, FIX_2_562915447);

  770.                     z3 = MULTIPLY(-z3, FIX_1_961570560);

  771.                     z4 = MULTIPLY(-d1, FIX_0_390180644);

  772. 

  773.                     z3 += z5;

  774.                     z4 += z5;

  775. 

  776.                     tmp0 += z1 + z3;

  777.                     tmp1 = z2 + z4;

  778.                     tmp2 += z2 + z3;

  779.                     tmp3 += z1 + z4;

  780.                 } else {

  781.                     /* d1 == 0, d3 != 0, d5 == 0, d7 != 0 */

  782.                     z3 = d7 + d3;

  783. 

  784.                     tmp0 = MULTIPLY(-d7, FIX_0_601344887);

  785.                     z1 = MULTIPLY(-d7, FIX_0_899976223);

  786.                     tmp2 = MULTIPLY(d3, FIX_0_509795579);

  787.                     z2 = MULTIPLY(-d3, FIX_2_562915447);

  788.                     z5 = MULTIPLY(z3, FIX_1_175875602);

  789.                     z3 = MULTIPLY(-z3, FIX_0_785694958);

  790. 

  791.                     tmp0 += z3;

  792.                     tmp1 = z2 + z5;

  793.                     tmp2 += z3;

  794.                     tmp3 = z1 + z5;

  795.                 }

  796.             } else {

  797.                 if (d1) {

  798.                     /* d1 != 0, d3 == 0, d5 == 0, d7 != 0 */

  799.                     z1 = d7 + d1;

  800.                     z5 = MULTIPLY(z1, FIX_1_175875602);

  801. 

  802.                     z1 = MULTIPLY(z1, FIX_0_275899380);

  803.                     z3 = MULTIPLY(-d7, FIX_1_961570560);

  804.                     tmp0 = MULTIPLY(-d7, FIX_1_662939225);

  805.                     z4 = MULTIPLY(-d1, FIX_0_390180644);

  806.                     tmp3 = MULTIPLY(d1, FIX_1_111140466);

  807. 

  808.                     tmp0 += z1;

  809.                     tmp1 = z4 + z5;

  810.                     tmp2 = z3 + z5;

  811.                     tmp3 += z1;

  812.                 } else {

  813.                     /* d1 == 0, d3 == 0, d5 == 0, d7 != 0 */

  814.                     tmp0 = MULTIPLY(-d7, FIX_1_387039845);

  815.                     tmp1 = MULTIPLY(d7, FIX_1_175875602);

  816.                     tmp2 = MULTIPLY(-d7, FIX_0_785694958);

  817.                     tmp3 = MULTIPLY(d7, FIX_0_275899380);

  818.                 }

  819.             }

  820.         }

  821.     } else {

  822.         if (d5) {

  823.             if (d3) {

  824.                 if (d1) {

  825.                     /* d1 != 0, d3 != 0, d5 != 0, d7 == 0 */

  826.                     z2 = d5 + d3;

  827.                     z4 = d5 + d1;

  828.                     z5 = MULTIPLY(d3 + z4, FIX_1_175875602);

  829. 

  830.                     tmp1 = MULTIPLY(d5, FIX_2_053119869);

  831.                     tmp2 = MULTIPLY(d3, FIX_3_072711026);

  832.                     tmp3 = MULTIPLY(d1, FIX_1_501321110);

  833.                     z1 = MULTIPLY(-d1, FIX_0_899976223);

  834.                     z2 = MULTIPLY(-z2, FIX_2_562915447);

  835.                     z3 = MULTIPLY(-d3, FIX_1_961570560);

  836.                     z4 = MULTIPLY(-z4, FIX_0_390180644);

  837. 

  838.                     z3 += z5;

  839.                     z4 += z5;

  840. 

  841.                     tmp0 = z1 + z3;

  842.                     tmp1 += z2 + z4;

  843.                     tmp2 += z2 + z3;

  844.                     tmp3 += z1 + z4;

  845.                 } else {

  846.                     /* d1 == 0, d3 != 0, d5 != 0, d7 == 0 */

  847.                     z2 = d5 + d3;

  848. 

  849.                     z5 = MULTIPLY(z2, FIX_1_175875602);

  850.                     tmp1 = MULTIPLY(d5, FIX_1_662939225);

  851.                     z4 = MULTIPLY(-d5, FIX_0_390180644);

  852.                     z2 = MULTIPLY(-z2, FIX_1_387039845);

  853.                     tmp2 = MULTIPLY(d3, FIX_1_111140466);

  854.                     z3 = MULTIPLY(-d3, FIX_1_961570560);

  855. 

  856.                     tmp0 = z3 + z5;

  857.                     tmp1 += z2;

  858.                     tmp2 += z2;

  859.                     tmp3 = z4 + z5;

  860.                 }

  861.             } else {

  862.                 if (d1) {

  863.                     /* d1 != 0, d3 == 0, d5 != 0, d7 == 0 */

  864.                     z4 = d5 + d1;

  865. 

  866.                     z5 = MULTIPLY(z4, FIX_1_175875602);

  867.                     z1 = MULTIPLY(-d1, FIX_0_899976223);

  868.                     tmp3 = MULTIPLY(d1, FIX_0_601344887);

  869.                     tmp1 = MULTIPLY(-d5, FIX_0_509795579);

  870.                     z2 = MULTIPLY(-d5, FIX_2_562915447);

  871.                     z4 = MULTIPLY(z4, FIX_0_785694958);

  872. 

  873.                     tmp0 = z1 + z5;

  874.                     tmp1 += z4;

  875.                     tmp2 = z2 + z5;

  876.                     tmp3 += z4;

  877.                 } else {

  878.                     /* d1 == 0, d3 == 0, d5 != 0, d7 == 0 */

  879.                     tmp0 = MULTIPLY(d5, FIX_1_175875602);

  880.                     tmp1 = MULTIPLY(d5, FIX_0_275899380);

  881.                     tmp2 = MULTIPLY(-d5, FIX_1_387039845);

  882.                     tmp3 = MULTIPLY(d5, FIX_0_785694958);

  883.                 }

  884.             }

  885.         } else {

  886.             if (d3) {

  887.                 if (d1) {

  888.                     /* d1 != 0, d3 != 0, d5 == 0, d7 == 0 */

  889.                     z5 = d1 + d3;

  890.                     tmp3 = MULTIPLY(d1, FIX_0_211164243);

  891.                     tmp2 = MULTIPLY(-d3, FIX_1_451774981);

  892.                     z1 = MULTIPLY(d1, FIX_1_061594337);

  893.                     z2 = MULTIPLY(-d3, FIX_2_172734803);

  894.                     z4 = MULTIPLY(z5, FIX_0_785694958);

  895.                     z5 = MULTIPLY(z5, FIX_1_175875602);

  896. 

  897.                     tmp0 = z1 - z4;

  898.                     tmp1 = z2 + z4;

  899.                     tmp2 += z5;

  900.                     tmp3 += z5;

  901.                 } else {

  902.                     /* d1 == 0, d3 != 0, d5 == 0, d7 == 0 */

  903.                     tmp0 = MULTIPLY(-d3, FIX_0_785694958);

  904.                     tmp1 = MULTIPLY(-d3, FIX_1_387039845);

  905.                     tmp2 = MULTIPLY(-d3, FIX_0_275899380);

  906.                     tmp3 = MULTIPLY(d3, FIX_1_175875602);

  907.                 }

  908.             } else {

  909.                 if (d1) {

  910.                     /* d1 != 0, d3 == 0, d5 == 0, d7 == 0 */

  911.                     tmp0 = MULTIPLY(d1, FIX_0_275899380);

  912.                     tmp1 = MULTIPLY(d1, FIX_0_785694958);

  913.                     tmp2 = MULTIPLY(d1, FIX_1_175875602);

  914.                     tmp3 = MULTIPLY(d1, FIX_1_387039845);

  915.                 } else {

  916.                     /* d1 == 0, d3 == 0, d5 == 0, d7 == 0 */

  917.                     tmp0 = tmp1 = tmp2 = tmp3 = 0;

  918.                 }

  919.             }

  920.         }

  921.     }

  922. 

  923.     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

  924. 

  925.     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp3,

  926.                                            CONST_BITS+PASS1_BITS+3);

  927.     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp10 - tmp3,

  928.                                            CONST_BITS+PASS1_BITS+3);

  929.     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp11 + tmp2,

  930.                                            CONST_BITS+PASS1_BITS+3);

  931.     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(tmp11 - tmp2,

  932.                                            CONST_BITS+PASS1_BITS+3);

  933.     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(tmp12 + tmp1,

  934.                                            CONST_BITS+PASS1_BITS+3);

  935.     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp12 - tmp1,

  936.                                            CONST_BITS+PASS1_BITS+3);

  937.     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp13 + tmp0,

  938.                                            CONST_BITS+PASS1_BITS+3);

  939.     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp13 - tmp0,

  940.                                            CONST_BITS+PASS1_BITS+3);

  941. 

  942.     dataptr++;                  /* advance pointer to next column */

  943.   }

  944. }

  945. 

  946. #undef DCTSIZE

  947. #define DCTSIZE 4

  948. #define DCTSTRIDE 8

  949. 

  950. void j_rev_dct4(DCTBLOCK data)

  951. {

  952.   int32_t tmp0, tmp1, tmp2, tmp3;

  953.   int32_t tmp10, tmp11, tmp12, tmp13;

  954.   int32_t z1;

  955.   int32_t d0, d2, d4, d6;

  956.   register DCTELEM *dataptr;

  957.   int rowctr;

  958. 

  959.   /* Pass 1: process rows. */

  960.   /* Note results are scaled up by sqrt(8) compared to a true IDCT; */

  961.   /* furthermore, we scale the results by 2**PASS1_BITS. */

  962. 

  963.   data[0] += 4;

  964. 

  965.   dataptr = data;

  966. 

  967.   for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {

  968.     /* Due to quantization, we will usually find that many of the input

  969.      * coefficients are zero, especially the AC terms.  We can exploit this

  970.      * by short-circuiting the IDCT calculation for any row in which all

  971.      * the AC terms are zero.  In that case each output is equal to the

  972.      * DC coefficient (with scale factor as needed).

  973.      * With typical images and quantization tables, half or more of the

  974.      * row DCT calculations can be simplified this way.

  975.      */

  976. 

  977.     register int *idataptr = (int*)dataptr;

  978. 

  979.     d0 = dataptr[0];

  980.     d2 = dataptr[1];

  981.     d4 = dataptr[2];

  982.     d6 = dataptr[3];

  983. 

  984.     if ((d2 | d4 | d6) == 0) {

  985.       /* AC terms all zero */

  986.       if (d0) {

  987.           /* Compute a 32 bit value to assign. */

  988.           DCTELEM dcval = (DCTELEM) (d0 << PASS1_BITS);

  989.           register int v = (dcval & 0xffff) | ((dcval << 16) & 0xffff0000);

  990. 

  991.           idataptr[0] = v;

  992.           idataptr[1] = v;

  993.       }

  994. 

  995.       dataptr += DCTSTRIDE;     /* advance pointer to next row */

  996.       continue;

  997.     }

  998. 

  999.     /* Even part: reverse the even part of the forward DCT. */

  1000.     /* The rotator is sqrt(2)*c(-6). */

  1001.     if (d6) {

  1002.             if (d2) {

  1003.                     /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */

  1004.                     z1 = MULTIPLY(d2 + d6, FIX_0_541196100);

  1005.                     tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);

  1006.                     tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);

  1007. 

  1008.                     tmp0 = (d0 + d4) << CONST_BITS;

  1009.                     tmp1 = (d0 - d4) << CONST_BITS;

  1010. 

  1011.                     tmp10 = tmp0 + tmp3;

  1012.                     tmp13 = tmp0 - tmp3;

  1013.                     tmp11 = tmp1 + tmp2;

  1014.                     tmp12 = tmp1 - tmp2;

  1015.             } else {

  1016.                     /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */

  1017.                     tmp2 = MULTIPLY(-d6, FIX_1_306562965);

  1018.                     tmp3 = MULTIPLY(d6, FIX_0_541196100);

  1019. 

  1020.                     tmp0 = (d0 + d4) << CONST_BITS;

  1021.                     tmp1 = (d0 - d4) << CONST_BITS;

  1022. 

  1023.                     tmp10 = tmp0 + tmp3;

  1024.                     tmp13 = tmp0 - tmp3;

  1025.                     tmp11 = tmp1 + tmp2;

  1026.                     tmp12 = tmp1 - tmp2;

  1027.             }

  1028.     } else {

  1029.             if (d2) {

  1030.                     /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */

  1031.                     tmp2 = MULTIPLY(d2, FIX_0_541196100);

  1032.                     tmp3 = MULTIPLY(d2, FIX_1_306562965);

  1033. 

  1034.                     tmp0 = (d0 + d4) << CONST_BITS;

  1035.                     tmp1 = (d0 - d4) << CONST_BITS;

  1036. 

  1037.                     tmp10 = tmp0 + tmp3;

  1038.                     tmp13 = tmp0 - tmp3;

  1039.                     tmp11 = tmp1 + tmp2;

  1040.                     tmp12 = tmp1 - tmp2;

  1041.             } else {

  1042.                     /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */

  1043.                     tmp10 = tmp13 = (d0 + d4) << CONST_BITS;

  1044.                     tmp11 = tmp12 = (d0 - d4) << CONST_BITS;

  1045.             }

  1046.       }

  1047. 

  1048.     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

  1049. 

  1050.     dataptr[0] = (DCTELEM) DESCALE(tmp10, CONST_BITS-PASS1_BITS);

  1051.     dataptr[1] = (DCTELEM) DESCALE(tmp11, CONST_BITS-PASS1_BITS);

  1052.     dataptr[2] = (DCTELEM) DESCALE(tmp12, CONST_BITS-PASS1_BITS);

  1053.     dataptr[3] = (DCTELEM) DESCALE(tmp13, CONST_BITS-PASS1_BITS);

  1054. 

  1055.     dataptr += DCTSTRIDE;       /* advance pointer to next row */

  1056.   }

  1057. 

  1058.   /* Pass 2: process columns. */

  1059.   /* Note that we must descale the results by a factor of 8 == 2**3, */

  1060.   /* and also undo the PASS1_BITS scaling. */

  1061. 

  1062.   dataptr = data;

  1063.   for (rowctr = DCTSIZE-1; rowctr >= 0; rowctr--) {

  1064.     /* Columns of zeroes can be exploited in the same way as we did with rows.

  1065.      * However, the row calculation has created many nonzero AC terms, so the

  1066.      * simplification applies less often (typically 5% to 10% of the time).

  1067.      * On machines with very fast multiplication, it's possible that the

  1068.      * test takes more time than it's worth.  In that case this section

  1069.      * may be commented out.

  1070.      */

  1071. 

  1072.     d0 = dataptr[DCTSTRIDE*0];

  1073.     d2 = dataptr[DCTSTRIDE*1];

  1074.     d4 = dataptr[DCTSTRIDE*2];

  1075.     d6 = dataptr[DCTSTRIDE*3];

  1076. 

  1077.     /* Even part: reverse the even part of the forward DCT. */

  1078.     /* The rotator is sqrt(2)*c(-6). */

  1079.     if (d6) {

  1080.             if (d2) {

  1081.                     /* d0 != 0, d2 != 0, d4 != 0, d6 != 0 */

  1082.                     z1 = MULTIPLY(d2 + d6, FIX_0_541196100);

  1083.                     tmp2 = z1 + MULTIPLY(-d6, FIX_1_847759065);

  1084.                     tmp3 = z1 + MULTIPLY(d2, FIX_0_765366865);

  1085. 

  1086.                     tmp0 = (d0 + d4) << CONST_BITS;

  1087.                     tmp1 = (d0 - d4) << CONST_BITS;

  1088. 

  1089.                     tmp10 = tmp0 + tmp3;

  1090.                     tmp13 = tmp0 - tmp3;

  1091.                     tmp11 = tmp1 + tmp2;

  1092.                     tmp12 = tmp1 - tmp2;

  1093.             } else {

  1094.                     /* d0 != 0, d2 == 0, d4 != 0, d6 != 0 */

  1095.                     tmp2 = MULTIPLY(-d6, FIX_1_306562965);

  1096.                     tmp3 = MULTIPLY(d6, FIX_0_541196100);

  1097. 

  1098.                     tmp0 = (d0 + d4) << CONST_BITS;

  1099.                     tmp1 = (d0 - d4) << CONST_BITS;

  1100. 

  1101.                     tmp10 = tmp0 + tmp3;

  1102.                     tmp13 = tmp0 - tmp3;

  1103.                     tmp11 = tmp1 + tmp2;

  1104.                     tmp12 = tmp1 - tmp2;

  1105.             }

  1106.     } else {

  1107.             if (d2) {

  1108.                     /* d0 != 0, d2 != 0, d4 != 0, d6 == 0 */

  1109.                     tmp2 = MULTIPLY(d2, FIX_0_541196100);

  1110.                     tmp3 = MULTIPLY(d2, FIX_1_306562965);

  1111. 

  1112.                     tmp0 = (d0 + d4) << CONST_BITS;

  1113.                     tmp1 = (d0 - d4) << CONST_BITS;

  1114. 

  1115.                     tmp10 = tmp0 + tmp3;

  1116.                     tmp13 = tmp0 - tmp3;

  1117.                     tmp11 = tmp1 + tmp2;

  1118.                     tmp12 = tmp1 - tmp2;

  1119.             } else {

  1120.                     /* d0 != 0, d2 == 0, d4 != 0, d6 == 0 */

  1121.                     tmp10 = tmp13 = (d0 + d4) << CONST_BITS;

  1122.                     tmp11 = tmp12 = (d0 - d4) << CONST_BITS;

  1123.             }

  1124.     }

  1125. 

  1126.     /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

  1127. 

  1128.     dataptr[DCTSTRIDE*0] = tmp10 >> (CONST_BITS+PASS1_BITS+3);

  1129.     dataptr[DCTSTRIDE*1] = tmp11 >> (CONST_BITS+PASS1_BITS+3);

  1130.     dataptr[DCTSTRIDE*2] = tmp12 >> (CONST_BITS+PASS1_BITS+3);

  1131.     dataptr[DCTSTRIDE*3] = tmp13 >> (CONST_BITS+PASS1_BITS+3);

  1132. 

  1133.     dataptr++;                  /* advance pointer to next column */

  1134.   }

  1135. }

  1136. 

  1137. void j_rev_dct2(DCTBLOCK data){

  1138.   int d00, d01, d10, d11;

  1139. 

  1140.   data[0] += 4;

  1141.   d00 = data[0+0*DCTSTRIDE] + data[1+0*DCTSTRIDE];

  1142.   d01 = data[0+0*DCTSTRIDE] - data[1+0*DCTSTRIDE];

  1143.   d10 = data[0+1*DCTSTRIDE] + data[1+1*DCTSTRIDE];

  1144.   d11 = data[0+1*DCTSTRIDE] - data[1+1*DCTSTRIDE];

  1145. 

  1146.   data[0+0*DCTSTRIDE]= (d00 + d10)>>3;

  1147.   data[1+0*DCTSTRIDE]= (d01 + d11)>>3;

  1148.   data[0+1*DCTSTRIDE]= (d00 - d10)>>3;

  1149.   data[1+1*DCTSTRIDE]= (d01 - d11)>>3;

  1150. }

  1151. 

  1152. void j_rev_dct1(DCTBLOCK data){

  1153.   data[0] = (data[0] + 4)>>3;

  1154. }

  1155. 

  1156. #undef FIX

  1157. #undef CONST_BITS