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FFmpeg/libavcodec/jfdctint.c

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  1. /*

  2.  * jfdctint.c

  3.  *

  4.  * Copyright (C) 1991-1996, Thomas G. Lane.

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

  6.  * For conditions of distribution and use, see the accompanying README file.

  7.  *

  8.  * This file contains a slow-but-accurate integer implementation of the

  9.  * forward DCT (Discrete Cosine Transform).

  10.  *

  11.  * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT

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

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

  14.  *

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

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

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

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

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

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

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

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

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

  24.  */

  25. 

  26. /**

  27.  * @file jfdctint.c

  28.  * Independent JPEG Group's slow & accurate dct.

  29.  */

  30.  

  31. #include <stdlib.h>

  32. #include <stdio.h>

  33. #include "common.h"

  34. #include "dsputil.h"

  35. 

  36. #define SHIFT_TEMPS

  37. #define DCTSIZE 8

  38. #define BITS_IN_JSAMPLE 8

  39. #define GLOBAL(x) x

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

  41. #define MULTIPLY16C16(var,const) ((var)*(const))

  42. 

  43. #if 1 //def USE_ACCURATE_ROUNDING

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

  45. #else

  46. #define DESCALE(x,n)  RIGHT_SHIFT(x, n)

  47. #endif

  48. 

  49. 

  50. /*

  51.  * This module is specialized to the case DCTSIZE = 8.

  52.  */

  53. 

  54. #if DCTSIZE != 8

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

  56. #endif

  57. 

  58. 

  59. /*

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

  61.  *

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

  63.  * larger than the true DCT outputs.  The final outputs are therefore

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

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

  66.  * this arrangement is that we save two multiplications per 1-D DCT,

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

  68.  * In the IJG code, this factor of 8 is removed by the quantization step

  69.  * (in jcdctmgr.c), NOT in this module.

  70.  *

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

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

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

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

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

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

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

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

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

  80.  * full fractional precision.

  81.  *

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

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

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

  85.  * with the recommended scaling.  (For 12-bit sample data, the intermediate

  86.  * array is int32_t anyway.)

  87.  *

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

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

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

  91.  */

  92. 

  93. #if BITS_IN_JSAMPLE == 8

  94. #define CONST_BITS  13

  95. #define PASS1_BITS  4		/* set this to 2 if 16x16 multiplies are faster */

  96. #else

  97. #define CONST_BITS  13

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

  99. #endif

  100. 

  101. /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus

  102.  * causing a lot of useless floating-point operations at run time.

  103.  * To get around this we use the following pre-calculated constants.

  104.  * If you change CONST_BITS you may want to add appropriate values.

  105.  * (With a reasonable C compiler, you can just rely on the FIX() macro...)

  106.  */

  107. 

  108. #if CONST_BITS == 13

  109. #define FIX_0_298631336  ((int32_t)  2446)	/* FIX(0.298631336) */

  110. #define FIX_0_390180644  ((int32_t)  3196)	/* FIX(0.390180644) */

  111. #define FIX_0_541196100  ((int32_t)  4433)	/* FIX(0.541196100) */

  112. #define FIX_0_765366865  ((int32_t)  6270)	/* FIX(0.765366865) */

  113. #define FIX_0_899976223  ((int32_t)  7373)	/* FIX(0.899976223) */

  114. #define FIX_1_175875602  ((int32_t)  9633)	/* FIX(1.175875602) */

  115. #define FIX_1_501321110  ((int32_t)  12299)	/* FIX(1.501321110) */

  116. #define FIX_1_847759065  ((int32_t)  15137)	/* FIX(1.847759065) */

  117. #define FIX_1_961570560  ((int32_t)  16069)	/* FIX(1.961570560) */

  118. #define FIX_2_053119869  ((int32_t)  16819)	/* FIX(2.053119869) */

  119. #define FIX_2_562915447  ((int32_t)  20995)	/* FIX(2.562915447) */

  120. #define FIX_3_072711026  ((int32_t)  25172)	/* FIX(3.072711026) */

  121. #else

  122. #define FIX_0_298631336  FIX(0.298631336)

  123. #define FIX_0_390180644  FIX(0.390180644)

  124. #define FIX_0_541196100  FIX(0.541196100)

  125. #define FIX_0_765366865  FIX(0.765366865)

  126. #define FIX_0_899976223  FIX(0.899976223)

  127. #define FIX_1_175875602  FIX(1.175875602)

  128. #define FIX_1_501321110  FIX(1.501321110)

  129. #define FIX_1_847759065  FIX(1.847759065)

  130. #define FIX_1_961570560  FIX(1.961570560)

  131. #define FIX_2_053119869  FIX(2.053119869)

  132. #define FIX_2_562915447  FIX(2.562915447)

  133. #define FIX_3_072711026  FIX(3.072711026)

  134. #endif

  135. 

  136. 

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

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

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

  140.  * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.

  141.  * For 12-bit samples, a full 32-bit multiplication will be needed.

  142.  */

  143. 

  144. #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2

  145. #define MULTIPLY(var,const)  MULTIPLY16C16(var,const)

  146. #else

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

  148. #endif

  149. 

  150. 

  151. static always_inline void row_fdct(DCTELEM * data){

  152.   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

  153.   int_fast32_t tmp10, tmp11, tmp12, tmp13;

  154.   int_fast32_t z1, z2, z3, z4, z5;

  155.   DCTELEM *dataptr;

  156.   int ctr;

  157.   SHIFT_TEMPS

  158. 

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

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

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

  162. 

  163.   dataptr = data;

  164.   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {

  165.     tmp0 = dataptr[0] + dataptr[7];

  166.     tmp7 = dataptr[0] - dataptr[7];

  167.     tmp1 = dataptr[1] + dataptr[6];

  168.     tmp6 = dataptr[1] - dataptr[6];

  169.     tmp2 = dataptr[2] + dataptr[5];

  170.     tmp5 = dataptr[2] - dataptr[5];

  171.     tmp3 = dataptr[3] + dataptr[4];

  172.     tmp4 = dataptr[3] - dataptr[4];

  173.     

  174.     /* Even part per LL&M figure 1 --- note that published figure is faulty;

  175.      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".

  176.      */

  177.     

  178.     tmp10 = tmp0 + tmp3;

  179.     tmp13 = tmp0 - tmp3;

  180.     tmp11 = tmp1 + tmp2;

  181.     tmp12 = tmp1 - tmp2;

  182.     

  183.     dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);

  184.     dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);

  185.     

  186.     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);

  187.     dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),

  188. 				   CONST_BITS-PASS1_BITS);

  189.     dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),

  190. 				   CONST_BITS-PASS1_BITS);

  191.     

  192.     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).

  193.      * cK represents cos(K*pi/16).

  194.      * i0..i3 in the paper are tmp4..tmp7 here.

  195.      */

  196.     

  197.     z1 = tmp4 + tmp7;

  198.     z2 = tmp5 + tmp6;

  199.     z3 = tmp4 + tmp6;

  200.     z4 = tmp5 + tmp7;

  201.     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

  202.     

  203.     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */

  204.     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */

  205.     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */

  206.     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */

  207.     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */

  208.     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */

  209.     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */

  210.     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */

  211.     

  212.     z3 += z5;

  213.     z4 += z5;

  214.     

  215.     dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);

  216.     dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);

  217.     dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);

  218.     dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);

  219.     

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

  221.   }

  222. }

  223. 

  224. /*

  225.  * Perform the forward DCT on one block of samples.

  226.  */

  227. 

  228. GLOBAL(void)

  229. ff_jpeg_fdct_islow (DCTELEM * data)

  230. {

  231.   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

  232.   int_fast32_t tmp10, tmp11, tmp12, tmp13;

  233.   int_fast32_t z1, z2, z3, z4, z5;

  234.   DCTELEM *dataptr;

  235.   int ctr;

  236.   SHIFT_TEMPS

  237. 

  238.   row_fdct(data);

  239. 

  240.   /* Pass 2: process columns.

  241.    * We remove the PASS1_BITS scaling, but leave the results scaled up

  242.    * by an overall factor of 8.

  243.    */

  244. 

  245.   dataptr = data;

  246.   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {

  247.     tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];

  248.     tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];

  249.     tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];

  250.     tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];

  251.     tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];

  252.     tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];

  253.     tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];

  254.     tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];

  255.     

  256.     /* Even part per LL&M figure 1 --- note that published figure is faulty;

  257.      * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".

  258.      */

  259.     

  260.     tmp10 = tmp0 + tmp3;

  261.     tmp13 = tmp0 - tmp3;

  262.     tmp11 = tmp1 + tmp2;

  263.     tmp12 = tmp1 - tmp2;

  264.     

  265.     dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);

  266.     dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);

  267.     

  268.     z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);

  269.     dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),

  270. 					   CONST_BITS+PASS1_BITS);

  271.     dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),

  272. 					   CONST_BITS+PASS1_BITS);

  273.     

  274.     /* Odd part per figure 8 --- note paper omits factor of sqrt(2).

  275.      * cK represents cos(K*pi/16).

  276.      * i0..i3 in the paper are tmp4..tmp7 here.

  277.      */

  278.     

  279.     z1 = tmp4 + tmp7;

  280.     z2 = tmp5 + tmp6;

  281.     z3 = tmp4 + tmp6;

  282.     z4 = tmp5 + tmp7;

  283.     z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

  284.     

  285.     tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */

  286.     tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */

  287.     tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */

  288.     tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */

  289.     z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */

  290.     z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */

  291.     z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */

  292.     z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */

  293.     

  294.     z3 += z5;

  295.     z4 += z5;

  296.     

  297.     dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,

  298. 					   CONST_BITS+PASS1_BITS);

  299.     dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,

  300. 					   CONST_BITS+PASS1_BITS);

  301.     dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,

  302. 					   CONST_BITS+PASS1_BITS);

  303.     dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,

  304. 					   CONST_BITS+PASS1_BITS);

  305.     

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

  307.   }

  308. }

  309. 

  310. /*

  311.  * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT

  312.  * on the rows and then, instead of doing even and odd, part on the colums

  313.  * you do even part two times.

  314.  */

  315. GLOBAL(void)

  316. ff_fdct248_islow (DCTELEM * data)

  317. {

  318.   int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;

  319.   int_fast32_t tmp10, tmp11, tmp12, tmp13;

  320.   int_fast32_t z1;

  321.   DCTELEM *dataptr;

  322.   int ctr;

  323.   SHIFT_TEMPS

  324. 

  325.   row_fdct(data);

  326. 

  327.   /* Pass 2: process columns.

  328.    * We remove the PASS1_BITS scaling, but leave the results scaled up

  329.    * by an overall factor of 8.

  330.    */

  331. 

  332.   dataptr = data;

  333.   for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {

  334.      tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1];

  335.      tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];

  336.      tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5];

  337.      tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7];

  338.      tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1];

  339.      tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];

  340.      tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5];

  341.      tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7];

  342.       

  343.      tmp10 = tmp0 + tmp3;

  344.      tmp11 = tmp1 + tmp2;

  345.      tmp12 = tmp1 - tmp2;

  346.      tmp13 = tmp0 - tmp3;

  347.      

  348.      dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);

  349.      dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);

  350.      

  351.      z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);

  352.      dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),

  353. 				            CONST_BITS+PASS1_BITS);

  354.      dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),

  355. 				            CONST_BITS+PASS1_BITS);

  356. 

  357.      tmp10 = tmp4 + tmp7;

  358.      tmp11 = tmp5 + tmp6;

  359.      tmp12 = tmp5 - tmp6;

  360.      tmp13 = tmp4 - tmp7;

  361. 

  362.      dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);

  363.      dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);

  364.      

  365.      z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);

  366.      dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),

  367. 				            CONST_BITS+PASS1_BITS);

  368.      dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),

  369. 				            CONST_BITS+PASS1_BITS);

  370.     

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

  372.   }

  373. }