jfdctint.c 16 KB

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  1. /*
  2. * jfdctint.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) 1991-1996, 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 a slow-but-accurate integer implementation of the
  42. * forward DCT (Discrete Cosine Transform).
  43. *
  44. * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
  45. * on each column. Direct algorithms are also available, but they are
  46. * much more complex and seem not to be any faster when reduced to code.
  47. *
  48. * This implementation is based on an algorithm described in
  49. * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
  50. * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
  51. * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
  52. * The primary algorithm described there uses 11 multiplies and 29 adds.
  53. * We use their alternate method with 12 multiplies and 32 adds.
  54. * The advantage of this method is that no data path contains more than one
  55. * multiplication; this allows a very simple and accurate implementation in
  56. * scaled fixed-point arithmetic, with a minimal number of shifts.
  57. */
  58. /**
  59. * @file libavcodec/jfdctint.c
  60. * Independent JPEG Group's slow & accurate dct.
  61. */
  62. #include <stdlib.h>
  63. #include <stdio.h>
  64. #include "libavutil/common.h"
  65. #include "dsputil.h"
  66. #define SHIFT_TEMPS
  67. #define DCTSIZE 8
  68. #define BITS_IN_JSAMPLE 8
  69. #define GLOBAL(x) x
  70. #define RIGHT_SHIFT(x, n) ((x) >> (n))
  71. #define MULTIPLY16C16(var,const) ((var)*(const))
  72. #if 1 //def USE_ACCURATE_ROUNDING
  73. #define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
  74. #else
  75. #define DESCALE(x,n) RIGHT_SHIFT(x, n)
  76. #endif
  77. /*
  78. * This module is specialized to the case DCTSIZE = 8.
  79. */
  80. #if DCTSIZE != 8
  81. Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  82. #endif
  83. /*
  84. * The poop on this scaling stuff is as follows:
  85. *
  86. * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
  87. * larger than the true DCT outputs. The final outputs are therefore
  88. * a factor of N larger than desired; since N=8 this can be cured by
  89. * a simple right shift at the end of the algorithm. The advantage of
  90. * this arrangement is that we save two multiplications per 1-D DCT,
  91. * because the y0 and y4 outputs need not be divided by sqrt(N).
  92. * In the IJG code, this factor of 8 is removed by the quantization step
  93. * (in jcdctmgr.c), NOT in this module.
  94. *
  95. * We have to do addition and subtraction of the integer inputs, which
  96. * is no problem, and multiplication by fractional constants, which is
  97. * a problem to do in integer arithmetic. We multiply all the constants
  98. * by CONST_SCALE and convert them to integer constants (thus retaining
  99. * CONST_BITS bits of precision in the constants). After doing a
  100. * multiplication we have to divide the product by CONST_SCALE, with proper
  101. * rounding, to produce the correct output. This division can be done
  102. * cheaply as a right shift of CONST_BITS bits. We postpone shifting
  103. * as long as possible so that partial sums can be added together with
  104. * full fractional precision.
  105. *
  106. * The outputs of the first pass are scaled up by PASS1_BITS bits so that
  107. * they are represented to better-than-integral precision. These outputs
  108. * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
  109. * with the recommended scaling. (For 12-bit sample data, the intermediate
  110. * array is int32_t anyway.)
  111. *
  112. * To avoid overflow of the 32-bit intermediate results in pass 2, we must
  113. * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
  114. * shows that the values given below are the most effective.
  115. */
  116. #if BITS_IN_JSAMPLE == 8
  117. #define CONST_BITS 13
  118. #define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */
  119. #else
  120. #define CONST_BITS 13
  121. #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
  122. #endif
  123. /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
  124. * causing a lot of useless floating-point operations at run time.
  125. * To get around this we use the following pre-calculated constants.
  126. * If you change CONST_BITS you may want to add appropriate values.
  127. * (With a reasonable C compiler, you can just rely on the FIX() macro...)
  128. */
  129. #if CONST_BITS == 13
  130. #define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */
  131. #define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */
  132. #define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */
  133. #define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */
  134. #define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */
  135. #define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */
  136. #define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */
  137. #define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */
  138. #define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */
  139. #define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */
  140. #define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */
  141. #define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */
  142. #else
  143. #define FIX_0_298631336 FIX(0.298631336)
  144. #define FIX_0_390180644 FIX(0.390180644)
  145. #define FIX_0_541196100 FIX(0.541196100)
  146. #define FIX_0_765366865 FIX(0.765366865)
  147. #define FIX_0_899976223 FIX(0.899976223)
  148. #define FIX_1_175875602 FIX(1.175875602)
  149. #define FIX_1_501321110 FIX(1.501321110)
  150. #define FIX_1_847759065 FIX(1.847759065)
  151. #define FIX_1_961570560 FIX(1.961570560)
  152. #define FIX_2_053119869 FIX(2.053119869)
  153. #define FIX_2_562915447 FIX(2.562915447)
  154. #define FIX_3_072711026 FIX(3.072711026)
  155. #endif
  156. /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
  157. * For 8-bit samples with the recommended scaling, all the variable
  158. * and constant values involved are no more than 16 bits wide, so a
  159. * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
  160. * For 12-bit samples, a full 32-bit multiplication will be needed.
  161. */
  162. #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
  163. #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
  164. #else
  165. #define MULTIPLY(var,const) ((var) * (const))
  166. #endif
  167. static av_always_inline void row_fdct(DCTELEM * data){
  168. int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  169. int_fast32_t tmp10, tmp11, tmp12, tmp13;
  170. int_fast32_t z1, z2, z3, z4, z5;
  171. DCTELEM *dataptr;
  172. int ctr;
  173. SHIFT_TEMPS
  174. /* Pass 1: process rows. */
  175. /* Note results are scaled up by sqrt(8) compared to a true DCT; */
  176. /* furthermore, we scale the results by 2**PASS1_BITS. */
  177. dataptr = data;
  178. for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
  179. tmp0 = dataptr[0] + dataptr[7];
  180. tmp7 = dataptr[0] - dataptr[7];
  181. tmp1 = dataptr[1] + dataptr[6];
  182. tmp6 = dataptr[1] - dataptr[6];
  183. tmp2 = dataptr[2] + dataptr[5];
  184. tmp5 = dataptr[2] - dataptr[5];
  185. tmp3 = dataptr[3] + dataptr[4];
  186. tmp4 = dataptr[3] - dataptr[4];
  187. /* Even part per LL&M figure 1 --- note that published figure is faulty;
  188. * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
  189. */
  190. tmp10 = tmp0 + tmp3;
  191. tmp13 = tmp0 - tmp3;
  192. tmp11 = tmp1 + tmp2;
  193. tmp12 = tmp1 - tmp2;
  194. dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
  195. dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
  196. z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
  197. dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
  198. CONST_BITS-PASS1_BITS);
  199. dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
  200. CONST_BITS-PASS1_BITS);
  201. /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
  202. * cK represents cos(K*pi/16).
  203. * i0..i3 in the paper are tmp4..tmp7 here.
  204. */
  205. z1 = tmp4 + tmp7;
  206. z2 = tmp5 + tmp6;
  207. z3 = tmp4 + tmp6;
  208. z4 = tmp5 + tmp7;
  209. z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
  210. tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
  211. tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
  212. tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
  213. tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
  214. z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
  215. z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
  216. z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
  217. z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
  218. z3 += z5;
  219. z4 += z5;
  220. dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
  221. dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
  222. dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
  223. dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
  224. dataptr += DCTSIZE; /* advance pointer to next row */
  225. }
  226. }
  227. /*
  228. * Perform the forward DCT on one block of samples.
  229. */
  230. GLOBAL(void)
  231. ff_jpeg_fdct_islow (DCTELEM * data)
  232. {
  233. int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  234. int_fast32_t tmp10, tmp11, tmp12, tmp13;
  235. int_fast32_t z1, z2, z3, z4, z5;
  236. DCTELEM *dataptr;
  237. int ctr;
  238. SHIFT_TEMPS
  239. row_fdct(data);
  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. dataptr = data;
  245. for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
  246. tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
  247. tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
  248. tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
  249. tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
  250. tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
  251. tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
  252. tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
  253. tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
  254. /* Even part per LL&M figure 1 --- note that published figure is faulty;
  255. * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
  256. */
  257. tmp10 = tmp0 + tmp3;
  258. tmp13 = tmp0 - tmp3;
  259. tmp11 = tmp1 + tmp2;
  260. tmp12 = tmp1 - tmp2;
  261. dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
  262. dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
  263. z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
  264. dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
  265. CONST_BITS+PASS1_BITS);
  266. dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
  267. CONST_BITS+PASS1_BITS);
  268. /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
  269. * cK represents cos(K*pi/16).
  270. * i0..i3 in the paper are tmp4..tmp7 here.
  271. */
  272. z1 = tmp4 + tmp7;
  273. z2 = tmp5 + tmp6;
  274. z3 = tmp4 + tmp6;
  275. z4 = tmp5 + tmp7;
  276. z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
  277. tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
  278. tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
  279. tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
  280. tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
  281. z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
  282. z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
  283. z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
  284. z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
  285. z3 += z5;
  286. z4 += z5;
  287. dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
  288. CONST_BITS+PASS1_BITS);
  289. dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
  290. CONST_BITS+PASS1_BITS);
  291. dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
  292. CONST_BITS+PASS1_BITS);
  293. dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
  294. CONST_BITS+PASS1_BITS);
  295. dataptr++; /* advance pointer to next column */
  296. }
  297. }
  298. /*
  299. * The secret of DCT2-4-8 is really simple -- you do the usual 1-DCT
  300. * on the rows and then, instead of doing even and odd, part on the colums
  301. * you do even part two times.
  302. */
  303. GLOBAL(void)
  304. ff_fdct248_islow (DCTELEM * data)
  305. {
  306. int_fast32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  307. int_fast32_t tmp10, tmp11, tmp12, tmp13;
  308. int_fast32_t z1;
  309. DCTELEM *dataptr;
  310. int ctr;
  311. SHIFT_TEMPS
  312. row_fdct(data);
  313. /* Pass 2: process columns.
  314. * We remove the PASS1_BITS scaling, but leave the results scaled up
  315. * by an overall factor of 8.
  316. */
  317. dataptr = data;
  318. for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
  319. tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*1];
  320. tmp1 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*3];
  321. tmp2 = dataptr[DCTSIZE*4] + dataptr[DCTSIZE*5];
  322. tmp3 = dataptr[DCTSIZE*6] + dataptr[DCTSIZE*7];
  323. tmp4 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*1];
  324. tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*3];
  325. tmp6 = dataptr[DCTSIZE*4] - dataptr[DCTSIZE*5];
  326. tmp7 = dataptr[DCTSIZE*6] - dataptr[DCTSIZE*7];
  327. tmp10 = tmp0 + tmp3;
  328. tmp11 = tmp1 + tmp2;
  329. tmp12 = tmp1 - tmp2;
  330. tmp13 = tmp0 - tmp3;
  331. dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
  332. dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
  333. z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
  334. dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
  335. CONST_BITS+PASS1_BITS);
  336. dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
  337. CONST_BITS+PASS1_BITS);
  338. tmp10 = tmp4 + tmp7;
  339. tmp11 = tmp5 + tmp6;
  340. tmp12 = tmp5 - tmp6;
  341. tmp13 = tmp4 - tmp7;
  342. dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
  343. dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
  344. z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
  345. dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
  346. CONST_BITS+PASS1_BITS);
  347. dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
  348. CONST_BITS+PASS1_BITS);
  349. dataptr++; /* advance pointer to next column */
  350. }
  351. }