You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.

298 lines
11KB

  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. * @file jfdctint.c
  27. * Independent JPEG Group's slow & accurate dct.
  28. */
  29. #include <stdlib.h>
  30. #include <stdio.h>
  31. #include "common.h"
  32. #include "dsputil.h"
  33. #define SHIFT_TEMPS
  34. #define DCTSIZE 8
  35. #define BITS_IN_JSAMPLE 8
  36. #define GLOBAL(x) x
  37. #define RIGHT_SHIFT(x, n) ((x) >> (n))
  38. #define MULTIPLY16C16(var,const) ((var)*(const))
  39. #if 1 //def USE_ACCURATE_ROUNDING
  40. #define DESCALE(x,n) RIGHT_SHIFT((x) + (1 << ((n) - 1)), n)
  41. #else
  42. #define DESCALE(x,n) RIGHT_SHIFT(x, n)
  43. #endif
  44. /*
  45. * This module is specialized to the case DCTSIZE = 8.
  46. */
  47. #if DCTSIZE != 8
  48. Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
  49. #endif
  50. /*
  51. * The poop on this scaling stuff is as follows:
  52. *
  53. * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
  54. * larger than the true DCT outputs. The final outputs are therefore
  55. * a factor of N larger than desired; since N=8 this can be cured by
  56. * a simple right shift at the end of the algorithm. The advantage of
  57. * this arrangement is that we save two multiplications per 1-D DCT,
  58. * because the y0 and y4 outputs need not be divided by sqrt(N).
  59. * In the IJG code, this factor of 8 is removed by the quantization step
  60. * (in jcdctmgr.c), NOT in this module.
  61. *
  62. * We have to do addition and subtraction of the integer inputs, which
  63. * is no problem, and multiplication by fractional constants, which is
  64. * a problem to do in integer arithmetic. We multiply all the constants
  65. * by CONST_SCALE and convert them to integer constants (thus retaining
  66. * CONST_BITS bits of precision in the constants). After doing a
  67. * multiplication we have to divide the product by CONST_SCALE, with proper
  68. * rounding, to produce the correct output. This division can be done
  69. * cheaply as a right shift of CONST_BITS bits. We postpone shifting
  70. * as long as possible so that partial sums can be added together with
  71. * full fractional precision.
  72. *
  73. * The outputs of the first pass are scaled up by PASS1_BITS bits so that
  74. * they are represented to better-than-integral precision. These outputs
  75. * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
  76. * with the recommended scaling. (For 12-bit sample data, the intermediate
  77. * array is int32_t anyway.)
  78. *
  79. * To avoid overflow of the 32-bit intermediate results in pass 2, we must
  80. * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
  81. * shows that the values given below are the most effective.
  82. */
  83. #if BITS_IN_JSAMPLE == 8
  84. #define CONST_BITS 13
  85. #define PASS1_BITS 4 /* set this to 2 if 16x16 multiplies are faster */
  86. #else
  87. #define CONST_BITS 13
  88. #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
  89. #endif
  90. /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
  91. * causing a lot of useless floating-point operations at run time.
  92. * To get around this we use the following pre-calculated constants.
  93. * If you change CONST_BITS you may want to add appropriate values.
  94. * (With a reasonable C compiler, you can just rely on the FIX() macro...)
  95. */
  96. #if CONST_BITS == 13
  97. #define FIX_0_298631336 ((int32_t) 2446) /* FIX(0.298631336) */
  98. #define FIX_0_390180644 ((int32_t) 3196) /* FIX(0.390180644) */
  99. #define FIX_0_541196100 ((int32_t) 4433) /* FIX(0.541196100) */
  100. #define FIX_0_765366865 ((int32_t) 6270) /* FIX(0.765366865) */
  101. #define FIX_0_899976223 ((int32_t) 7373) /* FIX(0.899976223) */
  102. #define FIX_1_175875602 ((int32_t) 9633) /* FIX(1.175875602) */
  103. #define FIX_1_501321110 ((int32_t) 12299) /* FIX(1.501321110) */
  104. #define FIX_1_847759065 ((int32_t) 15137) /* FIX(1.847759065) */
  105. #define FIX_1_961570560 ((int32_t) 16069) /* FIX(1.961570560) */
  106. #define FIX_2_053119869 ((int32_t) 16819) /* FIX(2.053119869) */
  107. #define FIX_2_562915447 ((int32_t) 20995) /* FIX(2.562915447) */
  108. #define FIX_3_072711026 ((int32_t) 25172) /* FIX(3.072711026) */
  109. #else
  110. #define FIX_0_298631336 FIX(0.298631336)
  111. #define FIX_0_390180644 FIX(0.390180644)
  112. #define FIX_0_541196100 FIX(0.541196100)
  113. #define FIX_0_765366865 FIX(0.765366865)
  114. #define FIX_0_899976223 FIX(0.899976223)
  115. #define FIX_1_175875602 FIX(1.175875602)
  116. #define FIX_1_501321110 FIX(1.501321110)
  117. #define FIX_1_847759065 FIX(1.847759065)
  118. #define FIX_1_961570560 FIX(1.961570560)
  119. #define FIX_2_053119869 FIX(2.053119869)
  120. #define FIX_2_562915447 FIX(2.562915447)
  121. #define FIX_3_072711026 FIX(3.072711026)
  122. #endif
  123. /* Multiply an int32_t variable by an int32_t constant to yield an int32_t result.
  124. * For 8-bit samples with the recommended scaling, all the variable
  125. * and constant values involved are no more than 16 bits wide, so a
  126. * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
  127. * For 12-bit samples, a full 32-bit multiplication will be needed.
  128. */
  129. #if BITS_IN_JSAMPLE == 8 && CONST_BITS<=13 && PASS1_BITS<=2
  130. #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
  131. #else
  132. #define MULTIPLY(var,const) ((var) * (const))
  133. #endif
  134. /*
  135. * Perform the forward DCT on one block of samples.
  136. */
  137. GLOBAL(void)
  138. ff_jpeg_fdct_islow (DCTELEM * data)
  139. {
  140. int32_t tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  141. int32_t tmp10, tmp11, tmp12, tmp13;
  142. int32_t z1, z2, z3, z4, z5;
  143. DCTELEM *dataptr;
  144. int ctr;
  145. SHIFT_TEMPS
  146. /* Pass 1: process rows. */
  147. /* Note results are scaled up by sqrt(8) compared to a true DCT; */
  148. /* furthermore, we scale the results by 2**PASS1_BITS. */
  149. dataptr = data;
  150. for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
  151. tmp0 = dataptr[0] + dataptr[7];
  152. tmp7 = dataptr[0] - dataptr[7];
  153. tmp1 = dataptr[1] + dataptr[6];
  154. tmp6 = dataptr[1] - dataptr[6];
  155. tmp2 = dataptr[2] + dataptr[5];
  156. tmp5 = dataptr[2] - dataptr[5];
  157. tmp3 = dataptr[3] + dataptr[4];
  158. tmp4 = dataptr[3] - dataptr[4];
  159. /* Even part per LL&M figure 1 --- note that published figure is faulty;
  160. * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
  161. */
  162. tmp10 = tmp0 + tmp3;
  163. tmp13 = tmp0 - tmp3;
  164. tmp11 = tmp1 + tmp2;
  165. tmp12 = tmp1 - tmp2;
  166. dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
  167. dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
  168. z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
  169. dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
  170. CONST_BITS-PASS1_BITS);
  171. dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
  172. CONST_BITS-PASS1_BITS);
  173. /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
  174. * cK represents cos(K*pi/16).
  175. * i0..i3 in the paper are tmp4..tmp7 here.
  176. */
  177. z1 = tmp4 + tmp7;
  178. z2 = tmp5 + tmp6;
  179. z3 = tmp4 + tmp6;
  180. z4 = tmp5 + tmp7;
  181. z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
  182. tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
  183. tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
  184. tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
  185. tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
  186. z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
  187. z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
  188. z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
  189. z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
  190. z3 += z5;
  191. z4 += z5;
  192. dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
  193. dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
  194. dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
  195. dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
  196. dataptr += DCTSIZE; /* advance pointer to next row */
  197. }
  198. /* Pass 2: process columns.
  199. * We remove the PASS1_BITS scaling, but leave the results scaled up
  200. * by an overall factor of 8.
  201. */
  202. dataptr = data;
  203. for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
  204. tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
  205. tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
  206. tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
  207. tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
  208. tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
  209. tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
  210. tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
  211. tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
  212. /* Even part per LL&M figure 1 --- note that published figure is faulty;
  213. * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
  214. */
  215. tmp10 = tmp0 + tmp3;
  216. tmp13 = tmp0 - tmp3;
  217. tmp11 = tmp1 + tmp2;
  218. tmp12 = tmp1 - tmp2;
  219. dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
  220. dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
  221. z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
  222. dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
  223. CONST_BITS+PASS1_BITS);
  224. dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
  225. CONST_BITS+PASS1_BITS);
  226. /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
  227. * cK represents cos(K*pi/16).
  228. * i0..i3 in the paper are tmp4..tmp7 here.
  229. */
  230. z1 = tmp4 + tmp7;
  231. z2 = tmp5 + tmp6;
  232. z3 = tmp4 + tmp6;
  233. z4 = tmp5 + tmp7;
  234. z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
  235. tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
  236. tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
  237. tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
  238. tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
  239. z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
  240. z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
  241. z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
  242. z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
  243. z3 += z5;
  244. z4 += z5;
  245. dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
  246. CONST_BITS+PASS1_BITS);
  247. dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
  248. CONST_BITS+PASS1_BITS);
  249. dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
  250. CONST_BITS+PASS1_BITS);
  251. dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
  252. CONST_BITS+PASS1_BITS);
  253. dataptr++; /* advance pointer to next column */
  254. }
  255. }