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  1. /*
  2. * jfdctfst.c
  3. *
  4. * Copyright (C) 1994-1996, 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 fast, not so 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 Arai, Agui, and Nakajima's algorithm for
  16. * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
  17. * Japanese, but the algorithm is described in the Pennebaker & Mitchell
  18. * JPEG textbook (see REFERENCES section in file README). The following code
  19. * is based directly on figure 4-8 in P&M.
  20. * While an 8-point DCT cannot be done in less than 11 multiplies, it is
  21. * possible to arrange the computation so that many of the multiplies are
  22. * simple scalings of the final outputs. These multiplies can then be
  23. * folded into the multiplications or divisions by the JPEG quantization
  24. * table entries. The AA&N method leaves only 5 multiplies and 29 adds
  25. * to be done in the DCT itself.
  26. * The primary disadvantage of this method is that with fixed-point math,
  27. * accuracy is lost due to imprecise representation of the scaled
  28. * quantization values. The smaller the quantization table entry, the less
  29. * precise the scaled value, so this implementation does worse with high-
  30. * quality-setting files than with low-quality ones.
  31. */
  32. /**
  33. * @file jfdctfst.c
  34. * Independent JPEG Group's fast AAN dct.
  35. */
  36. #include <stdlib.h>
  37. #include <stdio.h>
  38. #include "common.h"
  39. #include "dsputil.h"
  40. #define DCTSIZE 8
  41. #define GLOBAL(x) x
  42. #define RIGHT_SHIFT(x, n) ((x) >> (n))
  43. #define SHIFT_TEMPS
  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. /* Scaling decisions are generally the same as in the LL&M algorithm;
  51. * see jfdctint.c for more details. However, we choose to descale
  52. * (right shift) multiplication products as soon as they are formed,
  53. * rather than carrying additional fractional bits into subsequent additions.
  54. * This compromises accuracy slightly, but it lets us save a few shifts.
  55. * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples)
  56. * everywhere except in the multiplications proper; this saves a good deal
  57. * of work on 16-bit-int machines.
  58. *
  59. * Again to save a few shifts, the intermediate results between pass 1 and
  60. * pass 2 are not upscaled, but are represented only to integral precision.
  61. *
  62. * A final compromise is to represent the multiplicative constants to only
  63. * 8 fractional bits, rather than 13. This saves some shifting work on some
  64. * machines, and may also reduce the cost of multiplication (since there
  65. * are fewer one-bits in the constants).
  66. */
  67. #define CONST_BITS 8
  68. /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
  69. * causing a lot of useless floating-point operations at run time.
  70. * To get around this we use the following pre-calculated constants.
  71. * If you change CONST_BITS you may want to add appropriate values.
  72. * (With a reasonable C compiler, you can just rely on the FIX() macro...)
  73. */
  74. #if CONST_BITS == 8
  75. #define FIX_0_382683433 ((int32_t) 98) /* FIX(0.382683433) */
  76. #define FIX_0_541196100 ((int32_t) 139) /* FIX(0.541196100) */
  77. #define FIX_0_707106781 ((int32_t) 181) /* FIX(0.707106781) */
  78. #define FIX_1_306562965 ((int32_t) 334) /* FIX(1.306562965) */
  79. #else
  80. #define FIX_0_382683433 FIX(0.382683433)
  81. #define FIX_0_541196100 FIX(0.541196100)
  82. #define FIX_0_707106781 FIX(0.707106781)
  83. #define FIX_1_306562965 FIX(1.306562965)
  84. #endif
  85. /* We can gain a little more speed, with a further compromise in accuracy,
  86. * by omitting the addition in a descaling shift. This yields an incorrectly
  87. * rounded result half the time...
  88. */
  89. #ifndef USE_ACCURATE_ROUNDING
  90. #undef DESCALE
  91. #define DESCALE(x,n) RIGHT_SHIFT(x, n)
  92. #endif
  93. /* Multiply a DCTELEM variable by an int32_t constant, and immediately
  94. * descale to yield a DCTELEM result.
  95. */
  96. #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS))
  97. /*
  98. * Perform the forward DCT on one block of samples.
  99. */
  100. GLOBAL(void)
  101. fdct_ifast (DCTELEM * data)
  102. {
  103. DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
  104. DCTELEM tmp10, tmp11, tmp12, tmp13;
  105. DCTELEM z1, z2, z3, z4, z5, z11, z13;
  106. DCTELEM *dataptr;
  107. int ctr;
  108. SHIFT_TEMPS
  109. /* Pass 1: process rows. */
  110. dataptr = data;
  111. for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
  112. tmp0 = dataptr[0] + dataptr[7];
  113. tmp7 = dataptr[0] - dataptr[7];
  114. tmp1 = dataptr[1] + dataptr[6];
  115. tmp6 = dataptr[1] - dataptr[6];
  116. tmp2 = dataptr[2] + dataptr[5];
  117. tmp5 = dataptr[2] - dataptr[5];
  118. tmp3 = dataptr[3] + dataptr[4];
  119. tmp4 = dataptr[3] - dataptr[4];
  120. /* Even part */
  121. tmp10 = tmp0 + tmp3; /* phase 2 */
  122. tmp13 = tmp0 - tmp3;
  123. tmp11 = tmp1 + tmp2;
  124. tmp12 = tmp1 - tmp2;
  125. dataptr[0] = tmp10 + tmp11; /* phase 3 */
  126. dataptr[4] = tmp10 - tmp11;
  127. z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
  128. dataptr[2] = tmp13 + z1; /* phase 5 */
  129. dataptr[6] = tmp13 - z1;
  130. /* Odd part */
  131. tmp10 = tmp4 + tmp5; /* phase 2 */
  132. tmp11 = tmp5 + tmp6;
  133. tmp12 = tmp6 + tmp7;
  134. /* The rotator is modified from fig 4-8 to avoid extra negations. */
  135. z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
  136. z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
  137. z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
  138. z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
  139. z11 = tmp7 + z3; /* phase 5 */
  140. z13 = tmp7 - z3;
  141. dataptr[5] = z13 + z2; /* phase 6 */
  142. dataptr[3] = z13 - z2;
  143. dataptr[1] = z11 + z4;
  144. dataptr[7] = z11 - z4;
  145. dataptr += DCTSIZE; /* advance pointer to next row */
  146. }
  147. /* Pass 2: process columns. */
  148. dataptr = data;
  149. for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
  150. tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
  151. tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
  152. tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
  153. tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
  154. tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
  155. tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
  156. tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
  157. tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
  158. /* Even part */
  159. tmp10 = tmp0 + tmp3; /* phase 2 */
  160. tmp13 = tmp0 - tmp3;
  161. tmp11 = tmp1 + tmp2;
  162. tmp12 = tmp1 - tmp2;
  163. dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
  164. dataptr[DCTSIZE*4] = tmp10 - tmp11;
  165. z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */
  166. dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
  167. dataptr[DCTSIZE*6] = tmp13 - z1;
  168. /* Odd part */
  169. tmp10 = tmp4 + tmp5; /* phase 2 */
  170. tmp11 = tmp5 + tmp6;
  171. tmp12 = tmp6 + tmp7;
  172. /* The rotator is modified from fig 4-8 to avoid extra negations. */
  173. z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */
  174. z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */
  175. z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */
  176. z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */
  177. z11 = tmp7 + z3; /* phase 5 */
  178. z13 = tmp7 - z3;
  179. dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
  180. dataptr[DCTSIZE*3] = z13 - z2;
  181. dataptr[DCTSIZE*1] = z11 + z4;
  182. dataptr[DCTSIZE*7] = z11 - z4;
  183. dataptr++; /* advance pointer to next column */
  184. }
  185. }
  186. #undef GLOBAL
  187. #undef CONST_BITS
  188. #undef DESCALE
  189. #undef FIX_0_541196100
  190. #undef FIX_1_306562965