7 * Copyright (C) 1994, Thomas G. Lane.
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9 * This file is part of the Independent JPEG Group's software.
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11 * For conditions of distribution and use, see the accompanying README file.
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15 * This file contains a floating-point implementation of the
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17 * forward DCT (Discrete Cosine Transform).
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21 * This implementation should be more accurate than either of the integer
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23 * DCT implementations. However, it may not give the same results on all
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25 * machines because of differences in roundoff behavior. Speed will depend
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27 * on the hardware's floating point capacity.
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31 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
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33 * on each column. Direct algorithms are also available, but they are
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35 * much more complex and seem not to be any faster when reduced to code.
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39 * This implementation is based on Arai, Agui, and Nakajima's algorithm for
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41 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in
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43 * Japanese, but the algorithm is described in the Pennebaker & Mitchell
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45 * JPEG textbook (see REFERENCES section in file README). The following code
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47 * is based directly on figure 4-8 in P&M.
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49 * While an 8-point DCT cannot be done in less than 11 multiplies, it is
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51 * possible to arrange the computation so that many of the multiplies are
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53 * simple scalings of the final outputs. These multiplies can then be
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55 * folded into the multiplications or divisions by the JPEG quantization
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57 * table entries. The AA&N method leaves only 5 multiplies and 29 adds
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59 * to be done in the DCT itself.
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61 * The primary disadvantage of this method is that with a fixed-point
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63 * implementation, accuracy is lost due to imprecise representation of the
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65 * scaled quantization values. However, that problem does not arise if
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67 * we use floating point arithmetic.
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73 #define JPEG_INTERNALS
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75 #include "jinclude.h"
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77 #include "radiant_jpeglib.h"
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79 #include "jdct.h" /* Private declarations for DCT subsystem */
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83 #ifdef DCT_FLOAT_SUPPORTED
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91 * This module is specialized to the case DCTSIZE = 8.
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99 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
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109 * Perform the forward DCT on one block of samples.
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117 jpeg_fdct_float (FAST_FLOAT * data)
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121 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
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123 FAST_FLOAT tmp10, tmp11, tmp12, tmp13;
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125 FAST_FLOAT z1, z2, z3, z4, z5, z11, z13;
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127 FAST_FLOAT *dataptr;
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133 /* Pass 1: process rows. */
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139 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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141 tmp0 = dataptr[0] + dataptr[7];
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143 tmp7 = dataptr[0] - dataptr[7];
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145 tmp1 = dataptr[1] + dataptr[6];
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147 tmp6 = dataptr[1] - dataptr[6];
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149 tmp2 = dataptr[2] + dataptr[5];
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151 tmp5 = dataptr[2] - dataptr[5];
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153 tmp3 = dataptr[3] + dataptr[4];
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155 tmp4 = dataptr[3] - dataptr[4];
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163 tmp10 = tmp0 + tmp3; /* phase 2 */
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165 tmp13 = tmp0 - tmp3;
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167 tmp11 = tmp1 + tmp2;
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169 tmp12 = tmp1 - tmp2;
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173 dataptr[0] = tmp10 + tmp11; /* phase 3 */
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175 dataptr[4] = tmp10 - tmp11;
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179 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
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181 dataptr[2] = tmp13 + z1; /* phase 5 */
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183 dataptr[6] = tmp13 - z1;
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191 tmp10 = tmp4 + tmp5; /* phase 2 */
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193 tmp11 = tmp5 + tmp6;
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195 tmp12 = tmp6 + tmp7;
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199 /* The rotator is modified from fig 4-8 to avoid extra negations. */
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201 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
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203 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
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205 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
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207 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
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211 z11 = tmp7 + z3; /* phase 5 */
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217 dataptr[5] = z13 + z2; /* phase 6 */
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219 dataptr[3] = z13 - z2;
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221 dataptr[1] = z11 + z4;
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223 dataptr[7] = z11 - z4;
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227 dataptr += DCTSIZE; /* advance pointer to next row */
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233 /* Pass 2: process columns. */
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239 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
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241 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
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243 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
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245 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
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247 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
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249 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
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251 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
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253 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
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255 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
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263 tmp10 = tmp0 + tmp3; /* phase 2 */
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265 tmp13 = tmp0 - tmp3;
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267 tmp11 = tmp1 + tmp2;
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269 tmp12 = tmp1 - tmp2;
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273 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */
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275 dataptr[DCTSIZE*4] = tmp10 - tmp11;
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279 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */
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281 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */
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283 dataptr[DCTSIZE*6] = tmp13 - z1;
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291 tmp10 = tmp4 + tmp5; /* phase 2 */
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293 tmp11 = tmp5 + tmp6;
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295 tmp12 = tmp6 + tmp7;
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299 /* The rotator is modified from fig 4-8 to avoid extra negations. */
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301 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */
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303 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */
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305 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */
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307 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */
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311 z11 = tmp7 + z3; /* phase 5 */
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317 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */
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319 dataptr[DCTSIZE*3] = z13 - z2;
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321 dataptr[DCTSIZE*1] = z11 + z4;
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323 dataptr[DCTSIZE*7] = z11 - z4;
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327 dataptr++; /* advance pointer to next column */
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335 #endif /* DCT_FLOAT_SUPPORTED */
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