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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 #define JPEG_INTERNALS | |
| 27 #include "jinclude.h" | |
| 28 #include "jpeglib.h" | |
| 29 #include "jdct.h" /* Private declarations for DCT subsystem */ | |
| 30 | |
| 31 #ifdef DCT_ISLOW_SUPPORTED | |
| 32 | |
| 33 | |
| 34 /* | |
| 35 * This module is specialized to the case DCTSIZE = 8. | |
| 36 */ | |
| 37 | |
| 38 #if DCTSIZE != 8 | |
| 39 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ | |
| 40 #endif | |
| 41 | |
| 42 | |
| 43 /* | |
| 44 * The poop on this scaling stuff is as follows: | |
| 45 * | |
| 46 * Each 1-D DCT step produces outputs which are a factor of sqrt(N) | |
| 47 * larger than the true DCT outputs. The final outputs are therefore | |
| 48 * a factor of N larger than desired; since N=8 this can be cured by | |
| 49 * a simple right shift at the end of the algorithm. The advantage of | |
| 50 * this arrangement is that we save two multiplications per 1-D DCT, | |
| 51 * because the y0 and y4 outputs need not be divided by sqrt(N). | |
| 52 * In the IJG code, this factor of 8 is removed by the quantization step | |
| 53 * (in jcdctmgr.c), NOT in this module. | |
| 54 * | |
| 55 * We have to do addition and subtraction of the integer inputs, which | |
| 56 * is no problem, and multiplication by fractional constants, which is | |
| 57 * a problem to do in integer arithmetic. We multiply all the constants | |
| 58 * by CONST_SCALE and convert them to integer constants (thus retaining | |
| 59 * CONST_BITS bits of precision in the constants). After doing a | |
| 60 * multiplication we have to divide the product by CONST_SCALE, with proper | |
| 61 * rounding, to produce the correct output. This division can be done | |
| 62 * cheaply as a right shift of CONST_BITS bits. We postpone shifting | |
| 63 * as long as possible so that partial sums can be added together with | |
| 64 * full fractional precision. | |
| 65 * | |
| 66 * The outputs of the first pass are scaled up by PASS1_BITS bits so that | |
| 67 * they are represented to better-than-integral precision. These outputs | |
| 68 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word | |
| 69 * with the recommended scaling. (For 12-bit sample data, the intermediate | |
| 70 * array is INT32 anyway.) | |
| 71 * | |
| 72 * To avoid overflow of the 32-bit intermediate results in pass 2, we must | |
| 73 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis | |
| 74 * shows that the values given below are the most effective. | |
| 75 */ | |
| 76 | |
| 77 #if BITS_IN_JSAMPLE == 8 | |
| 78 #define CONST_BITS 13 | |
| 79 #define PASS1_BITS 2 | |
| 80 #else | |
| 81 #define CONST_BITS 13 | |
| 82 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ | |
| 83 #endif | |
| 84 | |
| 85 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus | |
| 86 * causing a lot of useless floating-point operations at run time. | |
| 87 * To get around this we use the following pre-calculated constants. | |
| 88 * If you change CONST_BITS you may want to add appropriate values. | |
| 89 * (With a reasonable C compiler, you can just rely on the FIX() macro...) | |
| 90 */ | |
| 91 | |
| 92 #if CONST_BITS == 13 | |
| 93 #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */ | |
| 94 #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */ | |
| 95 #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */ | |
| 96 #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */ | |
| 97 #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */ | |
| 98 #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */ | |
| 99 #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */ | |
| 100 #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */ | |
| 101 #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */ | |
| 102 #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */ | |
| 103 #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */ | |
| 104 #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */ | |
| 105 #else | |
| 106 #define FIX_0_298631336 FIX(0.298631336) | |
| 107 #define FIX_0_390180644 FIX(0.390180644) | |
| 108 #define FIX_0_541196100 FIX(0.541196100) | |
| 109 #define FIX_0_765366865 FIX(0.765366865) | |
| 110 #define FIX_0_899976223 FIX(0.899976223) | |
| 111 #define FIX_1_175875602 FIX(1.175875602) | |
| 112 #define FIX_1_501321110 FIX(1.501321110) | |
| 113 #define FIX_1_847759065 FIX(1.847759065) | |
| 114 #define FIX_1_961570560 FIX(1.961570560) | |
| 115 #define FIX_2_053119869 FIX(2.053119869) | |
| 116 #define FIX_2_562915447 FIX(2.562915447) | |
| 117 #define FIX_3_072711026 FIX(3.072711026) | |
| 118 #endif | |
| 119 | |
| 120 | |
| 121 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. | |
| 122 * For 8-bit samples with the recommended scaling, all the variable | |
| 123 * and constant values involved are no more than 16 bits wide, so a | |
| 124 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. | |
| 125 * For 12-bit samples, a full 32-bit multiplication will be needed. | |
| 126 */ | |
| 127 | |
| 128 #if BITS_IN_JSAMPLE == 8 | |
| 129 #define MULTIPLY(var,const) MULTIPLY16C16(var,const) | |
| 130 #else | |
| 131 #define MULTIPLY(var,const) ((var) * (const)) | |
| 132 #endif | |
| 133 | |
| 134 | |
| 135 /* | |
| 136 * Perform the forward DCT on one block of samples. | |
| 137 */ | |
| 138 | |
| 139 GLOBAL(void) | |
| 140 jpeg_fdct_islow (DCTELEM * data) | |
| 141 { | |
| 142 INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; | |
| 143 INT32 tmp10, tmp11, tmp12, tmp13; | |
| 144 INT32 z1, z2, z3, z4, z5; | |
| 145 DCTELEM *dataptr; | |
| 146 int ctr; | |
| 147 SHIFT_TEMPS | |
| 148 | |
| 149 /* Pass 1: process rows. */ | |
| 150 /* Note results are scaled up by sqrt(8) compared to a true DCT; */ | |
| 151 /* furthermore, we scale the results by 2**PASS1_BITS. */ | |
| 152 | |
| 153 dataptr = data; | |
| 154 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { | |
| 155 tmp0 = dataptr[0] + dataptr[7]; | |
| 156 tmp7 = dataptr[0] - dataptr[7]; | |
| 157 tmp1 = dataptr[1] + dataptr[6]; | |
| 158 tmp6 = dataptr[1] - dataptr[6]; | |
| 159 tmp2 = dataptr[2] + dataptr[5]; | |
| 160 tmp5 = dataptr[2] - dataptr[5]; | |
| 161 tmp3 = dataptr[3] + dataptr[4]; | |
| 162 tmp4 = dataptr[3] - dataptr[4]; | |
| 163 | |
| 164 /* Even part per LL&M figure 1 --- note that published figure is faulty; | |
| 165 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". | |
| 166 */ | |
| 167 | |
| 168 tmp10 = tmp0 + tmp3; | |
| 169 tmp13 = tmp0 - tmp3; | |
| 170 tmp11 = tmp1 + tmp2; | |
| 171 tmp12 = tmp1 - tmp2; | |
| 172 | |
| 173 dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); | |
| 174 dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); | |
| 175 | |
| 176 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); | |
| 177 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), | |
| 178 CONST_BITS-PASS1_BITS); | |
| 179 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), | |
| 180 CONST_BITS-PASS1_BITS); | |
| 181 | |
| 182 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). | |
| 183 * cK represents cos(K*pi/16). | |
| 184 * i0..i3 in the paper are tmp4..tmp7 here. | |
| 185 */ | |
| 186 | |
| 187 z1 = tmp4 + tmp7; | |
| 188 z2 = tmp5 + tmp6; | |
| 189 z3 = tmp4 + tmp6; | |
| 190 z4 = tmp5 + tmp7; | |
| 191 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ | |
| 192 | |
| 193 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ | |
| 194 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ | |
| 195 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ | |
| 196 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ | |
| 197 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ | |
| 198 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ | |
| 199 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ | |
| 200 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ | |
| 201 | |
| 202 z3 += z5; | |
| 203 z4 += z5; | |
| 204 | |
| 205 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); | |
| 206 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); | |
| 207 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); | |
| 208 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); | |
| 209 | |
| 210 dataptr += DCTSIZE; /* advance pointer to next row */ | |
| 211 } | |
| 212 | |
| 213 /* Pass 2: process columns. | |
| 214 * We remove the PASS1_BITS scaling, but leave the results scaled up | |
| 215 * by an overall factor of 8. | |
| 216 */ | |
| 217 | |
| 218 dataptr = data; | |
| 219 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { | |
| 220 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; | |
| 221 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; | |
| 222 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; | |
| 223 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; | |
| 224 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; | |
| 225 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; | |
| 226 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; | |
| 227 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; | |
| 228 | |
| 229 /* Even part per LL&M figure 1 --- note that published figure is faulty; | |
| 230 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". | |
| 231 */ | |
| 232 | |
| 233 tmp10 = tmp0 + tmp3; | |
| 234 tmp13 = tmp0 - tmp3; | |
| 235 tmp11 = tmp1 + tmp2; | |
| 236 tmp12 = tmp1 - tmp2; | |
| 237 | |
| 238 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); | |
| 239 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); | |
| 240 | |
| 241 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); | |
| 242 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865)
, | |
| 243 CONST_BITS+PASS1_BITS); | |
| 244 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_84775906
5), | |
| 245 CONST_BITS+PASS1_BITS); | |
| 246 | |
| 247 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). | |
| 248 * cK represents cos(K*pi/16). | |
| 249 * i0..i3 in the paper are tmp4..tmp7 here. | |
| 250 */ | |
| 251 | |
| 252 z1 = tmp4 + tmp7; | |
| 253 z2 = tmp5 + tmp6; | |
| 254 z3 = tmp4 + tmp6; | |
| 255 z4 = tmp5 + tmp7; | |
| 256 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ | |
| 257 | |
| 258 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ | |
| 259 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ | |
| 260 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ | |
| 261 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ | |
| 262 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ | |
| 263 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ | |
| 264 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ | |
| 265 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ | |
| 266 | |
| 267 z3 += z5; | |
| 268 z4 += z5; | |
| 269 | |
| 270 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, | |
| 271 CONST_BITS+PASS1_BITS); | |
| 272 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, | |
| 273 CONST_BITS+PASS1_BITS); | |
| 274 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, | |
| 275 CONST_BITS+PASS1_BITS); | |
| 276 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, | |
| 277 CONST_BITS+PASS1_BITS); | |
| 278 | |
| 279 dataptr++; /* advance pointer to next column */ | |
| 280 } | |
| 281 } | |
| 282 | |
| 283 #endif /* DCT_ISLOW_SUPPORTED */ | |
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Issue 1705523002:
Remove libjpeg and libjpeg_turbo. (Closed)
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