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annotate libs/libjpeg/jfdctint.c @ 7:a3c4fcc9f8f3

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author John Tsiombikas <nuclear@member.fsf.org>
date Thu, 24 Sep 2015 06:49:25 +0300
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nuclear@2 1 /*
nuclear@2 2 * jfdctint.c
nuclear@2 3 *
nuclear@2 4 * Copyright (C) 1991-1996, Thomas G. Lane.
nuclear@2 5 * This file is part of the Independent JPEG Group's software.
nuclear@2 6 * For conditions of distribution and use, see the accompanying README file.
nuclear@2 7 *
nuclear@2 8 * This file contains a slow-but-accurate integer implementation of the
nuclear@2 9 * forward DCT (Discrete Cosine Transform).
nuclear@2 10 *
nuclear@2 11 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
nuclear@2 12 * on each column. Direct algorithms are also available, but they are
nuclear@2 13 * much more complex and seem not to be any faster when reduced to code.
nuclear@2 14 *
nuclear@2 15 * This implementation is based on an algorithm described in
nuclear@2 16 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
nuclear@2 17 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
nuclear@2 18 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
nuclear@2 19 * The primary algorithm described there uses 11 multiplies and 29 adds.
nuclear@2 20 * We use their alternate method with 12 multiplies and 32 adds.
nuclear@2 21 * The advantage of this method is that no data path contains more than one
nuclear@2 22 * multiplication; this allows a very simple and accurate implementation in
nuclear@2 23 * scaled fixed-point arithmetic, with a minimal number of shifts.
nuclear@2 24 */
nuclear@2 25
nuclear@2 26 #define JPEG_INTERNALS
nuclear@2 27 #include "jinclude.h"
nuclear@2 28 #include "jpeglib.h"
nuclear@2 29 #include "jdct.h" /* Private declarations for DCT subsystem */
nuclear@2 30
nuclear@2 31 #ifdef DCT_ISLOW_SUPPORTED
nuclear@2 32
nuclear@2 33
nuclear@2 34 /*
nuclear@2 35 * This module is specialized to the case DCTSIZE = 8.
nuclear@2 36 */
nuclear@2 37
nuclear@2 38 #if DCTSIZE != 8
nuclear@2 39 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
nuclear@2 40 #endif
nuclear@2 41
nuclear@2 42
nuclear@2 43 /*
nuclear@2 44 * The poop on this scaling stuff is as follows:
nuclear@2 45 *
nuclear@2 46 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
nuclear@2 47 * larger than the true DCT outputs. The final outputs are therefore
nuclear@2 48 * a factor of N larger than desired; since N=8 this can be cured by
nuclear@2 49 * a simple right shift at the end of the algorithm. The advantage of
nuclear@2 50 * this arrangement is that we save two multiplications per 1-D DCT,
nuclear@2 51 * because the y0 and y4 outputs need not be divided by sqrt(N).
nuclear@2 52 * In the IJG code, this factor of 8 is removed by the quantization step
nuclear@2 53 * (in jcdctmgr.c), NOT in this module.
nuclear@2 54 *
nuclear@2 55 * We have to do addition and subtraction of the integer inputs, which
nuclear@2 56 * is no problem, and multiplication by fractional constants, which is
nuclear@2 57 * a problem to do in integer arithmetic. We multiply all the constants
nuclear@2 58 * by CONST_SCALE and convert them to integer constants (thus retaining
nuclear@2 59 * CONST_BITS bits of precision in the constants). After doing a
nuclear@2 60 * multiplication we have to divide the product by CONST_SCALE, with proper
nuclear@2 61 * rounding, to produce the correct output. This division can be done
nuclear@2 62 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
nuclear@2 63 * as long as possible so that partial sums can be added together with
nuclear@2 64 * full fractional precision.
nuclear@2 65 *
nuclear@2 66 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
nuclear@2 67 * they are represented to better-than-integral precision. These outputs
nuclear@2 68 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
nuclear@2 69 * with the recommended scaling. (For 12-bit sample data, the intermediate
nuclear@2 70 * array is INT32 anyway.)
nuclear@2 71 *
nuclear@2 72 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
nuclear@2 73 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
nuclear@2 74 * shows that the values given below are the most effective.
nuclear@2 75 */
nuclear@2 76
nuclear@2 77 #if BITS_IN_JSAMPLE == 8
nuclear@2 78 #define CONST_BITS 13
nuclear@2 79 #define PASS1_BITS 2
nuclear@2 80 #else
nuclear@2 81 #define CONST_BITS 13
nuclear@2 82 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
nuclear@2 83 #endif
nuclear@2 84
nuclear@2 85 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
nuclear@2 86 * causing a lot of useless floating-point operations at run time.
nuclear@2 87 * To get around this we use the following pre-calculated constants.
nuclear@2 88 * If you change CONST_BITS you may want to add appropriate values.
nuclear@2 89 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
nuclear@2 90 */
nuclear@2 91
nuclear@2 92 #if CONST_BITS == 13
nuclear@2 93 #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
nuclear@2 94 #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
nuclear@2 95 #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
nuclear@2 96 #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
nuclear@2 97 #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
nuclear@2 98 #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
nuclear@2 99 #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
nuclear@2 100 #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
nuclear@2 101 #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
nuclear@2 102 #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
nuclear@2 103 #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
nuclear@2 104 #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
nuclear@2 105 #else
nuclear@2 106 #define FIX_0_298631336 FIX(0.298631336)
nuclear@2 107 #define FIX_0_390180644 FIX(0.390180644)
nuclear@2 108 #define FIX_0_541196100 FIX(0.541196100)
nuclear@2 109 #define FIX_0_765366865 FIX(0.765366865)
nuclear@2 110 #define FIX_0_899976223 FIX(0.899976223)
nuclear@2 111 #define FIX_1_175875602 FIX(1.175875602)
nuclear@2 112 #define FIX_1_501321110 FIX(1.501321110)
nuclear@2 113 #define FIX_1_847759065 FIX(1.847759065)
nuclear@2 114 #define FIX_1_961570560 FIX(1.961570560)
nuclear@2 115 #define FIX_2_053119869 FIX(2.053119869)
nuclear@2 116 #define FIX_2_562915447 FIX(2.562915447)
nuclear@2 117 #define FIX_3_072711026 FIX(3.072711026)
nuclear@2 118 #endif
nuclear@2 119
nuclear@2 120
nuclear@2 121 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
nuclear@2 122 * For 8-bit samples with the recommended scaling, all the variable
nuclear@2 123 * and constant values involved are no more than 16 bits wide, so a
nuclear@2 124 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
nuclear@2 125 * For 12-bit samples, a full 32-bit multiplication will be needed.
nuclear@2 126 */
nuclear@2 127
nuclear@2 128 #if BITS_IN_JSAMPLE == 8
nuclear@2 129 #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
nuclear@2 130 #else
nuclear@2 131 #define MULTIPLY(var,const) ((var) * (const))
nuclear@2 132 #endif
nuclear@2 133
nuclear@2 134
nuclear@2 135 /*
nuclear@2 136 * Perform the forward DCT on one block of samples.
nuclear@2 137 */
nuclear@2 138
nuclear@2 139 GLOBAL(void)
nuclear@2 140 jpeg_fdct_islow (DCTELEM * data)
nuclear@2 141 {
nuclear@2 142 INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
nuclear@2 143 INT32 tmp10, tmp11, tmp12, tmp13;
nuclear@2 144 INT32 z1, z2, z3, z4, z5;
nuclear@2 145 DCTELEM *dataptr;
nuclear@2 146 int ctr;
nuclear@2 147 SHIFT_TEMPS
nuclear@2 148
nuclear@2 149 /* Pass 1: process rows. */
nuclear@2 150 /* Note results are scaled up by sqrt(8) compared to a true DCT; */
nuclear@2 151 /* furthermore, we scale the results by 2**PASS1_BITS. */
nuclear@2 152
nuclear@2 153 dataptr = data;
nuclear@2 154 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
nuclear@2 155 tmp0 = dataptr[0] + dataptr[7];
nuclear@2 156 tmp7 = dataptr[0] - dataptr[7];
nuclear@2 157 tmp1 = dataptr[1] + dataptr[6];
nuclear@2 158 tmp6 = dataptr[1] - dataptr[6];
nuclear@2 159 tmp2 = dataptr[2] + dataptr[5];
nuclear@2 160 tmp5 = dataptr[2] - dataptr[5];
nuclear@2 161 tmp3 = dataptr[3] + dataptr[4];
nuclear@2 162 tmp4 = dataptr[3] - dataptr[4];
nuclear@2 163
nuclear@2 164 /* Even part per LL&M figure 1 --- note that published figure is faulty;
nuclear@2 165 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
nuclear@2 166 */
nuclear@2 167
nuclear@2 168 tmp10 = tmp0 + tmp3;
nuclear@2 169 tmp13 = tmp0 - tmp3;
nuclear@2 170 tmp11 = tmp1 + tmp2;
nuclear@2 171 tmp12 = tmp1 - tmp2;
nuclear@2 172
nuclear@2 173 dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
nuclear@2 174 dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
nuclear@2 175
nuclear@2 176 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
nuclear@2 177 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
nuclear@2 178 CONST_BITS-PASS1_BITS);
nuclear@2 179 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
nuclear@2 180 CONST_BITS-PASS1_BITS);
nuclear@2 181
nuclear@2 182 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
nuclear@2 183 * cK represents cos(K*pi/16).
nuclear@2 184 * i0..i3 in the paper are tmp4..tmp7 here.
nuclear@2 185 */
nuclear@2 186
nuclear@2 187 z1 = tmp4 + tmp7;
nuclear@2 188 z2 = tmp5 + tmp6;
nuclear@2 189 z3 = tmp4 + tmp6;
nuclear@2 190 z4 = tmp5 + tmp7;
nuclear@2 191 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
nuclear@2 192
nuclear@2 193 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
nuclear@2 194 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
nuclear@2 195 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
nuclear@2 196 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
nuclear@2 197 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
nuclear@2 198 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
nuclear@2 199 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
nuclear@2 200 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
nuclear@2 201
nuclear@2 202 z3 += z5;
nuclear@2 203 z4 += z5;
nuclear@2 204
nuclear@2 205 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
nuclear@2 206 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
nuclear@2 207 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
nuclear@2 208 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
nuclear@2 209
nuclear@2 210 dataptr += DCTSIZE; /* advance pointer to next row */
nuclear@2 211 }
nuclear@2 212
nuclear@2 213 /* Pass 2: process columns.
nuclear@2 214 * We remove the PASS1_BITS scaling, but leave the results scaled up
nuclear@2 215 * by an overall factor of 8.
nuclear@2 216 */
nuclear@2 217
nuclear@2 218 dataptr = data;
nuclear@2 219 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
nuclear@2 220 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
nuclear@2 221 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
nuclear@2 222 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
nuclear@2 223 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
nuclear@2 224 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
nuclear@2 225 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
nuclear@2 226 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
nuclear@2 227 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
nuclear@2 228
nuclear@2 229 /* Even part per LL&M figure 1 --- note that published figure is faulty;
nuclear@2 230 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
nuclear@2 231 */
nuclear@2 232
nuclear@2 233 tmp10 = tmp0 + tmp3;
nuclear@2 234 tmp13 = tmp0 - tmp3;
nuclear@2 235 tmp11 = tmp1 + tmp2;
nuclear@2 236 tmp12 = tmp1 - tmp2;
nuclear@2 237
nuclear@2 238 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
nuclear@2 239 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
nuclear@2 240
nuclear@2 241 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
nuclear@2 242 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
nuclear@2 243 CONST_BITS+PASS1_BITS);
nuclear@2 244 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
nuclear@2 245 CONST_BITS+PASS1_BITS);
nuclear@2 246
nuclear@2 247 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
nuclear@2 248 * cK represents cos(K*pi/16).
nuclear@2 249 * i0..i3 in the paper are tmp4..tmp7 here.
nuclear@2 250 */
nuclear@2 251
nuclear@2 252 z1 = tmp4 + tmp7;
nuclear@2 253 z2 = tmp5 + tmp6;
nuclear@2 254 z3 = tmp4 + tmp6;
nuclear@2 255 z4 = tmp5 + tmp7;
nuclear@2 256 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
nuclear@2 257
nuclear@2 258 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
nuclear@2 259 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
nuclear@2 260 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
nuclear@2 261 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
nuclear@2 262 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
nuclear@2 263 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
nuclear@2 264 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
nuclear@2 265 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
nuclear@2 266
nuclear@2 267 z3 += z5;
nuclear@2 268 z4 += z5;
nuclear@2 269
nuclear@2 270 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
nuclear@2 271 CONST_BITS+PASS1_BITS);
nuclear@2 272 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
nuclear@2 273 CONST_BITS+PASS1_BITS);
nuclear@2 274 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
nuclear@2 275 CONST_BITS+PASS1_BITS);
nuclear@2 276 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
nuclear@2 277 CONST_BITS+PASS1_BITS);
nuclear@2 278
nuclear@2 279 dataptr++; /* advance pointer to next column */
nuclear@2 280 }
nuclear@2 281 }
nuclear@2 282
nuclear@2 283 #endif /* DCT_ISLOW_SUPPORTED */