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annotate libs/libjpeg/jfdctint.c @ 0:b2f14e535253

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author John Tsiombikas <nuclear@member.fsf.org>
date Sat, 01 Feb 2014 19:58:19 +0200
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nuclear@0 1 /*
nuclear@0 2 * jfdctint.c
nuclear@0 3 *
nuclear@0 4 * Copyright (C) 1991-1996, Thomas G. Lane.
nuclear@0 5 * This file is part of the Independent JPEG Group's software.
nuclear@0 6 * For conditions of distribution and use, see the accompanying README file.
nuclear@0 7 *
nuclear@0 8 * This file contains a slow-but-accurate integer implementation of the
nuclear@0 9 * forward DCT (Discrete Cosine Transform).
nuclear@0 10 *
nuclear@0 11 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT
nuclear@0 12 * on each column. Direct algorithms are also available, but they are
nuclear@0 13 * much more complex and seem not to be any faster when reduced to code.
nuclear@0 14 *
nuclear@0 15 * This implementation is based on an algorithm described in
nuclear@0 16 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
nuclear@0 17 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
nuclear@0 18 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
nuclear@0 19 * The primary algorithm described there uses 11 multiplies and 29 adds.
nuclear@0 20 * We use their alternate method with 12 multiplies and 32 adds.
nuclear@0 21 * The advantage of this method is that no data path contains more than one
nuclear@0 22 * multiplication; this allows a very simple and accurate implementation in
nuclear@0 23 * scaled fixed-point arithmetic, with a minimal number of shifts.
nuclear@0 24 */
nuclear@0 25
nuclear@0 26 #define JPEG_INTERNALS
nuclear@0 27 #include "jinclude.h"
nuclear@0 28 #include "jpeglib.h"
nuclear@0 29 #include "jdct.h" /* Private declarations for DCT subsystem */
nuclear@0 30
nuclear@0 31 #ifdef DCT_ISLOW_SUPPORTED
nuclear@0 32
nuclear@0 33
nuclear@0 34 /*
nuclear@0 35 * This module is specialized to the case DCTSIZE = 8.
nuclear@0 36 */
nuclear@0 37
nuclear@0 38 #if DCTSIZE != 8
nuclear@0 39 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
nuclear@0 40 #endif
nuclear@0 41
nuclear@0 42
nuclear@0 43 /*
nuclear@0 44 * The poop on this scaling stuff is as follows:
nuclear@0 45 *
nuclear@0 46 * Each 1-D DCT step produces outputs which are a factor of sqrt(N)
nuclear@0 47 * larger than the true DCT outputs. The final outputs are therefore
nuclear@0 48 * a factor of N larger than desired; since N=8 this can be cured by
nuclear@0 49 * a simple right shift at the end of the algorithm. The advantage of
nuclear@0 50 * this arrangement is that we save two multiplications per 1-D DCT,
nuclear@0 51 * because the y0 and y4 outputs need not be divided by sqrt(N).
nuclear@0 52 * In the IJG code, this factor of 8 is removed by the quantization step
nuclear@0 53 * (in jcdctmgr.c), NOT in this module.
nuclear@0 54 *
nuclear@0 55 * We have to do addition and subtraction of the integer inputs, which
nuclear@0 56 * is no problem, and multiplication by fractional constants, which is
nuclear@0 57 * a problem to do in integer arithmetic. We multiply all the constants
nuclear@0 58 * by CONST_SCALE and convert them to integer constants (thus retaining
nuclear@0 59 * CONST_BITS bits of precision in the constants). After doing a
nuclear@0 60 * multiplication we have to divide the product by CONST_SCALE, with proper
nuclear@0 61 * rounding, to produce the correct output. This division can be done
nuclear@0 62 * cheaply as a right shift of CONST_BITS bits. We postpone shifting
nuclear@0 63 * as long as possible so that partial sums can be added together with
nuclear@0 64 * full fractional precision.
nuclear@0 65 *
nuclear@0 66 * The outputs of the first pass are scaled up by PASS1_BITS bits so that
nuclear@0 67 * they are represented to better-than-integral precision. These outputs
nuclear@0 68 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
nuclear@0 69 * with the recommended scaling. (For 12-bit sample data, the intermediate
nuclear@0 70 * array is INT32 anyway.)
nuclear@0 71 *
nuclear@0 72 * To avoid overflow of the 32-bit intermediate results in pass 2, we must
nuclear@0 73 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis
nuclear@0 74 * shows that the values given below are the most effective.
nuclear@0 75 */
nuclear@0 76
nuclear@0 77 #if BITS_IN_JSAMPLE == 8
nuclear@0 78 #define CONST_BITS 13
nuclear@0 79 #define PASS1_BITS 2
nuclear@0 80 #else
nuclear@0 81 #define CONST_BITS 13
nuclear@0 82 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */
nuclear@0 83 #endif
nuclear@0 84
nuclear@0 85 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
nuclear@0 86 * causing a lot of useless floating-point operations at run time.
nuclear@0 87 * To get around this we use the following pre-calculated constants.
nuclear@0 88 * If you change CONST_BITS you may want to add appropriate values.
nuclear@0 89 * (With a reasonable C compiler, you can just rely on the FIX() macro...)
nuclear@0 90 */
nuclear@0 91
nuclear@0 92 #if CONST_BITS == 13
nuclear@0 93 #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */
nuclear@0 94 #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */
nuclear@0 95 #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */
nuclear@0 96 #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */
nuclear@0 97 #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */
nuclear@0 98 #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */
nuclear@0 99 #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */
nuclear@0 100 #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */
nuclear@0 101 #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */
nuclear@0 102 #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */
nuclear@0 103 #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */
nuclear@0 104 #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */
nuclear@0 105 #else
nuclear@0 106 #define FIX_0_298631336 FIX(0.298631336)
nuclear@0 107 #define FIX_0_390180644 FIX(0.390180644)
nuclear@0 108 #define FIX_0_541196100 FIX(0.541196100)
nuclear@0 109 #define FIX_0_765366865 FIX(0.765366865)
nuclear@0 110 #define FIX_0_899976223 FIX(0.899976223)
nuclear@0 111 #define FIX_1_175875602 FIX(1.175875602)
nuclear@0 112 #define FIX_1_501321110 FIX(1.501321110)
nuclear@0 113 #define FIX_1_847759065 FIX(1.847759065)
nuclear@0 114 #define FIX_1_961570560 FIX(1.961570560)
nuclear@0 115 #define FIX_2_053119869 FIX(2.053119869)
nuclear@0 116 #define FIX_2_562915447 FIX(2.562915447)
nuclear@0 117 #define FIX_3_072711026 FIX(3.072711026)
nuclear@0 118 #endif
nuclear@0 119
nuclear@0 120
nuclear@0 121 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
nuclear@0 122 * For 8-bit samples with the recommended scaling, all the variable
nuclear@0 123 * and constant values involved are no more than 16 bits wide, so a
nuclear@0 124 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
nuclear@0 125 * For 12-bit samples, a full 32-bit multiplication will be needed.
nuclear@0 126 */
nuclear@0 127
nuclear@0 128 #if BITS_IN_JSAMPLE == 8
nuclear@0 129 #define MULTIPLY(var,const) MULTIPLY16C16(var,const)
nuclear@0 130 #else
nuclear@0 131 #define MULTIPLY(var,const) ((var) * (const))
nuclear@0 132 #endif
nuclear@0 133
nuclear@0 134
nuclear@0 135 /*
nuclear@0 136 * Perform the forward DCT on one block of samples.
nuclear@0 137 */
nuclear@0 138
nuclear@0 139 GLOBAL(void)
nuclear@0 140 jpeg_fdct_islow (DCTELEM * data)
nuclear@0 141 {
nuclear@0 142 INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7;
nuclear@0 143 INT32 tmp10, tmp11, tmp12, tmp13;
nuclear@0 144 INT32 z1, z2, z3, z4, z5;
nuclear@0 145 DCTELEM *dataptr;
nuclear@0 146 int ctr;
nuclear@0 147 SHIFT_TEMPS
nuclear@0 148
nuclear@0 149 /* Pass 1: process rows. */
nuclear@0 150 /* Note results are scaled up by sqrt(8) compared to a true DCT; */
nuclear@0 151 /* furthermore, we scale the results by 2**PASS1_BITS. */
nuclear@0 152
nuclear@0 153 dataptr = data;
nuclear@0 154 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
nuclear@0 155 tmp0 = dataptr[0] + dataptr[7];
nuclear@0 156 tmp7 = dataptr[0] - dataptr[7];
nuclear@0 157 tmp1 = dataptr[1] + dataptr[6];
nuclear@0 158 tmp6 = dataptr[1] - dataptr[6];
nuclear@0 159 tmp2 = dataptr[2] + dataptr[5];
nuclear@0 160 tmp5 = dataptr[2] - dataptr[5];
nuclear@0 161 tmp3 = dataptr[3] + dataptr[4];
nuclear@0 162 tmp4 = dataptr[3] - dataptr[4];
nuclear@0 163
nuclear@0 164 /* Even part per LL&M figure 1 --- note that published figure is faulty;
nuclear@0 165 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
nuclear@0 166 */
nuclear@0 167
nuclear@0 168 tmp10 = tmp0 + tmp3;
nuclear@0 169 tmp13 = tmp0 - tmp3;
nuclear@0 170 tmp11 = tmp1 + tmp2;
nuclear@0 171 tmp12 = tmp1 - tmp2;
nuclear@0 172
nuclear@0 173 dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS);
nuclear@0 174 dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS);
nuclear@0 175
nuclear@0 176 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
nuclear@0 177 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
nuclear@0 178 CONST_BITS-PASS1_BITS);
nuclear@0 179 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
nuclear@0 180 CONST_BITS-PASS1_BITS);
nuclear@0 181
nuclear@0 182 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
nuclear@0 183 * cK represents cos(K*pi/16).
nuclear@0 184 * i0..i3 in the paper are tmp4..tmp7 here.
nuclear@0 185 */
nuclear@0 186
nuclear@0 187 z1 = tmp4 + tmp7;
nuclear@0 188 z2 = tmp5 + tmp6;
nuclear@0 189 z3 = tmp4 + tmp6;
nuclear@0 190 z4 = tmp5 + tmp7;
nuclear@0 191 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
nuclear@0 192
nuclear@0 193 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
nuclear@0 194 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
nuclear@0 195 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
nuclear@0 196 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
nuclear@0 197 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
nuclear@0 198 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
nuclear@0 199 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
nuclear@0 200 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
nuclear@0 201
nuclear@0 202 z3 += z5;
nuclear@0 203 z4 += z5;
nuclear@0 204
nuclear@0 205 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS);
nuclear@0 206 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS);
nuclear@0 207 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS);
nuclear@0 208 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS);
nuclear@0 209
nuclear@0 210 dataptr += DCTSIZE; /* advance pointer to next row */
nuclear@0 211 }
nuclear@0 212
nuclear@0 213 /* Pass 2: process columns.
nuclear@0 214 * We remove the PASS1_BITS scaling, but leave the results scaled up
nuclear@0 215 * by an overall factor of 8.
nuclear@0 216 */
nuclear@0 217
nuclear@0 218 dataptr = data;
nuclear@0 219 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) {
nuclear@0 220 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7];
nuclear@0 221 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7];
nuclear@0 222 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6];
nuclear@0 223 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6];
nuclear@0 224 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5];
nuclear@0 225 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5];
nuclear@0 226 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4];
nuclear@0 227 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4];
nuclear@0 228
nuclear@0 229 /* Even part per LL&M figure 1 --- note that published figure is faulty;
nuclear@0 230 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6".
nuclear@0 231 */
nuclear@0 232
nuclear@0 233 tmp10 = tmp0 + tmp3;
nuclear@0 234 tmp13 = tmp0 - tmp3;
nuclear@0 235 tmp11 = tmp1 + tmp2;
nuclear@0 236 tmp12 = tmp1 - tmp2;
nuclear@0 237
nuclear@0 238 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS);
nuclear@0 239 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS);
nuclear@0 240
nuclear@0 241 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100);
nuclear@0 242 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865),
nuclear@0 243 CONST_BITS+PASS1_BITS);
nuclear@0 244 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065),
nuclear@0 245 CONST_BITS+PASS1_BITS);
nuclear@0 246
nuclear@0 247 /* Odd part per figure 8 --- note paper omits factor of sqrt(2).
nuclear@0 248 * cK represents cos(K*pi/16).
nuclear@0 249 * i0..i3 in the paper are tmp4..tmp7 here.
nuclear@0 250 */
nuclear@0 251
nuclear@0 252 z1 = tmp4 + tmp7;
nuclear@0 253 z2 = tmp5 + tmp6;
nuclear@0 254 z3 = tmp4 + tmp6;
nuclear@0 255 z4 = tmp5 + tmp7;
nuclear@0 256 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */
nuclear@0 257
nuclear@0 258 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
nuclear@0 259 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
nuclear@0 260 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
nuclear@0 261 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
nuclear@0 262 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
nuclear@0 263 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
nuclear@0 264 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
nuclear@0 265 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */
nuclear@0 266
nuclear@0 267 z3 += z5;
nuclear@0 268 z4 += z5;
nuclear@0 269
nuclear@0 270 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3,
nuclear@0 271 CONST_BITS+PASS1_BITS);
nuclear@0 272 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4,
nuclear@0 273 CONST_BITS+PASS1_BITS);
nuclear@0 274 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3,
nuclear@0 275 CONST_BITS+PASS1_BITS);
nuclear@0 276 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4,
nuclear@0 277 CONST_BITS+PASS1_BITS);
nuclear@0 278
nuclear@0 279 dataptr++; /* advance pointer to next column */
nuclear@0 280 }
nuclear@0 281 }
nuclear@0 282
nuclear@0 283 #endif /* DCT_ISLOW_SUPPORTED */