1/* 2 * jfdctint.c 3 * 4 * This file was part of the Independent JPEG Group's software. 5 * Copyright (C) 1991-1996, Thomas G. Lane. 6 * libjpeg-turbo Modifications: 7 * Copyright (C) 2015, D. R. Commander. 8 * For conditions of distribution and use, see the accompanying README.ijg 9 * file. 10 * 11 * This file contains a slow-but-accurate integer implementation of the 12 * forward DCT (Discrete Cosine Transform). 13 * 14 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 15 * on each column. Direct algorithms are also available, but they are 16 * much more complex and seem not to be any faster when reduced to code. 17 * 18 * This implementation is based on an algorithm described in 19 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT 20 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, 21 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. 22 * The primary algorithm described there uses 11 multiplies and 29 adds. 23 * We use their alternate method with 12 multiplies and 32 adds. 24 * The advantage of this method is that no data path contains more than one 25 * multiplication; this allows a very simple and accurate implementation in 26 * scaled fixed-point arithmetic, with a minimal number of shifts. 27 */ 28 29#define JPEG_INTERNALS 30#include "jinclude.h" 31#include "jpeglib.h" 32#include "jdct.h" /* Private declarations for DCT subsystem */ 33 34#ifdef DCT_ISLOW_SUPPORTED 35 36 37/* 38 * This module is specialized to the case DCTSIZE = 8. 39 */ 40 41#if DCTSIZE != 8 42 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 43#endif 44 45 46/* 47 * The poop on this scaling stuff is as follows: 48 * 49 * Each 1-D DCT step produces outputs which are a factor of sqrt(N) 50 * larger than the true DCT outputs. The final outputs are therefore 51 * a factor of N larger than desired; since N=8 this can be cured by 52 * a simple right shift at the end of the algorithm. The advantage of 53 * this arrangement is that we save two multiplications per 1-D DCT, 54 * because the y0 and y4 outputs need not be divided by sqrt(N). 55 * In the IJG code, this factor of 8 is removed by the quantization step 56 * (in jcdctmgr.c), NOT in this module. 57 * 58 * We have to do addition and subtraction of the integer inputs, which 59 * is no problem, and multiplication by fractional constants, which is 60 * a problem to do in integer arithmetic. We multiply all the constants 61 * by CONST_SCALE and convert them to integer constants (thus retaining 62 * CONST_BITS bits of precision in the constants). After doing a 63 * multiplication we have to divide the product by CONST_SCALE, with proper 64 * rounding, to produce the correct output. This division can be done 65 * cheaply as a right shift of CONST_BITS bits. We postpone shifting 66 * as long as possible so that partial sums can be added together with 67 * full fractional precision. 68 * 69 * The outputs of the first pass are scaled up by PASS1_BITS bits so that 70 * they are represented to better-than-integral precision. These outputs 71 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word 72 * with the recommended scaling. (For 12-bit sample data, the intermediate 73 * array is JLONG anyway.) 74 * 75 * To avoid overflow of the 32-bit intermediate results in pass 2, we must 76 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis 77 * shows that the values given below are the most effective. 78 */ 79 80#if BITS_IN_JSAMPLE == 8 81#define CONST_BITS 13 82#define PASS1_BITS 2 83#else 84#define CONST_BITS 13 85#define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 86#endif 87 88/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 89 * causing a lot of useless floating-point operations at run time. 90 * To get around this we use the following pre-calculated constants. 91 * If you change CONST_BITS you may want to add appropriate values. 92 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 93 */ 94 95#if CONST_BITS == 13 96#define FIX_0_298631336 ((JLONG) 2446) /* FIX(0.298631336) */ 97#define FIX_0_390180644 ((JLONG) 3196) /* FIX(0.390180644) */ 98#define FIX_0_541196100 ((JLONG) 4433) /* FIX(0.541196100) */ 99#define FIX_0_765366865 ((JLONG) 6270) /* FIX(0.765366865) */ 100#define FIX_0_899976223 ((JLONG) 7373) /* FIX(0.899976223) */ 101#define FIX_1_175875602 ((JLONG) 9633) /* FIX(1.175875602) */ 102#define FIX_1_501321110 ((JLONG) 12299) /* FIX(1.501321110) */ 103#define FIX_1_847759065 ((JLONG) 15137) /* FIX(1.847759065) */ 104#define FIX_1_961570560 ((JLONG) 16069) /* FIX(1.961570560) */ 105#define FIX_2_053119869 ((JLONG) 16819) /* FIX(2.053119869) */ 106#define FIX_2_562915447 ((JLONG) 20995) /* FIX(2.562915447) */ 107#define FIX_3_072711026 ((JLONG) 25172) /* FIX(3.072711026) */ 108#else 109#define FIX_0_298631336 FIX(0.298631336) 110#define FIX_0_390180644 FIX(0.390180644) 111#define FIX_0_541196100 FIX(0.541196100) 112#define FIX_0_765366865 FIX(0.765366865) 113#define FIX_0_899976223 FIX(0.899976223) 114#define FIX_1_175875602 FIX(1.175875602) 115#define FIX_1_501321110 FIX(1.501321110) 116#define FIX_1_847759065 FIX(1.847759065) 117#define FIX_1_961570560 FIX(1.961570560) 118#define FIX_2_053119869 FIX(2.053119869) 119#define FIX_2_562915447 FIX(2.562915447) 120#define FIX_3_072711026 FIX(3.072711026) 121#endif 122 123 124/* Multiply an JLONG variable by an JLONG constant to yield an JLONG result. 125 * For 8-bit samples with the recommended scaling, all the variable 126 * and constant values involved are no more than 16 bits wide, so a 127 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. 128 * For 12-bit samples, a full 32-bit multiplication will be needed. 129 */ 130 131#if BITS_IN_JSAMPLE == 8 132#define MULTIPLY(var,const) MULTIPLY16C16(var,const) 133#else 134#define MULTIPLY(var,const) ((var) * (const)) 135#endif 136 137 138/* 139 * Perform the forward DCT on one block of samples. 140 */ 141 142GLOBAL(void) 143jpeg_fdct_islow (DCTELEM *data) 144{ 145 JLONG tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 146 JLONG tmp10, tmp11, tmp12, tmp13; 147 JLONG z1, z2, z3, z4, z5; 148 DCTELEM *dataptr; 149 int ctr; 150 SHIFT_TEMPS 151 152 /* Pass 1: process rows. */ 153 /* Note results are scaled up by sqrt(8) compared to a true DCT; */ 154 /* furthermore, we scale the results by 2**PASS1_BITS. */ 155 156 dataptr = data; 157 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 158 tmp0 = dataptr[0] + dataptr[7]; 159 tmp7 = dataptr[0] - dataptr[7]; 160 tmp1 = dataptr[1] + dataptr[6]; 161 tmp6 = dataptr[1] - dataptr[6]; 162 tmp2 = dataptr[2] + dataptr[5]; 163 tmp5 = dataptr[2] - dataptr[5]; 164 tmp3 = dataptr[3] + dataptr[4]; 165 tmp4 = dataptr[3] - dataptr[4]; 166 167 /* Even part per LL&M figure 1 --- note that published figure is faulty; 168 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 169 */ 170 171 tmp10 = tmp0 + tmp3; 172 tmp13 = tmp0 - tmp3; 173 tmp11 = tmp1 + tmp2; 174 tmp12 = tmp1 - tmp2; 175 176 dataptr[0] = (DCTELEM) LEFT_SHIFT(tmp10 + tmp11, PASS1_BITS); 177 dataptr[4] = (DCTELEM) LEFT_SHIFT(tmp10 - tmp11, PASS1_BITS); 178 179 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 180 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 181 CONST_BITS-PASS1_BITS); 182 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 183 CONST_BITS-PASS1_BITS); 184 185 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 186 * cK represents cos(K*pi/16). 187 * i0..i3 in the paper are tmp4..tmp7 here. 188 */ 189 190 z1 = tmp4 + tmp7; 191 z2 = tmp5 + tmp6; 192 z3 = tmp4 + tmp6; 193 z4 = tmp5 + tmp7; 194 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 195 196 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 197 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 198 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 199 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 200 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 201 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 202 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 203 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 204 205 z3 += z5; 206 z4 += z5; 207 208 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); 209 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); 210 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); 211 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); 212 213 dataptr += DCTSIZE; /* advance pointer to next row */ 214 } 215 216 /* Pass 2: process columns. 217 * We remove the PASS1_BITS scaling, but leave the results scaled up 218 * by an overall factor of 8. 219 */ 220 221 dataptr = data; 222 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 223 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 224 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 225 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 226 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 227 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 228 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 229 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 230 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 231 232 /* Even part per LL&M figure 1 --- note that published figure is faulty; 233 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 234 */ 235 236 tmp10 = tmp0 + tmp3; 237 tmp13 = tmp0 - tmp3; 238 tmp11 = tmp1 + tmp2; 239 tmp12 = tmp1 - tmp2; 240 241 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); 242 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); 243 244 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 245 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 246 CONST_BITS+PASS1_BITS); 247 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 248 CONST_BITS+PASS1_BITS); 249 250 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 251 * cK represents cos(K*pi/16). 252 * i0..i3 in the paper are tmp4..tmp7 here. 253 */ 254 255 z1 = tmp4 + tmp7; 256 z2 = tmp5 + tmp6; 257 z3 = tmp4 + tmp6; 258 z4 = tmp5 + tmp7; 259 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 260 261 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 262 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 263 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 264 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 265 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 266 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 267 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 268 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 269 270 z3 += z5; 271 z4 += z5; 272 273 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, 274 CONST_BITS+PASS1_BITS); 275 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, 276 CONST_BITS+PASS1_BITS); 277 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, 278 CONST_BITS+PASS1_BITS); 279 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, 280 CONST_BITS+PASS1_BITS); 281 282 dataptr++; /* advance pointer to next column */ 283 } 284} 285 286#endif /* DCT_ISLOW_SUPPORTED */ 287