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 file. 9 * 10 * This file contains a slow-but-accurate integer implementation of the 11 * forward DCT (Discrete Cosine Transform). 12 * 13 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 14 * on each column. Direct algorithms are also available, but they are 15 * much more complex and seem not to be any faster when reduced to code. 16 * 17 * This implementation is based on an algorithm described in 18 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT 19 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, 20 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. 21 * The primary algorithm described there uses 11 multiplies and 29 adds. 22 * We use their alternate method with 12 multiplies and 32 adds. 23 * The advantage of this method is that no data path contains more than one 24 * multiplication; this allows a very simple and accurate implementation in 25 * scaled fixed-point arithmetic, with a minimal number of shifts. 26 */ 27 28#define JPEG_INTERNALS 29#include "jinclude.h" 30#include "jpeglib.h" 31#include "jdct.h" /* Private declarations for DCT subsystem */ 32 33#ifdef DCT_ISLOW_SUPPORTED 34 35 36/* 37 * This module is specialized to the case DCTSIZE = 8. 38 */ 39 40#if DCTSIZE != 8 41 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 42#endif 43 44 45/* 46 * The poop on this scaling stuff is as follows: 47 * 48 * Each 1-D DCT step produces outputs which are a factor of sqrt(N) 49 * larger than the true DCT outputs. The final outputs are therefore 50 * a factor of N larger than desired; since N=8 this can be cured by 51 * a simple right shift at the end of the algorithm. The advantage of 52 * this arrangement is that we save two multiplications per 1-D DCT, 53 * because the y0 and y4 outputs need not be divided by sqrt(N). 54 * In the IJG code, this factor of 8 is removed by the quantization step 55 * (in jcdctmgr.c), NOT in this module. 56 * 57 * We have to do addition and subtraction of the integer inputs, which 58 * is no problem, and multiplication by fractional constants, which is 59 * a problem to do in integer arithmetic. We multiply all the constants 60 * by CONST_SCALE and convert them to integer constants (thus retaining 61 * CONST_BITS bits of precision in the constants). After doing a 62 * multiplication we have to divide the product by CONST_SCALE, with proper 63 * rounding, to produce the correct output. This division can be done 64 * cheaply as a right shift of CONST_BITS bits. We postpone shifting 65 * as long as possible so that partial sums can be added together with 66 * full fractional precision. 67 * 68 * The outputs of the first pass are scaled up by PASS1_BITS bits so that 69 * they are represented to better-than-integral precision. These outputs 70 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word 71 * with the recommended scaling. (For 12-bit sample data, the intermediate 72 * array is INT32 anyway.) 73 * 74 * To avoid overflow of the 32-bit intermediate results in pass 2, we must 75 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis 76 * shows that the values given below are the most effective. 77 */ 78 79#if BITS_IN_JSAMPLE == 8 80#define CONST_BITS 13 81#define PASS1_BITS 2 82#else 83#define CONST_BITS 13 84#define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 85#endif 86 87/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 88 * causing a lot of useless floating-point operations at run time. 89 * To get around this we use the following pre-calculated constants. 90 * If you change CONST_BITS you may want to add appropriate values. 91 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 92 */ 93 94#if CONST_BITS == 13 95#define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */ 96#define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */ 97#define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */ 98#define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */ 99#define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */ 100#define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */ 101#define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */ 102#define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */ 103#define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */ 104#define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */ 105#define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */ 106#define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */ 107#else 108#define FIX_0_298631336 FIX(0.298631336) 109#define FIX_0_390180644 FIX(0.390180644) 110#define FIX_0_541196100 FIX(0.541196100) 111#define FIX_0_765366865 FIX(0.765366865) 112#define FIX_0_899976223 FIX(0.899976223) 113#define FIX_1_175875602 FIX(1.175875602) 114#define FIX_1_501321110 FIX(1.501321110) 115#define FIX_1_847759065 FIX(1.847759065) 116#define FIX_1_961570560 FIX(1.961570560) 117#define FIX_2_053119869 FIX(2.053119869) 118#define FIX_2_562915447 FIX(2.562915447) 119#define FIX_3_072711026 FIX(3.072711026) 120#endif 121 122 123/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. 124 * For 8-bit samples with the recommended scaling, all the variable 125 * and constant values involved are no more than 16 bits wide, so a 126 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. 127 * For 12-bit samples, a full 32-bit multiplication will be needed. 128 */ 129 130#if BITS_IN_JSAMPLE == 8 131#define MULTIPLY(var,const) MULTIPLY16C16(var,const) 132#else 133#define MULTIPLY(var,const) ((var) * (const)) 134#endif 135 136 137/* 138 * Perform the forward DCT on one block of samples. 139 */ 140 141GLOBAL(void) 142jpeg_fdct_islow (DCTELEM * data) 143{ 144 INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 145 INT32 tmp10, tmp11, tmp12, tmp13; 146 INT32 z1, z2, z3, z4, z5; 147 DCTELEM *dataptr; 148 int ctr; 149 SHIFT_TEMPS 150 151 /* Pass 1: process rows. */ 152 /* Note results are scaled up by sqrt(8) compared to a true DCT; */ 153 /* furthermore, we scale the results by 2**PASS1_BITS. */ 154 155 dataptr = data; 156 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 157 tmp0 = dataptr[0] + dataptr[7]; 158 tmp7 = dataptr[0] - dataptr[7]; 159 tmp1 = dataptr[1] + dataptr[6]; 160 tmp6 = dataptr[1] - dataptr[6]; 161 tmp2 = dataptr[2] + dataptr[5]; 162 tmp5 = dataptr[2] - dataptr[5]; 163 tmp3 = dataptr[3] + dataptr[4]; 164 tmp4 = dataptr[3] - dataptr[4]; 165 166 /* Even part per LL&M figure 1 --- note that published figure is faulty; 167 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 168 */ 169 170 tmp10 = tmp0 + tmp3; 171 tmp13 = tmp0 - tmp3; 172 tmp11 = tmp1 + tmp2; 173 tmp12 = tmp1 - tmp2; 174 175 dataptr[0] = (DCTELEM) LEFT_SHIFT(tmp10 + tmp11, PASS1_BITS); 176 dataptr[4] = (DCTELEM) LEFT_SHIFT(tmp10 - tmp11, PASS1_BITS); 177 178 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 179 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 180 CONST_BITS-PASS1_BITS); 181 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 182 CONST_BITS-PASS1_BITS); 183 184 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 185 * cK represents cos(K*pi/16). 186 * i0..i3 in the paper are tmp4..tmp7 here. 187 */ 188 189 z1 = tmp4 + tmp7; 190 z2 = tmp5 + tmp6; 191 z3 = tmp4 + tmp6; 192 z4 = tmp5 + tmp7; 193 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 194 195 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 196 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 197 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 198 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 199 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 200 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 201 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 202 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 203 204 z3 += z5; 205 z4 += z5; 206 207 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); 208 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); 209 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); 210 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); 211 212 dataptr += DCTSIZE; /* advance pointer to next row */ 213 } 214 215 /* Pass 2: process columns. 216 * We remove the PASS1_BITS scaling, but leave the results scaled up 217 * by an overall factor of 8. 218 */ 219 220 dataptr = data; 221 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 222 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 223 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 224 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 225 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 226 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 227 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 228 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 229 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 230 231 /* Even part per LL&M figure 1 --- note that published figure is faulty; 232 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 233 */ 234 235 tmp10 = tmp0 + tmp3; 236 tmp13 = tmp0 - tmp3; 237 tmp11 = tmp1 + tmp2; 238 tmp12 = tmp1 - tmp2; 239 240 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); 241 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); 242 243 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 244 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 245 CONST_BITS+PASS1_BITS); 246 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 247 CONST_BITS+PASS1_BITS); 248 249 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 250 * cK represents cos(K*pi/16). 251 * i0..i3 in the paper are tmp4..tmp7 here. 252 */ 253 254 z1 = tmp4 + tmp7; 255 z2 = tmp5 + tmp6; 256 z3 = tmp4 + tmp6; 257 z4 = tmp5 + tmp7; 258 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 259 260 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 261 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 262 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 263 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 264 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 265 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 266 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 267 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 268 269 z3 += z5; 270 z4 += z5; 271 272 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, 273 CONST_BITS+PASS1_BITS); 274 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, 275 CONST_BITS+PASS1_BITS); 276 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, 277 CONST_BITS+PASS1_BITS); 278 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, 279 CONST_BITS+PASS1_BITS); 280 281 dataptr++; /* advance pointer to next column */ 282 } 283} 284 285#endif /* DCT_ISLOW_SUPPORTED */ 286