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 139GLOBAL(void) 140jpeg_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_847759065), 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 */ 284