1 #if !defined(_FX_JPEG_TURBO_) 2 /* 3 * jfdctint.c 4 * 5 * Copyright (C) 1991-1996, Thomas G. Lane. 6 * This file is part of the Independent JPEG Group's software. 7 * For conditions of distribution and use, see the accompanying README file. 8 * 9 * This file contains a slow-but-accurate integer implementation of the 10 * forward DCT (Discrete Cosine Transform). 11 * 12 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 13 * on each column. Direct algorithms are also available, but they are 14 * much more complex and seem not to be any faster when reduced to code. 15 * 16 * This implementation is based on an algorithm described in 17 * C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT 18 * Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics, 19 * Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991. 20 * The primary algorithm described there uses 11 multiplies and 29 adds. 21 * We use their alternate method with 12 multiplies and 32 adds. 22 * The advantage of this method is that no data path contains more than one 23 * multiplication; this allows a very simple and accurate implementation in 24 * scaled fixed-point arithmetic, with a minimal number of shifts. 25 */ 26 27 #define JPEG_INTERNALS 28 #include "jinclude.h" 29 #include "jpeglib.h" 30 #include "jdct.h" /* Private declarations for DCT subsystem */ 31 32 #ifdef DCT_ISLOW_SUPPORTED 33 34 35 /* 36 * This module is specialized to the case DCTSIZE = 8. 37 */ 38 39 #if DCTSIZE != 8 40 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 41 #endif 42 43 44 /* 45 * The poop on this scaling stuff is as follows: 46 * 47 * Each 1-D DCT step produces outputs which are a factor of sqrt(N) 48 * larger than the true DCT outputs. The final outputs are therefore 49 * a factor of N larger than desired; since N=8 this can be cured by 50 * a simple right shift at the end of the algorithm. The advantage of 51 * this arrangement is that we save two multiplications per 1-D DCT, 52 * because the y0 and y4 outputs need not be divided by sqrt(N). 53 * In the IJG code, this factor of 8 is removed by the quantization step 54 * (in jcdctmgr.c), NOT in this module. 55 * 56 * We have to do addition and subtraction of the integer inputs, which 57 * is no problem, and multiplication by fractional constants, which is 58 * a problem to do in integer arithmetic. We multiply all the constants 59 * by CONST_SCALE and convert them to integer constants (thus retaining 60 * CONST_BITS bits of precision in the constants). After doing a 61 * multiplication we have to divide the product by CONST_SCALE, with proper 62 * rounding, to produce the correct output. This division can be done 63 * cheaply as a right shift of CONST_BITS bits. We postpone shifting 64 * as long as possible so that partial sums can be added together with 65 * full fractional precision. 66 * 67 * The outputs of the first pass are scaled up by PASS1_BITS bits so that 68 * they are represented to better-than-integral precision. These outputs 69 * require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word 70 * with the recommended scaling. (For 12-bit sample data, the intermediate 71 * array is INT32 anyway.) 72 * 73 * To avoid overflow of the 32-bit intermediate results in pass 2, we must 74 * have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26. Error analysis 75 * shows that the values given below are the most effective. 76 */ 77 78 #if BITS_IN_JSAMPLE == 8 79 #define CONST_BITS 13 80 #define PASS1_BITS 2 81 #else 82 #define CONST_BITS 13 83 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 84 #endif 85 86 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 87 * causing a lot of useless floating-point operations at run time. 88 * To get around this we use the following pre-calculated constants. 89 * If you change CONST_BITS you may want to add appropriate values. 90 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 91 */ 92 93 #if CONST_BITS == 13 94 #define FIX_0_298631336 ((INT32) 2446) /* FIX(0.298631336) */ 95 #define FIX_0_390180644 ((INT32) 3196) /* FIX(0.390180644) */ 96 #define FIX_0_541196100 ((INT32) 4433) /* FIX(0.541196100) */ 97 #define FIX_0_765366865 ((INT32) 6270) /* FIX(0.765366865) */ 98 #define FIX_0_899976223 ((INT32) 7373) /* FIX(0.899976223) */ 99 #define FIX_1_175875602 ((INT32) 9633) /* FIX(1.175875602) */ 100 #define FIX_1_501321110 ((INT32) 12299) /* FIX(1.501321110) */ 101 #define FIX_1_847759065 ((INT32) 15137) /* FIX(1.847759065) */ 102 #define FIX_1_961570560 ((INT32) 16069) /* FIX(1.961570560) */ 103 #define FIX_2_053119869 ((INT32) 16819) /* FIX(2.053119869) */ 104 #define FIX_2_562915447 ((INT32) 20995) /* FIX(2.562915447) */ 105 #define FIX_3_072711026 ((INT32) 25172) /* FIX(3.072711026) */ 106 #else 107 #define FIX_0_298631336 FIX(0.298631336) 108 #define FIX_0_390180644 FIX(0.390180644) 109 #define FIX_0_541196100 FIX(0.541196100) 110 #define FIX_0_765366865 FIX(0.765366865) 111 #define FIX_0_899976223 FIX(0.899976223) 112 #define FIX_1_175875602 FIX(1.175875602) 113 #define FIX_1_501321110 FIX(1.501321110) 114 #define FIX_1_847759065 FIX(1.847759065) 115 #define FIX_1_961570560 FIX(1.961570560) 116 #define FIX_2_053119869 FIX(2.053119869) 117 #define FIX_2_562915447 FIX(2.562915447) 118 #define FIX_3_072711026 FIX(3.072711026) 119 #endif 120 121 122 /* Multiply an INT32 variable by an INT32 constant to yield an INT32 result. 123 * For 8-bit samples with the recommended scaling, all the variable 124 * and constant values involved are no more than 16 bits wide, so a 125 * 16x16->32 bit multiply can be used instead of a full 32x32 multiply. 126 * For 12-bit samples, a full 32-bit multiplication will be needed. 127 */ 128 129 #if BITS_IN_JSAMPLE == 8 130 #define MULTIPLY(var,const) MULTIPLY16C16(var,const) 131 #else 132 #define MULTIPLY(var,const) ((var) * (const)) 133 #endif 134 135 136 /* 137 * Perform the forward DCT on one block of samples. 138 */ 139 140 GLOBAL(void) 141 jpeg_fdct_islow (DCTELEM * data) 142 { 143 INT32 tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 144 INT32 tmp10, tmp11, tmp12, tmp13; 145 INT32 z1, z2, z3, z4, z5; 146 DCTELEM *dataptr; 147 int ctr; 148 SHIFT_TEMPS 149 150 /* Pass 1: process rows. */ 151 /* Note results are scaled up by sqrt(8) compared to a true DCT; */ 152 /* furthermore, we scale the results by 2**PASS1_BITS. */ 153 154 dataptr = data; 155 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 156 tmp0 = dataptr[0] + dataptr[7]; 157 tmp7 = dataptr[0] - dataptr[7]; 158 tmp1 = dataptr[1] + dataptr[6]; 159 tmp6 = dataptr[1] - dataptr[6]; 160 tmp2 = dataptr[2] + dataptr[5]; 161 tmp5 = dataptr[2] - dataptr[5]; 162 tmp3 = dataptr[3] + dataptr[4]; 163 tmp4 = dataptr[3] - dataptr[4]; 164 165 /* Even part per LL&M figure 1 --- note that published figure is faulty; 166 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 167 */ 168 169 tmp10 = tmp0 + tmp3; 170 tmp13 = tmp0 - tmp3; 171 tmp11 = tmp1 + tmp2; 172 tmp12 = tmp1 - tmp2; 173 174 dataptr[0] = (DCTELEM) ((tmp10 + tmp11) << PASS1_BITS); 175 dataptr[4] = (DCTELEM) ((tmp10 - tmp11) << PASS1_BITS); 176 177 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 178 dataptr[2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 179 CONST_BITS-PASS1_BITS); 180 dataptr[6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 181 CONST_BITS-PASS1_BITS); 182 183 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 184 * cK represents cos(K*pi/16). 185 * i0..i3 in the paper are tmp4..tmp7 here. 186 */ 187 188 z1 = tmp4 + tmp7; 189 z2 = tmp5 + tmp6; 190 z3 = tmp4 + tmp6; 191 z4 = tmp5 + tmp7; 192 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 193 194 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 195 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 196 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 197 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 198 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 199 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 200 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 201 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 202 203 z3 += z5; 204 z4 += z5; 205 206 dataptr[7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, CONST_BITS-PASS1_BITS); 207 dataptr[5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, CONST_BITS-PASS1_BITS); 208 dataptr[3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, CONST_BITS-PASS1_BITS); 209 dataptr[1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, CONST_BITS-PASS1_BITS); 210 211 dataptr += DCTSIZE; /* advance pointer to next row */ 212 } 213 214 /* Pass 2: process columns. 215 * We remove the PASS1_BITS scaling, but leave the results scaled up 216 * by an overall factor of 8. 217 */ 218 219 dataptr = data; 220 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 221 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 222 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 223 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 224 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 225 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 226 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 227 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 228 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 229 230 /* Even part per LL&M figure 1 --- note that published figure is faulty; 231 * rotator "sqrt(2)*c1" should be "sqrt(2)*c6". 232 */ 233 234 tmp10 = tmp0 + tmp3; 235 tmp13 = tmp0 - tmp3; 236 tmp11 = tmp1 + tmp2; 237 tmp12 = tmp1 - tmp2; 238 239 dataptr[DCTSIZE*0] = (DCTELEM) DESCALE(tmp10 + tmp11, PASS1_BITS); 240 dataptr[DCTSIZE*4] = (DCTELEM) DESCALE(tmp10 - tmp11, PASS1_BITS); 241 242 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_541196100); 243 dataptr[DCTSIZE*2] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp13, FIX_0_765366865), 244 CONST_BITS+PASS1_BITS); 245 dataptr[DCTSIZE*6] = (DCTELEM) DESCALE(z1 + MULTIPLY(tmp12, - FIX_1_847759065), 246 CONST_BITS+PASS1_BITS); 247 248 /* Odd part per figure 8 --- note paper omits factor of sqrt(2). 249 * cK represents cos(K*pi/16). 250 * i0..i3 in the paper are tmp4..tmp7 here. 251 */ 252 253 z1 = tmp4 + tmp7; 254 z2 = tmp5 + tmp6; 255 z3 = tmp4 + tmp6; 256 z4 = tmp5 + tmp7; 257 z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */ 258 259 tmp4 = MULTIPLY(tmp4, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */ 260 tmp5 = MULTIPLY(tmp5, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */ 261 tmp6 = MULTIPLY(tmp6, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */ 262 tmp7 = MULTIPLY(tmp7, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */ 263 z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */ 264 z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */ 265 z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */ 266 z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */ 267 268 z3 += z5; 269 z4 += z5; 270 271 dataptr[DCTSIZE*7] = (DCTELEM) DESCALE(tmp4 + z1 + z3, 272 CONST_BITS+PASS1_BITS); 273 dataptr[DCTSIZE*5] = (DCTELEM) DESCALE(tmp5 + z2 + z4, 274 CONST_BITS+PASS1_BITS); 275 dataptr[DCTSIZE*3] = (DCTELEM) DESCALE(tmp6 + z2 + z3, 276 CONST_BITS+PASS1_BITS); 277 dataptr[DCTSIZE*1] = (DCTELEM) DESCALE(tmp7 + z1 + z4, 278 CONST_BITS+PASS1_BITS); 279 280 dataptr++; /* advance pointer to next column */ 281 } 282 } 283 284 #endif /* DCT_ISLOW_SUPPORTED */ 285 286 #endif //_FX_JPEG_TURBO_ 287