jidctint.cpp (16274B)
1 /* 2 * jidctint.c 3 * 4 * Copyright (C) 1991-1994, 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 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine 10 * must also perform dequantization of the input coefficients. 11 * 12 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT 13 * on each row (or vice versa, but it's more convenient to emit a row at 14 * a time). Direct algorithms are also available, but they are much more 15 * 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 8 x8 DCTs. /* deliberate syntax err */ 42 #endif 43 44 45 /* 46 * The poop on this scaling stuff is as follows: 47 * 48 * Each 1-D IDCT step produces outputs which are a factor of sqrt(N) 49 * larger than the true IDCT 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 IDCT, 53 * because the y0 and y4 inputs need not be divided by sqrt(N). 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. (To scale up 12-bit sample data further, an 70 * intermediate INT32 array would be needed.) 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 /* Dequantize a coefficient by multiplying it by the multiplier-table 136 * entry; produce an int result. In this module, both inputs and result 137 * are 16 bits or less, so either int or short multiply will work. 138 */ 139 140 #define DEQUANTIZE( coef, quantval ) ( ( (ISLOW_MULT_TYPE) ( coef ) ) * ( quantval ) ) 141 142 143 /* 144 * Perform dequantization and inverse DCT on one block of coefficients. 145 */ 146 147 GLOBAL void 148 jpeg_idct_islow( j_decompress_ptr cinfo, jpeg_component_info * compptr, 149 JCOEFPTR coef_block, 150 JSAMPARRAY output_buf, JDIMENSION output_col ) { 151 INT32 tmp0, tmp1, tmp2, tmp3; 152 INT32 tmp10, tmp11, tmp12, tmp13; 153 INT32 z1, z2, z3, z4, z5; 154 JCOEFPTR inptr; 155 ISLOW_MULT_TYPE * quantptr; 156 int * wsptr; 157 JSAMPROW outptr; 158 JSAMPLE * range_limit = IDCT_range_limit( cinfo ); 159 int ctr; 160 int workspace[DCTSIZE2];/* buffers data between passes */ 161 SHIFT_TEMPS 162 163 /* Pass 1: process columns from input, store into work array. */ 164 /* Note results are scaled up by sqrt(8) compared to a true IDCT; */ 165 /* furthermore, we scale the results by 2**PASS1_BITS. */ 166 167 inptr = coef_block; 168 quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table; 169 wsptr = workspace; 170 for ( ctr = DCTSIZE; ctr > 0; ctr-- ) { 171 /* Due to quantization, we will usually find that many of the input 172 * coefficients are zero, especially the AC terms. We can exploit this 173 * by short-circuiting the IDCT calculation for any column in which all 174 * the AC terms are zero. In that case each output is equal to the 175 * DC coefficient (with scale factor as needed). 176 * With typical images and quantization tables, half or more of the 177 * column DCT calculations can be simplified this way. 178 */ 179 180 if ( ( inptr[DCTSIZE * 1] | inptr[DCTSIZE * 2] | inptr[DCTSIZE * 3] | 181 inptr[DCTSIZE * 4] | inptr[DCTSIZE * 5] | inptr[DCTSIZE * 6] | 182 inptr[DCTSIZE * 7] ) == 0 ) { 183 /* AC terms all zero */ 184 int dcval = DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] ) << PASS1_BITS; 185 186 wsptr[DCTSIZE * 0] = dcval; 187 wsptr[DCTSIZE * 1] = dcval; 188 wsptr[DCTSIZE * 2] = dcval; 189 wsptr[DCTSIZE * 3] = dcval; 190 wsptr[DCTSIZE * 4] = dcval; 191 wsptr[DCTSIZE * 5] = dcval; 192 wsptr[DCTSIZE * 6] = dcval; 193 wsptr[DCTSIZE * 7] = dcval; 194 195 inptr++; /* advance pointers to next column */ 196 quantptr++; 197 wsptr++; 198 continue; 199 } 200 201 /* Even part: reverse the even part of the forward DCT. */ 202 /* The rotator is sqrt(2)*c(-6). */ 203 204 z2 = DEQUANTIZE( inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] ); 205 z3 = DEQUANTIZE( inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] ); 206 207 z1 = MULTIPLY( z2 + z3, FIX_0_541196100 ); 208 tmp2 = z1 + MULTIPLY( z3, -FIX_1_847759065 ); 209 tmp3 = z1 + MULTIPLY( z2, FIX_0_765366865 ); 210 211 z2 = DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] ); 212 z3 = DEQUANTIZE( inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] ); 213 214 tmp0 = ( z2 + z3 ) << CONST_BITS; 215 tmp1 = ( z2 - z3 ) << CONST_BITS; 216 217 tmp10 = tmp0 + tmp3; 218 tmp13 = tmp0 - tmp3; 219 tmp11 = tmp1 + tmp2; 220 tmp12 = tmp1 - tmp2; 221 222 /* Odd part per figure 8; the matrix is unitary and hence its 223 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. 224 */ 225 226 tmp0 = DEQUANTIZE( inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] ); 227 tmp1 = DEQUANTIZE( inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] ); 228 tmp2 = DEQUANTIZE( inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] ); 229 tmp3 = DEQUANTIZE( inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1] ); 230 231 z1 = tmp0 + tmp3; 232 z2 = tmp1 + tmp2; 233 z3 = tmp0 + tmp2; 234 z4 = tmp1 + tmp3; 235 z5 = MULTIPLY( z3 + z4, FIX_1_175875602 );/* sqrt(2) * c3 */ 236 237 tmp0 = MULTIPLY( tmp0, FIX_0_298631336 );/* sqrt(2) * (-c1+c3+c5-c7) */ 238 tmp1 = MULTIPLY( tmp1, FIX_2_053119869 );/* sqrt(2) * ( c1+c3-c5+c7) */ 239 tmp2 = MULTIPLY( tmp2, FIX_3_072711026 );/* sqrt(2) * ( c1+c3+c5-c7) */ 240 tmp3 = MULTIPLY( tmp3, FIX_1_501321110 );/* sqrt(2) * ( c1+c3-c5-c7) */ 241 z1 = MULTIPLY( z1, -FIX_0_899976223 );/* sqrt(2) * (c7-c3) */ 242 z2 = MULTIPLY( z2, -FIX_2_562915447 );/* sqrt(2) * (-c1-c3) */ 243 z3 = MULTIPLY( z3, -FIX_1_961570560 );/* sqrt(2) * (-c3-c5) */ 244 z4 = MULTIPLY( z4, -FIX_0_390180644 );/* sqrt(2) * (c5-c3) */ 245 246 z3 += z5; 247 z4 += z5; 248 249 tmp0 += z1 + z3; 250 tmp1 += z2 + z4; 251 tmp2 += z2 + z3; 252 tmp3 += z1 + z4; 253 254 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ 255 256 wsptr[DCTSIZE * 0] = (int) DESCALE( tmp10 + tmp3, CONST_BITS - PASS1_BITS ); 257 wsptr[DCTSIZE * 7] = (int) DESCALE( tmp10 - tmp3, CONST_BITS - PASS1_BITS ); 258 wsptr[DCTSIZE * 1] = (int) DESCALE( tmp11 + tmp2, CONST_BITS - PASS1_BITS ); 259 wsptr[DCTSIZE * 6] = (int) DESCALE( tmp11 - tmp2, CONST_BITS - PASS1_BITS ); 260 wsptr[DCTSIZE * 2] = (int) DESCALE( tmp12 + tmp1, CONST_BITS - PASS1_BITS ); 261 wsptr[DCTSIZE * 5] = (int) DESCALE( tmp12 - tmp1, CONST_BITS - PASS1_BITS ); 262 wsptr[DCTSIZE * 3] = (int) DESCALE( tmp13 + tmp0, CONST_BITS - PASS1_BITS ); 263 wsptr[DCTSIZE * 4] = (int) DESCALE( tmp13 - tmp0, CONST_BITS - PASS1_BITS ); 264 265 inptr++; /* advance pointers to next column */ 266 quantptr++; 267 wsptr++; 268 } 269 270 /* Pass 2: process rows from work array, store into output array. */ 271 /* Note that we must descale the results by a factor of 8 == 2**3, */ 272 /* and also undo the PASS1_BITS scaling. */ 273 274 wsptr = workspace; 275 for ( ctr = 0; ctr < DCTSIZE; ctr++ ) { 276 outptr = output_buf[ctr] + output_col; 277 /* Rows of zeroes can be exploited in the same way as we did with columns. 278 * However, the column calculation has created many nonzero AC terms, so 279 * the simplification applies less often (typically 5% to 10% of the time). 280 * On machines with very fast multiplication, it's possible that the 281 * test takes more time than it's worth. In that case this section 282 * may be commented out. 283 */ 284 285 #ifndef NO_ZERO_ROW_TEST 286 if ( ( wsptr[1] | wsptr[2] | wsptr[3] | wsptr[4] | wsptr[5] | wsptr[6] | 287 wsptr[7] ) == 0 ) { 288 /* AC terms all zero */ 289 JSAMPLE dcval = range_limit[(int) DESCALE( (INT32) wsptr[0], PASS1_BITS + 3 ) 290 & RANGE_MASK]; 291 292 outptr[0] = dcval; 293 outptr[1] = dcval; 294 outptr[2] = dcval; 295 outptr[3] = dcval; 296 outptr[4] = dcval; 297 outptr[5] = dcval; 298 outptr[6] = dcval; 299 outptr[7] = dcval; 300 301 wsptr += DCTSIZE;/* advance pointer to next row */ 302 continue; 303 } 304 #endif 305 306 /* Even part: reverse the even part of the forward DCT. */ 307 /* The rotator is sqrt(2)*c(-6). */ 308 309 z2 = (INT32) wsptr[2]; 310 z3 = (INT32) wsptr[6]; 311 312 z1 = MULTIPLY( z2 + z3, FIX_0_541196100 ); 313 tmp2 = z1 + MULTIPLY( z3, -FIX_1_847759065 ); 314 tmp3 = z1 + MULTIPLY( z2, FIX_0_765366865 ); 315 316 tmp0 = ( (INT32) wsptr[0] + (INT32) wsptr[4] ) << CONST_BITS; 317 tmp1 = ( (INT32) wsptr[0] - (INT32) wsptr[4] ) << CONST_BITS; 318 319 tmp10 = tmp0 + tmp3; 320 tmp13 = tmp0 - tmp3; 321 tmp11 = tmp1 + tmp2; 322 tmp12 = tmp1 - tmp2; 323 324 /* Odd part per figure 8; the matrix is unitary and hence its 325 * transpose is its inverse. i0..i3 are y7,y5,y3,y1 respectively. 326 */ 327 328 tmp0 = (INT32) wsptr[7]; 329 tmp1 = (INT32) wsptr[5]; 330 tmp2 = (INT32) wsptr[3]; 331 tmp3 = (INT32) wsptr[1]; 332 333 z1 = tmp0 + tmp3; 334 z2 = tmp1 + tmp2; 335 z3 = tmp0 + tmp2; 336 z4 = tmp1 + tmp3; 337 z5 = MULTIPLY( z3 + z4, FIX_1_175875602 );/* sqrt(2) * c3 */ 338 339 tmp0 = MULTIPLY( tmp0, FIX_0_298631336 );/* sqrt(2) * (-c1+c3+c5-c7) */ 340 tmp1 = MULTIPLY( tmp1, FIX_2_053119869 );/* sqrt(2) * ( c1+c3-c5+c7) */ 341 tmp2 = MULTIPLY( tmp2, FIX_3_072711026 );/* sqrt(2) * ( c1+c3+c5-c7) */ 342 tmp3 = MULTIPLY( tmp3, FIX_1_501321110 );/* sqrt(2) * ( c1+c3-c5-c7) */ 343 z1 = MULTIPLY( z1, -FIX_0_899976223 );/* sqrt(2) * (c7-c3) */ 344 z2 = MULTIPLY( z2, -FIX_2_562915447 );/* sqrt(2) * (-c1-c3) */ 345 z3 = MULTIPLY( z3, -FIX_1_961570560 );/* sqrt(2) * (-c3-c5) */ 346 z4 = MULTIPLY( z4, -FIX_0_390180644 );/* sqrt(2) * (c5-c3) */ 347 348 z3 += z5; 349 z4 += z5; 350 351 tmp0 += z1 + z3; 352 tmp1 += z2 + z4; 353 tmp2 += z2 + z3; 354 tmp3 += z1 + z4; 355 356 /* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */ 357 358 outptr[0] = range_limit[(int) DESCALE( tmp10 + tmp3, 359 CONST_BITS + PASS1_BITS + 3 ) 360 & RANGE_MASK]; 361 outptr[7] = range_limit[(int) DESCALE( tmp10 - tmp3, 362 CONST_BITS + PASS1_BITS + 3 ) 363 & RANGE_MASK]; 364 outptr[1] = range_limit[(int) DESCALE( tmp11 + tmp2, 365 CONST_BITS + PASS1_BITS + 3 ) 366 & RANGE_MASK]; 367 outptr[6] = range_limit[(int) DESCALE( tmp11 - tmp2, 368 CONST_BITS + PASS1_BITS + 3 ) 369 & RANGE_MASK]; 370 outptr[2] = range_limit[(int) DESCALE( tmp12 + tmp1, 371 CONST_BITS + PASS1_BITS + 3 ) 372 & RANGE_MASK]; 373 outptr[5] = range_limit[(int) DESCALE( tmp12 - tmp1, 374 CONST_BITS + PASS1_BITS + 3 ) 375 & RANGE_MASK]; 376 outptr[3] = range_limit[(int) DESCALE( tmp13 + tmp0, 377 CONST_BITS + PASS1_BITS + 3 ) 378 & RANGE_MASK]; 379 outptr[4] = range_limit[(int) DESCALE( tmp13 - tmp0, 380 CONST_BITS + PASS1_BITS + 3 ) 381 & RANGE_MASK]; 382 383 wsptr += DCTSIZE; /* advance pointer to next row */ 384 } 385 } 386 387 #endif /* DCT_ISLOW_SUPPORTED */