jidctfst.cpp (14346B)
1 /* 2 * jidctfst.c 3 * 4 * Copyright (C) 1994-1995, 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 fast, not so 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 Arai, Agui, and Nakajima's algorithm for 18 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 19 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 20 * JPEG textbook (see REFERENCES section in file README). The following code 21 * is based directly on figure 4-8 in P&M. 22 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 23 * possible to arrange the computation so that many of the multiplies are 24 * simple scalings of the final outputs. These multiplies can then be 25 * folded into the multiplications or divisions by the JPEG quantization 26 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 27 * to be done in the DCT itself. 28 * The primary disadvantage of this method is that with fixed-point math, 29 * accuracy is lost due to imprecise representation of the scaled 30 * quantization values. The smaller the quantization table entry, the less 31 * precise the scaled value, so this implementation does worse with high- 32 * quality-setting files than with low-quality ones. 33 */ 34 35 #define JPEG_INTERNALS 36 #include "jinclude.h" 37 #include "jpeglib.h" 38 #include "jdct.h" /* Private declarations for DCT subsystem */ 39 40 #ifdef DCT_IFAST_SUPPORTED 41 42 43 /* 44 * This module is specialized to the case DCTSIZE = 8. 45 */ 46 47 #if DCTSIZE != 8 48 Sorry, this code only copes with 8 x8 DCTs. /* deliberate syntax err */ 49 #endif 50 51 52 /* Scaling decisions are generally the same as in the LL&M algorithm; 53 * see jidctint.c for more details. However, we choose to descale 54 * (right shift) multiplication products as soon as they are formed, 55 * rather than carrying additional fractional bits into subsequent additions. 56 * This compromises accuracy slightly, but it lets us save a few shifts. 57 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 58 * everywhere except in the multiplications proper; this saves a good deal 59 * of work on 16-bit-int machines. 60 * 61 * The dequantized coefficients are not integers because the AA&N scaling 62 * factors have been incorporated. We represent them scaled up by PASS1_BITS, 63 * so that the first and second IDCT rounds have the same input scaling. 64 * For 8-bit JSAMPLEs, we choose IFAST_SCALE_BITS = PASS1_BITS so as to 65 * avoid a descaling shift; this compromises accuracy rather drastically 66 * for small quantization table entries, but it saves a lot of shifts. 67 * For 12-bit JSAMPLEs, there's no hope of using 16x16 multiplies anyway, 68 * so we use a much larger scaling factor to preserve accuracy. 69 * 70 * A final compromise is to represent the multiplicative constants to only 71 * 8 fractional bits, rather than 13. This saves some shifting work on some 72 * machines, and may also reduce the cost of multiplication (since there 73 * are fewer one-bits in the constants). 74 */ 75 76 #if BITS_IN_JSAMPLE == 8 77 #define CONST_BITS 8 78 #define PASS1_BITS 2 79 #else 80 #define CONST_BITS 8 81 #define PASS1_BITS 1 /* lose a little precision to avoid overflow */ 82 #endif 83 84 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 85 * causing a lot of useless floating-point operations at run time. 86 * To get around this we use the following pre-calculated constants. 87 * If you change CONST_BITS you may want to add appropriate values. 88 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 89 */ 90 91 #if CONST_BITS == 8 92 #define FIX_1_082392200 ( (INT32) 277 ) /* FIX(1.082392200) */ 93 #define FIX_1_414213562 ( (INT32) 362 ) /* FIX(1.414213562) */ 94 #define FIX_1_847759065 ( (INT32) 473 ) /* FIX(1.847759065) */ 95 #define FIX_2_613125930 ( (INT32) 669 ) /* FIX(2.613125930) */ 96 #else 97 #define FIX_1_082392200 FIX( 1.082392200 ) 98 #define FIX_1_414213562 FIX( 1.414213562 ) 99 #define FIX_1_847759065 FIX( 1.847759065 ) 100 #define FIX_2_613125930 FIX( 2.613125930 ) 101 #endif 102 103 104 /* We can gain a little more speed, with a further compromise in accuracy, 105 * by omitting the addition in a descaling shift. This yields an incorrectly 106 * rounded result half the time... 107 */ 108 109 #ifndef USE_ACCURATE_ROUNDING 110 #undef DESCALE 111 #define DESCALE( x, n ) RIGHT_SHIFT( x, n ) 112 #endif 113 114 115 /* Multiply a DCTELEM variable by an INT32 constant, and immediately 116 * descale to yield a DCTELEM result. 117 */ 118 119 #define MULTIPLY( var, const ) ( (DCTELEM) DESCALE( ( var ) * ( const ), CONST_BITS ) ) 120 121 122 /* Dequantize a coefficient by multiplying it by the multiplier-table 123 * entry; produce a DCTELEM result. For 8-bit data a 16x16->16 124 * multiplication will do. For 12-bit data, the multiplier table is 125 * declared INT32, so a 32-bit multiply will be used. 126 */ 127 128 #if BITS_IN_JSAMPLE == 8 129 #define DEQUANTIZE( coef, quantval ) ( ( (IFAST_MULT_TYPE) ( coef ) ) * ( quantval ) ) 130 #else 131 #define DEQUANTIZE( coef, quantval ) \ 132 DESCALE( ( coef ) * ( quantval ), IFAST_SCALE_BITS - PASS1_BITS ) 133 #endif 134 135 136 /* Like DESCALE, but applies to a DCTELEM and produces an int. 137 * We assume that int right shift is unsigned if INT32 right shift is. 138 */ 139 140 #ifdef RIGHT_SHIFT_IS_UNSIGNED 141 #define ISHIFT_TEMPS DCTELEM ishift_temp; 142 #if BITS_IN_JSAMPLE == 8 143 #define DCTELEMBITS 16 /* DCTELEM may be 16 or 32 bits */ 144 #else 145 #define DCTELEMBITS 32 /* DCTELEM must be 32 bits */ 146 #endif 147 #define IRIGHT_SHIFT( x, shft ) \ 148 ( ( ishift_temp = ( x ) ) < 0 ? \ 149 ( ishift_temp >> ( shft ) ) | ( ( ~( (DCTELEM) 0 ) ) << ( DCTELEMBITS - ( shft ) ) ) : \ 150 ( ishift_temp >> ( shft ) ) ) 151 #else 152 #define ISHIFT_TEMPS 153 #define IRIGHT_SHIFT( x, shft ) ( ( x ) >> ( shft ) ) 154 #endif 155 156 #ifdef USE_ACCURATE_ROUNDING 157 #define IDESCALE( x, n ) ( (int) IRIGHT_SHIFT( ( x ) + ( 1 << ( ( n ) - 1 ) ), n ) ) 158 #else 159 #define IDESCALE( x, n ) ( (int) IRIGHT_SHIFT( x, n ) ) 160 #endif 161 162 163 /* 164 * Perform dequantization and inverse DCT on one block of coefficients. 165 */ 166 167 GLOBAL void 168 jpeg_idct_ifast( j_decompress_ptr cinfo, jpeg_component_info * compptr, 169 JCOEFPTR coef_block, 170 JSAMPARRAY output_buf, JDIMENSION output_col ) { 171 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 172 DCTELEM tmp10, tmp11, tmp12, tmp13; 173 DCTELEM z5, z10, z11, z12, z13; 174 JCOEFPTR inptr; 175 IFAST_MULT_TYPE * quantptr; 176 int * wsptr; 177 JSAMPROW outptr; 178 JSAMPLE * range_limit = IDCT_range_limit( cinfo ); 179 int ctr; 180 int workspace[DCTSIZE2];/* buffers data between passes */ 181 SHIFT_TEMPS /* for DESCALE */ 182 ISHIFT_TEMPS /* for IDESCALE */ 183 184 /* Pass 1: process columns from input, store into work array. */ 185 186 inptr = coef_block; 187 quantptr = (IFAST_MULT_TYPE *) compptr->dct_table; 188 wsptr = workspace; 189 for ( ctr = DCTSIZE; ctr > 0; ctr-- ) { 190 /* Due to quantization, we will usually find that many of the input 191 * coefficients are zero, especially the AC terms. We can exploit this 192 * by short-circuiting the IDCT calculation for any column in which all 193 * the AC terms are zero. In that case each output is equal to the 194 * DC coefficient (with scale factor as needed). 195 * With typical images and quantization tables, half or more of the 196 * column DCT calculations can be simplified this way. 197 */ 198 199 if ( ( inptr[DCTSIZE * 1] | inptr[DCTSIZE * 2] | inptr[DCTSIZE * 3] | 200 inptr[DCTSIZE * 4] | inptr[DCTSIZE * 5] | inptr[DCTSIZE * 6] | 201 inptr[DCTSIZE * 7] ) == 0 ) { 202 /* AC terms all zero */ 203 int dcval = (int) DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] ); 204 205 wsptr[DCTSIZE * 0] = dcval; 206 wsptr[DCTSIZE * 1] = dcval; 207 wsptr[DCTSIZE * 2] = dcval; 208 wsptr[DCTSIZE * 3] = dcval; 209 wsptr[DCTSIZE * 4] = dcval; 210 wsptr[DCTSIZE * 5] = dcval; 211 wsptr[DCTSIZE * 6] = dcval; 212 wsptr[DCTSIZE * 7] = dcval; 213 214 inptr++; /* advance pointers to next column */ 215 quantptr++; 216 wsptr++; 217 continue; 218 } 219 220 /* Even part */ 221 222 tmp0 = DEQUANTIZE( inptr[DCTSIZE * 0], quantptr[DCTSIZE * 0] ); 223 tmp1 = DEQUANTIZE( inptr[DCTSIZE * 2], quantptr[DCTSIZE * 2] ); 224 tmp2 = DEQUANTIZE( inptr[DCTSIZE * 4], quantptr[DCTSIZE * 4] ); 225 tmp3 = DEQUANTIZE( inptr[DCTSIZE * 6], quantptr[DCTSIZE * 6] ); 226 227 tmp10 = tmp0 + tmp2;/* phase 3 */ 228 tmp11 = tmp0 - tmp2; 229 230 tmp13 = tmp1 + tmp3;/* phases 5-3 */ 231 tmp12 = MULTIPLY( tmp1 - tmp3, FIX_1_414213562 ) - tmp13;/* 2*c4 */ 232 233 tmp0 = tmp10 + tmp13;/* phase 2 */ 234 tmp3 = tmp10 - tmp13; 235 tmp1 = tmp11 + tmp12; 236 tmp2 = tmp11 - tmp12; 237 238 /* Odd part */ 239 240 tmp4 = DEQUANTIZE( inptr[DCTSIZE * 1], quantptr[DCTSIZE * 1] ); 241 tmp5 = DEQUANTIZE( inptr[DCTSIZE * 3], quantptr[DCTSIZE * 3] ); 242 tmp6 = DEQUANTIZE( inptr[DCTSIZE * 5], quantptr[DCTSIZE * 5] ); 243 tmp7 = DEQUANTIZE( inptr[DCTSIZE * 7], quantptr[DCTSIZE * 7] ); 244 245 z13 = tmp6 + tmp5; /* phase 6 */ 246 z10 = tmp6 - tmp5; 247 z11 = tmp4 + tmp7; 248 z12 = tmp4 - tmp7; 249 250 tmp7 = z11 + z13; /* phase 5 */ 251 tmp11 = MULTIPLY( z11 - z13, FIX_1_414213562 );/* 2*c4 */ 252 253 z5 = MULTIPLY( z10 + z12, FIX_1_847759065 );/* 2*c2 */ 254 tmp10 = MULTIPLY( z12, FIX_1_082392200 ) - z5;/* 2*(c2-c6) */ 255 tmp12 = MULTIPLY( z10, -FIX_2_613125930 ) + z5;/* -2*(c2+c6) */ 256 257 tmp6 = tmp12 - tmp7;/* phase 2 */ 258 tmp5 = tmp11 - tmp6; 259 tmp4 = tmp10 + tmp5; 260 261 wsptr[DCTSIZE * 0] = (int) ( tmp0 + tmp7 ); 262 wsptr[DCTSIZE * 7] = (int) ( tmp0 - tmp7 ); 263 wsptr[DCTSIZE * 1] = (int) ( tmp1 + tmp6 ); 264 wsptr[DCTSIZE * 6] = (int) ( tmp1 - tmp6 ); 265 wsptr[DCTSIZE * 2] = (int) ( tmp2 + tmp5 ); 266 wsptr[DCTSIZE * 5] = (int) ( tmp2 - tmp5 ); 267 wsptr[DCTSIZE * 4] = (int) ( tmp3 + tmp4 ); 268 wsptr[DCTSIZE * 3] = (int) ( tmp3 - tmp4 ); 269 270 inptr++; /* advance pointers to next column */ 271 quantptr++; 272 wsptr++; 273 } 274 275 /* Pass 2: process rows from work array, store into output array. */ 276 /* Note that we must descale the results by a factor of 8 == 2**3, */ 277 /* and also undo the PASS1_BITS scaling. */ 278 279 wsptr = workspace; 280 for ( ctr = 0; ctr < DCTSIZE; ctr++ ) { 281 outptr = output_buf[ctr] + output_col; 282 /* Rows of zeroes can be exploited in the same way as we did with columns. 283 * However, the column calculation has created many nonzero AC terms, so 284 * the simplification applies less often (typically 5% to 10% of the time). 285 * On machines with very fast multiplication, it's possible that the 286 * test takes more time than it's worth. In that case this section 287 * may be commented out. 288 */ 289 290 #ifndef NO_ZERO_ROW_TEST 291 if ( ( wsptr[1] | wsptr[2] | wsptr[3] | wsptr[4] | wsptr[5] | wsptr[6] | 292 wsptr[7] ) == 0 ) { 293 /* AC terms all zero */ 294 JSAMPLE dcval = range_limit[IDESCALE( wsptr[0], PASS1_BITS + 3 ) 295 & RANGE_MASK]; 296 297 outptr[0] = dcval; 298 outptr[1] = dcval; 299 outptr[2] = dcval; 300 outptr[3] = dcval; 301 outptr[4] = dcval; 302 outptr[5] = dcval; 303 outptr[6] = dcval; 304 outptr[7] = dcval; 305 306 wsptr += DCTSIZE;/* advance pointer to next row */ 307 continue; 308 } 309 #endif 310 311 /* Even part */ 312 313 tmp10 = ( (DCTELEM) wsptr[0] + (DCTELEM) wsptr[4] ); 314 tmp11 = ( (DCTELEM) wsptr[0] - (DCTELEM) wsptr[4] ); 315 316 tmp13 = ( (DCTELEM) wsptr[2] + (DCTELEM) wsptr[6] ); 317 tmp12 = MULTIPLY( (DCTELEM) wsptr[2] - (DCTELEM) wsptr[6], FIX_1_414213562 ) 318 - tmp13; 319 320 tmp0 = tmp10 + tmp13; 321 tmp3 = tmp10 - tmp13; 322 tmp1 = tmp11 + tmp12; 323 tmp2 = tmp11 - tmp12; 324 325 /* Odd part */ 326 327 z13 = (DCTELEM) wsptr[5] + (DCTELEM) wsptr[3]; 328 z10 = (DCTELEM) wsptr[5] - (DCTELEM) wsptr[3]; 329 z11 = (DCTELEM) wsptr[1] + (DCTELEM) wsptr[7]; 330 z12 = (DCTELEM) wsptr[1] - (DCTELEM) wsptr[7]; 331 332 tmp7 = z11 + z13; /* phase 5 */ 333 tmp11 = MULTIPLY( z11 - z13, FIX_1_414213562 );/* 2*c4 */ 334 335 z5 = MULTIPLY( z10 + z12, FIX_1_847759065 );/* 2*c2 */ 336 tmp10 = MULTIPLY( z12, FIX_1_082392200 ) - z5;/* 2*(c2-c6) */ 337 tmp12 = MULTIPLY( z10, -FIX_2_613125930 ) + z5;/* -2*(c2+c6) */ 338 339 tmp6 = tmp12 - tmp7;/* phase 2 */ 340 tmp5 = tmp11 - tmp6; 341 tmp4 = tmp10 + tmp5; 342 343 /* Final output stage: scale down by a factor of 8 and range-limit */ 344 345 outptr[0] = range_limit[IDESCALE( tmp0 + tmp7, PASS1_BITS + 3 ) 346 & RANGE_MASK]; 347 outptr[7] = range_limit[IDESCALE( tmp0 - tmp7, PASS1_BITS + 3 ) 348 & RANGE_MASK]; 349 outptr[1] = range_limit[IDESCALE( tmp1 + tmp6, PASS1_BITS + 3 ) 350 & RANGE_MASK]; 351 outptr[6] = range_limit[IDESCALE( tmp1 - tmp6, PASS1_BITS + 3 ) 352 & RANGE_MASK]; 353 outptr[2] = range_limit[IDESCALE( tmp2 + tmp5, PASS1_BITS + 3 ) 354 & RANGE_MASK]; 355 outptr[5] = range_limit[IDESCALE( tmp2 - tmp5, PASS1_BITS + 3 ) 356 & RANGE_MASK]; 357 outptr[4] = range_limit[IDESCALE( tmp3 + tmp4, PASS1_BITS + 3 ) 358 & RANGE_MASK]; 359 outptr[3] = range_limit[IDESCALE( tmp3 - tmp4, PASS1_BITS + 3 ) 360 & RANGE_MASK]; 361 362 wsptr += DCTSIZE; /* advance pointer to next row */ 363 } 364 } 365 366 #endif /* DCT_IFAST_SUPPORTED */