1 /* 2 * jidctflt.c 3 * 4 * Copyright (C) 1994-1998, Thomas G. Lane. 5 * Modified 2010-2015 by Guido Vollbeding. 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 floating-point implementation of the 10 * inverse DCT (Discrete Cosine Transform). In the IJG code, this routine 11 * must also perform dequantization of the input coefficients. 12 * 13 * This implementation should be more accurate than either of the integer 14 * IDCT implementations. However, it may not give the same results on all 15 * machines because of differences in roundoff behavior. Speed will depend 16 * on the hardware's floating point capacity. 17 * 18 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT 19 * on each row (or vice versa, but it's more convenient to emit a row at 20 * a time). Direct algorithms are also available, but they are much more 21 * complex and seem not to be any faster when reduced to code. 22 * 23 * This implementation is based on Arai, Agui, and Nakajima's algorithm for 24 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 25 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 26 * JPEG textbook (see REFERENCES section in file README). The following code 27 * is based directly on figure 4-8 in P&M. 28 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 29 * possible to arrange the computation so that many of the multiplies are 30 * simple scalings of the final outputs. These multiplies can then be 31 * folded into the multiplications or divisions by the JPEG quantization 32 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 33 * to be done in the DCT itself. 34 * The primary disadvantage of this method is that with a fixed-point 35 * implementation, accuracy is lost due to imprecise representation of the 36 * scaled quantization values. However, that problem does not arise if 37 * we use floating point arithmetic. 38 */ 39 40 #define JPEG_INTERNALS 41 #include "jinclude.h" 42 #include "jpeglib.h" 43 #include "jdct.h" /* Private declarations for DCT subsystem */ 44 45 #ifdef DCT_FLOAT_SUPPORTED 46 47 48 /* 49 * This module is specialized to the case DCTSIZE = 8. 50 */ 51 52 #if DCTSIZE != 8 53 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 54 #endif 55 56 57 /* Dequantize a coefficient by multiplying it by the multiplier-table 58 * entry; produce a float result. 59 */ 60 61 #define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval)) 62 63 64 /* 65 * Perform dequantization and inverse DCT on one block of coefficients. 66 * 67 * cK represents cos(K*pi/16). 68 */ 69 70 GLOBAL(void) 71 jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr, 72 JCOEFPTR coef_block, 73 JSAMPARRAY output_buf, JDIMENSION output_col) 74 { 75 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 76 FAST_FLOAT tmp10, tmp11, tmp12, tmp13; 77 FAST_FLOAT z5, z10, z11, z12, z13; 78 JCOEFPTR inptr; 79 FLOAT_MULT_TYPE * quantptr; 80 FAST_FLOAT * wsptr; 81 JSAMPROW outptr; 82 JSAMPLE *range_limit = IDCT_range_limit(cinfo); 83 int ctr; 84 FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */ 85 86 /* Pass 1: process columns from input, store into work array. */ 87 88 inptr = coef_block; 89 quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table; 90 wsptr = workspace; 91 for (ctr = DCTSIZE; ctr > 0; ctr--) { 92 /* Due to quantization, we will usually find that many of the input 93 * coefficients are zero, especially the AC terms. We can exploit this 94 * by short-circuiting the IDCT calculation for any column in which all 95 * the AC terms are zero. In that case each output is equal to the 96 * DC coefficient (with scale factor as needed). 97 * With typical images and quantization tables, half or more of the 98 * column DCT calculations can be simplified this way. 99 */ 100 101 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && 102 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && 103 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && 104 inptr[DCTSIZE*7] == 0) { 105 /* AC terms all zero */ 106 FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 107 108 wsptr[DCTSIZE*0] = dcval; 109 wsptr[DCTSIZE*1] = dcval; 110 wsptr[DCTSIZE*2] = dcval; 111 wsptr[DCTSIZE*3] = dcval; 112 wsptr[DCTSIZE*4] = dcval; 113 wsptr[DCTSIZE*5] = dcval; 114 wsptr[DCTSIZE*6] = dcval; 115 wsptr[DCTSIZE*7] = dcval; 116 117 inptr++; /* advance pointers to next column */ 118 quantptr++; 119 wsptr++; 120 continue; 121 } 122 123 /* Even part */ 124 125 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 126 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 127 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 128 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 129 130 tmp10 = tmp0 + tmp2; /* phase 3 */ 131 tmp11 = tmp0 - tmp2; 132 133 tmp13 = tmp1 + tmp3; /* phases 5-3 */ 134 tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */ 135 136 tmp0 = tmp10 + tmp13; /* phase 2 */ 137 tmp3 = tmp10 - tmp13; 138 tmp1 = tmp11 + tmp12; 139 tmp2 = tmp11 - tmp12; 140 141 /* Odd part */ 142 143 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 144 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 145 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 146 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 147 148 z13 = tmp6 + tmp5; /* phase 6 */ 149 z10 = tmp6 - tmp5; 150 z11 = tmp4 + tmp7; 151 z12 = tmp4 - tmp7; 152 153 tmp7 = z11 + z13; /* phase 5 */ 154 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */ 155 156 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ 157 tmp10 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */ 158 tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 2*(c2+c6) */ 159 160 tmp6 = tmp12 - tmp7; /* phase 2 */ 161 tmp5 = tmp11 - tmp6; 162 tmp4 = tmp10 - tmp5; 163 164 wsptr[DCTSIZE*0] = tmp0 + tmp7; 165 wsptr[DCTSIZE*7] = tmp0 - tmp7; 166 wsptr[DCTSIZE*1] = tmp1 + tmp6; 167 wsptr[DCTSIZE*6] = tmp1 - tmp6; 168 wsptr[DCTSIZE*2] = tmp2 + tmp5; 169 wsptr[DCTSIZE*5] = tmp2 - tmp5; 170 wsptr[DCTSIZE*3] = tmp3 + tmp4; 171 wsptr[DCTSIZE*4] = tmp3 - tmp4; 172 173 inptr++; /* advance pointers to next column */ 174 quantptr++; 175 wsptr++; 176 } 177 178 /* Pass 2: process rows from work array, store into output array. */ 179 180 wsptr = workspace; 181 for (ctr = 0; ctr < DCTSIZE; ctr++) { 182 outptr = output_buf[ctr] + output_col; 183 /* Rows of zeroes can be exploited in the same way as we did with columns. 184 * However, the column calculation has created many nonzero AC terms, so 185 * the simplification applies less often (typically 5% to 10% of the time). 186 * And testing floats for zero is relatively expensive, so we don't bother. 187 */ 188 189 /* Even part */ 190 191 /* Prepare range-limit and float->int conversion */ 192 z5 = wsptr[0] + (((FAST_FLOAT) RANGE_CENTER) + ((FAST_FLOAT) 0.5)); 193 tmp10 = z5 + wsptr[4]; 194 tmp11 = z5 - wsptr[4]; 195 196 tmp13 = wsptr[2] + wsptr[6]; 197 tmp12 = (wsptr[2] - wsptr[6]) * 198 ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */ 199 200 tmp0 = tmp10 + tmp13; 201 tmp3 = tmp10 - tmp13; 202 tmp1 = tmp11 + tmp12; 203 tmp2 = tmp11 - tmp12; 204 205 /* Odd part */ 206 207 z13 = wsptr[5] + wsptr[3]; 208 z10 = wsptr[5] - wsptr[3]; 209 z11 = wsptr[1] + wsptr[7]; 210 z12 = wsptr[1] - wsptr[7]; 211 212 tmp7 = z11 + z13; /* phase 5 */ 213 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */ 214 215 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ 216 tmp10 = z5 - z12 * ((FAST_FLOAT) 1.082392200); /* 2*(c2-c6) */ 217 tmp12 = z5 - z10 * ((FAST_FLOAT) 2.613125930); /* 2*(c2+c6) */ 218 219 tmp6 = tmp12 - tmp7; /* phase 2 */ 220 tmp5 = tmp11 - tmp6; 221 tmp4 = tmp10 - tmp5; 222 223 /* Final output stage: float->int conversion and range-limit */ 224 225 outptr[0] = range_limit[(int) (tmp0 + tmp7) & RANGE_MASK]; 226 outptr[7] = range_limit[(int) (tmp0 - tmp7) & RANGE_MASK]; 227 outptr[1] = range_limit[(int) (tmp1 + tmp6) & RANGE_MASK]; 228 outptr[6] = range_limit[(int) (tmp1 - tmp6) & RANGE_MASK]; 229 outptr[2] = range_limit[(int) (tmp2 + tmp5) & RANGE_MASK]; 230 outptr[5] = range_limit[(int) (tmp2 - tmp5) & RANGE_MASK]; 231 outptr[3] = range_limit[(int) (tmp3 + tmp4) & RANGE_MASK]; 232 outptr[4] = range_limit[(int) (tmp3 - tmp4) & RANGE_MASK]; 233 234 wsptr += DCTSIZE; /* advance pointer to next row */ 235 } 236 } 237 238 #endif /* DCT_FLOAT_SUPPORTED */ 239