1 /* 2 * jidctflt.c 3 * 4 * Copyright (C) 1994-1998, 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 floating-point 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 * This implementation should be more accurate than either of the integer 13 * IDCT implementations. However, it may not give the same results on all 14 * machines because of differences in roundoff behavior. Speed will depend 15 * on the hardware's floating point capacity. 16 * 17 * A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT 18 * on each row (or vice versa, but it's more convenient to emit a row at 19 * a time). Direct algorithms are also available, but they are much more 20 * complex and seem not to be any faster when reduced to code. 21 * 22 * This implementation is based on Arai, Agui, and Nakajima's algorithm for 23 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 24 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 25 * JPEG textbook (see REFERENCES section in file README). The following code 26 * is based directly on figure 4-8 in P&M. 27 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 28 * possible to arrange the computation so that many of the multiplies are 29 * simple scalings of the final outputs. These multiplies can then be 30 * folded into the multiplications or divisions by the JPEG quantization 31 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 32 * to be done in the DCT itself. 33 * The primary disadvantage of this method is that with a fixed-point 34 * implementation, accuracy is lost due to imprecise representation of the 35 * scaled quantization values. However, that problem does not arise if 36 * we use floating point arithmetic. 37 */ 38 39 #define JPEG_INTERNALS 40 #include "jinclude.h" 41 #include "jpeglib.h" 42 #include "jdct.h" /* Private declarations for DCT subsystem */ 43 44 #ifdef DCT_FLOAT_SUPPORTED 45 46 47 /* 48 * This module is specialized to the case DCTSIZE = 8. 49 */ 50 51 #if DCTSIZE != 8 52 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 53 #endif 54 55 56 /* Dequantize a coefficient by multiplying it by the multiplier-table 57 * entry; produce a float result. 58 */ 59 60 #define DEQUANTIZE(coef,quantval) (((FAST_FLOAT) (coef)) * (quantval)) 61 62 63 /* 64 * Perform dequantization and inverse DCT on one block of coefficients. 65 */ 66 67 GLOBAL(void) 68 jpeg_idct_float (j_decompress_ptr cinfo, jpeg_component_info * compptr, 69 JCOEFPTR coef_block, 70 JSAMPARRAY output_buf, JDIMENSION output_col) 71 { 72 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 73 FAST_FLOAT tmp10, tmp11, tmp12, tmp13; 74 FAST_FLOAT z5, z10, z11, z12, z13; 75 JCOEFPTR inptr; 76 FLOAT_MULT_TYPE * quantptr; 77 FAST_FLOAT * wsptr; 78 JSAMPROW outptr; 79 JSAMPLE *range_limit = IDCT_range_limit(cinfo); 80 int ctr; 81 FAST_FLOAT workspace[DCTSIZE2]; /* buffers data between passes */ 82 SHIFT_TEMPS 83 84 /* Pass 1: process columns from input, store into work array. */ 85 86 inptr = coef_block; 87 quantptr = (FLOAT_MULT_TYPE *) compptr->dct_table; 88 wsptr = workspace; 89 for (ctr = DCTSIZE; ctr > 0; ctr--) { 90 /* Due to quantization, we will usually find that many of the input 91 * coefficients are zero, especially the AC terms. We can exploit this 92 * by short-circuiting the IDCT calculation for any column in which all 93 * the AC terms are zero. In that case each output is equal to the 94 * DC coefficient (with scale factor as needed). 95 * With typical images and quantization tables, half or more of the 96 * column DCT calculations can be simplified this way. 97 */ 98 99 if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 && 100 inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 && 101 inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 && 102 inptr[DCTSIZE*7] == 0) { 103 /* AC terms all zero */ 104 FAST_FLOAT dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 105 106 wsptr[DCTSIZE*0] = dcval; 107 wsptr[DCTSIZE*1] = dcval; 108 wsptr[DCTSIZE*2] = dcval; 109 wsptr[DCTSIZE*3] = dcval; 110 wsptr[DCTSIZE*4] = dcval; 111 wsptr[DCTSIZE*5] = dcval; 112 wsptr[DCTSIZE*6] = dcval; 113 wsptr[DCTSIZE*7] = dcval; 114 115 inptr++; /* advance pointers to next column */ 116 quantptr++; 117 wsptr++; 118 continue; 119 } 120 121 /* Even part */ 122 123 tmp0 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]); 124 tmp1 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]); 125 tmp2 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]); 126 tmp3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]); 127 128 tmp10 = tmp0 + tmp2; /* phase 3 */ 129 tmp11 = tmp0 - tmp2; 130 131 tmp13 = tmp1 + tmp3; /* phases 5-3 */ 132 tmp12 = (tmp1 - tmp3) * ((FAST_FLOAT) 1.414213562) - tmp13; /* 2*c4 */ 133 134 tmp0 = tmp10 + tmp13; /* phase 2 */ 135 tmp3 = tmp10 - tmp13; 136 tmp1 = tmp11 + tmp12; 137 tmp2 = tmp11 - tmp12; 138 139 /* Odd part */ 140 141 tmp4 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]); 142 tmp5 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]); 143 tmp6 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]); 144 tmp7 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]); 145 146 z13 = tmp6 + tmp5; /* phase 6 */ 147 z10 = tmp6 - tmp5; 148 z11 = tmp4 + tmp7; 149 z12 = tmp4 - tmp7; 150 151 tmp7 = z11 + z13; /* phase 5 */ 152 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); /* 2*c4 */ 153 154 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ 155 tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ 156 tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ 157 158 tmp6 = tmp12 - tmp7; /* phase 2 */ 159 tmp5 = tmp11 - tmp6; 160 tmp4 = tmp10 + tmp5; 161 162 wsptr[DCTSIZE*0] = tmp0 + tmp7; 163 wsptr[DCTSIZE*7] = tmp0 - tmp7; 164 wsptr[DCTSIZE*1] = tmp1 + tmp6; 165 wsptr[DCTSIZE*6] = tmp1 - tmp6; 166 wsptr[DCTSIZE*2] = tmp2 + tmp5; 167 wsptr[DCTSIZE*5] = tmp2 - tmp5; 168 wsptr[DCTSIZE*4] = tmp3 + tmp4; 169 wsptr[DCTSIZE*3] = tmp3 - tmp4; 170 171 inptr++; /* advance pointers to next column */ 172 quantptr++; 173 wsptr++; 174 } 175 176 /* Pass 2: process rows from work array, store into output array. */ 177 /* Note that we must descale the results by a factor of 8 == 2**3. */ 178 179 wsptr = workspace; 180 for (ctr = 0; ctr < DCTSIZE; ctr++) { 181 outptr = output_buf[ctr] + output_col; 182 /* Rows of zeroes can be exploited in the same way as we did with columns. 183 * However, the column calculation has created many nonzero AC terms, so 184 * the simplification applies less often (typically 5% to 10% of the time). 185 * And testing floats for zero is relatively expensive, so we don't bother. 186 */ 187 188 /* Even part */ 189 190 tmp10 = wsptr[0] + wsptr[4]; 191 tmp11 = wsptr[0] - wsptr[4]; 192 193 tmp13 = wsptr[2] + wsptr[6]; 194 tmp12 = (wsptr[2] - wsptr[6]) * ((FAST_FLOAT) 1.414213562) - tmp13; 195 196 tmp0 = tmp10 + tmp13; 197 tmp3 = tmp10 - tmp13; 198 tmp1 = tmp11 + tmp12; 199 tmp2 = tmp11 - tmp12; 200 201 /* Odd part */ 202 203 z13 = wsptr[5] + wsptr[3]; 204 z10 = wsptr[5] - wsptr[3]; 205 z11 = wsptr[1] + wsptr[7]; 206 z12 = wsptr[1] - wsptr[7]; 207 208 tmp7 = z11 + z13; 209 tmp11 = (z11 - z13) * ((FAST_FLOAT) 1.414213562); 210 211 z5 = (z10 + z12) * ((FAST_FLOAT) 1.847759065); /* 2*c2 */ 212 tmp10 = ((FAST_FLOAT) 1.082392200) * z12 - z5; /* 2*(c2-c6) */ 213 tmp12 = ((FAST_FLOAT) -2.613125930) * z10 + z5; /* -2*(c2+c6) */ 214 215 tmp6 = tmp12 - tmp7; 216 tmp5 = tmp11 - tmp6; 217 tmp4 = tmp10 + tmp5; 218 219 /* Final output stage: scale down by a factor of 8 and range-limit */ 220 221 outptr[0] = range_limit[(int) DESCALE((INT32) (tmp0 + tmp7), 3) 222 & RANGE_MASK]; 223 outptr[7] = range_limit[(int) DESCALE((INT32) (tmp0 - tmp7), 3) 224 & RANGE_MASK]; 225 outptr[1] = range_limit[(int) DESCALE((INT32) (tmp1 + tmp6), 3) 226 & RANGE_MASK]; 227 outptr[6] = range_limit[(int) DESCALE((INT32) (tmp1 - tmp6), 3) 228 & RANGE_MASK]; 229 outptr[2] = range_limit[(int) DESCALE((INT32) (tmp2 + tmp5), 3) 230 & RANGE_MASK]; 231 outptr[5] = range_limit[(int) DESCALE((INT32) (tmp2 - tmp5), 3) 232 & RANGE_MASK]; 233 outptr[4] = range_limit[(int) DESCALE((INT32) (tmp3 + tmp4), 3) 234 & RANGE_MASK]; 235 outptr[3] = range_limit[(int) DESCALE((INT32) (tmp3 - tmp4), 3) 236 & RANGE_MASK]; 237 238 wsptr += DCTSIZE; /* advance pointer to next row */ 239 } 240 } 241 242 #endif /* DCT_FLOAT_SUPPORTED */ 243