1 /* 2 * jfdctfst.c 3 * 4 * Copyright (C) 1994-1996, Thomas G. Lane. 5 * Modified 2003-2017 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 fast, not so 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 Arai, Agui, and Nakajima's algorithm for 17 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 18 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 19 * JPEG textbook (see REFERENCES section in file README). The following code 20 * is based directly on figure 4-8 in P&M. 21 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 22 * possible to arrange the computation so that many of the multiplies are 23 * simple scalings of the final outputs. These multiplies can then be 24 * folded into the multiplications or divisions by the JPEG quantization 25 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 26 * to be done in the DCT itself. 27 * The primary disadvantage of this method is that with fixed-point math, 28 * accuracy is lost due to imprecise representation of the scaled 29 * quantization values. The smaller the quantization table entry, the less 30 * precise the scaled value, so this implementation does worse with high- 31 * quality-setting files than with low-quality ones. 32 */ 33 34 #define JPEG_INTERNALS 35 #include "jinclude.h" 36 #include "jpeglib.h" 37 #include "jdct.h" /* Private declarations for DCT subsystem */ 38 39 #ifdef DCT_IFAST_SUPPORTED 40 41 42 /* 43 * This module is specialized to the case DCTSIZE = 8. 44 */ 45 46 #if DCTSIZE != 8 47 Sorry, this code only copes with 8x8 DCT blocks. /* deliberate syntax err */ 48 #endif 49 50 51 /* Scaling decisions are generally the same as in the LL&M algorithm; 52 * see jfdctint.c for more details. However, we choose to descale 53 * (right shift) multiplication products as soon as they are formed, 54 * rather than carrying additional fractional bits into subsequent additions. 55 * This compromises accuracy slightly, but it lets us save a few shifts. 56 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 57 * everywhere except in the multiplications proper; this saves a good deal 58 * of work on 16-bit-int machines. 59 * 60 * Again to save a few shifts, the intermediate results between pass 1 and 61 * pass 2 are not upscaled, but are represented only to integral precision. 62 * 63 * A final compromise is to represent the multiplicative constants to only 64 * 8 fractional bits, rather than 13. This saves some shifting work on some 65 * machines, and may also reduce the cost of multiplication (since there 66 * are fewer one-bits in the constants). 67 */ 68 69 #define CONST_BITS 8 70 71 72 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 73 * causing a lot of useless floating-point operations at run time. 74 * To get around this we use the following pre-calculated constants. 75 * If you change CONST_BITS you may want to add appropriate values. 76 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 77 */ 78 79 #if CONST_BITS == 8 80 #define FIX_0_382683433 ((INT32) 98) /* FIX(0.382683433) */ 81 #define FIX_0_541196100 ((INT32) 139) /* FIX(0.541196100) */ 82 #define FIX_0_707106781 ((INT32) 181) /* FIX(0.707106781) */ 83 #define FIX_1_306562965 ((INT32) 334) /* FIX(1.306562965) */ 84 #else 85 #define FIX_0_382683433 FIX(0.382683433) 86 #define FIX_0_541196100 FIX(0.541196100) 87 #define FIX_0_707106781 FIX(0.707106781) 88 #define FIX_1_306562965 FIX(1.306562965) 89 #endif 90 91 92 /* We can gain a little more speed, with a further compromise in accuracy, 93 * by omitting the addition in a descaling shift. This yields an incorrectly 94 * rounded result half the time... 95 */ 96 97 #ifndef USE_ACCURATE_ROUNDING 98 #undef DESCALE 99 #define DESCALE(x,n) RIGHT_SHIFT(x, n) 100 #endif 101 102 103 /* Multiply a DCTELEM variable by an INT32 constant, and immediately 104 * descale to yield a DCTELEM result. 105 */ 106 107 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 108 109 110 /* 111 * Perform the forward DCT on one block of samples. 112 * 113 * cK represents cos(K*pi/16). 114 */ 115 116 GLOBAL(void) 117 jpeg_fdct_ifast (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col) 118 { 119 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 120 DCTELEM tmp10, tmp11, tmp12, tmp13; 121 DCTELEM z1, z2, z3, z4, z5, z11, z13; 122 DCTELEM *dataptr; 123 JSAMPROW elemptr; 124 int ctr; 125 SHIFT_TEMPS 126 127 /* Pass 1: process rows. */ 128 129 dataptr = data; 130 for (ctr = 0; ctr < DCTSIZE; ctr++) { 131 elemptr = sample_data[ctr] + start_col; 132 133 /* Load data into workspace */ 134 tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]); 135 tmp7 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]); 136 tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]); 137 tmp6 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]); 138 tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]); 139 tmp5 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]); 140 tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]); 141 tmp4 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]); 142 143 /* Even part */ 144 145 tmp10 = tmp0 + tmp3; /* phase 2 */ 146 tmp13 = tmp0 - tmp3; 147 tmp11 = tmp1 + tmp2; 148 tmp12 = tmp1 - tmp2; 149 150 /* Apply unsigned->signed conversion. */ 151 dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* phase 3 */ 152 dataptr[4] = tmp10 - tmp11; 153 154 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ 155 dataptr[2] = tmp13 + z1; /* phase 5 */ 156 dataptr[6] = tmp13 - z1; 157 158 /* Odd part */ 159 160 tmp10 = tmp4 + tmp5; /* phase 2 */ 161 tmp11 = tmp5 + tmp6; 162 tmp12 = tmp6 + tmp7; 163 164 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 165 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ 166 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ 167 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ 168 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ 169 170 z11 = tmp7 + z3; /* phase 5 */ 171 z13 = tmp7 - z3; 172 173 dataptr[5] = z13 + z2; /* phase 6 */ 174 dataptr[3] = z13 - z2; 175 dataptr[1] = z11 + z4; 176 dataptr[7] = z11 - z4; 177 178 dataptr += DCTSIZE; /* advance pointer to next row */ 179 } 180 181 /* Pass 2: process columns. */ 182 183 dataptr = data; 184 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 185 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 186 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 187 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 188 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 189 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 190 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 191 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 192 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 193 194 /* Even part */ 195 196 tmp10 = tmp0 + tmp3; /* phase 2 */ 197 tmp13 = tmp0 - tmp3; 198 tmp11 = tmp1 + tmp2; 199 tmp12 = tmp1 - tmp2; 200 201 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ 202 dataptr[DCTSIZE*4] = tmp10 - tmp11; 203 204 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ 205 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ 206 dataptr[DCTSIZE*6] = tmp13 - z1; 207 208 /* Odd part */ 209 210 tmp10 = tmp4 + tmp5; /* phase 2 */ 211 tmp11 = tmp5 + tmp6; 212 tmp12 = tmp6 + tmp7; 213 214 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 215 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ 216 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ 217 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ 218 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ 219 220 z11 = tmp7 + z3; /* phase 5 */ 221 z13 = tmp7 - z3; 222 223 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ 224 dataptr[DCTSIZE*3] = z13 - z2; 225 dataptr[DCTSIZE*1] = z11 + z4; 226 dataptr[DCTSIZE*7] = z11 - z4; 227 228 dataptr++; /* advance pointer to next column */ 229 } 230 } 231 232 #endif /* DCT_IFAST_SUPPORTED */ 233