1 /* 2 * jfdctfst.c 3 * 4 * This file was part of the Independent JPEG Group's software: 5 * Copyright (C) 1994-1996, Thomas G. Lane. 6 * libjpeg-turbo Modifications: 7 * Copyright (C) 2015, D. R. Commander. 8 * For conditions of distribution and use, see the accompanying README.ijg 9 * file. 10 * 11 * This file contains a fast, not so accurate integer implementation of the 12 * forward DCT (Discrete Cosine Transform). 13 * 14 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 15 * on each column. Direct algorithms are also available, but they are 16 * much more complex and seem not to be any faster when reduced to code. 17 * 18 * This implementation is based on Arai, Agui, and Nakajima's algorithm for 19 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 20 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 21 * JPEG textbook (see REFERENCES section in file README.ijg). The following 22 * code is based directly on figure 4-8 in P&M. 23 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 24 * possible to arrange the computation so that many of the multiplies are 25 * simple scalings of the final outputs. These multiplies can then be 26 * folded into the multiplications or divisions by the JPEG quantization 27 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 28 * to be done in the DCT itself. 29 * The primary disadvantage of this method is that with fixed-point math, 30 * accuracy is lost due to imprecise representation of the scaled 31 * quantization values. The smaller the quantization table entry, the less 32 * precise the scaled value, so this implementation does worse with high- 33 * quality-setting files than with low-quality ones. 34 */ 35 36 #define JPEG_INTERNALS 37 #include "jinclude.h" 38 #include "jpeglib.h" 39 #include "jdct.h" /* Private declarations for DCT subsystem */ 40 41 #ifdef DCT_IFAST_SUPPORTED 42 43 44 /* 45 * This module is specialized to the case DCTSIZE = 8. 46 */ 47 48 #if DCTSIZE != 8 49 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 50 #endif 51 52 53 /* Scaling decisions are generally the same as in the LL&M algorithm; 54 * see jfdctint.c for more details. However, we choose to descale 55 * (right shift) multiplication products as soon as they are formed, 56 * rather than carrying additional fractional bits into subsequent additions. 57 * This compromises accuracy slightly, but it lets us save a few shifts. 58 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 59 * everywhere except in the multiplications proper; this saves a good deal 60 * of work on 16-bit-int machines. 61 * 62 * Again to save a few shifts, the intermediate results between pass 1 and 63 * pass 2 are not upscaled, but are represented only to integral precision. 64 * 65 * A final compromise is to represent the multiplicative constants to only 66 * 8 fractional bits, rather than 13. This saves some shifting work on some 67 * machines, and may also reduce the cost of multiplication (since there 68 * are fewer one-bits in the constants). 69 */ 70 71 #define CONST_BITS 8 72 73 74 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 75 * causing a lot of useless floating-point operations at run time. 76 * To get around this we use the following pre-calculated constants. 77 * If you change CONST_BITS you may want to add appropriate values. 78 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 79 */ 80 81 #if CONST_BITS == 8 82 #define FIX_0_382683433 ((JLONG) 98) /* FIX(0.382683433) */ 83 #define FIX_0_541196100 ((JLONG) 139) /* FIX(0.541196100) */ 84 #define FIX_0_707106781 ((JLONG) 181) /* FIX(0.707106781) */ 85 #define FIX_1_306562965 ((JLONG) 334) /* FIX(1.306562965) */ 86 #else 87 #define FIX_0_382683433 FIX(0.382683433) 88 #define FIX_0_541196100 FIX(0.541196100) 89 #define FIX_0_707106781 FIX(0.707106781) 90 #define FIX_1_306562965 FIX(1.306562965) 91 #endif 92 93 94 /* We can gain a little more speed, with a further compromise in accuracy, 95 * by omitting the addition in a descaling shift. This yields an incorrectly 96 * rounded result half the time... 97 */ 98 99 #ifndef USE_ACCURATE_ROUNDING 100 #undef DESCALE 101 #define DESCALE(x,n) RIGHT_SHIFT(x, n) 102 #endif 103 104 105 /* Multiply a DCTELEM variable by an JLONG constant, and immediately 106 * descale to yield a DCTELEM result. 107 */ 108 109 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 110 111 112 /* 113 * Perform the forward DCT on one block of samples. 114 */ 115 116 GLOBAL(void) 117 jpeg_fdct_ifast (DCTELEM *data) 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 int ctr; 124 SHIFT_TEMPS 125 126 /* Pass 1: process rows. */ 127 128 dataptr = data; 129 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 130 tmp0 = dataptr[0] + dataptr[7]; 131 tmp7 = dataptr[0] - dataptr[7]; 132 tmp1 = dataptr[1] + dataptr[6]; 133 tmp6 = dataptr[1] - dataptr[6]; 134 tmp2 = dataptr[2] + dataptr[5]; 135 tmp5 = dataptr[2] - dataptr[5]; 136 tmp3 = dataptr[3] + dataptr[4]; 137 tmp4 = dataptr[3] - dataptr[4]; 138 139 /* Even part */ 140 141 tmp10 = tmp0 + tmp3; /* phase 2 */ 142 tmp13 = tmp0 - tmp3; 143 tmp11 = tmp1 + tmp2; 144 tmp12 = tmp1 - tmp2; 145 146 dataptr[0] = tmp10 + tmp11; /* phase 3 */ 147 dataptr[4] = tmp10 - tmp11; 148 149 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ 150 dataptr[2] = tmp13 + z1; /* phase 5 */ 151 dataptr[6] = tmp13 - z1; 152 153 /* Odd part */ 154 155 tmp10 = tmp4 + tmp5; /* phase 2 */ 156 tmp11 = tmp5 + tmp6; 157 tmp12 = tmp6 + tmp7; 158 159 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 160 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ 161 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ 162 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ 163 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ 164 165 z11 = tmp7 + z3; /* phase 5 */ 166 z13 = tmp7 - z3; 167 168 dataptr[5] = z13 + z2; /* phase 6 */ 169 dataptr[3] = z13 - z2; 170 dataptr[1] = z11 + z4; 171 dataptr[7] = z11 - z4; 172 173 dataptr += DCTSIZE; /* advance pointer to next row */ 174 } 175 176 /* Pass 2: process columns. */ 177 178 dataptr = data; 179 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 180 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 181 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 182 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 183 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 184 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 185 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 186 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 187 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 188 189 /* Even part */ 190 191 tmp10 = tmp0 + tmp3; /* phase 2 */ 192 tmp13 = tmp0 - tmp3; 193 tmp11 = tmp1 + tmp2; 194 tmp12 = tmp1 - tmp2; 195 196 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ 197 dataptr[DCTSIZE*4] = tmp10 - tmp11; 198 199 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ 200 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ 201 dataptr[DCTSIZE*6] = tmp13 - z1; 202 203 /* Odd part */ 204 205 tmp10 = tmp4 + tmp5; /* phase 2 */ 206 tmp11 = tmp5 + tmp6; 207 tmp12 = tmp6 + tmp7; 208 209 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 210 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ 211 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ 212 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ 213 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ 214 215 z11 = tmp7 + z3; /* phase 5 */ 216 z13 = tmp7 - z3; 217 218 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ 219 dataptr[DCTSIZE*3] = z13 - z2; 220 dataptr[DCTSIZE*1] = z11 + z4; 221 dataptr[DCTSIZE*7] = z11 - z4; 222 223 dataptr++; /* advance pointer to next column */ 224 } 225 } 226 227 #endif /* DCT_IFAST_SUPPORTED */ 228
