1 /* 2 * jfdctfst.c 3 * 4 * Copyright (C) 1994-1996, 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 * forward DCT (Discrete Cosine Transform). 10 * 11 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 12 * on each column. Direct algorithms are also available, but they are 13 * much more complex and seem not to be any faster when reduced to code. 14 * 15 * This implementation is based on Arai, Agui, and Nakajima's algorithm for 16 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 17 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 18 * JPEG textbook (see REFERENCES section in file README). The following code 19 * is based directly on figure 4-8 in P&M. 20 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 21 * possible to arrange the computation so that many of the multiplies are 22 * simple scalings of the final outputs. These multiplies can then be 23 * folded into the multiplications or divisions by the JPEG quantization 24 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 25 * to be done in the DCT itself. 26 * The primary disadvantage of this method is that with fixed-point math, 27 * accuracy is lost due to imprecise representation of the scaled 28 * quantization values. The smaller the quantization table entry, the less 29 * precise the scaled value, so this implementation does worse with high- 30 * quality-setting files than with low-quality ones. 31 */ 32 33 #define JPEG_INTERNALS 34 #include "jinclude.h" 35 #include "jpeglib.h" 36 #include "jdct.h" /* Private declarations for DCT subsystem */ 37 38 #ifdef DCT_IFAST_SUPPORTED 39 40 41 /* 42 * This module is specialized to the case DCTSIZE = 8. 43 */ 44 45 #if DCTSIZE != 8 46 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 47 #endif 48 49 50 /* Scaling decisions are generally the same as in the LL&M algorithm; 51 * see jfdctint.c for more details. However, we choose to descale 52 * (right shift) multiplication products as soon as they are formed, 53 * rather than carrying additional fractional bits into subsequent additions. 54 * This compromises accuracy slightly, but it lets us save a few shifts. 55 * More importantly, 16-bit arithmetic is then adequate (for 8-bit samples) 56 * everywhere except in the multiplications proper; this saves a good deal 57 * of work on 16-bit-int machines. 58 * 59 * Again to save a few shifts, the intermediate results between pass 1 and 60 * pass 2 are not upscaled, but are represented only to integral precision. 61 * 62 * A final compromise is to represent the multiplicative constants to only 63 * 8 fractional bits, rather than 13. This saves some shifting work on some 64 * machines, and may also reduce the cost of multiplication (since there 65 * are fewer one-bits in the constants). 66 */ 67 68 #define CONST_BITS 8 69 70 71 /* Some C compilers fail to reduce "FIX(constant)" at compile time, thus 72 * causing a lot of useless floating-point operations at run time. 73 * To get around this we use the following pre-calculated constants. 74 * If you change CONST_BITS you may want to add appropriate values. 75 * (With a reasonable C compiler, you can just rely on the FIX() macro...) 76 */ 77 78 #if CONST_BITS == 8 79 #define FIX_0_382683433 ((INT32) 98) /* FIX(0.382683433) */ 80 #define FIX_0_541196100 ((INT32) 139) /* FIX(0.541196100) */ 81 #define FIX_0_707106781 ((INT32) 181) /* FIX(0.707106781) */ 82 #define FIX_1_306562965 ((INT32) 334) /* FIX(1.306562965) */ 83 #else 84 #define FIX_0_382683433 FIX(0.382683433) 85 #define FIX_0_541196100 FIX(0.541196100) 86 #define FIX_0_707106781 FIX(0.707106781) 87 #define FIX_1_306562965 FIX(1.306562965) 88 #endif 89 90 91 /* We can gain a little more speed, with a further compromise in accuracy, 92 * by omitting the addition in a descaling shift. This yields an incorrectly 93 * rounded result half the time... 94 */ 95 96 #ifndef USE_ACCURATE_ROUNDING 97 #undef DESCALE 98 #define DESCALE(x,n) RIGHT_SHIFT(x, n) 99 #endif 100 101 102 /* Multiply a DCTELEM variable by an INT32 constant, and immediately 103 * descale to yield a DCTELEM result. 104 */ 105 106 #define MULTIPLY(var,const) ((DCTELEM) DESCALE((var) * (const), CONST_BITS)) 107 108 109 /* 110 * Perform the forward DCT on one block of samples. 111 */ 112 113 GLOBAL(void) 114 jpeg_fdct_ifast (DCTELEM * data) 115 { 116 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 117 DCTELEM tmp10, tmp11, tmp12, tmp13; 118 DCTELEM z1, z2, z3, z4, z5, z11, z13; 119 DCTELEM *dataptr; 120 int ctr; 121 SHIFT_TEMPS 122 123 /* Pass 1: process rows. */ 124 125 dataptr = data; 126 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 127 tmp0 = dataptr[0] + dataptr[7]; 128 tmp7 = dataptr[0] - dataptr[7]; 129 tmp1 = dataptr[1] + dataptr[6]; 130 tmp6 = dataptr[1] - dataptr[6]; 131 tmp2 = dataptr[2] + dataptr[5]; 132 tmp5 = dataptr[2] - dataptr[5]; 133 tmp3 = dataptr[3] + dataptr[4]; 134 tmp4 = dataptr[3] - dataptr[4]; 135 136 /* Even part */ 137 138 tmp10 = tmp0 + tmp3; /* phase 2 */ 139 tmp13 = tmp0 - tmp3; 140 tmp11 = tmp1 + tmp2; 141 tmp12 = tmp1 - tmp2; 142 143 dataptr[0] = tmp10 + tmp11; /* phase 3 */ 144 dataptr[4] = tmp10 - tmp11; 145 146 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ 147 dataptr[2] = tmp13 + z1; /* phase 5 */ 148 dataptr[6] = tmp13 - z1; 149 150 /* Odd part */ 151 152 tmp10 = tmp4 + tmp5; /* phase 2 */ 153 tmp11 = tmp5 + tmp6; 154 tmp12 = tmp6 + tmp7; 155 156 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 157 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ 158 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ 159 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ 160 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ 161 162 z11 = tmp7 + z3; /* phase 5 */ 163 z13 = tmp7 - z3; 164 165 dataptr[5] = z13 + z2; /* phase 6 */ 166 dataptr[3] = z13 - z2; 167 dataptr[1] = z11 + z4; 168 dataptr[7] = z11 - z4; 169 170 dataptr += DCTSIZE; /* advance pointer to next row */ 171 } 172 173 /* Pass 2: process columns. */ 174 175 dataptr = data; 176 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 177 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 178 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 179 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 180 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 181 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 182 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 183 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 184 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 185 186 /* Even part */ 187 188 tmp10 = tmp0 + tmp3; /* phase 2 */ 189 tmp13 = tmp0 - tmp3; 190 tmp11 = tmp1 + tmp2; 191 tmp12 = tmp1 - tmp2; 192 193 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ 194 dataptr[DCTSIZE*4] = tmp10 - tmp11; 195 196 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ 197 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ 198 dataptr[DCTSIZE*6] = tmp13 - z1; 199 200 /* Odd part */ 201 202 tmp10 = tmp4 + tmp5; /* phase 2 */ 203 tmp11 = tmp5 + tmp6; 204 tmp12 = tmp6 + tmp7; 205 206 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 207 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ 208 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ 209 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ 210 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ 211 212 z11 = tmp7 + z3; /* phase 5 */ 213 z13 = tmp7 - z3; 214 215 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ 216 dataptr[DCTSIZE*3] = z13 - z2; 217 dataptr[DCTSIZE*1] = z11 + z4; 218 dataptr[DCTSIZE*7] = z11 - z4; 219 220 dataptr++; /* advance pointer to next column */ 221 } 222 } 223 224 #endif /* DCT_IFAST_SUPPORTED */ 225
