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| 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 */ | |
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