1/* 2 * jfdctfst.c 3 * 4 * Copyright (C) 1994-1996, Thomas G. Lane. 5 * Modified 2003-2009 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 DCTs. /* 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 114GLOBAL(void) 115jpeg_fdct_ifast (DCTELEM * data, JSAMPARRAY sample_data, JDIMENSION start_col) 116{ 117 DCTELEM tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 118 DCTELEM tmp10, tmp11, tmp12, tmp13; 119 DCTELEM z1, z2, z3, z4, z5, z11, z13; 120 DCTELEM *dataptr; 121 JSAMPROW elemptr; 122 int ctr; 123 SHIFT_TEMPS 124 125 /* Pass 1: process rows. */ 126 127 dataptr = data; 128 for (ctr = 0; ctr < DCTSIZE; ctr++) { 129 elemptr = sample_data[ctr] + start_col; 130 131 /* Load data into workspace */ 132 tmp0 = GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7]); 133 tmp7 = GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7]); 134 tmp1 = GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6]); 135 tmp6 = GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6]); 136 tmp2 = GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5]); 137 tmp5 = GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5]); 138 tmp3 = GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4]); 139 tmp4 = GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4]); 140 141 /* Even part */ 142 143 tmp10 = tmp0 + tmp3; /* phase 2 */ 144 tmp13 = tmp0 - tmp3; 145 tmp11 = tmp1 + tmp2; 146 tmp12 = tmp1 - tmp2; 147 148 /* Apply unsigned->signed conversion */ 149 dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* phase 3 */ 150 dataptr[4] = tmp10 - tmp11; 151 152 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ 153 dataptr[2] = tmp13 + z1; /* phase 5 */ 154 dataptr[6] = tmp13 - z1; 155 156 /* Odd part */ 157 158 tmp10 = tmp4 + tmp5; /* phase 2 */ 159 tmp11 = tmp5 + tmp6; 160 tmp12 = tmp6 + tmp7; 161 162 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 163 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ 164 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ 165 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ 166 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ 167 168 z11 = tmp7 + z3; /* phase 5 */ 169 z13 = tmp7 - z3; 170 171 dataptr[5] = z13 + z2; /* phase 6 */ 172 dataptr[3] = z13 - z2; 173 dataptr[1] = z11 + z4; 174 dataptr[7] = z11 - z4; 175 176 dataptr += DCTSIZE; /* advance pointer to next row */ 177 } 178 179 /* Pass 2: process columns. */ 180 181 dataptr = data; 182 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 183 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 184 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 185 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 186 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 187 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 188 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 189 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 190 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 191 192 /* Even part */ 193 194 tmp10 = tmp0 + tmp3; /* phase 2 */ 195 tmp13 = tmp0 - tmp3; 196 tmp11 = tmp1 + tmp2; 197 tmp12 = tmp1 - tmp2; 198 199 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ 200 dataptr[DCTSIZE*4] = tmp10 - tmp11; 201 202 z1 = MULTIPLY(tmp12 + tmp13, FIX_0_707106781); /* c4 */ 203 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ 204 dataptr[DCTSIZE*6] = tmp13 - z1; 205 206 /* Odd part */ 207 208 tmp10 = tmp4 + tmp5; /* phase 2 */ 209 tmp11 = tmp5 + tmp6; 210 tmp12 = tmp6 + tmp7; 211 212 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 213 z5 = MULTIPLY(tmp10 - tmp12, FIX_0_382683433); /* c6 */ 214 z2 = MULTIPLY(tmp10, FIX_0_541196100) + z5; /* c2-c6 */ 215 z4 = MULTIPLY(tmp12, FIX_1_306562965) + z5; /* c2+c6 */ 216 z3 = MULTIPLY(tmp11, FIX_0_707106781); /* c4 */ 217 218 z11 = tmp7 + z3; /* phase 5 */ 219 z13 = tmp7 - z3; 220 221 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ 222 dataptr[DCTSIZE*3] = z13 - z2; 223 dataptr[DCTSIZE*1] = z11 + z4; 224 dataptr[DCTSIZE*7] = z11 - z4; 225 226 dataptr++; /* advance pointer to next column */ 227 } 228} 229 230#endif /* DCT_IFAST_SUPPORTED */ 231