1 /* 2 * jfdctflt.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.ijg 7 * file. 8 * 9 * This file contains a floating-point implementation of the 10 * forward DCT (Discrete Cosine Transform). 11 * 12 * This implementation should be more accurate than either of the integer 13 * DCT implementations. However, it may not give the same results on all 14 * machines because of differences in roundoff behavior. Speed will depend 15 * on the hardware's floating point capacity. 16 * 17 * A 2-D DCT can be done by 1-D DCT on each row followed by 1-D DCT 18 * on each column. Direct algorithms are also available, but they are 19 * much more complex and seem not to be any faster when reduced to code. 20 * 21 * This implementation is based on Arai, Agui, and Nakajima's algorithm for 22 * scaled DCT. Their original paper (Trans. IEICE E-71(11):1095) is in 23 * Japanese, but the algorithm is described in the Pennebaker & Mitchell 24 * JPEG textbook (see REFERENCES section in file README.ijg). The following 25 * code is based directly on figure 4-8 in P&M. 26 * While an 8-point DCT cannot be done in less than 11 multiplies, it is 27 * possible to arrange the computation so that many of the multiplies are 28 * simple scalings of the final outputs. These multiplies can then be 29 * folded into the multiplications or divisions by the JPEG quantization 30 * table entries. The AA&N method leaves only 5 multiplies and 29 adds 31 * to be done in the DCT itself. 32 * The primary disadvantage of this method is that with a fixed-point 33 * implementation, accuracy is lost due to imprecise representation of the 34 * scaled quantization values. However, that problem does not arise if 35 * we use floating point arithmetic. 36 */ 37 38 #define JPEG_INTERNALS 39 #include "jinclude.h" 40 #include "jpeglib.h" 41 #include "jdct.h" /* Private declarations for DCT subsystem */ 42 43 #ifdef DCT_FLOAT_SUPPORTED 44 45 46 /* 47 * This module is specialized to the case DCTSIZE = 8. 48 */ 49 50 #if DCTSIZE != 8 51 Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */ 52 #endif 53 54 55 /* 56 * Perform the forward DCT on one block of samples. 57 */ 58 59 GLOBAL(void) 60 jpeg_fdct_float (FAST_FLOAT *data) 61 { 62 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 63 FAST_FLOAT tmp10, tmp11, tmp12, tmp13; 64 FAST_FLOAT z1, z2, z3, z4, z5, z11, z13; 65 FAST_FLOAT *dataptr; 66 int ctr; 67 68 /* Pass 1: process rows. */ 69 70 dataptr = data; 71 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 72 tmp0 = dataptr[0] + dataptr[7]; 73 tmp7 = dataptr[0] - dataptr[7]; 74 tmp1 = dataptr[1] + dataptr[6]; 75 tmp6 = dataptr[1] - dataptr[6]; 76 tmp2 = dataptr[2] + dataptr[5]; 77 tmp5 = dataptr[2] - dataptr[5]; 78 tmp3 = dataptr[3] + dataptr[4]; 79 tmp4 = dataptr[3] - dataptr[4]; 80 81 /* Even part */ 82 83 tmp10 = tmp0 + tmp3; /* phase 2 */ 84 tmp13 = tmp0 - tmp3; 85 tmp11 = tmp1 + tmp2; 86 tmp12 = tmp1 - tmp2; 87 88 dataptr[0] = tmp10 + tmp11; /* phase 3 */ 89 dataptr[4] = tmp10 - tmp11; 90 91 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */ 92 dataptr[2] = tmp13 + z1; /* phase 5 */ 93 dataptr[6] = tmp13 - z1; 94 95 /* Odd part */ 96 97 tmp10 = tmp4 + tmp5; /* phase 2 */ 98 tmp11 = tmp5 + tmp6; 99 tmp12 = tmp6 + tmp7; 100 101 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 102 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */ 103 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */ 104 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */ 105 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */ 106 107 z11 = tmp7 + z3; /* phase 5 */ 108 z13 = tmp7 - z3; 109 110 dataptr[5] = z13 + z2; /* phase 6 */ 111 dataptr[3] = z13 - z2; 112 dataptr[1] = z11 + z4; 113 dataptr[7] = z11 - z4; 114 115 dataptr += DCTSIZE; /* advance pointer to next row */ 116 } 117 118 /* Pass 2: process columns. */ 119 120 dataptr = data; 121 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 122 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 123 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 124 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 125 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 126 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 127 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 128 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 129 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 130 131 /* Even part */ 132 133 tmp10 = tmp0 + tmp3; /* phase 2 */ 134 tmp13 = tmp0 - tmp3; 135 tmp11 = tmp1 + tmp2; 136 tmp12 = tmp1 - tmp2; 137 138 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ 139 dataptr[DCTSIZE*4] = tmp10 - tmp11; 140 141 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */ 142 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ 143 dataptr[DCTSIZE*6] = tmp13 - z1; 144 145 /* Odd part */ 146 147 tmp10 = tmp4 + tmp5; /* phase 2 */ 148 tmp11 = tmp5 + tmp6; 149 tmp12 = tmp6 + tmp7; 150 151 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 152 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */ 153 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */ 154 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */ 155 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */ 156 157 z11 = tmp7 + z3; /* phase 5 */ 158 z13 = tmp7 - z3; 159 160 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ 161 dataptr[DCTSIZE*3] = z13 - z2; 162 dataptr[DCTSIZE*1] = z11 + z4; 163 dataptr[DCTSIZE*7] = z11 - z4; 164 165 dataptr++; /* advance pointer to next column */ 166 } 167 } 168 169 #endif /* DCT_FLOAT_SUPPORTED */ 170