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