1 /* 2 * jfdctflt.c 3 * 4 * Copyright (C) 1994-1996, Thomas G. Lane. 5 * Modified 2003-2017 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 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). The following code 25 * 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 DCT blocks. /* deliberate syntax err */ 52 #endif 53 54 55 /* 56 * Perform the forward DCT on one block of samples. 57 * 58 * cK represents cos(K*pi/16). 59 */ 60 61 GLOBAL(void) 62 jpeg_fdct_float (FAST_FLOAT * data, JSAMPARRAY sample_data, JDIMENSION start_col) 63 { 64 FAST_FLOAT tmp0, tmp1, tmp2, tmp3, tmp4, tmp5, tmp6, tmp7; 65 FAST_FLOAT tmp10, tmp11, tmp12, tmp13; 66 FAST_FLOAT z1, z2, z3, z4, z5, z11, z13; 67 FAST_FLOAT *dataptr; 68 JSAMPROW elemptr; 69 int ctr; 70 71 /* Pass 1: process rows. */ 72 73 dataptr = data; 74 for (ctr = 0; ctr < DCTSIZE; ctr++) { 75 elemptr = sample_data[ctr] + start_col; 76 77 /* Load data into workspace */ 78 tmp0 = (FAST_FLOAT) (GETJSAMPLE(elemptr[0]) + GETJSAMPLE(elemptr[7])); 79 tmp7 = (FAST_FLOAT) (GETJSAMPLE(elemptr[0]) - GETJSAMPLE(elemptr[7])); 80 tmp1 = (FAST_FLOAT) (GETJSAMPLE(elemptr[1]) + GETJSAMPLE(elemptr[6])); 81 tmp6 = (FAST_FLOAT) (GETJSAMPLE(elemptr[1]) - GETJSAMPLE(elemptr[6])); 82 tmp2 = (FAST_FLOAT) (GETJSAMPLE(elemptr[2]) + GETJSAMPLE(elemptr[5])); 83 tmp5 = (FAST_FLOAT) (GETJSAMPLE(elemptr[2]) - GETJSAMPLE(elemptr[5])); 84 tmp3 = (FAST_FLOAT) (GETJSAMPLE(elemptr[3]) + GETJSAMPLE(elemptr[4])); 85 tmp4 = (FAST_FLOAT) (GETJSAMPLE(elemptr[3]) - GETJSAMPLE(elemptr[4])); 86 87 /* Even part */ 88 89 tmp10 = tmp0 + tmp3; /* phase 2 */ 90 tmp13 = tmp0 - tmp3; 91 tmp11 = tmp1 + tmp2; 92 tmp12 = tmp1 - tmp2; 93 94 /* Apply unsigned->signed conversion. */ 95 dataptr[0] = tmp10 + tmp11 - 8 * CENTERJSAMPLE; /* phase 3 */ 96 dataptr[4] = tmp10 - tmp11; 97 98 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */ 99 dataptr[2] = tmp13 + z1; /* phase 5 */ 100 dataptr[6] = tmp13 - z1; 101 102 /* Odd part */ 103 104 tmp10 = tmp4 + tmp5; /* phase 2 */ 105 tmp11 = tmp5 + tmp6; 106 tmp12 = tmp6 + tmp7; 107 108 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 109 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */ 110 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */ 111 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */ 112 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */ 113 114 z11 = tmp7 + z3; /* phase 5 */ 115 z13 = tmp7 - z3; 116 117 dataptr[5] = z13 + z2; /* phase 6 */ 118 dataptr[3] = z13 - z2; 119 dataptr[1] = z11 + z4; 120 dataptr[7] = z11 - z4; 121 122 dataptr += DCTSIZE; /* advance pointer to next row */ 123 } 124 125 /* Pass 2: process columns. */ 126 127 dataptr = data; 128 for (ctr = DCTSIZE-1; ctr >= 0; ctr--) { 129 tmp0 = dataptr[DCTSIZE*0] + dataptr[DCTSIZE*7]; 130 tmp7 = dataptr[DCTSIZE*0] - dataptr[DCTSIZE*7]; 131 tmp1 = dataptr[DCTSIZE*1] + dataptr[DCTSIZE*6]; 132 tmp6 = dataptr[DCTSIZE*1] - dataptr[DCTSIZE*6]; 133 tmp2 = dataptr[DCTSIZE*2] + dataptr[DCTSIZE*5]; 134 tmp5 = dataptr[DCTSIZE*2] - dataptr[DCTSIZE*5]; 135 tmp3 = dataptr[DCTSIZE*3] + dataptr[DCTSIZE*4]; 136 tmp4 = dataptr[DCTSIZE*3] - dataptr[DCTSIZE*4]; 137 138 /* Even part */ 139 140 tmp10 = tmp0 + tmp3; /* phase 2 */ 141 tmp13 = tmp0 - tmp3; 142 tmp11 = tmp1 + tmp2; 143 tmp12 = tmp1 - tmp2; 144 145 dataptr[DCTSIZE*0] = tmp10 + tmp11; /* phase 3 */ 146 dataptr[DCTSIZE*4] = tmp10 - tmp11; 147 148 z1 = (tmp12 + tmp13) * ((FAST_FLOAT) 0.707106781); /* c4 */ 149 dataptr[DCTSIZE*2] = tmp13 + z1; /* phase 5 */ 150 dataptr[DCTSIZE*6] = tmp13 - z1; 151 152 /* Odd part */ 153 154 tmp10 = tmp4 + tmp5; /* phase 2 */ 155 tmp11 = tmp5 + tmp6; 156 tmp12 = tmp6 + tmp7; 157 158 /* The rotator is modified from fig 4-8 to avoid extra negations. */ 159 z5 = (tmp10 - tmp12) * ((FAST_FLOAT) 0.382683433); /* c6 */ 160 z2 = ((FAST_FLOAT) 0.541196100) * tmp10 + z5; /* c2-c6 */ 161 z4 = ((FAST_FLOAT) 1.306562965) * tmp12 + z5; /* c2+c6 */ 162 z3 = tmp11 * ((FAST_FLOAT) 0.707106781); /* c4 */ 163 164 z11 = tmp7 + z3; /* phase 5 */ 165 z13 = tmp7 - z3; 166 167 dataptr[DCTSIZE*5] = z13 + z2; /* phase 6 */ 168 dataptr[DCTSIZE*3] = z13 - z2; 169 dataptr[DCTSIZE*1] = z11 + z4; 170 dataptr[DCTSIZE*7] = z11 - z4; 171 172 dataptr++; /* advance pointer to next column */ 173 } 174 } 175 176 #endif /* DCT_FLOAT_SUPPORTED */ 177