5 void idct_reference(const int16_t* input, const uint32_t* quant_table, uint8_t* output)
9 for (unsigned y = 0; y < 8; ++y) {
10 for (unsigned x = 0; x < 8; ++x) {
12 for (unsigned u = 0; u < 8; ++u) {
13 for (unsigned v = 0; v < 8; ++v) {
14 double c_u = (u == 0) ? 1/sqrt(2.0) : 1.0;
15 double c_v = (v == 0) ? 1/sqrt(2.0) : 1.0;
17 * input[u * DCTSIZE + v] * quant_table[u * DCTSIZE + v]
18 * cos((2 * x + 1) * v * M_PI / 16.0)
19 * cos((2 * y + 1) * u * M_PI / 16.0);
22 temp[y * DCTSIZE + x] = 0.25 * acc;
26 for (unsigned y = 0; y < 8; ++y) {
27 for (unsigned x = 0; x < 8; ++x) {
28 double val = temp[y * DCTSIZE + x];
30 output[y * DCTSIZE + x] = 0;
31 } else if (val >= 255.0) {
32 output[y * DCTSIZE + x] = 255;
34 output[y * DCTSIZE + x] = (uint8_t)(val + 0.5);
40 // AA&N (Arai, Agui and Nakajima) floating-point IDCT.
41 // This IDCT is based on the same DCT that libjpeg uses -- in fact, exactly the
42 // same figure from the same book ("JPEG: Still Image Data Compression Standard",
43 // page 52, figure 4-8). However, it is coded from scratch, and uses the
44 // transposition method for converting DCT -> IDCT suggested in the book.
45 // (libjpeg seems to use some other method that yields similar, but not
48 // As this is generally meant as a reference and not useful code (we expect
49 // a SIMD fixed-point algorithm to be used in most cases), it has not been
50 // attempted significantly optimized. We assume the compiler will be smart
51 // enough to do all the variable propagation for us anyway.
53 // Scale factors; 1.0 / (sqrt(2.0) * cos(k * M_PI / 16.0)), except for the first which is 1.
54 static const double scalefac[] = {
55 1.0, 0.7209598220069479, 0.765366864730180, 0.8504300947672564,
56 1.0, 1.2727585805728336, 1.847759065022573, 3.6245097854115502
60 static inline void idct1d_float(double y0, double y1, double y2, double y3, double y4, double y5, double y6, double y7, double *x)
63 const double a1 = 0.7071067811865474; // sqrt(2)
64 const double a2 = 0.5411961001461971; // cos(3/8 pi) * sqrt(2)
66 const double a4 = 1.3065629648763766; // cos(pi/8) * sqrt(2)
67 const double a5 = 0.5 * (a4 - a2);
70 const double p1_0 = y0 * scalefac[0];
71 const double p1_1 = y4 * scalefac[4];
72 const double p1_2 = y2 * scalefac[2];
73 const double p1_3 = y6 * scalefac[6];
74 const double p1_4 = y5 * scalefac[5];
75 const double p1_5 = y1 * scalefac[1];
76 const double p1_6 = y7 * scalefac[7];
77 const double p1_7 = y3 * scalefac[3];
80 const double p2_0 = p1_0;
81 const double p2_1 = p1_1;
82 const double p2_2 = p1_2;
83 const double p2_3 = p1_3;
84 const double p2_4 = p1_4 - p1_7;
85 const double p2_5 = p1_5 + p1_6;
86 const double p2_6 = p1_5 - p1_6;
87 const double p2_7 = p1_4 + p1_7;
90 const double p3_0 = p2_0;
91 const double p3_1 = p2_1;
92 const double p3_2 = p2_2 - p2_3;
93 const double p3_3 = p2_2 + p2_3;
94 const double p3_4 = p2_4;
95 const double p3_5 = p2_5 - p2_7;
96 const double p3_6 = p2_6;
97 const double p3_7 = p2_5 + p2_7;
100 const double p4_0 = p3_0;
101 const double p4_1 = p3_1;
102 const double p4_2 = a1 * p3_2;
103 const double p4_3 = p3_3;
104 const double p4_4 = p3_4 * -a2 + (p3_4 + p3_6) * -a5;
105 const double p4_5 = a3 * p3_5;
106 const double p4_6 = p3_6 * a4 + (p3_4 + p3_6) * -a5;
107 const double p4_7 = p3_7;
110 const double p5_0 = p4_0 + p4_1;
111 const double p5_1 = p4_0 - p4_1;
112 const double p5_2 = p4_2;
113 const double p5_3 = p4_2 + p4_3;
114 const double p5_4 = p4_4;
115 const double p5_5 = p4_5;
116 const double p5_6 = p4_6;
117 const double p5_7 = p4_7;
120 const double p6_0 = p5_0 + p5_3;
121 const double p6_1 = p5_1 + p5_2;
122 const double p6_2 = p5_1 - p5_2;
123 const double p6_3 = p5_0 - p5_3;
124 const double p6_4 = -p5_4;
125 const double p6_5 = p5_5 - p5_4;
126 const double p6_6 = p5_5 + p5_6;
127 const double p6_7 = p5_6 + p5_7;
140 void idct_float(const int16_t* input, const uint32_t* quant_table, uint8_t* output)
142 double temp[DCTSIZE2];
145 for (unsigned x = 0; x < DCTSIZE; ++x) {
146 idct1d_float(input[DCTSIZE * 0 + x] * (int32_t)quant_table[DCTSIZE * 0 + x],
147 input[DCTSIZE * 1 + x] * (int32_t)quant_table[DCTSIZE * 1 + x],
148 input[DCTSIZE * 2 + x] * (int32_t)quant_table[DCTSIZE * 2 + x],
149 input[DCTSIZE * 3 + x] * (int32_t)quant_table[DCTSIZE * 3 + x],
150 input[DCTSIZE * 4 + x] * (int32_t)quant_table[DCTSIZE * 4 + x],
151 input[DCTSIZE * 5 + x] * (int32_t)quant_table[DCTSIZE * 5 + x],
152 input[DCTSIZE * 6 + x] * (int32_t)quant_table[DCTSIZE * 6 + x],
153 input[DCTSIZE * 7 + x] * (int32_t)quant_table[DCTSIZE * 7 + x],
158 for (unsigned y = 0; y < DCTSIZE; ++y) {
159 double temp2[DCTSIZE];
160 idct1d_float(temp[DCTSIZE * 0 + y],
161 temp[DCTSIZE * 1 + y],
162 temp[DCTSIZE * 2 + y],
163 temp[DCTSIZE * 3 + y],
164 temp[DCTSIZE * 4 + y],
165 temp[DCTSIZE * 5 + y],
166 temp[DCTSIZE * 6 + y],
167 temp[DCTSIZE * 7 + y],
169 for (unsigned x = 0; x < DCTSIZE; ++x) {
170 double val = (1.0/8.0) * temp2[x];
172 output[y * DCTSIZE + x] = 0;
173 } else if (val >= 255.0) {
174 output[y * DCTSIZE + x] = 255;
176 output[y * DCTSIZE + x] = (uint8_t)(val + 0.5);