2 // MMX32 iDCT algorithm (IEEE-1180 compliant) :: idct_mmx32()
6 // v0.16B33 initial release
8 // This was one of the harder pieces of work to code.
9 // Intel's app-note focuses on the numerical issues of the algorithm, but
10 // assumes the programmer is familiar with IDCT mathematics, leaving the
11 // form of the complete function up to the programmer's imagination.
20 // I played around with the code for quite a few hours. I came up
21 // with *A* working IDCT algorithm, however I'm not sure whether my routine
22 // is "the correct one." But rest assured, my code passes all six IEEE
23 // accuracy tests with plenty of margin.
25 // My IDCT algorithm consists of 4 steps:
27 // 1) IDCT-row transformation (using the IDCT-row function) on all 8 rows
28 // This yields an intermediate 8x8 matrix.
30 // 2) intermediate matrix transpose (mandatory)
32 // 3) IDCT-row transformation (2nd time) on all 8 rows of the intermediate
33 // matrix. The output is the final-result, in transposed form.
35 // 4) post-transformation matrix transpose
36 // (not necessary if the input-data is already transposed, this could
37 // be done during the MPEG "zig-zag" scan, but since my algorithm
38 // requires at least one transpose operation, why not re-use the
41 // Although the (1st) and (3rd) steps use the SAME row-transform operation,
42 // the (3rd) step uses different shift&round constants (explained later.)
44 // Also note that the intermediate transpose (2) would not be neccessary,
45 // if the subsequent operation were a iDCT-column transformation. Since
46 // we only have the iDCT-row transform, we transpose the intermediate
47 // matrix and use the iDCT-row transform a 2nd time.
49 // I had to change some constants/variables for my method to work :
51 // As given by Intel, the #defines for SHIFT_INV_COL and RND_INV_COL are
52 // wrong. Not surprising since I'm not using a true column-transform
53 // operation, but the row-transform operation (as mentioned earlier.)
54 // round_inv_col[], which is given as "4 int16_t" values, should have the
55 // same dimensions as round_inv_row[]. The corrected variables are
58 // Intel's code defines a different table for each each row operation.
59 // The tables given are 0/4, 1/7, 2/6, and 5/3. My code only uses row#0.
60 // Using the other rows messes up the overall transform.
62 // IMPLEMENTATION DETAILs
63 // ----------------------
65 // I divided the algorithm's work into two subroutines,
66 // 1) idct_mmx32_rows() - transforms 8 rows, then transpose
67 // 2) idct_mmx32_cols() - transforms 8 rows, then transpose
68 // yields final result ("drop-in" direct replacement for INT32 IDCT)
70 // The 2nd function is a clone of the 1st, with changes made only to the
71 // shift&rounding instructions.
73 // In the 1st function (rows), the shift & round instructions use
74 // SHIFT_INV_ROW & round_inv_row[] (renamed to r_inv_row[])
76 // In the 2nd function (cols)-> r_inv_col[], and
77 // SHIFT_INV_COL & round_inv_col[] (renamed to r_inv_col[])
79 // Each function contains an integrated transpose-operator, which comes
80 // AFTER the primary transformation operation. In the future, I'll optimize
81 // the code to do more of the transpose-work "in-place". Right now, I've
82 // left the code as two subroutines and a main calling function, so other
83 // people can read the code more easily.
85 // liaor@umcc.ais.org http://members.tripod.com/~liaor
88 //;=============================================================================
90 //; AP-922 http://developer.intel.com/vtune/cbts/strmsimd
91 //; These examples contain code fragments for first stage iDCT 8x8
92 //; (for rows) and first stage DCT 8x8 (for columns)
94 //;=============================================================================
96 #define BITS_INV_ACC 4 //; 4 or 5 for IEEE
97 // 5 yields higher accuracy, but lessens dynamic range on the input matrix
98 #define SHIFT_INV_ROW (16 - BITS_INV_ACC)
99 #define SHIFT_INV_COL (1 + BITS_INV_ACC +14 ) // changed from Intel's val)
102 #define RND_INV_ROW (1 << (SHIFT_INV_ROW-1))
103 #define RND_INV_COL (1 << (SHIFT_INV_COL-1))
104 #define RND_INV_CORR (RND_INV_COL - 1) //; correction -1.0 and round
106 /* TODO: This should *really* be aligned on 16-byte boundaries... */
108 const int idct_r_inv_row[2] = { RND_INV_ROW, RND_INV_ROW};
109 const int idct_r_inv_col[2] = {RND_INV_COL, RND_INV_COL};
110 const int idct_r_inv_corr[2] = {RND_INV_CORR, RND_INV_CORR };
112 /* Unused and thus redundant...
113 const long long dct_one_corr = 0x0001000100010001;
117 ;=============================================================================
119 ; The first stage iDCT 8x8 - inverse DCTs of rows
121 ;-----------------------------------------------------------------------------
122 ; The 8-point inverse DCT direct algorithm
123 ;-----------------------------------------------------------------------------
125 ; static const int16_t w[32] = {
126 ; FIX(cos_4_16), FIX(cos_2_16), FIX(cos_4_16), FIX(cos_6_16),
127 ; FIX(cos_4_16), FIX(cos_6_16), -FIX(cos_4_16), -FIX(cos_2_16),
128 ; FIX(cos_4_16), -FIX(cos_6_16), -FIX(cos_4_16), FIX(cos_2_16),
129 ; FIX(cos_4_16), -FIX(cos_2_16), FIX(cos_4_16), -FIX(cos_6_16),
130 ; FIX(cos_1_16), FIX(cos_3_16), FIX(cos_5_16), FIX(cos_7_16),
131 ; FIX(cos_3_16), -FIX(cos_7_16), -FIX(cos_1_16), -FIX(cos_5_16),
132 ; FIX(cos_5_16), -FIX(cos_1_16), FIX(cos_7_16), FIX(cos_3_16),
133 ; FIX(cos_7_16), -FIX(cos_5_16), FIX(cos_3_16), -FIX(cos_1_16) };
135 ; #define DCT_8_INV_ROW(x, y)
138 ; int a0, a1, a2, a3, b0, b1, b2, b3;
140 ; a0 =x[0]*w[0]+x[2]*w[1]+x[4]*w[2]+x[6]*w[3];
141 ; a1 =x[0]*w[4]+x[2]*w[5]+x[4]*w[6]+x[6]*w[7];
142 ; a2 = x[0] * w[ 8] + x[2] * w[ 9] + x[4] * w[10] + x[6] * w[11];
143 ; a3 = x[0] * w[12] + x[2] * w[13] + x[4] * w[14] + x[6] * w[15];
144 ; b0 = x[1] * w[16] + x[3] * w[17] + x[5] * w[18] + x[7] * w[19];
145 ; b1 = x[1] * w[20] + x[3] * w[21] + x[5] * w[22] + x[7] * w[23];
146 ; b2 = x[1] * w[24] + x[3] * w[25] + x[5] * w[26] + x[7] * w[27];
147 ; b3 = x[1] * w[28] + x[3] * w[29] + x[5] * w[30] + x[7] * w[31];
149 ; y[0] = SHIFT_ROUND ( a0 + b0 );
150 ; y[1] = SHIFT_ROUND ( a1 + b1 );
151 ; y[2] = SHIFT_ROUND ( a2 + b2 );
152 ; y[3] = SHIFT_ROUND ( a3 + b3 );
153 ; y[4] = SHIFT_ROUND ( a3 - b3 );
154 ; y[5] = SHIFT_ROUND ( a2 - b2 );
155 ; y[6] = SHIFT_ROUND ( a1 - b1 );
156 ; y[7] = SHIFT_ROUND ( a0 - b0 );
159 ;-----------------------------------------------------------------------------
161 ; In this implementation the outputs of the iDCT-1D are multiplied
162 ; for rows 0,4 - by cos_4_16,
163 ; for rows 1,7 - by cos_1_16,
164 ; for rows 2,6 - by cos_2_16,
165 ; for rows 3,5 - by cos_3_16
166 ; and are shifted to the left for better accuracy
168 ; For the constants used,
169 ; FIX(float_const) = (int16_t) (float_const * (1<<15) + 0.5)
171 ;=============================================================================
174 /* CONCATENATED TABLE, rows 0,1,2,3,4,5,6,7 (in order )
176 In our implementation, however, we only use row0 !
179 const int16_t idct_tab_01234567[] = {
180 //row0, this row is required
181 16384, 16384, 16384, -16384, // ; movq-> w06 w04 w02 w00
182 21407, 8867, 8867, -21407, // w07 w05 w03 w01
183 16384, -16384, 16384, 16384, //; w14 w12 w10 w08
184 -8867, 21407, -21407, -8867, //; w15 w13 w11 w09
185 22725, 12873, 19266, -22725, //; w22 w20 w18 w16
186 19266, 4520, -4520, -12873, //; w23 w21 w19 w17
187 12873, 4520, 4520, 19266, //; w30 w28 w26 w24
188 -22725, 19266, -12873, -22725, //w31 w29 w27 w25
190 // the rest of these rows (1-7), aren't used !
193 22725, 22725, 22725, -22725, // ; movq-> w06 w04 w02 w00
194 29692, 12299, 12299, -29692, // ; w07 w05 w03 w01
195 22725, -22725, 22725, 22725, //; w14 w12 w10 w08
196 -12299, 29692, -29692, -12299, //; w15 w13 w11 w09
197 31521, 17855, 26722, -31521, //; w22 w20 w18 w16
198 26722, 6270, -6270, -17855, //; w23 w21 w19 w17
199 17855, 6270, 6270, 26722, //; w30 w28 w26 w24
200 -31521, 26722, -17855, -31521, // w31 w29 w27 w25
203 21407, 21407, 21407, -21407, // ; movq-> w06 w04 w02 w00
204 27969, 11585, 11585, -27969, // ; w07 w05 w03 w01
205 21407, -21407, 21407, 21407, // ; w14 w12 w10 w08
206 -11585, 27969, -27969, -11585, // ;w15 w13 w11 w09
207 29692, 16819, 25172, -29692, // ;w22 w20 w18 w16
208 25172, 5906, -5906, -16819, // ;w23 w21 w19 w17
209 16819, 5906, 5906, 25172, // ;w30 w28 w26 w24
210 -29692, 25172, -16819, -29692, // ;w31 w29 w27 w25
213 19266, 19266, 19266, -19266, //; movq-> w06 w04 w02 w00
214 25172, 10426, 10426, -25172, //; w07 w05 w03 w01
215 19266, -19266, 19266, 19266, //; w14 w12 w10 w08
216 -10426, 25172, -25172, -10426, //; w15 w13 w11 w09
217 26722, 15137, 22654, -26722, //; w22 w20 w18 w16
218 22654, 5315, -5315, -15137, //; w23 w21 w19 w17
219 15137, 5315, 5315, 22654, //; w30 w28 w26 w24
220 -26722, 22654, -15137, -26722, //; w31 w29 w27 w25
223 16384, 16384, 16384, -16384, // ; movq-> w06 w04 w02 w00
224 21407, 8867, 8867, -21407, // w07 w05 w03 w01
225 16384, -16384, 16384, 16384, //; w14 w12 w10 w08
226 -8867, 21407, -21407, -8867, //; w15 w13 w11 w09
227 22725, 12873, 19266, -22725, //; w22 w20 w18 w16
228 19266, 4520, -4520, -12873, //; w23 w21 w19 w17
229 12873, 4520, 4520, 19266, //; w30 w28 w26 w24
230 -22725, 19266, -12873, -22725, //w31 w29 w27 w25
233 19266, 19266, 19266, -19266, //; movq-> w06 w04 w02 w00
234 25172, 10426, 10426, -25172, //; w07 w05 w03 w01
235 19266, -19266, 19266, 19266, //; w14 w12 w10 w08
236 -10426, 25172, -25172, -10426, //; w15 w13 w11 w09
237 26722, 15137, 22654, -26722, //; w22 w20 w18 w16
238 22654, 5315, -5315, -15137, //; w23 w21 w19 w17
239 15137, 5315, 5315, 22654, //; w30 w28 w26 w24
240 -26722, 22654, -15137, -26722, //; w31 w29 w27 w25
243 21407, 21407, 21407, -21407, // ; movq-> w06 w04 w02 w00
244 27969, 11585, 11585, -27969, // ; w07 w05 w03 w01
245 21407, -21407, 21407, 21407, // ; w14 w12 w10 w08
246 -11585, 27969, -27969, -11585, // ;w15 w13 w11 w09
247 29692, 16819, 25172, -29692, // ;w22 w20 w18 w16
248 25172, 5906, -5906, -16819, // ;w23 w21 w19 w17
249 16819, 5906, 5906, 25172, // ;w30 w28 w26 w24
250 -29692, 25172, -16819, -29692, // ;w31 w29 w27 w25
253 22725, 22725, 22725, -22725, // ; movq-> w06 w04 w02 w00
254 29692, 12299, 12299, -29692, // ; w07 w05 w03 w01
255 22725, -22725, 22725, 22725, //; w14 w12 w10 w08
256 -12299, 29692, -29692, -12299, //; w15 w13 w11 w09
257 31521, 17855, 26722, -31521, //; w22 w20 w18 w16
258 26722, 6270, -6270, -17855, //; w23 w21 w19 w17
259 17855, 6270, 6270, 26722, //; w30 w28 w26 w24
260 -31521, 26722, -17855, -31521}; // w31 w29 w27 w25