// // MMX32 iDCT algorithm (IEEE-1180 compliant) :: idct_mmx32() // // MPEG2AVI // -------- // v0.16B33 initial release // // This was one of the harder pieces of work to code. // Intel's app-note focuses on the numerical issues of the algorithm, but // assumes the programmer is familiar with IDCT mathematics, leaving the // form of the complete function up to the programmer's imagination. #include "config.h" #include "mpeg2enc.h" #include "global.h" #include "simd.h" // ALGORITHM OVERVIEW // ------------------ // I played around with the code for quite a few hours. I came up // with *A* working IDCT algorithm, however I'm not sure whether my routine // is "the correct one." But rest assured, my code passes all six IEEE // accuracy tests with plenty of margin. // // My IDCT algorithm consists of 4 steps: // // 1) IDCT-row transformation (using the IDCT-row function) on all 8 rows // This yields an intermediate 8x8 matrix. // // 2) intermediate matrix transpose (mandatory) // // 3) IDCT-row transformation (2nd time) on all 8 rows of the intermediate // matrix. The output is the final-result, in transposed form. // // 4) post-transformation matrix transpose // (not necessary if the input-data is already transposed, this could // be done during the MPEG "zig-zag" scan, but since my algorithm // requires at least one transpose operation, why not re-use the // transpose-code.) // // Although the (1st) and (3rd) steps use the SAME row-transform operation, // the (3rd) step uses different shift&round constants (explained later.) // // Also note that the intermediate transpose (2) would not be neccessary, // if the subsequent operation were a iDCT-column transformation. Since // we only have the iDCT-row transform, we transpose the intermediate // matrix and use the iDCT-row transform a 2nd time. // // I had to change some constants/variables for my method to work : // // As given by Intel, the #defines for SHIFT_INV_COL and RND_INV_COL are // wrong. Not surprising since I'm not using a true column-transform // operation, but the row-transform operation (as mentioned earlier.) // round_inv_col[], which is given as "4 int16_t" values, should have the // same dimensions as round_inv_row[]. The corrected variables are // shown. // // Intel's code defines a different table for each each row operation. // The tables given are 0/4, 1/7, 2/6, and 5/3. My code only uses row#0. // Using the other rows messes up the overall transform. // // IMPLEMENTATION DETAILs // ---------------------- // // I divided the algorithm's work into two subroutines, // 1) idct_mmx32_rows() - transforms 8 rows, then transpose // 2) idct_mmx32_cols() - transforms 8 rows, then transpose // yields final result ("drop-in" direct replacement for INT32 IDCT) // // The 2nd function is a clone of the 1st, with changes made only to the // shift&rounding instructions. // // In the 1st function (rows), the shift & round instructions use // SHIFT_INV_ROW & round_inv_row[] (renamed to r_inv_row[]) // // In the 2nd function (cols)-> r_inv_col[], and // SHIFT_INV_COL & round_inv_col[] (renamed to r_inv_col[]) // // Each function contains an integrated transpose-operator, which comes // AFTER the primary transformation operation. In the future, I'll optimize // the code to do more of the transpose-work "in-place". Right now, I've // left the code as two subroutines and a main calling function, so other // people can read the code more easily. // // liaor@umcc.ais.org http://members.tripod.com/~liaor // //;============================================================================= //; //; AP-922 http://developer.intel.com/vtune/cbts/strmsimd //; These examples contain code fragments for first stage iDCT 8x8 //; (for rows) and first stage DCT 8x8 (for columns) //; //;============================================================================= #define BITS_INV_ACC 4 //; 4 or 5 for IEEE // 5 yields higher accuracy, but lessens dynamic range on the input matrix #define SHIFT_INV_ROW (16 - BITS_INV_ACC) #define SHIFT_INV_COL (1 + BITS_INV_ACC +14 ) // changed from Intel's val) #define RND_INV_ROW (1 << (SHIFT_INV_ROW-1)) #define RND_INV_COL (1 << (SHIFT_INV_COL-1)) #define RND_INV_CORR (RND_INV_COL - 1) //; correction -1.0 and round /* TODO: This should *really* be aligned on 16-byte boundaries... */ const int idct_r_inv_row[2] = { RND_INV_ROW, RND_INV_ROW}; const int idct_r_inv_col[2] = {RND_INV_COL, RND_INV_COL}; const int idct_r_inv_corr[2] = {RND_INV_CORR, RND_INV_CORR }; /* Unused and thus redundant... const long long dct_one_corr = 0x0001000100010001; */ /* ;============================================================================= ; ; The first stage iDCT 8x8 - inverse DCTs of rows ; ;----------------------------------------------------------------------------- ; The 8-point inverse DCT direct algorithm ;----------------------------------------------------------------------------- ; ; static const int16_t w[32] = { ; FIX(cos_4_16), FIX(cos_2_16), FIX(cos_4_16), FIX(cos_6_16), ; FIX(cos_4_16), FIX(cos_6_16), -FIX(cos_4_16), -FIX(cos_2_16), ; FIX(cos_4_16), -FIX(cos_6_16), -FIX(cos_4_16), FIX(cos_2_16), ; FIX(cos_4_16), -FIX(cos_2_16), FIX(cos_4_16), -FIX(cos_6_16), ; FIX(cos_1_16), FIX(cos_3_16), FIX(cos_5_16), FIX(cos_7_16), ; FIX(cos_3_16), -FIX(cos_7_16), -FIX(cos_1_16), -FIX(cos_5_16), ; FIX(cos_5_16), -FIX(cos_1_16), FIX(cos_7_16), FIX(cos_3_16), ; FIX(cos_7_16), -FIX(cos_5_16), FIX(cos_3_16), -FIX(cos_1_16) }; ; ; #define DCT_8_INV_ROW(x, y) ;{ ; int a0, a1, a2, a3, b0, b1, b2, b3; ; ; a0 =x[0]*w[0]+x[2]*w[1]+x[4]*w[2]+x[6]*w[3]; ; a1 =x[0]*w[4]+x[2]*w[5]+x[4]*w[6]+x[6]*w[7]; ; a2 = x[0] * w[ 8] + x[2] * w[ 9] + x[4] * w[10] + x[6] * w[11]; ; a3 = x[0] * w[12] + x[2] * w[13] + x[4] * w[14] + x[6] * w[15]; ; b0 = x[1] * w[16] + x[3] * w[17] + x[5] * w[18] + x[7] * w[19]; ; b1 = x[1] * w[20] + x[3] * w[21] + x[5] * w[22] + x[7] * w[23]; ; b2 = x[1] * w[24] + x[3] * w[25] + x[5] * w[26] + x[7] * w[27]; ; b3 = x[1] * w[28] + x[3] * w[29] + x[5] * w[30] + x[7] * w[31]; ; ; y[0] = SHIFT_ROUND ( a0 + b0 ); ; y[1] = SHIFT_ROUND ( a1 + b1 ); ; y[2] = SHIFT_ROUND ( a2 + b2 ); ; y[3] = SHIFT_ROUND ( a3 + b3 ); ; y[4] = SHIFT_ROUND ( a3 - b3 ); ; y[5] = SHIFT_ROUND ( a2 - b2 ); ; y[6] = SHIFT_ROUND ( a1 - b1 ); ; y[7] = SHIFT_ROUND ( a0 - b0 ); ;} ; ;----------------------------------------------------------------------------- ; ; In this implementation the outputs of the iDCT-1D are multiplied ; for rows 0,4 - by cos_4_16, ; for rows 1,7 - by cos_1_16, ; for rows 2,6 - by cos_2_16, ; for rows 3,5 - by cos_3_16 ; and are shifted to the left for better accuracy ; ; For the constants used, ; FIX(float_const) = (int16_t) (float_const * (1<<15) + 0.5) ; ;============================================================================= */ /* CONCATENATED TABLE, rows 0,1,2,3,4,5,6,7 (in order ) In our implementation, however, we only use row0 ! */ const int16_t idct_tab_01234567[] = { //row0, this row is required 16384, 16384, 16384, -16384, // ; movq-> w06 w04 w02 w00 21407, 8867, 8867, -21407, // w07 w05 w03 w01 16384, -16384, 16384, 16384, //; w14 w12 w10 w08 -8867, 21407, -21407, -8867, //; w15 w13 w11 w09 22725, 12873, 19266, -22725, //; w22 w20 w18 w16 19266, 4520, -4520, -12873, //; w23 w21 w19 w17 12873, 4520, 4520, 19266, //; w30 w28 w26 w24 -22725, 19266, -12873, -22725, //w31 w29 w27 w25 // the rest of these rows (1-7), aren't used ! //row1 22725, 22725, 22725, -22725, // ; movq-> w06 w04 w02 w00 29692, 12299, 12299, -29692, // ; w07 w05 w03 w01 22725, -22725, 22725, 22725, //; w14 w12 w10 w08 -12299, 29692, -29692, -12299, //; w15 w13 w11 w09 31521, 17855, 26722, -31521, //; w22 w20 w18 w16 26722, 6270, -6270, -17855, //; w23 w21 w19 w17 17855, 6270, 6270, 26722, //; w30 w28 w26 w24 -31521, 26722, -17855, -31521, // w31 w29 w27 w25 //row2 21407, 21407, 21407, -21407, // ; movq-> w06 w04 w02 w00 27969, 11585, 11585, -27969, // ; w07 w05 w03 w01 21407, -21407, 21407, 21407, // ; w14 w12 w10 w08 -11585, 27969, -27969, -11585, // ;w15 w13 w11 w09 29692, 16819, 25172, -29692, // ;w22 w20 w18 w16 25172, 5906, -5906, -16819, // ;w23 w21 w19 w17 16819, 5906, 5906, 25172, // ;w30 w28 w26 w24 -29692, 25172, -16819, -29692, // ;w31 w29 w27 w25 //row3 19266, 19266, 19266, -19266, //; movq-> w06 w04 w02 w00 25172, 10426, 10426, -25172, //; w07 w05 w03 w01 19266, -19266, 19266, 19266, //; w14 w12 w10 w08 -10426, 25172, -25172, -10426, //; w15 w13 w11 w09 26722, 15137, 22654, -26722, //; w22 w20 w18 w16 22654, 5315, -5315, -15137, //; w23 w21 w19 w17 15137, 5315, 5315, 22654, //; w30 w28 w26 w24 -26722, 22654, -15137, -26722, //; w31 w29 w27 w25 //row4 16384, 16384, 16384, -16384, // ; movq-> w06 w04 w02 w00 21407, 8867, 8867, -21407, // w07 w05 w03 w01 16384, -16384, 16384, 16384, //; w14 w12 w10 w08 -8867, 21407, -21407, -8867, //; w15 w13 w11 w09 22725, 12873, 19266, -22725, //; w22 w20 w18 w16 19266, 4520, -4520, -12873, //; w23 w21 w19 w17 12873, 4520, 4520, 19266, //; w30 w28 w26 w24 -22725, 19266, -12873, -22725, //w31 w29 w27 w25 //row5 19266, 19266, 19266, -19266, //; movq-> w06 w04 w02 w00 25172, 10426, 10426, -25172, //; w07 w05 w03 w01 19266, -19266, 19266, 19266, //; w14 w12 w10 w08 -10426, 25172, -25172, -10426, //; w15 w13 w11 w09 26722, 15137, 22654, -26722, //; w22 w20 w18 w16 22654, 5315, -5315, -15137, //; w23 w21 w19 w17 15137, 5315, 5315, 22654, //; w30 w28 w26 w24 -26722, 22654, -15137, -26722, //; w31 w29 w27 w25 //row6 21407, 21407, 21407, -21407, // ; movq-> w06 w04 w02 w00 27969, 11585, 11585, -27969, // ; w07 w05 w03 w01 21407, -21407, 21407, 21407, // ; w14 w12 w10 w08 -11585, 27969, -27969, -11585, // ;w15 w13 w11 w09 29692, 16819, 25172, -29692, // ;w22 w20 w18 w16 25172, 5906, -5906, -16819, // ;w23 w21 w19 w17 16819, 5906, 5906, 25172, // ;w30 w28 w26 w24 -29692, 25172, -16819, -29692, // ;w31 w29 w27 w25 //row7 22725, 22725, 22725, -22725, // ; movq-> w06 w04 w02 w00 29692, 12299, 12299, -29692, // ; w07 w05 w03 w01 22725, -22725, 22725, 22725, //; w14 w12 w10 w08 -12299, 29692, -29692, -12299, //; w15 w13 w11 w09 31521, 17855, 26722, -31521, //; w22 w20 w18 w16 26722, 6270, -6270, -17855, //; w23 w21 w19 w17 17855, 6270, 6270, 26722, //; w30 w28 w26 w24 -31521, 26722, -17855, -31521}; // w31 w29 w27 w25