trigtabs.hpp

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/* ***** BEGIN LICENSE BLOCK ***** 
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/**************************************************************************************
 * Fixed-point MP3 decoder
 * Jon Recker (jrecker@real.com), Ken Cooke (kenc@real.com)
 * June 2003
 *
 * trigtabs.c - global ROM tables for pre-calculated trig coefficients
 **************************************************************************************/
 
// constants in RAM are not significantly faster
 
#include "coder.h"
#include "fl/stl/stdint.h"
 
namespace fl {
namespace third_party {
 
/* post-IMDCT window, win[blockType][i]
 * format = Q31
 * Fused sin window with final stage of IMDCT
 * includes 1/sqrt(2) scaling, since we scale by sqrt(2) in dequant in order
 *   for fast IMDCT36 to be usable
 * 
 *  for(i=0;i<9;i++)   win[0][i] = sin(pi/36 *(i+0.5));
 *  for(i=9;i<36;i++)  win[0][i] = -sin(pi/36 *(i+0.5));
 * 
 *  for(i=0;i<9;i++)   win[1][i] = sin(pi/36 *(i+0.5));
 *  for(i=9;i<18;i++)  win[1][i] = -sin(pi/36 *(i+0.5));
 *  for(i=18;i<24;i++) win[1][i] = -1;
 *  for(i=24;i<30;i++) win[1][i] = -sin(pi/12 *(i+0.5-18));
 *  for(i=30;i<36;i++) win[1][i] = 0;
 * 
 *  for(i=0;i<6;i++)   win[3][i] = 0;
 *  for(i=6;i<9;i++)   win[3][i] = sin(pi/12 *(i+0.5-6));
 *  for(i=9;i<12;i++)  win[3][i] = -sin(pi/12 *(i+0.5-6));
 *  for(i=12;i<18;i++) win[3][i] = -1;
 *  for(i=18;i<36;i++) win[3][i] = -sin(pi/36*(i+0.5));
 * 
 *  for(i=0;i<3;i++)   win[2][i] = sin(pi/12*(i+0.5));
 *  for(i=3;i<12;i++)  win[2][i] = -sin(pi/12*(i+0.5));
 *  for(i=12;i<36;i++) win[2][i] = 0;
 * 
 *  for (i = 0; i < 4; i++) {
 *      if (i == 2) {
 *          win[i][8]  *= cos(pi/12 * (0+0.5));
 *          win[i][9]  *= cos(pi/12 * (0+0.5));
 *          win[i][7]  *= cos(pi/12 * (1+0.5));
 *          win[i][10] *= cos(pi/12 * (1+0.5));
 *          win[i][6]  *= cos(pi/12 * (2+0.5));
 *          win[i][11] *= cos(pi/12 * (2+0.5));
 *          win[i][0]  *= cos(pi/12 * (3+0.5));
 *          win[i][5]  *= cos(pi/12 * (3+0.5));
 *          win[i][1]  *= cos(pi/12 * (4+0.5));
 *          win[i][4]  *= cos(pi/12 * (4+0.5));
 *          win[i][2]  *= cos(pi/12 * (5+0.5));
 *          win[i][3]  *= cos(pi/12 * (5+0.5));
 *      } else {
 *          for (j = 0; j < 9; j++) {
 *              win[i][8-j] *= cos(pi/36 * (17-j+0.5));
 *              win[i][9+j] *= cos(pi/36 * (17-j+0.5));
 *          }
 *          for (j = 0; j < 9; j++) {
 *              win[i][18+8-j] *= cos(pi/36 * (j+0.5));
 *              win[i][18+9+j] *= cos(pi/36 * (j+0.5));
 *          }
 *      }
 *  }
 *  for (i = 0; i < 4; i++)
 *      for (j = 0; j < 36; j++)
 *          win[i][j] *= 1.0 / sqrt(2);
 */
 
const int32_t imdctWin[4][36] = {
    {
    0x02aace8b, 0x07311c28, 0x0a868fec, 0x0c913b52, 0x0d413ccd, 0x0c913b52, 0x0a868fec, 0x07311c28, 
    0x02aace8b, (int32_t)0xfd16d8dd, (int32_t)0xf6a09e66, (int32_t)0xef7a6275, (int32_t)0xe7dbc161, (int32_t)0xe0000000, (int32_t)0xd8243e9f, (int32_t)0xd0859d8b, 
    (int32_t)0xc95f619a, (int32_t)0xc2e92723, (int32_t)0xbd553175, (int32_t)0xb8cee3d8, (int32_t)0xb5797014, (int32_t)0xb36ec4ae, (int32_t)0xb2bec333, (int32_t)0xb36ec4ae, 
    (int32_t)0xb5797014, (int32_t)0xb8cee3d8, (int32_t)0xbd553175, (int32_t)0xc2e92723, (int32_t)0xc95f619a, (int32_t)0xd0859d8b, (int32_t)0xd8243e9f, (int32_t)0xe0000000, 
    (int32_t)0xe7dbc161, (int32_t)0xef7a6275, (int32_t)0xf6a09e66, (int32_t)0xfd16d8dd, 
    },
    {
    0x02aace8b, 0x07311c28, 0x0a868fec, 0x0c913b52, 0x0d413ccd, 0x0c913b52, 0x0a868fec, 0x07311c28, 
    0x02aace8b, (int32_t)0xfd16d8dd, (int32_t)0xf6a09e66, (int32_t)0xef7a6275, (int32_t)0xe7dbc161, (int32_t)0xe0000000, (int32_t)0xd8243e9f, (int32_t)0xd0859d8b, 
    (int32_t)0xc95f619a, (int32_t)0xc2e92723, (int32_t)0xbd44ef14, (int32_t)0xb831a052, (int32_t)0xb3aa3837, (int32_t)0xafb789a4, (int32_t)0xac6145bb, (int32_t)0xa9adecdc, 
    (int32_t)0xa864491f, (int32_t)0xad1868f0, (int32_t)0xb8431f49, (int32_t)0xc8f42236, (int32_t)0xdda8e6b1, (int32_t)0xf47755dc, 0x00000000, 0x00000000, 
    0x00000000, 0x00000000, 0x00000000, 0x00000000, 
    },
    {
    0x07311c28, 0x0d413ccd, 0x07311c28, (int32_t)0xf6a09e66, (int32_t)0xe0000000, (int32_t)0xc95f619a, (int32_t)0xb8cee3d8, (int32_t)0xb2bec333, 
    (int32_t)0xb8cee3d8, (int32_t)0xc95f619a, (int32_t)0xe0000000, (int32_t)0xf6a09e66, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 
    0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 
    0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 
    0x00000000, 0x00000000, 0x00000000, 0x00000000, 
    },
    {
    0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x028e9709, 0x04855ec0, 
    0x026743a1, (int32_t)0xfcde2c10, (int32_t)0xf515dc82, (int32_t)0xec93e53b, (int32_t)0xe4c880f8, (int32_t)0xdd5d0b08, (int32_t)0xd63510b7, (int32_t)0xcf5e834a, 
    (int32_t)0xc8e6b562, (int32_t)0xc2da4105, (int32_t)0xbd553175, (int32_t)0xb8cee3d8, (int32_t)0xb5797014, (int32_t)0xb36ec4ae, (int32_t)0xb2bec333, (int32_t)0xb36ec4ae, 
    (int32_t)0xb5797014, (int32_t)0xb8cee3d8, (int32_t)0xbd553175, (int32_t)0xc2e92723, (int32_t)0xc95f619a, (int32_t)0xd0859d8b, (int32_t)0xd8243e9f, (int32_t)0xe0000000, 
    (int32_t)0xe7dbc161, (int32_t)0xef7a6275, (int32_t)0xf6a09e66, (int32_t)0xfd16d8dd, 
    },
};
 
/* indexing = [mid-side off/on][intensity scale factor]
 * format = Q30, range = [0.0, 1.414]
 *
 * mid-side off: 
 *   ISFMpeg1[0][i] = tan(i*pi/12) / [1 + tan(i*pi/12)]  (left scalefactor)
 *                  =      1       / [1 + tan(i*pi/12)]  (right scalefactor)
 *
 * mid-side on: 
 *   ISFMpeg1[1][i] = sqrt(2) * ISFMpeg1[0][i]
 *
 * output L = ISFMpeg1[midSide][isf][0] * input L
 * output R = ISFMpeg1[midSide][isf][1] * input L
 *
 * obviously left scalefactor + right scalefactor = 1 (m-s off) or sqrt(2) (m-s on)
 *   so just store left and calculate right as 1 - left 
 *  (can derive as right = ISFMpeg1[x][6] - left)
 *
 * if mid-side enabled, multiply joint stereo scale factors by sqrt(2)
 *   - we scaled whole spectrum by 1/sqrt(2) in Dequant for the M+S/sqrt(2) in MidSideProc
 *   - but the joint stereo part of the spectrum doesn't need this, so we have to undo it
 *
 * if scale factor is and illegal intensity position, this becomes a passthrough
 *   - gain = [1, 0] if mid-side off, since L is coded directly and R = 0 in this region
 *   - gain = [1, 1] if mid-side on, since L = (M+S)/sqrt(2), R = (M-S)/sqrt(2)
 *     - and since S = 0 in the joint stereo region (above NZB right) then L = R = M * 1.0
 */
const int32_t ISFMpeg1[2][7] = {
    {0x00000000, 0x0d8658ba, 0x176cf5d0, 0x20000000, 0x28930a2f, 0x3279a745, 0x40000000},
    {0x00000000, 0x13207f5c, 0x2120fb83, 0x2d413ccc, 0x39617e16, 0x4761fa3d, 0x5a827999}
};
 
/* indexing = [intensity scale on/off][mid-side off/on][intensity scale factor]
 * format = Q30, range = [0.0, 1.414]
 *
 * if (isf == 0)                 kl = 1.0             kr = 1.0
 * else if (isf & 0x01 == 0x01)  kl = i0^((isf+1)/2), kr = 1.0
 * else if (isf & 0x01 == 0x00)  kl = 1.0,            kr = i0^(isf/2)
 *
 * if (intensityScale == 1)      i0 = 1/sqrt(2)       = 0x2d413ccc (Q30)
 * else                          i0 = 1/sqrt(sqrt(2)) = 0x35d13f32 (Q30)
 *
 * see comments for ISFMpeg1 (just above) regarding scaling, sqrt(2), etc.
 *
 * compress the MPEG2 table using the obvious identities above...
 * for isf = [0, 1, 2, ... 30], let sf = table[(isf+1) >> 1] 
 *   - if isf odd,  L = sf*L,     R = tab[0]*R
 *   - if isf even, L = tab[0]*L, R = sf*R
 */
const int32_t ISFMpeg2[2][2][16] = {
{
    {
        /* intensityScale off, mid-side off */
        0x40000000, 0x35d13f32, 0x2d413ccc, 0x260dfc14, 0x1fffffff, 0x1ae89f99, 0x16a09e66, 0x1306fe0a, 
        0x0fffffff, 0x0d744fcc, 0x0b504f33, 0x09837f05, 0x07ffffff, 0x06ba27e6, 0x05a82799, 0x04c1bf82,
    },
    {
        /* intensityScale off, mid-side on */
        0x5a827999, 0x4c1bf827, 0x3fffffff, 0x35d13f32, 0x2d413ccc, 0x260dfc13, 0x1fffffff, 0x1ae89f99, 
        0x16a09e66, 0x1306fe09, 0x0fffffff, 0x0d744fcc, 0x0b504f33, 0x09837f04, 0x07ffffff, 0x06ba27e6, 
    },
},
{
    {
        /* intensityScale on, mid-side off */
        0x40000000, 0x2d413ccc, 0x20000000, 0x16a09e66, 0x10000000, 0x0b504f33, 0x08000000, 0x05a82799, 
        0x04000000, 0x02d413cc, 0x02000000, 0x016a09e6, 0x01000000, 0x00b504f3, 0x00800000, 0x005a8279, 
    },
        /* intensityScale on, mid-side on */
    {
        0x5a827999, 0x3fffffff, 0x2d413ccc, 0x1fffffff, 0x16a09e66, 0x0fffffff, 0x0b504f33, 0x07ffffff, 
        0x05a82799, 0x03ffffff, 0x02d413cc, 0x01ffffff, 0x016a09e6, 0x00ffffff, 0x00b504f3, 0x007fffff, 
    }
}
};
 
/* indexing = [intensity scale on/off][left/right]
 * format = Q30, range = [0.0, 1.414]
 *
 * illegal intensity position scalefactors (see comments on ISFMpeg1)
 */
const int32_t ISFIIP[2][2] = {
    {0x40000000, 0x00000000}, /* mid-side off */
    {0x40000000, 0x40000000}, /* mid-side on */
};
 
const unsigned char uniqueIDTab[8] = {0x5f, 0x4b, 0x43, 0x5f, 0x5f, 0x4a, 0x52, 0x5f};
 
/* anti-alias coefficients - see spec Annex B, table 3-B.9 
 *   csa[0][i] = CSi, csa[1][i] = CAi
 * format = Q31
 */
const int32_t csa[8][2] = {
    {0x6dc253f0, (int32_t)0xbe2500aa}, 
    {0x70dcebe4, (int32_t)0xc39e4949},
    {0x798d6e73, (int32_t)0xd7e33f4a},
    {0x7ddd40a7, (int32_t)0xe8b71176},
    {0x7f6d20b7, (int32_t)0xf3e4fe2f},
    {0x7fe47e40, (int32_t)0xfac1a3c7}, 
    {0x7ffcb263, (int32_t)0xfe2ebdc6}, 
    {0x7fffc694, (int32_t)0xff86c25d}, 
};
 
/* format = Q30, range = [0.0981, 1.9976]
 *
 * n = 16;
 * k = 0;
 * for(i=0; i<5; i++, n=n/2) {
 *   for(p=0; p<n; p++, k++) {
 *     t = (PI / (4*n)) * (2*p + 1);
 *     coef32[k] = 2.0 * cos(t);
 *   }
 * }
 * coef32[30] *= 0.5;   / *** for initial back butterfly (i.e. two-point DCT) *** /
 */
const int32_t coef32[31] = {
    0x7fd8878d, 0x7e9d55fc, 0x7c29fbee, 0x78848413, 0x73b5ebd0, 0x6dca0d14, 0x66cf811f, 0x5ed77c89, 
    0x55f5a4d2, 0x4c3fdff3, 0x41ce1e64, 0x36ba2013, 0x2b1f34eb, 0x1f19f97b, 0x12c8106e, 0x0647d97c, 
    0x7f62368f, 0x7a7d055b, 0x70e2cbc6, 0x62f201ac, 0x5133cc94, 0x3c56ba70, 0x25280c5d, 0x0c8bd35e, 
    0x7d8a5f3f, 0x6a6d98a4, 0x471cece6, 0x18f8b83c, 0x7641af3c, 0x30fbc54d, 0x2d413ccc, 
};
 
/* format = Q30, right shifted by 12 (sign bits only in top 12 - undo this when rounding to short)
 *   this is to enable early-terminating multiplies on ARM
 * range = [-1.144287109, 1.144989014]
 * max gain of filter (per output sample) ~= 2.731
 *
 * new (properly sign-flipped) values 
 *  - these actually are correct to 32 bits, (floating-pt coefficients in spec
 *      chosen such that only ~20 bits are required)
 *
 * Reordering - see table 3-B.3 in spec (appendix B)
 *
 * polyCoef[i] = 
 *   D[ 0, 32, 64, ... 480],   i = [  0, 15]
 *   D[ 1, 33, 65, ... 481],   i = [ 16, 31]
 *   D[ 2, 34, 66, ... 482],   i = [ 32, 47]
 *     ...
 *   D[15, 47, 79, ... 495],   i = [240,255]
 *
 * also exploits symmetry: D[i] = -D[512 - i], for i = [1, 255]
 * 
 * polyCoef[256, 257, ... 263] are for special case of sample 16 (out of 0)
 *   see PolyphaseStereo() and PolyphaseMono()
 */
const int32_t polyCoef[264] = {
    /* shuffled vs. original from 0, 1, ... 15 to 0, 15, 2, 13, ... 14, 1 */
    0x00000000, 0x00000074, 0x00000354, 0x0000072c, 0x00001fd4, 0x00005084, 0x000066b8, 0x000249c4,
    0x00049478, (int32_t)0xfffdb63c, 0x000066b8, (int32_t)0xffffaf7c, 0x00001fd4, (int32_t)0xfffff8d4, 0x00000354, (int32_t)0xffffff8c,
    (int32_t)0xfffffffc, 0x00000068, 0x00000368, 0x00000644, 0x00001f40, 0x00004ad0, 0x00005d1c, 0x00022ce0,
    0x000493c0, (int32_t)0xfffd9960, 0x00006f78, (int32_t)0xffffa9cc, 0x0000203c, (int32_t)0xfffff7e4, 0x00000340, (int32_t)0xffffff84,
    (int32_t)0xfffffffc, 0x00000060, 0x00000378, 0x0000056c, 0x00001e80, 0x00004524, 0x000052a0, 0x00020ffc,
    0x000491a0, (int32_t)0xfffd7ca0, 0x00007760, (int32_t)0xffffa424, 0x00002080, (int32_t)0xfffff6ec, 0x00000328, (int32_t)0xffffff74,
    (int32_t)0xfffffffc, 0x00000054, 0x00000384, 0x00000498, 0x00001d94, 0x00003f7c, 0x00004744, 0x0001f32c,
    0x00048e18, (int32_t)0xfffd6008, 0x00007e70, (int32_t)0xffff9e8c, 0x0000209c, (int32_t)0xfffff5ec, 0x00000310, (int32_t)0xffffff68,
    (int32_t)0xfffffffc, 0x0000004c, 0x0000038c, 0x000003d0, 0x00001c78, 0x000039e4, 0x00003b00, 0x0001d680,
    0x00048924, (int32_t)0xfffd43ac, 0x000084b0, (int32_t)0xffff990c, 0x00002094, (int32_t)0xfffff4e4, 0x000002f8, (int32_t)0xffffff5c,
    (int32_t)0xfffffffc, 0x00000044, 0x00000390, 0x00000314, 0x00001b2c, 0x0000345c, 0x00002ddc, 0x0001ba04,
    0x000482d0, (int32_t)0xfffd279c, 0x00008a20, (int32_t)0xffff93a4, 0x0000206c, (int32_t)0xfffff3d4, 0x000002dc, (int32_t)0xffffff4c,
    (int32_t)0xfffffffc, 0x00000040, 0x00000390, 0x00000264, 0x000019b0, 0x00002ef0, 0x00001fd4, 0x00019dc8,
    0x00047b1c, (int32_t)0xfffd0be8, 0x00008ecc, (int32_t)0xffff8e64, 0x00002024, (int32_t)0xfffff2c0, 0x000002c0, (int32_t)0xffffff3c,
    (int32_t)0xfffffff8, 0x00000038, 0x0000038c, 0x000001bc, 0x000017fc, 0x0000299c, 0x000010e8, 0x000181d8,
    0x0004720c, (int32_t)0xfffcf09c, 0x000092b4, (int32_t)0xffff894c, 0x00001fc0, (int32_t)0xfffff1a4, 0x000002a4, (int32_t)0xffffff2c,
    (int32_t)0xfffffff8, 0x00000034, 0x00000380, 0x00000120, 0x00001618, 0x00002468, 0x00000118, 0x00016644,
    0x000467a4, (int32_t)0xfffcd5cc, 0x000095e0, (int32_t)0xffff8468, 0x00001f44, (int32_t)0xfffff084, 0x00000284, (int32_t)0xffffff18,
    (int32_t)0xfffffff8, 0x0000002c, 0x00000374, 0x00000090, 0x00001400, 0x00001f58, (int32_t)0xfffff068, 0x00014b14,
    0x00045bf0, (int32_t)0xfffcbb88, 0x00009858, (int32_t)0xffff7fbc, 0x00001ea8, (int32_t)0xffffef60, 0x00000268, (int32_t)0xffffff04,
    (int32_t)0xfffffff8, 0x00000028, 0x0000035c, 0x00000008, 0x000011ac, 0x00001a70, (int32_t)0xffffded8, 0x00013058,
    0x00044ef8, (int32_t)0xfffca1d8, 0x00009a1c, (int32_t)0xffff7b54, 0x00001dfc, (int32_t)0xffffee3c, 0x0000024c, (int32_t)0xfffffef0,
    (int32_t)0xfffffff4, 0x00000024, 0x00000340, (int32_t)0xffffff8c, 0x00000f28, 0x000015b0, (int32_t)0xffffcc70, 0x0001161c,
    0x000440bc, (int32_t)0xfffc88d8, 0x00009b3c, (int32_t)0xffff7734, 0x00001d38, (int32_t)0xffffed18, 0x0000022c, (int32_t)0xfffffedc,
    (int32_t)0xfffffff4, 0x00000020, 0x00000320, (int32_t)0xffffff1c, 0x00000c68, 0x0000111c, (int32_t)0xffffb92c, 0x0000fc6c,
    0x00043150, (int32_t)0xfffc708c, 0x00009bb8, (int32_t)0xffff7368, 0x00001c64, (int32_t)0xffffebf4, 0x00000210, (int32_t)0xfffffec4,
    (int32_t)0xfffffff0, 0x0000001c, 0x000002f4, (int32_t)0xfffffeb4, 0x00000974, 0x00000cb8, (int32_t)0xffffa518, 0x0000e350,
    0x000420b4, (int32_t)0xfffc5908, 0x00009b9c, (int32_t)0xffff6ff4, 0x00001b7c, (int32_t)0xffffead0, 0x000001f4, (int32_t)0xfffffeac,
    (int32_t)0xfffffff0, 0x0000001c, 0x000002c4, (int32_t)0xfffffe58, 0x00000648, 0x00000884, (int32_t)0xffff9038, 0x0000cad0,
    0x00040ef8, (int32_t)0xfffc425c, 0x00009af0, (int32_t)0xffff6ce0, 0x00001a88, (int32_t)0xffffe9b0, 0x000001d4, (int32_t)0xfffffe94,
    (int32_t)0xffffffec, 0x00000018, 0x0000028c, (int32_t)0xfffffe04, 0x000002e4, 0x00000480, (int32_t)0xffff7a90, 0x0000b2fc,
    0x0003fc28, (int32_t)0xfffc2c90, 0x000099b8, (int32_t)0xffff6a3c, 0x00001988, (int32_t)0xffffe898, 0x000001bc, (int32_t)0xfffffe7c,
    0x000001a0, 0x0000187c, 0x000097fc, 0x0003e84c, (int32_t)0xffff6424, (int32_t)0xffffff4c, 0x00000248, (int32_t)0xffffffec,
};
 
}  // namespace third_party
}  // namespace fl