frameworks/base/media/libstagefright/codecs/amrwbenc/src/math_op.c

   1 /*\r
   2  ** Copyright 2003-2010, VisualOn, Inc.\r
   3  **\r
   4  ** Licensed under the Apache License, Version 2.0 (the "License");\r
   5  ** you may not use this file except in compliance with the License.\r
   6  ** You may obtain a copy of the License at\r
   7  **\r
   8  **     http://www.apache.org/licenses/LICENSE-2.0\r
   9  **\r
  10  ** Unless required by applicable law or agreed to in writing, software\r
  11  ** distributed under the License is distributed on an "AS IS" BASIS,\r
  12  ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\r
  13  ** See the License for the specific language governing permissions and\r
  14  ** limitations under the License.\r
  15  */\r
  16 \r
  17 /*___________________________________________________________________________\r
  18 |                                                                           |\r
  19 |  This file contains mathematic operations in fixed point.                 |\r
  20 |                                                                           |\r
  21 |  Isqrt()              : inverse square root (16 bits precision).          |\r
  22 |  Pow2()               : 2^x  (16 bits precision).                         |\r
  23 |  Log2()               : log2 (16 bits precision).                         |\r
  24 |  Dot_product()        : scalar product of <x[],y[]>                       |\r
  25 |                                                                           |\r
  26 |  These operations are not standard double precision operations.           |\r
  27 |  They are used where low complexity is important and the full 32 bits     |\r
  28 |  precision is not necessary. For example, the function Div_32() has a     |\r
  29 |  24 bits precision which is enough for our purposes.                      |\r
  30 |                                                                           |\r
  31 |  In this file, the values use theses representations:                     |\r
  32 |                                                                           |\r
  33 |  Word32 L_32     : standard signed 32 bits format                         |\r
  34 |  Word16 hi, lo   : L_32 = hi<<16 + lo<<1  (DPF - Double Precision Format) |\r
  35 |  Word32 frac, Word16 exp : L_32 = frac << exp-31  (normalised format)     |\r
  36 |  Word16 int, frac        : L_32 = int.frac        (fractional format)     |\r
  37 |___________________________________________________________________________|\r
  38 */\r
  39 #include "typedef.h"\r
  40 #include "basic_op.h"\r
  41 #include "math_op.h"\r
  42 \r
  43 /*___________________________________________________________________________\r
  44 |                                                                           |\r
  45 |   Function Name : Isqrt                                                   |\r
  46 |                                                                           |\r
  47 |       Compute 1/sqrt(L_x).                                                |\r
  48 |       if L_x is negative or zero, result is 1 (7fffffff).                 |\r
  49 |---------------------------------------------------------------------------|\r
  50 |  Algorithm:                                                               |\r
  51 |                                                                           |\r
  52 |   1- Normalization of L_x.                                                |\r
  53 |   2- call Isqrt_n(L_x, exponant)                                          |\r
  54 |   3- L_y = L_x << exponant                                                |\r
  55 |___________________________________________________________________________|\r
  56 */\r
  57 Word32 Isqrt(                              /* (o) Q31 : output value (range: 0<=val<1)         */\r
  58                 Word32 L_x                            /* (i) Q0  : input value  (range: 0<=val<=7fffffff) */\r
  59             )\r
  60 {\r
  61         Word16 exp;\r
  62         Word32 L_y;\r
  63         exp = norm_l(L_x);\r
  64         L_x = (L_x << exp);                 /* L_x is normalized */\r
  65         exp = (31 - exp);\r
  66         Isqrt_n(&L_x, &exp);\r
  67         L_y = (L_x << exp);                 /* denormalization   */\r
  68         return (L_y);\r
  69 }\r
  70 \r
  71 /*___________________________________________________________________________\r
  72 |                                                                           |\r
  73 |   Function Name : Isqrt_n                                                 |\r
  74 |                                                                           |\r
  75 |       Compute 1/sqrt(value).                                              |\r
  76 |       if value is negative or zero, result is 1 (frac=7fffffff, exp=0).   |\r
  77 |---------------------------------------------------------------------------|\r
  78 |  Algorithm:                                                               |\r
  79 |                                                                           |\r
  80 |   The function 1/sqrt(value) is approximated by a table and linear        |\r
  81 |   interpolation.                                                          |\r
  82 |                                                                           |\r
  83 |   1- If exponant is odd then shift fraction right once.                   |\r
  84 |   2- exponant = -((exponant-1)>>1)                                        |\r
  85 |   3- i = bit25-b30 of fraction, 16 <= i <= 63 ->because of normalization. |\r
  86 |   4- a = bit10-b24                                                        |\r
  87 |   5- i -=16                                                               |\r
  88 |   6- fraction = table[i]<<16 - (table[i] - table[i+1]) * a * 2            |\r
  89 |___________________________________________________________________________|\r
  90 */\r
  91 static Word16 table_isqrt[49] =\r
  92 {\r
  93         32767, 31790, 30894, 30070, 29309, 28602, 27945, 27330, 26755, 26214,\r
  94         25705, 25225, 24770, 24339, 23930, 23541, 23170, 22817, 22479, 22155,\r
  95         21845, 21548, 21263, 20988, 20724, 20470, 20225, 19988, 19760, 19539,\r
  96         19326, 19119, 18919, 18725, 18536, 18354, 18176, 18004, 17837, 17674,\r
  97         17515, 17361, 17211, 17064, 16921, 16782, 16646, 16514, 16384\r
  98 };\r
  99 \r
 100 void Isqrt_n(\r
 101                 Word32 * frac,                        /* (i/o) Q31: normalized value (1.0 < frac <= 0.5) */\r
 102                 Word16 * exp                          /* (i/o)    : exponent (value = frac x 2^exponent) */\r
 103             )\r
 104 {\r
 105         Word16 i, a, tmp;\r
 106 \r
 107         if (*frac <= (Word32) 0)\r
 108         {\r
 109                 *exp = 0;                          \r
 110                 *frac = 0x7fffffffL;               \r
 111                 return;\r
 112         }\r
 113 \r
 114         if((*exp & 1) == 1)                       /*If exponant odd -> shift right */\r
 115                 *frac = (*frac) >> 1;\r
 116 \r
 117         *exp = negate((*exp - 1) >> 1);   \r
 118 \r
 119         *frac = (*frac >> 9);               \r
 120         i = extract_h(*frac);                  /* Extract b25-b31 */\r
 121         *frac = (*frac >> 1);              \r
 122         a = (Word16)(*frac);                  /* Extract b10-b24 */\r
 123         a = (Word16) (a & (Word16) 0x7fff);    \r
 124         i -= 16;\r
 125         *frac = L_deposit_h(table_isqrt[i]);   /* table[i] << 16         */\r
 126         tmp = vo_sub(table_isqrt[i], table_isqrt[i + 1]);      /* table[i] - table[i+1]) */\r
 127         *frac = vo_L_msu(*frac, tmp, a);          /* frac -=  tmp*a*2       */\r
 128 \r
 129         return;\r
 130 }\r
 131 \r
 132 /*___________________________________________________________________________\r
 133 |                                                                           |\r
 134 |   Function Name : Pow2()                                                  |\r
 135 |                                                                           |\r
 136 |     L_x = pow(2.0, exponant.fraction)         (exponant = interger part)  |\r
 137 |         = pow(2.0, 0.fraction) << exponant                                |\r
 138 |---------------------------------------------------------------------------|\r
 139 |  Algorithm:                                                               |\r
 140 |                                                                           |\r
 141 |   The function Pow2(L_x) is approximated by a table and linear            |\r
 142 |   interpolation.                                                          |\r
 143 |                                                                           |\r
 144 |   1- i = bit10-b15 of fraction,   0 <= i <= 31                            |\r
 145 |   2- a = bit0-b9   of fraction                                            |\r
 146 |   3- L_x = table[i]<<16 - (table[i] - table[i+1]) * a * 2                 |\r
 147 |   4- L_x = L_x >> (30-exponant)     (with rounding)                       |\r
 148 |___________________________________________________________________________|\r
 149 */\r
 150 static Word16 table_pow2[33] =\r
 151 {\r
 152         16384, 16743, 17109, 17484, 17867, 18258, 18658, 19066, 19484, 19911,\r
 153         20347, 20792, 21247, 21713, 22188, 22674, 23170, 23678, 24196, 24726,\r
 154         25268, 25821, 26386, 26964, 27554, 28158, 28774, 29405, 30048, 30706,\r
 155         31379, 32066, 32767\r
 156 };\r
 157 \r
 158 Word32 Pow2(                               /* (o) Q0  : result       (range: 0<=val<=0x7fffffff) */\r
 159                 Word16 exponant,                      /* (i) Q0  : Integer part.      (range: 0<=val<=30)   */\r
 160                 Word16 fraction                       /* (i) Q15 : Fractionnal part.  (range: 0.0<=val<1.0) */\r
 161            )\r
 162 {\r
 163         Word16 exp, i, a, tmp;\r
 164         Word32 L_x;\r
 165 \r
 166         L_x = vo_L_mult(fraction, 32);            /* L_x = fraction<<6           */\r
 167         i = extract_h(L_x);                    /* Extract b10-b16 of fraction */\r
 168         L_x =L_x >> 1;\r
 169         a = (Word16)(L_x);                    /* Extract b0-b9   of fraction */\r
 170         a = (Word16) (a & (Word16) 0x7fff); \r
 171 \r
 172         L_x = L_deposit_h(table_pow2[i]);      /* table[i] << 16        */\r
 173         tmp = vo_sub(table_pow2[i], table_pow2[i + 1]);        /* table[i] - table[i+1] */\r
 174         L_x -= (tmp * a)<<1;              /* L_x -= tmp*a*2        */\r
 175 \r
 176         exp = vo_sub(30, exponant);\r
 177         L_x = vo_L_shr_r(L_x, exp);\r
 178 \r
 179         return (L_x);\r
 180 }\r
 181 \r
 182 /*___________________________________________________________________________\r
 183 |                                                                           |\r
 184 |   Function Name : Dot_product12()                                         |\r
 185 |                                                                           |\r
 186 |       Compute scalar product of <x[],y[]> using accumulator.              |\r
 187 |                                                                           |\r
 188 |       The result is normalized (in Q31) with exponent (0..30).            |\r
 189 |---------------------------------------------------------------------------|\r
 190 |  Algorithm:                                                               |\r
 191 |                                                                           |\r
 192 |       dot_product = sum(x[i]*y[i])     i=0..N-1                           |\r
 193 |___________________________________________________________________________|\r
 194 */\r
 195 \r
 196 Word32 Dot_product12(                      /* (o) Q31: normalized result (1 < val <= -1) */\r
 197                 Word16 x[],                           /* (i) 12bits: x vector                       */\r
 198                 Word16 y[],                           /* (i) 12bits: y vector                       */\r
 199                 Word16 lg,                            /* (i)    : vector length                     */\r
 200                 Word16 * exp                          /* (o)    : exponent of result (0..+30)       */\r
 201                 )\r
 202 {\r
 203         Word16 sft;\r
 204         Word32 i, L_sum;\r
 205         L_sum = 0;\r
 206         for (i = 0; i < lg; i++)\r
 207         {\r
 208                 L_sum += x[i] * y[i];\r
 209         }\r
 210         L_sum = (L_sum << 1) + 1;\r
 211         /* Normalize acc in Q31 */\r
 212         sft = norm_l(L_sum);\r
 213         L_sum = L_sum << sft;\r
 214         *exp = 30 - sft;            /* exponent = 0..30 */\r
 215         return (L_sum);\r
 216 \r
 217 }\r
 218 \r
 219 \r