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      1 /*
      2  ** Copyright 2003-2010, VisualOn, Inc.
      3  **
      4  ** Licensed under the Apache License, Version 2.0 (the "License");
      5  ** you may not use this file except in compliance with the License.
      6  ** You may obtain a copy of the License at
      7  **
      8  **     http://www.apache.org/licenses/LICENSE-2.0
      9  **
     10  ** Unless required by applicable law or agreed to in writing, software
     11  ** distributed under the License is distributed on an "AS IS" BASIS,
     12  ** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     13  ** See the License for the specific language governing permissions and
     14  ** limitations under the License.
     15  */
     16 
     17 /*****************************************************************************
     18  *  This file contains operations in double precision.                       *
     19  *  These operations are not standard double precision operations.           *
     20  *  They are used where single precision is not enough but the full 32 bits  *
     21  *  precision is not necessary. For example, the function Div_32() has a     *
     22  *  24 bits precision which is enough for our purposes.                      *
     23  *                                                                           *
     24  *  The double precision numbers use a special representation:               *
     25  *                                                                           *
     26  *     L_32 = hi<<16 + lo<<1                                                 *
     27  *                                                                           *
     28  *  L_32 is a 32 bit integer.                                                *
     29  *  hi and lo are 16 bit signed integers.                                    *
     30  *  As the low part also contains the sign, this allows fast multiplication. *
     31  *                                                                           *
     32  *      0x8000 0000 <= L_32 <= 0x7fff fffe.                                  *
     33  *                                                                           *
     34  *  We will use DPF (Double Precision Format )in this file to specify        *
     35  *  this special format.                                                     *
     36  *****************************************************************************
     37 */
     38 #include "typedef.h"
     39 #include "basic_op.h"
     40 #include "oper_32b.h"
     41 
     42 /*****************************************************************************
     43  *                                                                           *
     44  *  Function L_Extract()                                                     *
     45  *                                                                           *
     46  *  Extract from a 32 bit integer two 16 bit DPF.                            *
     47  *                                                                           *
     48  *  Arguments:                                                               *
     49  *                                                                           *
     50  *   L_32      : 32 bit integer.                                             *
     51  *               0x8000 0000 <= L_32 <= 0x7fff ffff.                         *
     52  *   hi        : b16 to b31 of L_32                                          *
     53  *   lo        : (L_32 - hi<<16)>>1                                          *
     54  *****************************************************************************
     55 */
     56 
     57 __inline void VO_L_Extract (Word32 L_32, Word16 *hi, Word16 *lo)
     58 {
     59     *hi = (Word16)(L_32 >> 16);
     60     *lo = (Word16)((L_32 & 0xffff) >> 1);
     61     return;
     62 }
     63 
     64 /*****************************************************************************
     65  *                                                                           *
     66  *  Function L_Comp()                                                        *
     67  *                                                                           *
     68  *  Compose from two 16 bit DPF a 32 bit integer.                            *
     69  *                                                                           *
     70  *     L_32 = hi<<16 + lo<<1                                                 *
     71  *                                                                           *
     72  *  Arguments:                                                               *
     73  *                                                                           *
     74  *   hi        msb                                                           *
     75  *   lo        lsf (with sign)                                               *
     76  *                                                                           *
     77  *   Return Value :                                                          *
     78  *                                                                           *
     79  *             32 bit long signed integer (Word32) whose value falls in the  *
     80  *             range : 0x8000 0000 <= L_32 <= 0x7fff fff0.                   *
     81  *                                                                           *
     82  *****************************************************************************
     83 */
     84 
     85 Word32 L_Comp (Word16 hi, Word16 lo)
     86 {
     87     Word32 L_32;
     88 
     89     L_32 = L_deposit_h (hi);
     90 
     91     return (L_mac (L_32, lo, 1));       /* = hi<<16 + lo<<1 */
     92 }
     93 
     94 /*****************************************************************************
     95  * Function Mpy_32()                                                         *
     96  *                                                                           *
     97  *   Multiply two 32 bit integers (DPF). The result is divided by 2**31      *
     98  *                                                                           *
     99  *   L_32 = (hi1*hi2)<<1 + ( (hi1*lo2)>>15 + (lo1*hi2)>>15 )<<1              *
    100  *                                                                           *
    101  *   This operation can also be viewed as the multiplication of two Q31      *
    102  *   number and the result is also in Q31.                                   *
    103  *                                                                           *
    104  * Arguments:                                                                *
    105  *                                                                           *
    106  *  hi1         hi part of first number                                      *
    107  *  lo1         lo part of first number                                      *
    108  *  hi2         hi part of second number                                     *
    109  *  lo2         lo part of second number                                     *
    110  *                                                                           *
    111  *****************************************************************************
    112 */
    113 
    114 __inline Word32  Mpy_32 (Word16 hi1, Word16 lo1, Word16 hi2, Word16 lo2)
    115 {
    116     Word32 L_32;
    117     L_32 = (hi1 * hi2);
    118     L_32 += (hi1 * lo2) >> 15;
    119     L_32 += (lo1 * hi2) >> 15;
    120     L_32 <<= 1;
    121 
    122     return (L_32);
    123 }
    124 
    125 /*****************************************************************************
    126  * Function Mpy_32_16()                                                      *
    127  *                                                                           *
    128  *   Multiply a 16 bit integer by a 32 bit (DPF). The result is divided      *
    129  *   by 2**15                                                                *
    130  *                                                                           *
    131  *                                                                           *
    132  *   L_32 = (hi1*lo2)<<1 + ((lo1*lo2)>>15)<<1                                *
    133  *                                                                           *
    134  * Arguments:                                                                *
    135  *                                                                           *
    136  *  hi          hi part of 32 bit number.                                    *
    137  *  lo          lo part of 32 bit number.                                    *
    138  *  n           16 bit number.                                               *
    139  *                                                                           *
    140  *****************************************************************************
    141 */
    142 
    143 __inline Word32 Mpy_32_16 (Word16 hi, Word16 lo, Word16 n)
    144 {
    145     Word32 L_32;
    146 
    147     L_32 = (hi * n)<<1;
    148     L_32 += (((lo * n)>>15)<<1);
    149 
    150     return (L_32);
    151 }
    152 
    153 /*****************************************************************************
    154  *                                                                           *
    155  *   Function Name : Div_32                                                  *
    156  *                                                                           *
    157  *   Purpose :                                                               *
    158  *             Fractional integer division of two 32 bit numbers.            *
    159  *             L_num / L_denom.                                              *
    160  *             L_num and L_denom must be positive and L_num < L_denom.       *
    161  *             L_denom = denom_hi<<16 + denom_lo<<1                          *
    162  *             denom_hi is a normalize number.                               *
    163  *                                                                           *
    164  *   Inputs :                                                                *
    165  *                                                                           *
    166  *    L_num                                                                  *
    167  *             32 bit long signed integer (Word32) whose value falls in the  *
    168  *             range : 0x0000 0000 < L_num < L_denom                         *
    169  *                                                                           *
    170  *    L_denom = denom_hi<<16 + denom_lo<<1      (DPF)                        *
    171  *                                                                           *
    172  *       denom_hi                                                            *
    173  *             16 bit positive normalized integer whose value falls in the   *
    174  *             range : 0x4000 < hi < 0x7fff                                  *
    175  *       denom_lo                                                            *
    176  *             16 bit positive integer whose value falls in the              *
    177  *             range : 0 < lo < 0x7fff                                       *
    178  *                                                                           *
    179  *   Return Value :                                                          *
    180  *                                                                           *
    181  *    L_div                                                                  *
    182  *             32 bit long signed integer (Word32) whose value falls in the  *
    183  *             range : 0x0000 0000 <= L_div <= 0x7fff ffff.                  *
    184  *                                                                           *
    185  *  Algorithm:                                                               *
    186  *                                                                           *
    187  *  - find = 1/L_denom.                                                      *
    188  *      First approximation: approx = 1 / denom_hi                           *
    189  *      1/L_denom = approx * (2.0 - L_denom * approx )                       *
    190  *                                                                           *
    191  *  -  result = L_num * (1/L_denom)                                          *
    192  *****************************************************************************
    193 */
    194 
    195 Word32 Div_32 (Word32 L_num, Word16 denom_hi, Word16 denom_lo)
    196 {
    197     Word16 approx, hi, lo, n_hi, n_lo;
    198     Word32 L_32;
    199 
    200     /* First approximation: 1 / L_denom = 1/denom_hi */
    201 
    202     approx = div_s ((Word16) 0x3fff, denom_hi);
    203 
    204     /* 1/L_denom = approx * (2.0 - L_denom * approx) */
    205 
    206     L_32 = Mpy_32_16 (denom_hi, denom_lo, approx);
    207 
    208     L_32 = L_sub ((Word32) 0x7fffffffL, L_32);
    209     hi = L_32 >> 16;
    210     lo = (L_32 & 0xffff) >> 1;
    211 
    212     L_32 = Mpy_32_16 (hi, lo, approx);
    213 
    214     /* L_num * (1/L_denom) */
    215     hi = L_32 >> 16;
    216     lo = (L_32 & 0xffff) >> 1;
    217     VO_L_Extract (L_num, &n_hi, &n_lo);
    218     L_32 = Mpy_32 (n_hi, n_lo, hi, lo);
    219     L_32 = L_shl2(L_32, 2);
    220 
    221     return (L_32);
    222 }
    223 
    224