?? oper_32b.c
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/* Version 3.3 Last modified: December 26, 1995 */
#include "typedef.h"
#include "basic_op.h"
#include "oper_32b.h"
/*___________________________________________________________________________
| |
| This file contains operations in double precision. |
| These operations are not standard double precision operations. |
| They are used where single precision is not enough but the full 32 bits |
| precision is not necessary. For example, the function Div_32() has a |
| 24 bits precision which is enough for our purposes. |
| |
| The double precision numbers use a special representation: |
| |
| L_32 = hi<<16 + lo<<1 |
| |
| L_32 is a 32 bit integer. |
| hi and lo are 16 bit signed integers. |
| As the low part also contains the sign, this allows fast multiplication. |
| |
| 0x8000 0000 <= L_32 <= 0x7fff fffe. |
| |
| We will use DPF (Double Precision Format )in this file to specify |
| this special format. |
|___________________________________________________________________________|
*/
/*___________________________________________________________________________
| |
| Function L_Extract() |
| |
| Extract from a 32 bit integer two 16 bit DPF. |
| |
| Arguments: |
| |
| L_32 : 32 bit integer. |
| 0x8000 0000 <= L_32 <= 0x7fff ffff. |
| hi : b16 to b31 of L_32 |
| lo : (L_32 - hi<<16)>>1 |
|___________________________________________________________________________|
*/
void L_Extract(Word32 L_32, Word16 *hi, Word16 *lo)
{
*hi = extract_h(L_32);
*lo = extract_l( L_msu( L_shr(L_32, 1) , *hi, 16384)); /* lo = L_32>>1 */
return;
}
/*___________________________________________________________________________
| |
| Function L_Comp() |
| |
| Compose from two 16 bit DPF a 32 bit integer. |
| |
| L_32 = hi<<16 + lo<<1 |
| |
| Arguments: |
| |
| hi msb |
| lo lsf (with sign) |
| |
| Return Value : |
| |
| 32 bit long signed integer (Word32) whose value falls in the |
| range : 0x8000 0000 <= L_32 <= 0x7fff fff0. |
| |
|___________________________________________________________________________|
*/
Word32 L_Comp(Word16 hi, Word16 lo)
{
Word32 L_32;
L_32 = L_deposit_h(hi);
return( L_mac(L_32, lo, 1)); /* = hi<<16 + lo<<1 */
}
/*___________________________________________________________________________
| Function Mpy_32() |
| |
| Multiply two 32 bit integers (DPF). The result is divided by 2**31 |
| |
| L_32 = (hi1*hi2)<<1 + ( (hi1*lo2)>>15 + (lo1*hi2)>>15 )<<1 |
| |
| This operation can also be viewed as the multiplication of two Q31 |
| number and the result is also in Q31. |
| |
| Arguments: |
| |
| hi1 hi part of first number |
| lo1 lo part of first number |
| hi2 hi part of second number |
| lo2 lo part of second number |
| |
|___________________________________________________________________________|
*/
Word32 Mpy_32(Word16 hi1, Word16 lo1, Word16 hi2, Word16 lo2)
{
Word32 L_32;
L_32 = L_mult(hi1, hi2);
L_32 = L_mac(L_32, mult(hi1, lo2) , 1);
L_32 = L_mac(L_32, mult(lo1, hi2) , 1);
return( L_32 );
}
/*___________________________________________________________________________
| Function Mpy_32_16() |
| |
| Multiply a 16 bit integer by a 32 bit (DPF). The result is divided |
| by 2**15 |
| |
| This operation can also be viewed as the multiplication of a Q31 |
| number by a Q15 number, the result is in Q31. |
| |
| L_32 = (hi1*lo2)<<1 + ((lo1*lo2)>>15)<<1 |
| |
| Arguments: |
| |
| hi hi part of 32 bit number. |
| lo lo part of 32 bit number. |
| n 16 bit number. |
| |
|___________________________________________________________________________|
*/
Word32 Mpy_32_16(Word16 hi, Word16 lo, Word16 n)
{
Word32 L_32;
L_32 = L_mult(hi, n);
L_32 = L_mac(L_32, mult(lo, n) , 1);
return( L_32 );
}
/*___________________________________________________________________________
| |
| Function Name : Div_32 |
| |
| Purpose : |
| Fractional integer division of two 32 bit numbers. |
| L_num / L_denom. |
| L_num and L_denom must be positive and L_num < L_denom. |
| L_denom = denom_hi<<16 + denom_lo<<1 |
| denom_hi is a normalize number. |
| The result is in Q30. |
| |
| Inputs : |
| |
| L_num |
| 32 bit long signed integer (Word32) whose value falls in the |
| range : 0x0000 0000 < L_num < L_denom |
| |
| L_denom = denom_hi<<16 + denom_lo<<1 (DPF) |
| |
| denom_hi |
| 16 bit positive normalized integer whose value falls in the |
| range : 0x4000 < hi < 0x7fff |
| denom_lo |
| 16 bit positive integer whose value falls in the |
| range : 0 < lo < 0x7fff |
| |
| Return Value : |
| |
| L_div |
| 32 bit long signed integer (Word32) whose value falls in the |
| range : 0x0000 0000 <= L_div <= 0x7fff ffff. |
| It's a Q31 value |
| |
| Algorithm: |
| |
| - find = 1/L_denom. |
| First approximation: approx = 1 / denom_hi |
| 1/L_denom = approx * (2.0 - L_denom * approx ) |
| |
| - result = L_num * (1/L_denom) |
|___________________________________________________________________________|
*/
Word32 Div_32(Word32 L_num, Word16 denom_hi, Word16 denom_lo)
{
Word16 approx, hi, lo, n_hi, n_lo;
Word32 L_32;
/* First approximation: 1 / L_denom = 1/denom_hi */
approx = div_s( (Word16)0x3fff, denom_hi); /* result in Q14 */
/* Note: 3fff = 0.5 in Q15 */
/* 1/L_denom = approx * (2.0 - L_denom * approx) */
L_32 = Mpy_32_16(denom_hi, denom_lo, approx); /* result in Q30 */
L_32 = L_sub( (Word32)0x7fffffffL, L_32); /* result in Q30 */
L_Extract(L_32, &hi, &lo);
L_32 = Mpy_32_16(hi, lo, approx); /* = 1/L_denom in Q29 */
/* L_num * (1/L_denom) */
L_Extract(L_32, &hi, &lo);
L_Extract(L_num, &n_hi, &n_lo);
L_32 = Mpy_32(n_hi, n_lo, hi, lo); /* result in Q29 */
L_32 = L_shl(L_32, 2); /* From Q29 to Q31 */
return( L_32 );
}
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