Motorola DSP Developer's Kit

log-r.asm

Y = mot###_log(X)

Description

This function returns the natural logarithm elements of input vector X. The input vector X is a real vector

Input/Output

Input: Real vector X

Output: Real vector Y

Algorithm

Input:

Z in a1  (a2 = 0, a0 = 0)

Note    The input should be a positive fraction.

Output:

log(Z) in a1
    
(a2 is sign extended and a0=don't care).
log(Z) = log2(Z)*log(2)
log2(Z)=  pi3*(Z**3) +pi2*(Z**2) + pi1*Z + pi0
     i = 1, 2, 3.   
The range of the input number is divided into three different 
subranges and corresponding pij's (i=1,2,3; j=0,1,2,3) are used for 
each range. 
Range 1:
1 > Z > 0.8
    p13 =  0.6651550174712363
    p12 = -2.691225081621167
    p11 =  4.830861130814611
    p10 = -2.8047790282999791

Range 2:
0.8 >= Z > 0.64
    p23 =  1.299130893496323
    p22 = -4.205039190029353
    p21 =  6.038576413515295
    p20 = -3.126707123185897

Range 3:
0.64 >= Z >= 0.5

    p33 =  2.62317472043452
    p32 = -6.720343733123614
    p31 =  7.635399480799159
    p30 = -3.465490657054861

In the following pseudocode cij = pij/8 (i=1,2,3)
 (j=0,1,2,3)
log2nrm(Z) = [log2(ZS)/8 + (-S)/8]/2

Find S such that ZS = (2**S)*Z lies in the range [0.5,1]
Find the range of ZS.
If 1 > ZS > 0.8
Range 1:
   Find Term1_1 = c13* ZS + c12
   Find Term1_2 = Term1_1*ZS + c11 
   Find log2(ZS)/8 = Term1_2 * ZS + c10 

If 0.8 >= ZS > 0.64
Range  2:
   Find Term2_1 = c23 * ZS + c22
   Find Term2_2 = Term2_1 * ZS +c21
   Find log2(ZS)/8 = Term2_3 * ZS + c20

If  0.64 >= ZS >= 0.5
Range 3:
   Find Term3_1 = c33 * ZS + c32
   Find Term3_2 = Term3_1 * ZS +c31
   Find log2(ZS)/8 = Term3_2 * ZS + c30

Memory & Register

Memory allocation

X memory:

• #IN1 & #OUT1 stores the location of vector A

Y memory:

• $0 stores the coefficient of the polynomial

Register usage:

• R6 stores the length of vector A
• R3 is used for the shift bit:

6 for dsp56300

5 for dsp56600

• R0 stores the index of vector A
• R1 stores the index of the coefficient
• R6 is used as loop control
• R2 stores the address for the vector tmp
• R3 is used for the input shift bit
• R4, R5, and R7 are unused

Assumes M{0...7} = $ffff

Status Register

The assembly function log-r.asm does not set explicitly any status registers/bits during the function execution.

Data Size Limit

The length of vector X can't be larger than the continuous available data memory size.

Data Range Limit

The value of input vector X must be between -1.0 and +1.0.

Precision

In the case of DSP563, precision is 16 bits.

In the case of DSP566, precision is 12 bits.

interp-c.asm

log-c.asm