Motorola DSP Developer's Kit

log10-r.asm

Y = mot###_log10(X)

Description

This function computes the base 10 logarithm of real vector X

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:

log10(Z) in a1    
(a2 is sign extended and a0=don't care)

log10(Z) = log2(Z)*log10(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)*Zlies inthe range [0.5,1)
Find the range of ZS.

If 1 > ZS > 0.8

Range1:

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

Range2:

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 are used for vector A

Y memory:

• $0 is used for the coefficient of 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 coefficient
• R6 is used as loop control
• R2 stores the address for the tmp vector
• R3 is used for the input shift bit
• R4, R5, and R7 are unused

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

Status Register

The assembly function log10-r.asm does not explicitly set 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.

log-c.asm

log10-c.asm