Propeller Manual

Appendix B: Math Samples and Function Tables
Like the multiplier routine, this divider routine could be recoded with a sequence of 16
CMPSUB + RCL instruction pairs to get rid of the DJNZ and cut execution time by ~1/3. By
making such changes, speed can often be gained at the expense of code size.
Here is a square-root routine that uses the
CMPSUB instruction:
'
' Compute square-root of y[31..0] into x[15..0]
'
root mov a,#0 'reset accumulator
mov x,#0 'reset root
mov t,#16 'ready for 16 root bits
:loop shl y,#1 wc 'rotate top two bits of y to accumulator
rcl a,#1
shl y,#1 wc
rcl a,#1
shl x,#2 'determine next bit of root
or x,#1
cmpsub a,x wc
shr x,#2
rcl x,#1
djnz t,#:loop 'loop until done
root_ret ret 'square root in x[15..0]
Many complex math functions can be realized by additions, subtractions, and shifts. Though
specific examples were given here, these types of algorithms may be coded in many different
ways to best suit the application.
Log and Anti-Log Tables ($C000-DFFF)
The log and anti-log tables are useful for converting values between their number form and
exponent form.
When numbers are encoded into exponent form, simple math operations take on more
complex effects. For example ‘add’ and ‘subtract’ become ‘multiply’ and ‘divide,’ ‘shift-left’
becomes ‘square’ and ‘shift-right’ becomes ‘square-root,’ and ‘divide by 3’ will produce
‘cube root.’ Once the exponent is converted back to a number, the result will be apparent.
This process is imperfect, but quite fast.
For applications where many multiplies and divides must be performed in the absence of
many additions and subtractions, exponential encoding can greatly speed things up.
Exponential encoding is also useful for compressing numbers into fewer bits – sacrificing
resolution at higher magnitude. In many applications, such as audio synthesis, the nature of
signals is logarithmic in both frequency and magnitude. Processing such data in exponent
Propeller Manual v1.1 · Page 381