reciprocal calculation

Archiver

Hi,
I need to calculate the following:
Given S and T
0<=S<=16
1<=T<57000
calculate
(T*10) / ((1<<S)*2.54) which is always >1 and must be rescaled to 65536/F

Question: how do I calculate F?

65536/F can be written as I + (R/65536)
Question: how do I calculate I and R from F

All used vars are 16bit unsigned.
At Tracy Allen's site I found calculating a reciprocal value using 24bit
(shortcut #3)
http://www.emesystems.com/BS2math2.htm#Reciprocal
There is a input contraint that F must be >= 256.
In my case F is frequently <256. How to workaround that?

regards peter

Archiver

Hi Peter,

Use binary long division per this URL
http://www.emesystems.com/BS2math2.htm#longdivision


The integer part comes directly from your calculation:
D = ((1<<S)*2.54)
I = (T*10) / D
and the fraction numerator N from,
N = (T*10) // D ' note //
then apply the long division loop,
'

---

binary division loop

---

for J=15 to 0 ' 16 bits
N=N//D<<1 ' remainder*2
R.bit0(J)=N/D ' next bit
next
'

---

The result is the value R you want, with the 65536 implied.

If you need to re-scale R/65536 to be a decimal fraction (say for
display), then use,
R = R ** 10000 ' 0.0000 to 0.9999


-- Tracy


>Hi,
>I need to calculate the following:
>Given S and T
>0<=S<=16
>1<=T<57000
>calculate
>(T*10) / ((1<<S)*2.54) which is always >1 and must be rescaled to 65536/F
>
>Question: how do I calculate F?
>
>65536/F can be written as I + (R/65536)
>Question: how do I calculate I and R from F
>
>All used vars are 16bit unsigned.
>At Tracy Allen's site I found calculating a reciprocal value using 24bit
>(shortcut #3)
>http://www.emesystems.com/BS2math2.htm#Reciprocal
>There is a input contraint that F must be >= 256.
>In my case F is frequently <256. How to workaround that?
>
>regards peter