logarithm implementation

[ammassk]

For my project, I need to write VHDL code for natural logarithm(base 'e').For simplicity I am planning to write code using log series. But ln(x)=(x-1)-((x-1)^2)/2+((x-1)^3/3)--- will work only when x<1. But my x values are real numbers >1. How can I implement natural logarithm then?

 

[TrickyDicky]

you can use the floating point cores aavaiable from xilinx or altera. All your numbers are probably then 32 bit std_logic_vectors that represent 32 bit floating point. But this will use a lot of resources and have a long latency (but that does not affect throughput)
Have you investigated fixed point?

and what about using a look up table? its simpler than a taylor series.

 

[ammassk]

I am using fixed point format here.Also this log function is not for constant numbers. These are varying. Then how can i use look up table?

 

[TrickyDicky]

the varying input becomes the address value for the LUT.

 

[mrflibble]

For my project, I need to write VHDL code for natural logarithm(base 'e').For simplicity I am planning to write code using log series. But ln(x)=(x-1)-((x-1)^2)/2+((x-1)^3/3)--- will work only when x<1. But my x values are real numbers >1. How can I implement natural logarithm then?

On a more theoretical (yet still entirely practical ) note, you can do a Taylor expansion around any central value you like. It doesn't have to be x=1, it's just that that happens to be a popular way to do it for ln.

Anyways, as usual with this sort of thing ... what is your:
- input range
- input precision
- required output precision
- etc

Without any further details on your requirements the autopilot advice would be fixed point LUT + interpolation aaaand you're done.

 

[zorro]

The efficient way is to work in base 2 (i.e. find log2(x)) in the following steps:

a) obtain mantissa and exponent, i.e. x=mant*2^expon where mant is between 1/2 and 1
b) calculate log2(mant)
c) log2(x)=log2(mant)+expon
d) if you need ln: ln(x)=log2(x)*ln(2)

step (a) is trivial if you have x in floating point yet. If it is fixed point, it is a simple combinatorial logic or by shifting method.
steb (b) can use a polynomial approximation (best suited is Horner method), although there is a better algorithm (that i don't remember) using a small LUT (one entry per bit, if i'm not wrong). "Brute force" LUT is good if limited precision is OK.

Regards

Z