Electronic – How to code in assembly language for floating point exponentiation

assemblyfloating pointpic

I have problem calculating raise a to the power of b (a^b) where b is a floating point number.
In my case, b=-1.45. So the expression is a^(-1.45).
I'm using PIC18F4520 microcontroller and I don't know how to implement it in assembly language or its routine as well.

Best Answer

Note that just because b isn't an integer, it doesn't mean that it is necessarily floating-point. For example, it could be expressed as the integer ratio \$-1.45 = \frac{-29}{20}\$.

You need to specify what the type and range of a is, and what kind of accuracy you require in your application. You also haven't specified what you want the output to look like. As @jonathanjo pointed out, all answers except for a=1 are fractions less than 0.5. Also, since exponentiation is a nonlinear operation, it's important to understand what real-world values the integer values of 'a' represent.

For what it's worth, arbitrary exponentiation is usually implemented as a 3-step process: log, multiply, exponentiate:

$$a^b \equiv \exp(b \cdot \log(a))$$

You can use any convenient base for the log() and exp() operations, as long as they're the same. 2, \$e\$ and 10 are popular choices.

CORDIC is one way to implement log() and exp() on small systems. See also cordic.

But depending on your requirements, piecewise linear or polynomial approximation of the overall function might be more appropriate. These just require a few multiplies and adds. It's also possible that \$\frac{1}{polynomial}\$ or \$\frac{1}{\sqrt{polynomial}}\$ would be a good fit for your function. These operations are similarly easy to add to the mix using Newton-Raphson.

Related Solutions

System Generator: a block to change sign of a floating point

Negating a floating point number involves inverting the sign bit.

(For fixed-point numbers there's a Negate block in the sysgen library which should avoid using a multiplier)

Be aware though, that sysgen is not designed for use with floating-point - you might find yourself jumping through all sorts of hoops!

Electronic – How to split a floating point number into individual digits

There's numerous ways of doing it. You may find your compiler has a library function to do it for you. It may be possible with:

sprintf() / snprintf()
dtostrf()
dtoa()

Alternatively, it's not too hard to write your own routine to do it. It's just a case of first working out how many digits before the decimal point there are, dividing it by 10 that many times, then taking the integer portion repeatedly while multiplying by 10, making sure you add the decimal point in at the right place.

So in pseudo-code it may look something like:

If the value < 0.0:
    Insert - into string
    Subtract value from 0.0 to make it positive.
While the value <= 10.0:
    Divide by 10
    Increment decimal counter
For each digit of required precision:
    Take the integer portion of the value and place it in the string
    Subtract the integer portion from the value
    Decrement decimal counter
    If decimal counter is 0:
        Insert decimal point
    Multiply the value by 10.

Best Answer

Related Solutions

System Generator: a block to change sign of a floating point

Electronic – How to split a floating point number into individual digits

Related Topic