exp Generator

The exp generator uses a Taylor series approximation to calculate the fixed point value of the natural exponential function e^x. The Maclaurin series for the function can be written as:

e^x = 1 + x + x^2/2! + x^3/3! + ... + x^n/n!

where n is the nth degree or order of the polynomial.

For signed values, we can take the reciprocal value:

e^(-x) = 1/e^x

The fp_pow_full component can calculate the value of b^x where b and x are any fixed point numbers. This can be calculated by first observing:

b^x = e^(ln(b^x)) = e^(x*ln(b))

Therefore, we just calculate x*ln(b), and then we can feed the result into the exp
component to get our answer.

To calculate ln(p) for fixed point values p, we use the second order Padé Approximant of ln(p). We calculated the approximant using Wolfram Alpha.

The gen_exp.py file can generate an entire Calyx program for testing purposes. gen_exp.py can generate two different types of designs, depending on the base_is_e flag: if base_is_e is true, then the design can only caclulate values for e^x. The main component contains memories x (for the input) and ret for the result of e^x. If base_is_e is false, then the design can calculate values for b^x for any base e. Therefore, the main component contains memories x (the exponent input), b (the base intput), and ret for the result of b^x. In order to generate an example program (that can only calculate exponent values with base e), with degree 4, bit width 32, integer bit width 16, and x interpreted as a signed value:

./calyx-py/calyx/gen_exp.py -d 4 -w 32 -i 16 -s true -e true

Similarly, it provides a function to produce only the necessary components to be dropped into other Calyx programs.

Installation

Install the calyx-py library.

Command Line Options

The command line options configure the degree (or order) of the taylor series, bit width, integer bit width, and sign.

  • --degree: The degree of the Taylor polynomial.
  • --width: The bit width of the value x.
  • --int_width: The integer bit width of the value x. The fractional bit width is then inferred as width - int_width.
  • --is_signed: The signed interpretation of the value x. If x is a signed value, this should be true and otherwise, false.
  • --base_is_e: A boolean that determines whether or not to generate components needed to just calculate e^x, or to generate components needed to calculate b^x for any base b.