====== Namespace math ======

This namespace is used to provide support functions for math operations.

===== Functions =====

<code act>
template<pint Worig, Wnew> function sign_extend (int<Worig> x) : int<Wnew>;
</code>

This function takes an integer ''x'' of width ''Worig'', and sign extends its most significant bit to return a result that has width ''Wnew''. It assumes that ''Wnew'' is at least ''Worig.''


<code act>
template<pint Worig, Wnew> function zero_extend (int<Worig> x) : int<Wnew>;
</code>

This function takes an integer ''x'' of width ''Worig'', and zero extends it to return a result that has width ''Wnew''. It assumes that ''Wnew'' is at least ''Worig.''




===== Namespace math::fxp =====

==== Functions ====

The ''math::fxp'' namespace contains simple definitions for fixed-point arithmetic functions. Functions take two parameters ''A'' and ''B'', and integers use the standard Q-format where the representation Q(A,B) corresponds to A digits for the integer part and B digits for the fractional part. The representation uses 2's complement for negative
numbers, so addition and subtraction are the same for signed and unsigned arithmetic.

<code act>
template<pint A,B> function add (int<A+B> x, y) : int<A+B>;
</code>
This returns the sum of two Q(A,B) numbers ''x'' and ''y''.

<code act>
template<pint A,B> function sub (int<A+B> x, y) : int<A+B>;
</code>
This returns the difference of two Q(A,B) numbers ''x'' and ''y''.

<code act>
template<pint A,B> function multu (int<A+B> x, y) : int<A+B>;
</code>
This returns the unsigned product of two Q(A,B) numbers ''x'' and ''y''.

<code act>
template<pint A,B> function divu (int<A+B> x, y) : int<A+B>;
</code>
This returns the unsigned division result ''x/y'' of two Q(A,B) numbers ''x'' and ''y''.

<code act>
template<pint A,B> function mults (int<A+B> x, y) : int<A+B>;
</code>
This returns the signed product of two Q(A,B) numbers ''x'' and ''y''.

<code act>
template<pint A,B> function divs (int<A+B> x, y) : int<A+B>;
</code>
This returns the signed division result ''x/y'' of two Q(A,B) numbers ''x'' and ''y''.

<code act>
template<pint A,B> function uminus (int<A+B> x) : int<A+B>;
</code>
This returns the negated value of a signed Q(A,B) number ''x''.

<code act>
template<pint A,B> function positive (int<A+B> x) : bool;
</code>
This is true if the fixed point number is positive (greater than zero), and false otherwise.

<code act>
template<pint A,B> function negative (int<A+B> x) : bool;
</code>
This is true if the fixed point number is negative, and false otherwise

<code act>
template<pint A,B> function le(int<A+B> x, y) : bool;
</code>
This tests if the value in ''x'' is less than or equal to ''y''.

<code act>
function conv_to_fxp(pint A, B; preal v) : pint;
</code>
This can be used to convert a real constant value into its fixed point representation. Note that since ''pint'' values are 64-bit wide (max), this only works when ''A+B'' is at most 64.