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--- math:start [2022/07/30 15:38] – [Namespace math] rajit
+++ math:start [2025/09/23 11:02] (current) – [Fixed point data type] rajit
@@ Line 4: / Line 4: @@
 ===== 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.''
+===== Fixed point data type =====
+The standard math library has a fixed point data type.
+<code act>
+export template <pint A, B> deftype fixpoint(int<A+B> x);
+</code>
+This datatype uses the standard Q(A,B) fixed point format, where A bits are used for the integer part and B bits are used for the fractional part. This datatype defines operators for addition, subtraction, multiplication, division, as well as comparison operators.
+The following code fragment initializes the fixed point value ''x'' to 5.25. ''x.const(5.25)'' returns a parameterized integer corresponding to translating the real number 5.25 to the fixed point representation used by ''x''. Note that ''x.const()'' returns a ''pint'', so it is limited to 64 bits. ''x.set()'' is a macro that takes an integer of bitwidth (A+B) and sets ''x'' to the specified fixed point number.
+<code act>
+math::fixpoint<8,3> x;
+...
+chp {
+    x.set(x.const(5.25));
+    ...
+}
+</code>
+Other ways to initialize ''x'' to the fixed point number corresponding to the integer representation ''0x0f'' (which corresponds to 1.875 for Q(8,3)) are:
+<code act>
+...
+chp {
+   x.x := 0x0f;
+   ...
+   x.set(0x0f);
+   ...
+}
+</code>
+For debugging purposes, two macros are also provided for displaying the value of a fixed point number. The ''log()'' macro just displays the number using the ''log()'' statement, while the ''log_p()'' displays it without a new line.
+<code act>
+chp {
+   ...
+   x.log();
+   ...
+}
+</code>
@@ Line 48: / Line 101: @@
 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.
+These functions are used by the fixed point data type.