Signed-saturate
(signed-saturate n x) coerces the integer x into an n-bit
signed integer by signed saturation, then returns the result as an n-bit
unsigned number.
Normally signed saturation to n bits is understood as:
- If x is too small (less than -2^{n-1}) it becomes -2^{n-1}.
- If x is too big (2^{n-1} or more) it becomes 2^{n-1} - 1.
- Otherwise x is unchanged.
This is almost what we compute. The twist is: after saturating as
above, we mask the above with 2^{n-1} to obtain an unsigned, n-bit
result.
signed-saturate is actually a macro. Generally it expands into a call
of signed-saturate-fn. But, in the common cases where n is
explicitly 8, 16, 32, or 64, it instead expands into a call of an optimized,
inlined function.
Macro: signed-saturate
(defmacro signed-saturate (n x)
(cond ((eql n 8)
(cons 'signed-saturate8 (cons x 'nil)))
((eql n 16)
(cons 'signed-saturate16 (cons x 'nil)))
((eql n 32)
(cons 'signed-saturate32 (cons x 'nil)))
((eql n 64)
(cons 'signed-saturate64 (cons x 'nil)))
(t (cons 'signed-saturate-fn
(cons n (cons x 'nil))))))
Subtopics
- Signed-saturate-fn
- Logical definition of signed-saturate, and also its executable
implementation in the general case.
- Signed-saturate64
- Optimized implementation of 64-bit signed saturation.
- Signed-saturate32
- Optimized implementation of 32-bit signed saturation.
- Signed-saturate16
- Optimized implementation of 16-bit signed saturation.
- Signed-saturate8
- Optimized implementation of 8-bit signed saturation.
