diff options
| author | Schuyler Eldridge | 2020-02-06 10:35:36 -0500 |
|---|---|---|
| committer | GitHub | 2020-02-06 10:35:36 -0500 |
| commit | 39f8563c5e3e737610f46a82f6ceaa52120ef654 (patch) | |
| tree | 8112fc8fe606962ebe55d2f0d4a3bbcf0fd81ecc /spec | |
| parent | bf0ea92752cfb3db1797b8ffc8ff0c776552b1cf (diff) | |
| parent | 7e3a4240f0ddc24d8effac515b7449df588277da (diff) | |
Merge pull request #1362 from freechipsproject/andr-reduction-base-case
Change zero-width base case for Andr
Diffstat (limited to 'spec')
| -rw-r--r-- | spec/spec.pdf | bin | 274485 -> 275421 bytes | |||
| -rw-r--r-- | spec/spec.tex | 2 |
2 files changed, 2 insertions, 0 deletions
diff --git a/spec/spec.pdf b/spec/spec.pdf Binary files differindex 8b7fd125..e49441ad 100644 --- a/spec/spec.pdf +++ b/spec/spec.pdf diff --git a/spec/spec.tex b/spec/spec.tex index 68a404a8..a8a40da4 100644 --- a/spec/spec.tex +++ b/spec/spec.tex @@ -1533,6 +1533,8 @@ andr,orr,xorr & (e) & () & (UInt) & UInt & 1\\ The bitwise reduction operations correspond to a bitwise and, or, and exclusive or operation, reduced over every bit in \vv{e}. +In all cases, the reduction incorporates as an inductive base case the ``identity value'' associated with each operator. This is defined as the value that preserves the value of the other argument: one for \vv{and} (as $x \wedge 1 = x$), zero for \vv{or} (as $x \vee 0 = x$), and zero for \vv{xor} (as $x \oplus 0 = x$). Note that the logical consequence is that the and-reduction of a zero-width expression returns a one, while the or- and xor-reductions of a zero-width expression both return zero. + \subsection{Concatenate Operation} \begin{figure}[H] |