<table border="1" cellspacing="0" cellpadding="8">
    <tr>
        <th>Issue</th>
        <td>
            <a href=https://github.com/llvm/llvm-project/issues/60546>60546</a>
        </td>
    </tr>

    <tr>
        <th>Summary</th>
        <td>
            Simplify `urem` to `icmp+select` in `(x + 1) % n`
        </td>
    </tr>

    <tr>
      <th>Labels</th>
      <td>
            new issue
      </td>
    </tr>

    <tr>
      <th>Assignees</th>
      <td>
      </td>
    </tr>

    <tr>
      <th>Reporter</th>
      <td>
          scottmcm
      </td>
    </tr>
</table>

<pre>
    (Inspired by someone doing `self.write_index = (self.write_index + 1) % self.container.len();` in a circular buffer.)

If `x < n` (such as because it was just used to index an array of that length), then there's no need to modulo in `(x + 1) % n`, since there's only one case where the modulo does anything, and thus we could detect that case instead.

Alive2 proof: <https://alive2.llvm.org/ce/z/UNmz9j>

```llvm
define i64 @src(i64 noundef %x, i64 noundef %n) noundef {
%start:
  %_3 = icmp ult i64 noundef %x, noundef %n
  assume i1 %_3
  %_6 = add nuw i64 noundef %x, 1
  %0 = urem i64 %_6, noundef %n
  ret i64 %0
}
; =>
define i64 @tgt(i64 noundef %x, i64 noundef %n) noundef {
%start:
  %_3 = icmp ult i64 noundef %x, noundef %n
  assume i1 %_3
  %_6 = add nuw i64 noundef %x, 1
  %w = icmp eq i64 %_6, noundef %n
  %0 = select i1 %w, i64 0, i64 %_6
  ret i64 %0
}
; Transformation seems to be correct!
```

Repro in opt: <https://llvm.godbolt.org/z/5vP7T8fE7>
</pre>
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