The Javascript code below is a rough equivalent to the simple_format Show archive.org snapshot helper that ships with Rails:

function simpleFormat(str) {
  str = str.replace(/\r\n?/, "\n");
  str = $.trim(str);
  if (str.length > 0) {
    str = str.replace(/\n\n+/g, '</p><p>');
    str = str.replace(/\n/g, '<br />');
    str = '<p>' + str + '</p>';
  }
  return str;
}

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Read more Show archive.org snapshot

Unlike the Rails helper, this does not preserve whitespace. You probably don't care.