adverb (r)

• in an uncontrolled manner(adv.all)

  Example:
  She fought back madly.
  

  Synonym:
  frantically, uncontrollably
  

  source: wordnet30
• in an insane manner(adv.all)

  Example:
  The witch cackled madly.
  

  Synonym:
  crazily, dementedly, insanely
  Antonym:
  sanely
  

  source: wordnet30
• (used as intensives) extremely(adv.all)

  Example:
  She was madly in love.
  

  Synonym:
  deadly, deucedly, devilishly, insanely
  

  source: wordnet30
• In a mad manner; without reason or understanding; wildly.(adverb)

  source: webster1913