Diadenylate cyclase that catalyzes the condensation of 2 ATP molecules into cyclic di-AMP (c-di-AMP) (PubMed:25965978). c-di-AMP is a second messenger for intracellular signal transduction involved in the control of important regulatory processes such as osmoregulation (By similarity). 2 ATP = 3',3'-c-di-AMP + 2 diphosphate Belongs to the adenylate cyclase family. DacZ subfamily.