This depends on the data. ippsPhase_64f use 64 bit float point as calculation. unlikely the fixed-accuracy vector functions ( ippsAtan2_64f_A53 etc), it does not guaranteed level of accuracy. In most of the cases, 64f is sufficient, and work well for most of the applications. But in some corner cases and some special values, it does not guarantee to the accuracy to some least important bits.
Fixed-accuracy vector functions have a precisely determined process. Only it reach some precession of some level. Then the calculation will be finished.