The high performance and capacity of current FPGAs makes them suitable as acceleration co-processors. This article studies the implementation, for such accelerators, of the floating-point power function $x^y$ as defined by the C99 and IEEE 754-2008 standards, generalized here to arbitrary exponent and mantissa sizes. Last-bit accuracy at the smallest possible cost is obtained thanks to a careful study of the various subcomponents: a floating-point logarithm, a modified floating-point exponential, and a truncated floating-point multiplier. A parameterized architecture generator in the open-source FloPoCo project is presented in details and evaluated.