The present embodiments relate to integrated circuits with circuitry that efficiently performs mixed-precision floating-point arithmetic operations. Such circuitry may be implemented in specialized processing blocks. The specialized processing blocks may include configurable interconnect circuitry to support a variety of different use modes. For example, the specialized processing blocks may implement fixed-point addition, floating-point addition, fixed-point multiplication, floating-point multiplication, sum of two multiplications in a first floating-point precision, with or without casting to a second floating-point precision and the latter followed by a subsequent addition in the second floating-point precision, if desired, just to name a few. In some embodiments, two or more specialized processing blocks may be arranged in a cascade chain and perform together more complex operations such as a recursive mode dot product of two vectors of floating-point numbers having a first floating-point precision and output the dot product in a second floating-point precision.