The present embodiments relate to performing reduced-precision floating-point arithmetic operations using specialized processing blocks with higher-precision floating-point arithmetic circuitry. A specialized processing block may receive four floating-point numbers that represent two single-precision floating-point numbers, each separated into an LSB portion and an MSB portion, or four half-precision floating-point numbers. A first partial product generator may generate a first partial product of first and second input signals, while a second partial product generator may generate a second partial product of third and fourth input signals. A compressor circuit may generate carry and sum vector signals based on the first and second partial products; and circuitry may anticipate rounding and normalization operations by generating in parallel based on the carry and sum vector signals at least two results when performing the single-precision floating-point operation and at least four results when performing the two half-precision floating-point operations.