FMA3FMA4

FMA3FMA4 is a shorthand reference to two related, but distinct, fused multiply-add instruction formats used on x86 CPUs: FMA3 and FMA4. Both execute a multiply and an addition as a single operation with a single rounding step, which can improve numerical accuracy and performance compared to separate multiply and add instructions. The two formats differ in how many operands they use and how the result is written back to registers.

FMA3 refers to the three-operand fused multiply-add form. In FMA3, the operation computes a*b + c in one instruction, with the result written to a destination register that is typically one of the three operands. This design allows compact encoding and is widely supported by modern Intel and AMD processors. FMA3 reduces rounding errors relative to performing multiply and add separately and can improve throughput in floating-point heavy code.

FMA4 is a four-operand variant that explicitly separates the destination from the input operands. Its canonical form is d = a*b + c, where d is distinct from a, b, and c. FMA4 originated with AMD’s Bulldozer-era architectures and provides greater flexibility in register usage, which can reduce the need to overwrite input registers. However, FMA4 has seen limited adoption beyond certain AMD generations and is not as broadly supported as FMA3 on many modern CPUs.

In practice, most current software targets FMA3 capabilities, using compiler intrinsics or auto-vectorization to emit FMA3 instructions. FMA4 support is less common and can complicate portability across processors. Understanding the specific microarchitecture and compiler support is important when optimizing numerical code for fused multiply-add operations.