Issue #
Multiplication/addition combo can result in the compiler emitting two operations, multiplication and addition, instead of one operation fused multiply-add (FMA).
Actions #
Replace a combination of multiplication and addition a + b * c, with a call to the fma function.
Relevance #
Modern hardware often provides a fused multiply-add (FMA) instruction that performs multiplication and addition in a single instruction. Compilers, with an ISA supporting FMA instruction, will fuse independent multiplications and additions into a single FMA operation.
Most compilers do this automatically when proper optimization flags are provided. But, if the compiler is configured to work with strict IEEE 754 compliance, then FMA instructions will not be emitted automatically. In that case, the developer has an option to explicitly use FMA instruction through a function fma available in math.h (or std::fma available in cmath).
Code examples #
Have a look at the following code:
double calc_fma(double a, double b, double c) {
return a + b * c;
}
In the above example, the expression a + b * c is effectively a FMA operation and it can be replaced with a call to fma:
double calc_fma(double a, double b, double c) {
return fma(b, c, a);
}
Note
The above optimization makes sense under the following conditions: (1) The compiler is configured with strict IEEE 754 compliance (-ffp-contract=off or -ffp-contract=on on GCC and CLANG); and (2) The underlying ISA supports FMA and the compiler is allowed to use FMA instruction either using -mfma or -march=ARCH, where ARCH supports FMA instruction.
