Performance has always been a high priority for C++, yet there are many examples both in the language and the standard library where compilers produce code that is significantly slower than what a machine is capable of. In this blog post, I’m going to explore one such example from the standard math library.
Suppose we’re tasked with computing the square roots of an array of floating point numbers. We might write a function like this to perform the operation:
If we’re using gcc, we can compile the code with
g++ -c -O3 -march=native sqrt1.cpp
-O3, gcc will optimize the code heavily but will still produce code that is standard compliant. The
-march=native option tells gcc to produce code targeting the native architecture’s instruction set. The resulting binaries may not be portable even between different x86-64 CPUs.
Now, let’s benchmark the function. We’ll use google benchmark to measure how long it takes to compute the square roots of
Compiling our benchmark and running we get
g++ -O3 -march=native -o benchmark benchmark.cpp sqrt1.o
Can we do better? Let try this version:
and compile with
g++ -c -O3 -march=native -fno-math-errno sqrt2.cpp
The only difference between
compute_sqrt2 is that we added the extra option
-fno-math-errno when compiling. I’ll explain later what
-fno-math-errno does; but for now, I’ll only point out that the produced code is no longer standard compliant.
g++ -O3 -march=native -o benchmark benchmark.cpp sqrt2.o
compute_sqrt2 is more than 4 times faster than
What’s different? Let’s drill down into the assembly to find out. We can produce the assembly for the code by running
g++ -S -c -O3 -march=native sqrt1.cpp
The result will depend on what architecture you’re using, but looking at sqrt1.s on my architecture, we see this section
Let’s break down the first few instructions:
1: vmovsd (%rdi), %xmm0
What are instructions 3 and 4 for? Recall that for real numbers, sqrt is undefined on negative values. When
std::sqrt is passed a negative number, the C++ standard requires that it return the special floating point value
NaN and that it set the global variable
EDOM. But that error handling ends up being really expensive.
If we look at sqrt2.s, we see these instructions for the main loop:
Without the burden of having to do error handling, gcc can produce much faster code.
vsqrtpd is what’s known as a Single Instruction Multiple Data (SIMD) instruction. It computes the the square root of four double precision floating point numbers at a time. For computationally expensive functions like sqrt, vectorization helps a lot.
It’s unfortunate that the standard requires such error handling. It’s so much slower to do the error checking that many compilers like Intel’s icc and Apple’s default clang-based compiler opt out of the error handling by default. Even if we want
std::sqrt do error handling, we can’t portably rely on major compilers to do so.
The complete benchmark can be found at rnburn/cmath-bechmark.