### Libmvec

Libmvec is vector math library added in Glibc 2.22.

Vector math library was added to support SIMD constructs of OpenMP4.0 (#2.8 in http://www.openmp.org/mp-documents/OpenMP4.0.0.pdf) by adding vector implementations of vector math functions.

Vector math functions are vector variants of corresponding scalar math operations implemented using SIMD ISA extensions (e.g. SSE or AVX for x86_64). They take packed vector arguments, perform the operation on each element of the packed vector argument, and return a packed vector result. Using vector math functions is faster than repeatedly calling the scalar math routines.

The library can be disabled with --disable-mathvec configure option.

The library libmvec.so is linked in as needed when using *-lm*, no need to specify *-lmvec* explicitly.

For static builds with gcc needed to add both options with the following order: -lmvec -lm.

For static builds with g++ needed to add only -lmvec (-lm passed to linker by driver).

#### Libmvec on x86_64

Build and testing enabled by default.

Vector versions differ from the scalar analogues in accuracy and behavior on special values.

Functions are optimized for performance in their respective domains if processing doesnâ€™t incur special values like denormal values, over- and under-flow, and out of range. Special values processing is done in a scalar fashion via respective scalar routine calls. Additionally functions like trigonometric may resort to scalar processing of huge (or other) arguments that do not necessarily cause special values, but rather require different and less SIMD-friendly handling.

These functions were tested (via reasonable random sampling) to pass 4-ulp maximum relative error criterion on their domains in round-to-nearest computation mode. Known limitations:

C99 compliance in terms of special values, errno:

- Functions may not raise exceptions as required by C language standard. Functions may raise spurious exceptions. This is considered an artifact of SIMD processing and may be fixed in the future on the case-by-case basis
- Functions may not change errno in some of the required cases, e.g. if the SIMD friendly algorithm is done branch-free without a libm call for that value. This is done for performance reasons
- As the implementation is dependent on libm, some accuracy and special case problems may be inherent to this fact
- Functions do not guarantee fully correct results in computation modes different from round-to-nearest one

#### Vector ABI

For x86_64 vector functions names are created based on #2.6. Vector Function Name Mangling from Vector ABI VectorABI.txt which has been discussed at X86-64 System V Application Binary Interface mailing list (thread is https://groups.google.com/forum/#!topic/x86-64-abi/LmppCfN1rZ4).

#### Usage model and examples for x86_64

##### Example 1

Use of the vector math functions could be enabled with *-fopenmp -ffast-math* starting from optimization level *-O1* (for GCC starting from version 4.9.0) and appropriate usage of OpenMP SIMD constructs.

The following code in file cos.c:

#include <math.h> int N = 3200; double b[3200]; double a[3200]; int main (void) { int i; #pragma omp simd for (i = 0; i < N; i += 1) { b[i] = cos (a[i]); } return (0); }

being built by GCC 4.9.0 with the following command:

*gcc ./cos.c -O1 -fopenmp -ffast-math -lm -mavx2*

produces binary with call to AVX2 version of vectorized cos (which name is _ZGVdN4v_cos) if Glibc installed system-wide with not disabled Libmvec. In the case of not system-wide installation use additional -I/PATH_TO_GLIBC_INSTALL/include/ -L/PATH_TO_GLIBC_INSTALL/lib/ options.

##### Example 2

Starting from Glibc 2.23 vector math functions can be used also w/o OpenMP with compilers supporting *__attribute__ ((__simd__))*, for instance with GCC 6.* (and later) with options *-ftree-loop-vectorize -ffast-math* starting from optimization level *-O1*.

The following code in file sin.c:

#include <math.h> int N = 3200; double b[3200]; double a[3200]; int main (void) { int i; for (i = 0; i < N; i += 1) { b[i] = sin (a[i]); } return (0); }

being built by GCC 6.* with the following command:

*gcc ./sin.c -O1 -ftree-loop-vectorize -ffast-math -lm -mavx*

produces binary with call to AVX version of vectorized sin (which name is _ZGVcN4v_sin) if Glibc installed system-wide with not disabled Libmvec (in the case of not system-wide installation additional options -I/PATH_TO_GLIBC_INSTALL/include/ -L/PATH_TO_GLIBC_INSTALL/lib/ needed).