Update: Added before/after results for Pi(1e9) to emphasize the performance increase.

I did an experiment on an i7-Broadwell machine running CentOS 7.3. The system gmp-devel libraries were built to support the least common denominator. Thus, leaving out optimizations for newer CPU instructions.

# default package build
MPN_PATH=" x86_64/k8 x86_64 generic"

# manually on the broadwell machine, includes extra optimizations
MPN_PATH=" x86_64/coreibwl x86_64/coreihwl x86_64/coreisbr x86_64/core
+inhm x86_64/core2 x86_64 generic"
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I have everything point to the /opt/perl-5.26.1 folder to not impact the system in any way. Then, re-installed GMP modules including Math::Prime::Util.

cd gmp-6.1.2
./configure --prefix=/opt/perl-5.26.1
make -j 4
make check
make install

cd Math-GMP-2.15
/opt/perl-5.26.1/bin/perl Makefile.PL INC="-I/opt/perl-5.26.1/include"
+ LIBS="-L/opt/perl-5.26.1/lib -lgmp"
make
make test
make install

cd Math-BigInt-GMP-1.6004
/opt/perl-5.26.1/bin/perl Makefile.PL INC="-I/opt/perl-5.26.1/include"
+ LIBS="-L/opt/perl-5.26.1/lib -lgmp"
make
make test
make install

cd Math-Prime-Util-GMP-0.46
/opt/perl-5.26.1/bin/perl Makefile.PL INC="-I/opt/perl-5.26.1/include"
+ LIBS="-L/opt/perl-5.26.1/lib -lgmp"
make
make test
make install

cd Math-Prime-Util-master
/opt/perl-5.26.1/bin/perl Makefile.PL INC="-I/opt/perl-5.26.1/include"
+ LIBS="-L/opt/perl-5.26.1/lib -lgmp"
make
make test
make install
[download]

Beyond 20% gain is possible by simply building GMP manually. That will set MPN_PATH to utilize the full capabilities of the processor.

time /opt/perl-5.26.1/bin/perl -Mntheory=:all -E 'say Pi(1e6)' | wc -c
1000002

 0m  1.524s  using system gmp libraries
 0m  1.168s  using gmp libraries from /opt/perl-5.26.1/lib

time /opt/perl-5.26.1/bin/perl -Mntheory=:all -E 'say Pi(1e9)' | wc -c
1000000002

91m  7.581s  using system gmp libraries
67m 40.951s  using gmp libraries from /opt/perl-5.26.1/lib
[download]

Regards, Mario