GCC bug at -O2 and above for recent GCC and a -O3 and above for older compilers

Compile example (not working)

-> g++ -v -save-temps -O3 test.cpp -I/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/ -o wrong.gccy
Using built-in specs.
COLLECT_GCC=g++
COLLECT_LTO_WRAPPER=/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/lto-wrapper
Target: x86_64-pc-linux-gnu
Configured with: /build/gcc/src/gcc/configure --enable-languages=ada,c,c++,d,fortran,go,lto,objc,obj-c++ --enable-bootstrap --prefix=/usr --libdir=/usr/lib --libexecdir=/usr/lib --mandir=/usr/share/man --infodir=/usr/share/info --with-bugurl=https://bugs.archlinux.org/ --with-build-config=bootstrap-lto --with-linker-hash-style=gnu --with-system-zlib --enable-__cxa_atexit --enable-cet=auto --enable-checking=release --enable-clocale=gnu --enable-default-pie --enable-default-ssp --enable-gnu-indirect-function --enable-gnu-unique-object --enable-libstdcxx-backtrace --enable-link-serialization=1 --enable-linker-build-id --enable-lto --enable-multilib --enable-plugin --enable-shared --enable-threads=posix --disable-libssp --disable-libstdcxx-pch --disable-werror
Thread model: posix
Supported LTO compression algorithms: zlib zstd
gcc version 13.1.1 20230429 (GCC)
COLLECT_GCC_OPTIONS='-v' '-save-temps' '-O3' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'wrong.gccy' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'wrong.gccy-'
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/cc1plus -E -quiet -v -I /home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/ -D_GNU_SOURCE test.cpp -mtune=generic -march=x86-64 -O3 -fpch-preprocess -o wrong.gccy-test.ii
ignoring nonexistent directory "/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../x86_64-pc-linux-gnu/include"
#include "..." search starts here:
#include <...> search starts here:
 /home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../include/c++/13.1.1
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../include/c++/13.1.1/x86_64-pc-linux-gnu
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../include/c++/13.1.1/backward
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/include
 /usr/local/include
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/include-fixed
 /usr/include
End of search list.
COLLECT_GCC_OPTIONS='-v' '-save-temps' '-O3' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'wrong.gccy' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'wrong.gccy-'
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/cc1plus -fpreprocessed wrong.gccy-test.ii -quiet -dumpdir wrong.gccy- -dumpbase test.cpp -dumpbase-ext .cpp -mtune=generic -march=x86-64 -O3 -version -o wrong.gccy-test.s
GNU C++17 (GCC) version 13.1.1 20230429 (x86_64-pc-linux-gnu)
        compiled by GNU C version 13.1.1 20230429, GMP version 6.2.1, MPFR version 4.2.0, MPC version 1.3.1, isl version isl-0.26-GMP

warning: MPFR header version 4.2.0 differs from library version 4.2.0-p9.
GGC heuristics: --param ggc-min-expand=100 --param ggc-min-heapsize=131072
Compiler executable checksum: e149eaca55f4ee2a0171ba2b54b0dc8d
COLLECT_GCC_OPTIONS='-v' '-save-temps' '-O3' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'wrong.gccy' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'wrong.gccy-'
 as -v -I /home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/ --64 -o wrong.gccy-test.o wrong.gccy-test.s
GNU assembler version 2.40.0 (x86_64-pc-linux-gnu) using BFD version (GNU Binutils) 2.40.0
COMPILER_PATH=/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/:/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/:/usr/lib/gcc/x86_64-pc-linux-gnu/:/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/:/usr/lib/gcc/x86_64-pc-linux-gnu/
LIBRARY_PATH=/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/:/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib/:/lib/../lib/:/usr/lib/../lib/:/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../:/lib/:/usr/lib/
COLLECT_GCC_OPTIONS='-v' '-save-temps' '-O3' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'wrong.gccy' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'wrong.gccy.'
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/collect2 -plugin /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/liblto_plugin.so -plugin-opt=/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/lto-wrapper -plugin-opt=-fresolution=wrong.gccy.res -plugin-opt=-pass-through=-lgcc_s -plugin-opt=-pass-through=-lgcc -plugin-opt=-pass-through=-lc -plugin-opt=-pass-through=-lgcc_s -plugin-opt=-pass-through=-lgcc --build-id --eh-frame-hdr --hash-style=gnu -m elf_x86_64 -dynamic-linker /lib64/ld-linux-x86-64.so.2 -pie -o wrong.gccy /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib/Scrt1.o /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib/crti.o /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/crtbeginS.o -L/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1 -L/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib -L/lib/../lib -L/usr/lib/../lib -L/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../.. wrong.gccy-test.o -lstdc++ -lm -lgcc_s -lgcc -lc -lgcc_s -lgcc /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/crtendS.o /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib/crtn.o
COLLECT_GCC_OPTIONS='-v' '-save-temps' '-O3' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'wrong.gccy' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'wrong.gccy.'

tmp on  bg-search-index [!?]
-> ./wrong.gcc
wut?
high: 5.16756e+06 2.06703e+06 3.10054e+06
low:         0         0 0.0220723
diff: 0.132647

Compile Example (working)

-> g++ -v -save-temps -O1 test.cpp -I/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/ -o right.gcc
Using built-in specs.
COLLECT_GCC=g++
COLLECT_LTO_WRAPPER=/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/lto-wrapper
Target: x86_64-pc-linux-gnu
Configured with: /build/gcc/src/gcc/configure --enable-languages=ada,c,c++,d,fortran,go,lto,objc,obj-c++ --enable-bootstrap --prefix=/usr --libdir=/usr/lib --libexecdir=/usr/lib --mandir=/usr/share/man --infodir=/usr/share/info --with-bugurl=https://bugs.archlinux.org/ --with-build-config=bootstrap-lto --with-linker-hash-style=gnu --with-system-zlib --enable-__cxa_atexit --enable-cet=auto --enable-checking=release --enable-clocale=gnu --enable-default-pie --enable-default-ssp --enable-gnu-indirect-function --enable-gnu-unique-object --enable-libstdcxx-backtrace --enable-link-serialization=1 --enable-linker-build-id --enable-lto --enable-multilib --enable-plugin --enable-shared --enable-threads=posix --disable-libssp --disable-libstdcxx-pch --disable-werror
Thread model: posix
Supported LTO compression algorithms: zlib zstd
gcc version 13.1.1 20230429 (GCC)
COLLECT_GCC_OPTIONS='-v' '-save-temps' '-O1' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'right.gcc' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'right.gcc-'
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/cc1plus -E -quiet -v -I /home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/ -D_GNU_SOURCE test.cpp -mtune=generic -march=x86-64 -O1 -fpch-preprocess -o right.gcc-test.ii
ignoring nonexistent directory "/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../x86_64-pc-linux-gnu/include"
#include "..." search starts here:
#include <...> search starts here:
 /home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../include/c++/13.1.1
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../include/c++/13.1.1/x86_64-pc-linux-gnu
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../include/c++/13.1.1/backward
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/include
 /usr/local/include
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/include-fixed
 /usr/include
End of search list.
COLLECT_GCC_OPTIONS='-v' '-save-temps' '-O1' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'right.gcc' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'right.gcc-'
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/cc1plus -fpreprocessed right.gcc-test.ii -quiet -dumpdir right.gcc- -dumpbase test.cpp -dumpbase-ext .cpp -mtune=generic -march=x86-64 -O1 -version -o right.gcc-test.s
GNU C++17 (GCC) version 13.1.1 20230429 (x86_64-pc-linux-gnu)
        compiled by GNU C version 13.1.1 20230429, GMP version 6.2.1, MPFR version 4.2.0, MPC version 1.3.1, isl version isl-0.26-GMP

warning: MPFR header version 4.2.0 differs from library version 4.2.0-p9.
GGC heuristics: --param ggc-min-expand=100 --param ggc-min-heapsize=131072
Compiler executable checksum: e149eaca55f4ee2a0171ba2b54b0dc8d
./rightCOLLECT_GCC_OPTIONS='-v' '-save-temps' '-O1' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'right.gcc' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'right.gcc-'
 as -v -I /home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/ --64 -o right.gcc-test.o right.gcc-test.s
GNU assembler version 2.40.0 (x86_64-pc-linux-gnu) using BFD version (GNU Binutils) 2.40.0
COMPILER_PATH=/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/:/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/:/usr/lib/gcc/x86_64-pc-linux-gnu/:/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/:/usr/lib/gcc/x86_64-pc-linux-gnu/
LIBRARY_PATH=/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/:/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib/:/lib/../lib/:/usr/lib/../lib/:/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../:/lib/:/usr/lib/
COLLECT_GCC_OPTIONS='-v' '-save-temps' '-O1' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'right.gcc' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'right.gcc.'
 /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/collect2 -plugin /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/liblto_plugin.so -plugin-opt=/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/lto-wrapper -plugin-opt=-fresolution=right.gcc.res -plugin-opt=-pass-through=-lgcc_s -plugin-opt=-pass-through=-lgcc -plugin-opt=-pass-through=-lc -plugin-opt=-pass-through=-lgcc_s -plugin-opt=-pass-through=-lgcc --build-id --eh-frame-hdr --hash-style=gnu -m elf_x86_64 -dynamic-linker /lib64/ld-linux-x86-64.so.2 -pie -o right.gcc /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib/Scrt1.o /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib/crti.o /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/crtbeginS.o -L/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1 -L/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib -L/lib/../lib -L/usr/lib/../lib -L/usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../.. right.gcc-test.o -lstdc++ -lm -lgcc_s -lgcc -lc -lgcc_s -lgcc /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/crtendS.o /usr/lib/gcc/x86_64-pc-linux-gnu/13.1.1/../../../../lib/crtn.o
.gCOLLECT_GCC_OPTIONS='-v' '-save-temps' '-O1' '-I' '/home/lakin/.conan/data/eigen/3.4.0/_/_/package/5ab84d6acfe1f23c4fae0ab88f26e3a396351ac9/include/eigen3/' '-o' 'right.gcc' '-shared-libgcc' '-mtune=generic' '-march=x86-64' '-dumpdir' 'right.gcc.'

tmp on  bg-search-index [!?]
-> ./right.gcc
wut?
high: 5.16756e+06 2.06703e+06 3.10054e+06
low:   -0.12988 -0.0269518  0.0220723
diff: 4.75454e-09

test.cpp

#include <iostream>

#include <Eigen/Core>

using f64 = double;
using f32 = float;
template<typename T>
using vec3 = Eigen::Matrix<T, 3, 1>;

const f64 RADIUS_EARTH_M = 6371000.0;

auto main() -> int {
    std::cout << "wut?" << std::endl;
    vec3<f64> pos{0.5, 0.2, 0.3};
    pos = pos.normalized() * RADIUS_EARTH_M;
 
    // This code is attempting to represent double floating point values 
    // as two float values.  At high optimization levels two of the values
    // of low end up as zero. 
    vec3<f32> high = pos.cast<f32>();
    vec3<f32> low  = (pos - high.cast<f64>()).cast<f32>();

    std::cout << "high: " << high.transpose() << std::endl;
    std::cout << "low: " << low.transpose() << std::endl;

    vec3<f64> posRecreated = (high.cast<f64>() + low.cast<f64>());
    vec3<f64> diff         = posRecreated - pos;
    std::cout << "diff: " << diff.norm() << std::endl;
}