使用std::vector中的std::complex<double>为何出现机器精度级差异？

• 调试单元测试时发现：直接对临时构造的std::complex<double>调用std::pow，与对std::vector中存储的std::complex<double>调用std::pow的结果，存在机器精度（约1.11022e-16）级的差异，该现象仅在-O3编译优化下出现。
• 复现环境：AMD EPYC 7713 64核处理器，GCC 11.2.0、12.1.0版本均可复现。
• 无差异情况：使用float、double或std::complex<float>时未发现该精度差异。

测试代码 #

#include <complex>
#include <iostream>
#include <vector>

int main(int argc, const char * argv[]) {
    std::vector<std::complex<double>> base(1, 4.0);
    std::vector<std::complex<double>> exp(1, -0.23);

    std::cout << std::pow(std::complex(4.0), std::complex(-0.23)) - 
                 std::pow(base.at(0),        exp.at(0)) << std::endl;
    
    return 0;
}

GCC 11.2.0编译运行结果 #

perlmutter:~/bug> /opt/cray/pe/gcc/11.2.0/bin/c++ --version
c++ (GCC) 11.2.0 20210728 (Cray Inc.)
Copyright (C) 2021 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

perlmutter:~/bug> /opt/cray/pe/gcc/11.2.0/bin/c++ -O3 -o test test.cpp
perlmutter:~/bug> ./test
(1.11022e-16,-0)

GCC 12.1.0编译运行结果 #

(base) perlmutter:~/bug> gcc --version
gcc (GCC) 12.1.0 20220506 (HPE)
Copyright (C) 2022 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

perlmutter:~/bug> g++ -O3 -o test test.cpp
perlmutter:~/bug> ./test
(1.11022e-16,-0)

内容的提问来源于stack exchange，提问作者user1139069