Is there a fast C or C++ standard library function for double precision inverse square root?

No. No, there isn't. Not in C++. Nope.

You can use this function for faster inverse square root computing
There's an article on wikipedia on how it works: https://en.wikipedia.org/wiki/Fast_inverse_square_root
Also there's a C version of this algorithm.

float invSqrt( float number ){
    union {
        float f;
        uint32_t i;
    } conv;

    float x2;
    const float threehalfs = 1.5F;

    x2 = number * 0.5F;
    conv.f  = number;
    conv.i  = 0x5f3759df - ( conv.i >> 1 );
    conv.f  = conv.f * ( threehalfs - ( x2 * conv.f * conv.f ) );
    return conv.f;
}