Is there a way to programmatically get the double that is closest to 1.0, but isn't actually 1.0?
One hacky way to do this would be to memcpy the double to a same-sized integer, and then subtract one. The way IEEE754 floating-point formats work, this would end up decreasing the exponent by one while changing the fractional part from all zeros (1.000000000000) to all ones (1.111111111111). However there exist machines where integers are stored little-endian while floating-point is stored big-endian, so that won't always work.
Since C++11, you may use nextafter to get next representable value in given direction:
std::nextafter(1., 0.); // 0.99999999999999989
std::nextafter(1., 2.); // 1.0000000000000002