[C++] DECIMAL's precision and scale compute rules in add/substract and divide is different with doc #40123

Describe the bug, including details regarding any error messages, version, and platform.

Our decimal compute rules are compatible with Redshift’s decimal promotion rules.
In doc: https://arrow.apache.org/docs/cpp/compute.html#arithmetic-functions, we have the rules:

But during we add the decimal binary kernels, when we compute out_type, the rules are different in add/subtract and divide.

Add/subtract:

        const int32_t scale = s1;
        const int32_t precision = std::max(p1 - s1, p2 - s2) + scale + 1;
        return std::make_pair(precision, scale);

Divide:

        const int32_t scale = s1 - s2;
        const int32_t precision = p1;
        return std::make_pair(precision, scale);

Obviously they are wrong, did i miss some background knowledge?

Component(s)

C++