About one bit (in binary equivalent) per naive iteration? Better with some linear interpolation (pseudo-Newton)? IIRC, before e.g. continued fraction represent

About one bit (in binary equivalent) per naive iteration? Better with some linear interpolation (pseudo-Newton)? IIRC, before e.g. continued fraction representations/approximations became available, high precision estimates of pi were based upon geometric subdivisions of a circle and computation of hundreds of terms.