The paper [ON THE RAPID COMPUTATION OF VARIOUS POLYLOGARITHMIC CONSTANTS](http://www.davidhbailey.com/dhbpapers/digits.pdf) by Bailey, Borwein, and Plouffe gives sophisticated calculations which I will not summarize. But they remark



> 
> We are interested in computing in polynomially logarithmic space and
>  polynomial time. This class is usually denoted SC (space = logO(1)(d)
>  and time = dO(1) where d is the place of the “digit” to be computed).
>  ... It is not known whether division is possible in SC, similarly it is
>  not known whether base change is possible in SC.
> 
> 
> 


I suppose good bounds are known for space and time complexity of division and base change. What is known about them?



What is known about space and time complexity of division and base change?
The paper is outdated. Division was proved to be computable in logarithmic space (and a fortiori SC) by Chiu, Davida, and Litow [1]. In fact, they proved it to be in logspace-uniform $\mathrm{NC^1}$; this was improved by Hesse, Allender, and Barrington [2], who proved it is in fully uniform $\mathrm{TC^0}$. The same results also hold for base conversion.


[1] Andrew Chiu, George Davida and Bruce Litow: *Division in logspace-uniform $\mathit{NC}^1$*, RAIRO – Theoretical Informatics and Applications 35 (2001), no. 3, pp. 259–275, doi: [10.1051/ita:2001119](https://doi.org/10.1051/ita:2001119).


[2] William Hesse, Eric Allender, David A. Mix Barrington: *Uniform constant-depth threshold circuits for division and iterated multiplication*, Journal of Computer and System Sciences 65 (2002), no. 4, pp. 695–716, doi: [10.1016/S0022-0000(02)00025-9](https://doi.org/10.1016/S0022-0000(02)00025-9).


