International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. F, ch. 25.2, pp. 717718

The most timeconsuming calculations in refinement are the calculation of structure factors from atomic coordinates and the calculation of derivatives of the part of the residual dependent upon the diffraction data with respect to the atomic parameters. The quickest means of performing these calculations requires the use of spacegroupoptimized fast Fourier transforms (FFTs). The initial implementation of TNT used FFTs to calculate structure factors, but the much slower direct summation method to calculate the derivatives. Within a few years, Agarwal's method (Agarwal, 1978; Agarwal et al., 1981) was incorporated into TNT and from then on all crystallographic calculations were performed with FFTs.
The FFT programs of Ten Eyck (1973, 1977) made very efficient use of computer memory. Another means of saving memory was to recognize that the code for calculating stereochemical restraints did not need to be in the memory when the crystallographic calculations were being performed and vice versa. There were two ways to save memory using this information. One could create a series of `overlays' or one could break the calculation into a series of separate programs. The means for defining an overlay structure were never standardized and could not be ported from one type of computer to another and were, therefore, never attempted in TNT. For this reason, and a number of others mentioned here, TNT is not a single program but a collection of programs, each with a well defined and specialized purpose.
References
Agarwal, R. C. (1978). A new leastsquares technique based on the fast Fourier transform algorithm. Acta Cryst. A34, 791–809.Google ScholarAgarwal, R. C., Lifchitz, A. & Dodson, E. (1981). Block diagonal least squares refinement using fast Fourier techniques. In Refinement of protein structures, edited by P. A. Machin, J. W. Campbell & M. Elder. Warrington: Daresbury Laboratory.Google Scholar
Ten Eyck, L. F. (1973). Crystallographic fast Fourier transforms. Acta Cryst. A29, 183–191.Google Scholar
Ten Eyck, L. F. (1977). Efficient structurefactor calculation for large molecules by the fast Fourier transform. Acta Cryst. A33, 486–492.Google Scholar