  Truncated Conformal Space Approach (TCSA) is a highly efficient method to
compute spectra, operator matrix elements and time evolution in quantum field
theories defined as relevant perturbations of 1+1-dimensional conformal field
theories. However, similarly to other exact diagonalisation methods, TCSA is
ridden with the "curse of dimensionality": the dimension of the Hilbert space
increases exponentially with the (square root of the) truncation level,
limiting its precision by the available memory resources. Here we describe an
algorithm which exploits the chiral factorisation property of conformal field
theory with periodic boundary conditions to achieve a substantial improvement
in the truncation level. The Chirally Factorised TCSA (CFTCSA) algorithm
presented here works with inputs describing the necessary CFT data in a
specified format. It makes possible much more precise calculations with given
computing resources and extends the reach of the method to problems requiring
large Hilbert space dimensions. In fact, it has already been used in a number
of recent works ranging from determination of form factors, through studying
confinement of topological excitations to non-equilibrium dynamics. Besides the
description of the algorithm, a MATLAB implementation of the algorithm is also
provided as an ancillary file package, supplemented with example codes
computing spectra, matrix elements and time evolution, and with CFT data for
three different quantum field theories. We also give a detailed how-to guide
for constructing the required CFT data for Virasoro minimal models with central
charge c<1, and for the massless free boson with c=1.
