  We introduce an approach of Riemann--Roch theorem to the boundedness problem
of minimal log discrepancies in fixed dimension. After reducing it to the case
of a Gorenstein terminal singularity, firstly we prove that its minimal log
discrepancy is bounded if either multiplicity or embedding dimension is
bounded. Secondly we recover the characterisation of a Gorenstein terminal
three-fold singularity by Reid, and the precise boundary of its minimal log
discrepancy by Markushevich, without explicit classification. Finally we
provide the precise boundary for a special four-fold singularity, whose general
hyperplane section has a terminal piece.
