  We discuss the systematic evaluation of 3-loop vacuum integrals with
arbitrary masses. Using integration by parts, the general integral of this type
can be reduced algebraically to a few basis integrals. We define a set of
modified finite basis integrals that are particularly convenient for expressing
renormalized quantities. The basis integrals can be computed numerically by
solving coupled first-order differential equations, using as boundary
conditions the analytically known special cases that depend on only one mass
scale. We provide the results necessary to carry this out, and introduce an
implementation in the form of a public software package called 3VIL (3-loop
Vacuum Integral Library), which efficiently computes the numerical values of
the basis integrals for any specified masses. 3VIL is written in C, and can be
linked from C, C++, or FORTRAN code.
