We present a method for sampling singular functions defined on (nested) multiparticle phase spaces, based on a generalisation of parton-shower phase-space generation techniques. At the heart of the method are three key ingredients: (1) the Sudakov sampling by which shower-style calculations sweep across phase space in an ordered manner, from hard to soft; (2) the sequential nesting of multiparticle phase spaces; and (3) the factorisations obeyed by singular multiparton amplitudes on the edges of these phase spaces. We demonstrate a C++ implementation of the proposed algorithm, dubbed Sunshine (loosely derived from Sudakov Nesting of Hard Integrals), for hadronic Z decays, and use it to test the tree-level accuracy of the Vincia sector shower through 𝒪(α _s^2) .
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