Design

Bounded integers

Element i maps stream word i by Lemire's multiply-and-reject method, and a rejected word retries on a fallback generator derived by the global draw index, the aligned start position over the word width plus i, so a fill uses exactly n words and a fill cut at any element equals the whole fill. It reads 32-bit words, or 64-bit words for max above 2^32.

Normals

Normals use the 1024-layer ziggurat: element i comes from the 64-bit draw i, a draw outside the inner rectangles continues on a fallback generator keyed by its global draw index, and a fill cut at any element equals the whole fill.

Exponentials

Exponentials follow Appendix A of the specification: element i is -log(1 - u) / rate for the Float64 draw u number i, one draw each, so a fill is random access and uses exactly n draws. At rate = 1 the values are bit identical across ports. Base R has no user-supplied hook for exponentials, so rexp() after RNGkind("user-supplied") runs R's own algorithm on the Tandem uniforms and does not return them.