Joseph Ferano
a0278378ab
rand-int, rand, rand-bool, rand-int-range and rand-float-range, at the widths the author ruled: a u64 draw and an f64 in [0, 1). rand-seed and rand-state keep their names. The four old names are not names, and each is refused by the one that is, with a call that compiles — in both the call and the bare-name position, because a Lisp-1 makes the second a real thing to write. The generator's step is untouched, so a seed means what it meant. Its output function is not: PCG-XSH-RR folded the state to 32 bits, and no honest u64 or 53-bit f64 comes out of 32 bits without a second step. PCG-RXS-M-XS 64 answers 64 from the same one, so all five still cost exactly one draw and a seeded run is reproducible. The price, written where it lives: the permutation is a bijection of the state, which is what 64 output bits from 64 state bits costs. The sequence is therefore a different one, and programs/rand.flan pins it — reproducibility across the five, the single-draw cost of each, the half-open boundaries, and rand-bool's count over a thousand flips. sand.flan is not touched. It calls rand-f32, so the cases that compile or re-evaluate it skip themselves on the fixture rather than on a comment: fix its two calls and every one of them runs again. Its hash is the old generator's grid and gets re-taken then.
103 lines
4.1 KiB
Plaintext
103 lines
4.1 KiB
Plaintext
;;;; The five randomness functions, pinned.
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;;;;
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;;;; Three properties are asserted here and each is asserted as a *number* off
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;;;; a fixed seed rather than as a range, because a range would still pass if
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;;;; the derivation changed under it:
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;;;;
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;;;; 1. A seed fixes the sequence. The same five calls after the same seed
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;;;; print the same five lines.
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;;;; 2. A call that answers a number costs exactly one draw. Each block seeds,
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;;;; makes one call, and prints the *next* rand-int: all five print the
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;;;; same number, which is only true if each consumed one step of the
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;;;; generator. The one call that is not a draw is the one that is not a
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;;;; number — a range with nothing in it answers lo and leaves the
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;;;; generator where it was, which is asserted under 3.
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;;;; 3. The ranges are half-open and never divide by zero: [5, 5) and a
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;;;; reversed range answer lo, a range of one always answers lo, a loop
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;;;; over [0, 4) never produces 4, and the whole of i64 is a range like any
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;;;; other — its span only exists by wrapping.
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;;;;
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;;;; And rand-bool over a thousand draws, which is the only one of the five
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;;;; whose distribution a single number can check.
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(defn main [] i32
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;; 1. Reproducibility: two identical blocks, and therefore two identical
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;; pairs of lines in the expected output.
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(dotimes [round 2]
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(rand-seed 20260921)
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(print (rand-int)) (print " ")
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(print (rand)) (print " ")
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(print (rand-bool)) (print " ")
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(print (rand-int-range -10 10)) (print " ")
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(print (rand-float-range 2.0 3.0))
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(println ""))
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;; 2. One draw each. The first line is the second draw after seed 1, and
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;; every line under it is that same draw reached through a different one of
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;; the five.
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(rand-seed 1) (rand-int) (println (rand-int))
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(rand-seed 1) (rand) (println (rand-int))
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(rand-seed 1) (rand-bool) (println (rand-int))
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(rand-seed 1) (rand-int-range 0 100) (println (rand-int))
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(rand-seed 1) (rand-float-range 0.0 1.0) (println (rand-int))
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;; 3. The boundaries. An empty range, a reversed one, and a range of one
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;; answer lo without dividing; a range at the extremes of i64 still lands
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;; inside it.
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(print (rand-int-range 5 5)) (print " ")
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(print (rand-int-range 5 -5)) (print " ")
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(let [ones 0]
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(dotimes [i 20]
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(when (= (rand-int-range 7 8) 7) (set ones (+ ones 1))))
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(print ones))
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(println "")
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;; And an empty range is not a draw: two of them either side of a rand-int
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;; leave it the number it would have been on its own. Seeded twice so the
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;; two lines are the same number, which is the whole assertion.
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(rand-seed 1) (println (rand-int))
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(rand-seed 1)
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(rand-int-range 5 5)
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(rand-int-range 9 -9)
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(println (rand-int))
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;; And the widest range there is. hi - lo is 2^64 - 1 here and only reaches
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;; that by wrapping, which is what the u64 it is read as makes right: the
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;; answer has to be an i64 and not a number outside one.
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(rand-seed 3)
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(println (rand-int-range -9223372036854775808 9223372036854775807))
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;; hi is excluded, and lo is reachable: over 2000 draws on [0, 4) the top
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;; value seen is 3 and the bottom is 0.
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(let [top 0
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bottom 3
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fours 0]
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(dotimes [i 2000]
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(let [v (i32 (rand-int-range 0 4))]
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(set top (max top v))
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(set bottom (min bottom v))
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(when (= v 4) (set fours (+ fours 1)))))
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(print top) (print " ") (print bottom) (print " ") (print fours)
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(println ""))
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;; The float range is half-open for the same reason: rand never reaches 1.0,
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;; so nothing here reaches hi.
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(let [over 0]
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(dotimes [i 2000]
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(let [v (rand-float-range -1.0 1.0)]
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(when (or (>= v 1.0) (< v -1.0)) (set over (+ over 1)))))
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(print over)
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(println ""))
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;; rand-bool over a thousand draws. The count is pinned, and a fair coin puts
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;; it near 500 — a generator that had lost a bit would sit at 0 or 1000, and
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;; one biased enough to matter would miss the band.
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(rand-seed 99)
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(let [heads 0]
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(dotimes [i 1000]
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(when (rand-bool) (set heads (+ heads 1))))
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(print heads) (print " ")
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(print (and (> heads 450) (< heads 550)))
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(println ""))
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0)
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