60dd8d065f
renamed `partition-count' to `partitions' to be consistent with `permutations', and gave better examples in `multinomial' docs * (flulp-error +inf.0 +nan.0) was returning +nan.0 instead of +inf.0 * Type of `multinomial' didn't match its docs or `flmultinomial' * Reworded docs for `diagonal-array' * Reworked/reordered quite a few things in docs for `math/bigfloat' * Fixed first identity given in `gamma-inc' docs * Fixed descrption for `+max.0', etc.
68 lines
2.6 KiB
Racket
68 lines
2.6 KiB
Racket
#lang typed/racket/base
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(require "../unsafe.rkt")
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(provide factorial permutations multinomial)
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(define-predicate nonnegative-fixnum? Nonnegative-Fixnum)
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;; The number of factorials whose flonum representation is finite
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;; Makes generating the flonum table in gamma.rkt fast
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(: fact-table-size Positive-Fixnum)
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(define fact-table-size 171)
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(: fact-table (Vectorof Positive-Integer))
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(define fact-table
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(list->vector
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(reverse
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(foldl (λ: ([n : Positive-Integer]
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[ns : (Listof Positive-Integer)])
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(cons (* n (car ns)) ns))
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'(1)
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(build-list (- fact-table-size 1) add1)))))
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(: simple-cutoff Positive-Fixnum)
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;; The point at which it seems to be faster to use a more complicated recurrence
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(define simple-cutoff 244)
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(: factorial-simple (Nonnegative-Fixnum -> Positive-Integer))
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(define (factorial-simple n)
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(cond [(n . < . fact-table-size) (vector-ref fact-table n)]
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[else (* n (factorial-simple (- n 1)))]))
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(: factorial (case-> (Zero -> One)
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(One -> One)
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(Integer -> Positive-Integer)))
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(define (factorial n)
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(cond [(negative? n) (raise-argument-error 'factorial "Natural" n)]
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[(not (fixnum? n)) (raise-argument-error 'factorial "Nonnegative-Fixnum" n)]
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[(eqv? n 0) 1]
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[(eqv? n 1) 1]
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[(n . < . simple-cutoff) (factorial-simple n)]
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[else
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(let: loop : Positive-Integer ([n : Positive-Fixnum n]
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[m : Positive-Fixnum 1])
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(define n-m (- n m))
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(cond [(n-m . <= . 0) n]
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[else (define 2m (unsafe-fx* m 2))
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(* (loop n 2m) (loop n-m 2m))]))]))
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(: permutations (case-> (Integer Zero -> One)
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(One One -> One)
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(Integer Integer -> Natural)))
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(define (permutations n k)
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(cond [(negative? n) (raise-argument-error 'permutations "Natural" 0 n k)]
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[(negative? k) (raise-argument-error 'permutations "Natural" 1 n k)]
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[(zero? k) 1]
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[(k . > . n) 0]
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[else (assert (/ (factorial n) (factorial (- n k)))
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exact-nonnegative-integer?)]))
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(: multinomial (Integer (Listof Integer) -> Natural))
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(define (multinomial n ks)
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(cond [(negative? n) (raise-argument-error 'multinomial "Natural" 0 n ks)]
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[(ormap negative? ks) (raise-argument-error 'multinomial "(Listof Natural)" 1 n ks)]
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[(not (= n (apply + ks))) 0]
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[else (assert (apply / (factorial n) (map factorial ks))
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exact-nonnegative-integer?)]))
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