f2dc2027f6
in the original GitHub fork: https://github.com/ntoronto/racket Some things about this are known to be broken (most egregious is that the array tests DO NOT RUN because of a problem in typed/rackunit), about half has no coverage in the tests, and half has no documentation. Fixes and docs are coming. This is committed now to allow others to find errors and inconsistency in the things that appear to be working, and to give the author a (rather incomplete) sense of closure.
42 lines
1.4 KiB
Racket
42 lines
1.4 KiB
Racket
#lang typed/racket/base
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;; Computes the lower gamma series (found by unfolding its recursive characterization infinitely)
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(require "../../../flonum.rkt"
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"../log-gamma.rkt"
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"gamma-utils.rkt")
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(provide flgamma-lower-series fllog-gamma-lower-series get-series-iters)
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(define: series-iters : Flonum 0.0)
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(define (get-series-iters) series-iters)
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(: flgamma-lower-iter (Float Float -> Float))
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(define (flgamma-lower-iter k x)
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(let: loop : Float ([y : Float 0.0]
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[dy : Float (fl/ x (fl+ k 1.0))]
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[i : Float 0.0])
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(define new-y (fl+ y dy))
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(cond [(or (not (rational? new-y))
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((flabs dy) . fl<= . (flabs (fl* epsilon.0 new-y))))
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(set! series-iters i)
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new-y]
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[else
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(loop new-y (fl/ (fl* dy x) (fl+ (fl+ 2.0 i) k)) (fl+ i 1.0))])))
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(: flgamma-lower-series (Float Float -> Float))
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(define (flgamma-lower-series k x)
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(set! series-iters 0.0)
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(define z (flgamma-series-const k x))
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(cond [(fl= z 0.0) 0.0]
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[else
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(define y (flgamma-lower-iter k x))
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;; Avoid adding 1.0 if y is near zero
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(if (y . fl< . 1.0) (fl+ z (fl* z y)) (fl* z (fl+ y 1.0)))]))
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(: fllog-gamma-lower-series (Float Float -> Float))
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(define (fllog-gamma-lower-series k x)
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(define y (flgamma-lower-iter k x))
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(define log-z (fllog-gamma-series-const k x))
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(fl+ log-z (fllog1p (fl y))))
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