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.
124 lines
4.8 KiB
Racket
124 lines
4.8 KiB
Racket
#lang typed/racket/base
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Rational Chebyshev Approximations for the Inverse of the Error Function
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J. M. Blair, C. A. Edwards and J. H. Johnson
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Mathematics of Computation, Vol. 30, No. 136 (Oct., 1976), pp. 827-830
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Cribbed from LGPL Fortran implementation in:
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ALGORITHM 715: SPECFUN - A Portable FORTRAN Package of Special Function Routines and Test Drivers
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W. J. Cody
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ACM Transactions on Mathematical Software, Vol. 19 (1993), pp. 22-32
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Error is <= 3 ulps for both log and non-log functions
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|#
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(require "../../../flonum.rkt"
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"../../../base.rkt"
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"normal-utils.rkt")
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(provide standard-flnormal-log-cdf
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standard-flnormal-cdf)
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(: R0 (Float Any -> Float))
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(define (R0 x log?)
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(cond [log? (if (x . >= . 0.0)
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(lg+ (fllog 0.5) (lg/ (fllog x) logsqrt2pi.0))
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(lg- (fllog 0.5) (lg/ (fllog (- x)) logsqrt2pi.0)))]
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[else (+ 0.5 (/ x sqrt2pi.0))]))
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(: R1 (Float Any -> Float))
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(define (R1 x log?)
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(define x^2 (fl* x x))
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(let* ([r 6.5682337918207449113e-2]
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[r (fl+ (fl* r x^2) 2.2352520354606839287e0)]
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[r (fl+ (fl* r x^2) 1.6102823106855587881e2)]
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[r (fl+ (fl* r x^2) 1.0676894854603709582e3)]
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[r (fl+ (fl* r x^2) 1.8154981253343561249e4)]
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[s 1.0]
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[s (fl+ (fl* s x^2) 4.7202581904688241870e1)]
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[s (fl+ (fl* s x^2) 9.7609855173777669322e2)]
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[s (fl+ (fl* s x^2) 1.0260932208618978205e4)]
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[s (fl+ (fl* s x^2) 4.5507789335026729956e4)])
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(cond [log? (if (x . fl>= . 0.0)
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(lg+ (fllog 0.5) (lg* (fllog x) (lg/ (fllog r) (fllog s))))
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(lg- (fllog 0.5) (lg* (fllog (- x)) (lg/ (fllog r) (fllog s)))))]
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[else (fl+ 0.5 (fl* x (fl/ r s)))])))
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(: R2-post (Flonum Flonum Any -> Flonum))
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(define (R2-post x q log?)
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(cond [log?
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(cond [(x . fl> . 0.0) (fllog1p (- (fl* (flexp-1/2*x^2 x) q)))]
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[else (fl+ (fl* (fl* -0.5 x) x) (fllog q))])]
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[else
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(define z (fl* (flexp-1/2*x^2 x) q))
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(if (x . fl> . 0.0) (fl- 1.0 z) z)]))
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(: R2 (Float Any -> Float))
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(define (R2 x log?)
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(define y (flabs x))
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(let* ([r 1.0765576773720192317e-8]
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[r (fl+ (fl* r y) 3.9894151208813466764e-1)]
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[r (fl+ (fl* r y) 8.8831497943883759412e0)]
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[r (fl+ (fl* r y) 9.3506656132177855979e1)]
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[r (fl+ (fl* r y) 5.9727027639480026226e2)]
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[r (fl+ (fl* r y) 2.4945375852903726711e3)]
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[r (fl+ (fl* r y) 6.8481904505362823326e3)]
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[r (fl+ (fl* r y) 1.1602651437647350124e4)]
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[r (fl+ (fl* r y) 9.8427148383839780218e3)]
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[s 1.0]
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[s (fl+ (fl* s y) 2.2266688044328115691e1)]
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[s (fl+ (fl* s y) 2.3538790178262499861e2)]
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[s (fl+ (fl* s y) 1.5193775994075548050e3)]
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[s (fl+ (fl* s y) 6.4855582982667607550e3)]
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[s (fl+ (fl* s y) 1.8615571640885098091e4)]
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[s (fl+ (fl* s y) 3.4900952721145977266e4)]
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[s (fl+ (fl* s y) 3.8912003286093271411e4)]
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[s (fl+ (fl* s y) 1.9685429676859990727e4)])
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(R2-post x (fl/ r s) log?)))
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(: R3 (Float Any -> Float))
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(define (R3 x log?)
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(define x^2 (fl/ (fl/ 1.0 x) x))
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(let* ([r 2.307344176494017303e-2]
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[r (fl+ (fl* r x^2) 2.158985340579569900e-1)]
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[r (fl+ (fl* r x^2) 1.274011611602473639e-1)]
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[r (fl+ (fl* r x^2) 2.223527787064980700e-2)]
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[r (fl+ (fl* r x^2) 1.421619193227893466e-3)]
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[r (fl+ (fl* r x^2) 2.9112874951168792e-5)]
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[s 1.0]
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[s (fl+ (fl* s x^2) 1.28426009614491121e0)]
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[s (fl+ (fl* s x^2) 4.68238212480865118e-1)]
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[s (fl+ (fl* s x^2) 6.59881378689285515e-2)]
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[s (fl+ (fl* s x^2) 3.78239633202758244e-3)]
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[s (fl+ (fl* s x^2) 7.29751555083966205e-5)])
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(R2-post x (fl/ (fl- 1/sqrt2pi.0 (fl* x^2 (fl/ r s)))
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(flabs x))
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log?)))
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(: standard-flnormal-log-cdf (Float -> Float))
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(define (standard-flnormal-log-cdf x)
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(define y (flabs x))
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(cond [(y . fl<= . 1e-5) (R0 x #t)]
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[(y . fl<= . 0.6744897501960817) (R1 x #t)]
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[(y . fl<= . (flsqrt 32.0)) (R2 x #t)]
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[(x . fl< . -standard-normal-log-cdf-max.0) -inf.0]
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[(x . fl> . +standard-normal-log-cdf-max.0) 0.0]
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[else (R3 x #t)]))
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(: standard-flnormal-cdf (Float -> Float))
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(define (standard-flnormal-cdf x)
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(define y (flabs x))
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(cond [(y . fl<= . 1e-16) 0.5]
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[(y . fl<= . 1e-6) (R0 x #f)]
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[(y . fl<= . 0.6744897501960817) (R1 x #f)]
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[(y . fl<= . (flsqrt 32.0)) (R2 x #f)]
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[(x . fl< . -38.456870800437045)
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(cond [(x . fl< . -standard-normal-cdf-max.0) 0.0]
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[else +min.0])]
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[(x . fl> . 8.160707840858583)
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(cond [(x . fl> . +standard-normal-cdf-max.0) 1.0]
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[else 0.9999999999999999])]
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[else (R3 x #f)]))
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