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.
107 lines
3.9 KiB
Racket
107 lines
3.9 KiB
Racket
#lang typed/racket/base
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(require racket/performance-hint
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(only-in racket/math pi)
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"flonum-functions.rkt"
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"flonum-constants.rkt"
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"flonum-exp.rkt"
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"flonum-sum.rkt"
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"flonum-syntax.rkt")
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(provide fllog1p fllog+
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lg1+ lg+ lg1- lg- lgsum
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fllog-quotient)
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(begin-encourage-inline
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(: fllog1p (Float -> Float))
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;; Computes the value of log(1+x) in a way that is accurate for small x
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(define (fllog1p x)
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(define ax (flabs x))
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(cond [(ax . fl>= . 1.0) (fllog (fl+ 1.0 x))]
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[(ax . fl>= . (fl* 0.5 epsilon.0))
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(define y (fl+ 1.0 x))
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(fl- (fllog y) (fl/ (fl- (fl- y 1.0) x) y))]
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[else x]))
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(: fllog+ (Flonum Flonum -> Flonum))
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;; Computes log(a+b) in a way that is accurate for a+b near 1.0
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(define (fllog+ a b)
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(define a+b (+ a b))
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(cond [((flabs (- a+b 1.0)) . < . (fllog 2.0))
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;; a+b is too close to 1.0, so compute in higher precision
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(define-values (a+b a+b-lo) (fast-fl+/error a b))
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(- (fllog a+b) (fllog1p (- (/ a+b-lo a+b))))]
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[(a+b . = . +inf.0)
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;; a+b overflowed, so reduce the arguments
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(+ (fllog 2.0) (fllog (+ (* 0.5 a) (* 0.5 b))))]
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[else
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(fllog a+b)]))
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(: lg1+ (Float -> Float))
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(define (lg1+ log-x)
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(cond [(log-x . fl>= . 0.0) (fl+ log-x (fllog1p (flexp (- log-x))))]
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[else (fllog1p (flexp log-x))]))
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(: lg+ (Float Float -> Float))
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(define (lg+ log-x log-y)
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(let ([log-x (flmax log-x log-y)]
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[log-y (flmin log-x log-y)])
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(cond [(fl= log-x -inf.0) -inf.0]
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[else (fl+ log-x (fllog1p (flexp (fl- log-y log-x))))])))
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(: lg1- (Float -> Float))
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(define (lg1- log-x)
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(cond [(log-x . fl> . (fllog 0.5)) (fllog (- (flexpm1 log-x)))]
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[else (fllog1p (- (flexp log-x)))]))
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(: lg- (Float Float -> Float))
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(define (lg- log-x log-y)
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(cond [(log-y . fl> . log-x) +nan.0]
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[else (fl+ log-x (lg1- (fl- log-y log-x)))]))
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) ; begin-encourage-inline
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(: flmax* ((Listof Flonum) -> Flonum))
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(define (flmax* xs)
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(let loop ([xs xs] [mx -inf.0])
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(if (null? xs) mx (loop (cdr xs) (flmax mx (car xs))))))
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(: lgsum ((Listof Flonum) -> Flonum))
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(define (lgsum log-xs)
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(if (null? log-xs)
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0.0
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(let ([log-x0 (car log-xs)]
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[log-xs (cdr log-xs)])
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(if (null? log-xs)
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log-x0
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(let ([log-x1 (car log-xs)]
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[log-xs (cdr log-xs)])
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(if (null? log-xs)
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(lg+ log-x0 log-x1)
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(let ([max-log-x (flmax (flmax log-x0 log-x1) (flmax* log-xs))])
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(if (fl= max-log-x -inf.0)
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-inf.0
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(let ([s (flsum
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(list* -1.0 ; for the max element; faster than removing it
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(flexp (- log-x0 max-log-x))
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(flexp (- log-x1 max-log-x))
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(map (λ: ([log-x : Flonum]) (flexp (- log-x max-log-x)))
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log-xs)))])
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;; Yes, we subtract 1.0 and then add 1.0 before taking the log; this
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;; helps with precision a bit when s is near zero
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(+ max-log-x (fllog1p s)))))))))))
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(: fllog-quotient (Flonum Flonum -> Flonum))
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;; Computes (fllog (/ x y)) in a way that reduces error and avoids under-/overflow
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(define (fllog-quotient x y)
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(let ([x (flabs x)]
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[y (flabs y)]
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[s (fl/ (flsgn x) (flsgn y))])
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(cond [(s . fl> . 0.0)
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(define z (fl/ x y))
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(cond [(and (z . fl> . +max-subnormal.0) (z . fl< . +inf.0)) (fllog (fl* s z))]
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[else (fl+ (fllog x) (- (fllog y)))])]
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[(s . fl= . 0.0) -inf.0]
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[else +nan.0])))
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