e55a31480e
additions/changes * More accurate `flulp-error' * Added `flonum->fields', `fields->flonum', `flonum->sig+exp', `sig+exp->flonum' (currently undocumented) * Correctly rounded, robust `bigfloat->fl2' and `fl2' * Correctly rounded, robust `fl+/error', `fl-/error', `fl*/error', `flsqr/error', `fl//error' * Much faster but slightly less accurate fl2 ops (shamelessly stolen from crlibm, which is LGPL) * Added `fl2ulp', `fl2ulp-error', `fl2?' (which detects overlap), `+max-fl2-subnormal.0' (which was tricky), `fl2abs' * Added deterministic and randomized flonum op tests (against MPFR) * Added deterministic and randomized flonum/error op tests (against MPFR) * Added deterministic and randomized fl2 op tests (against MPFR) * Exposed FPU tests in `math/utils' (currently undocumented)
108 lines
3.9 KiB
Racket
108 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-error.rkt"
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"flvector.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-x . fl< . log-y) +nan.0]
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[(fl= log-x -inf.0) -inf.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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