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.
103 lines
3.5 KiB
Racket
103 lines
3.5 KiB
Racket
#lang typed/racket/base
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(require racket/flonum
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"../flonum/flonum-sum.rkt"
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"../flonum/flonum-functions.rkt"
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"../flonum/flonum-more-functions.rkt")
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(provide power-of-two?
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absolute-error
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relative-error
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sum
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asinh acosh atanh)
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;; Returns #t if x is an integer power of 2
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(: power-of-two? (Real -> Boolean))
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(define (power-of-two? x)
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(cond [(not (positive? x)) #f]
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[(flonum? x) (fl= x (flexpt 2.0 (flround (fl/ (fllog x) (fllog 2.0)))))]
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[(single-flonum? x) (power-of-two? (fl x))]
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[(integer? x) (= x (expt 2 (- (integer-length x) 1)))]
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[else (and (= 1 (numerator x))
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(power-of-two? (denominator x)))]))
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(: fix-exact-return (Real Real Real -> Real))
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(define (fix-exact-return x r e)
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(cond [(or (single-flonum? x) (single-flonum? r)) (real->single-flonum e)]
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[(or (flonum? x) (flonum? r)) (fl e)]
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[else e]))
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(: absolute-error (Real Real -> Real))
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(define (absolute-error x r)
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(fix-exact-return
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x r (cond [(eqv? x r) 0]
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[(and (rational? x) (rational? r))
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(abs (- (inexact->exact x) (inexact->exact r)))]
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[else +inf.0])))
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(: relative-error (Real Real -> Real))
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(define (relative-error x r)
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(fix-exact-return
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x r (cond [(eqv? x r) 0]
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[(and (zero? x) (zero? r)) 0]
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[(zero? r) +inf.0]
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[(and (rational? x) (rational? r))
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(define exact-r (inexact->exact r))
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(abs (/ (- (inexact->exact x) exact-r) exact-r))]
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[else +inf.0])))
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(: sum ((Listof Real) -> Real))
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(define (sum xs)
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(let loop ([xs xs]
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[#{r : Exact-Rational} 0]
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[#{fs : (Listof Flonum)} null])
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(cond [(null? xs)
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(cond [(null? fs) r]
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[(zero? r) (flsum fs)]
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[else (fl (+ r (inexact->exact (flsum fs))))])]
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[else
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(let ([x (car xs)]
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[xs (cdr xs)])
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(cond [(double-flonum? x) (loop xs r (cons x fs))]
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[(single-flonum? x) (loop xs r (cons (fl x) fs))]
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[else (loop xs (+ x r) fs)]))])))
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;; ===================================================================================================
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;; Inverse hyperbolic
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(: asinh (case-> (Zero -> Zero)
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(Float -> Float)
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(Real -> Real)
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(Float-Complex -> Float-Complex)
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(Number -> Number)))
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(define (asinh x)
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(cond [(flonum? x) (flasinh x)]
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[(eqv? x 0) 0]
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[(real? x) (flasinh (fl x))]
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[(float-complex? x) (log (+ x (sqrt (+ (* x x) 1.0))))]
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[else (log (+ x (sqrt (+ (* x x) 1))))]))
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(: acosh (case-> (One -> Zero)
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(Float -> Float)
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(Real -> Number)
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(Float-Complex -> Float-Complex)
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(Number -> Number)))
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(define (acosh x)
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(cond [(flonum? x) (flacosh x)]
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[(eqv? x 1) 0]
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[(and (real? x) (x . >= . 1)) (flacosh (fl x))]
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[(float-complex? x) (log (+ x (* (sqrt (+ x 1.0)) (sqrt (- x 1.0)))))]
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[else (log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))]))
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(: atanh (case-> (Zero -> Zero)
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(Float -> Float)
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(Real -> Real)
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(Float-Complex -> Float-Complex)
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(Number -> Number)))
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(define (atanh x)
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(cond [(flonum? x) (flatanh x)]
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[(eqv? x 0) 0]
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[(real? x) (flatanh (fl x))]
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[(float-complex? x) (* 0.5 (- (log (+ 1.0 x)) (log (- 1.0 x))))]
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[else (* 1/2 (- (log (+ 1 x)) (log (- 1 x))))]))
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