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Safe addition: Difference between revisions
→{{header|Racket}}
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>>> fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
1.0</lang>
=={{header|Racket}}==
<lang Racket>
#lang racket
;; 1. Racket has exact unlimited integers and fractions, which can be
;; used to perform exact operations. For example, given an inexact
;; flonum, we can convert it to an exact fraction and work with that:
(define (exact+ x y)
(+ (inexact->exact x) (inexact->exact y)))
;; (A variant of this would be to keep all numbers exact, so the default
;; operations never get to inexact numbers)
;; 2. We can implement the required operation using a bunch of
;; functionality provided by the math library, for example, use
;; `flnext' and `flprev' to get the surrounding numbers for both
;; inputs and use them to produce the resulting interval:
(require math)
(define (interval+ x y)
(cons (+ (flprev x) (flprev y)) (+ (flnext x) (flnext y))))
(interval+ 1.14 2000.0) ; -> '(2001.1399999999999 . 2001.1400000000003)
;; (Note: I'm not a numeric expert in any way, so there must be room for
;; improvement here...)
;; 3. Yet another option is to use the math library's bigfloats, with an
;; arbitrary precision:
(bf-precision 1024) ; 1024 bit floats
;; add two numbers, specified as strings to avoid rounding of number
;; literals
(bf+ (bf "1.14") (bf "2000.0"))
</lang>
=={{header|REXX}}==
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