# [plt-scheme] order of magnitude

Some browsing did not lead me to finding a function that accepts an exact positive rational number and returns its order of magnitude (an exact integer number) Something like:
(define log10 (inexact->exact (log 10)))
(define (order-of-magnitude q) (floor (/ (inexact->exact (log q)) log10)))
However, due to inexactness of function log we find:
(/ (inexact->exact (log #e1000e1000000)) log10) --> close to but sligtly less than 1000003
and hence:
(order-of-magnitude #e1000e1000000) ; --> 1000002
The wanted answer is 1000003. So I did the following:
(define order-of-magnitude
(let*
((log10 (inexact->exact (log 10)))
(10log (λ (q) (/ (inexact->exact (log q)) log10))))
(λ (q)
(unless (and (rational? q) (exact? q) (positive? q))
(raise-type-error 'magnitude "positive exact rational number" q))
(let* ((m (floor (10log q))) (k (expt 10 m)))
; From now on all arithmetic operations and their operands are exact.
(let loop ((m m) (lower (* k 1/10)) (middle k) (upper (* k 10)))
(cond
((<= q lower) (loop (sub1 m) (* lower 1/10) lower middle))
((>= q upper) (loop (add1 m) middle upper (* upper 10)))
(else m)))))))
(order-of-magnitude #e1000e1000000) ; --> 1000003
However, this seems rather complicated. Does someone have or know of a simpler and faster function for this purpose?
Thanks, Jos
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