racket/collects/plot/common/ticks.rkt
2011-11-10 12:59:41 -07:00

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#lang racket/base
;; Data structure that represents a tick, and functions that produce ticks.
(require racket/string racket/list racket/contract racket/pretty racket/match
"math.rkt"
"format.rkt"
"utils.rkt"
"contract.rkt"
"contract-doc.rkt"
"date-time.rkt"
"axis-transform.rkt"
"currency.rkt")
(provide (struct-out pre-tick) (struct-out tick) (struct-out ticks)
;; No ticks
no-ticks-layout no-ticks-format no-ticks
;; Linear ticks
linear-ticks-base linear-ticks-divisors
linear-ticks-layout linear-ticks-format linear-ticks
;; Uniform ticks
uniform-ticks-layout uniform-ticks
;; Log-scale ticks
log-ticks-base
log-ticks-layout log-ticks-format log-ticks
;; Date ticks
date-ticks-formats 24h-descending-date-ticks-formats 12h-descending-date-ticks-formats
date-ticks-layout date-ticks-format date-ticks
;; Time ticks
time-ticks-formats descending-time-ticks-formats
time-ticks-layout time-ticks-format time-ticks
;; Bit/byte ticks
bit/byte-ticks-format bit/byte-ticks
;; Currency ticks and formats
currency-scale-suffixes
us-currency-scale-suffixes uk-currency-scale-suffixes eu-currency-scale-suffixes
currency-format-strings
us-currency-format-strings uk-currency-format-strings eu-currency-format-strings
currency-ticks-format currency-ticks
;; Fractions
fraction-ticks-format fraction-ticks
)
(define-struct/contract pre-tick ([value real?] [major? boolean?]) #:transparent)
(define-struct/contract (tick pre-tick) ([label string?]) #:transparent)
(defcontract ticks-layout/c
(real? real? exact-positive-integer? axis-transform/c . -> . (listof pre-tick?)))
(defcontract ticks-format/c
(real? real? (listof pre-tick?) . -> . (listof string?)))
(define-struct/contract ticks ([layout ticks-layout/c] [format ticks-format/c]) #:transparent
#:property prop:procedure
(λ (t x-min x-max max-ticks transform)
(match-define (ticks layout format) t)
(define ts (layout x-min x-max max-ticks transform))
(match-define (list (pre-tick xs majors) ...) ts)
(map tick xs majors (format x-min x-max ts))))
;; ===================================================================================================
;; Helpers
(define-syntax-rule (with-exact-bounds x-min x-max body ...)
(cond [(x-min . >= . x-max)
(error 'bounds-check "expected min < max; given min = ~e and max = ~e" x-min x-max)]
[else (let ([x-min (inexact->exact x-min)]
[x-max (inexact->exact x-max)])
body ...)]))
(define (linear-seq-args x-min x-max step)
(define start (* (ceiling (/ x-min step)) step))
(define end (* (floor (/ x-max step)) step))
(define num (+ 1 (inexact->exact (round (/ (- end start) step)))))
(values start end num))
(define (linear-major-values/step x-min x-max step)
(define-values (start end num) (linear-seq-args x-min x-max step))
(linear-seq start end num))
(defproc (linear-minor-values/step [major-xs (listof real?)] [major-step real?]
[minor-ticks exact-nonnegative-integer?]) (listof real?)
(cond [(or (zero? minor-ticks) (empty? major-xs)) empty]
[else
(define major-start (first major-xs))
(define minor-step (/ major-step (+ minor-ticks 1)))
(for*/list ([x (in-list (cons (- major-start major-step) major-xs))]
[i (in-range 1 (+ minor-ticks 1))])
(+ x (* i minor-step)))]))
(defproc (tick-values->pre-ticks [major-xs (listof real?)] [minor-xs (listof real?)]
) (listof pre-tick?)
(define major-ts (map (λ (x) (pre-tick x #t)) major-xs))
(define minor-ts (map (λ (x) (pre-tick x #f)) minor-xs))
(sort (append major-ts minor-ts) < #:key pre-tick-value))
;; ===================================================================================================
;; No ticks
(defthing no-ticks-layout ticks-layout/c
(λ (x-min x-max max-ticks transform)
empty))
(defthing no-ticks-format ticks-format/c
(λ (x-min x-max ts)
empty))
(defthing no-ticks ticks?
(ticks no-ticks-layout no-ticks-format))
;; ===================================================================================================
;; Linear ticks (default tick function, evenly spaced)
(defparam linear-ticks-base (and/c exact-integer? (>=/c 2)) 10)
(defparam linear-ticks-divisors (listof exact-positive-integer?) '(1 2 5))
(defproc (linear-tick-step+divisor [x-min real?] [x-max real?]
[max-ticks exact-positive-integer?]
[base (and/c exact-integer? (>=/c 2))]
[divisors (listof exact-positive-integer?)]
) (values real? exact-positive-integer?)
(define range (- x-max x-min))
(define mag (expt base (floor-log/base base range)))
(define ds (sort divisors >))
(let/ec break
(for* ([e (in-range (floor-log/base base max-ticks) -2 -1)]
[d (in-list ds)])
;(printf "new-d = ~v~n" (* d (expt base e)))
(define step (/ mag d (expt base e)))
(define-values (_start _end num) (linear-seq-args x-min x-max step))
(when (num . <= . max-ticks)
(break step d)))
;(printf "default!~n")
(values (/ range max-ticks) max-ticks)))
(defproc (linear-tick-values [x-min real?] [x-max real?]
[max-ticks exact-positive-integer?]
[base (and/c exact-integer? (>=/c 2))]
[divisors (listof exact-positive-integer?)]
) (values (listof real?) (listof real?))
(with-exact-bounds
x-min x-max
(define-values (step d) (linear-tick-step+divisor x-min x-max max-ticks base divisors))
(define major-xs (linear-major-values/step x-min x-max step))
(define major-ticks (length major-xs))
(define ns (filter (λ (n) (zero? (remainder (* n d) base))) divisors))
(define n
(cond [(empty? ns) 1]
[else (argmin (λ (n) (abs (- (* n major-ticks) max-ticks))) (sort ns <))]))
(define minor-xs (linear-minor-values/step major-xs step (- n 1)))
(values major-xs (filter (λ (x) (<= x-min x x-max)) minor-xs))))
(defproc (linear-ticks-layout [#:base base (and/c exact-integer? (>=/c 2)) (linear-ticks-base)]
[#:divisors divisors (listof exact-positive-integer?)
(linear-ticks-divisors)]
) ticks-layout/c
(λ (x-min x-max max-ticks transform)
(define-values (major-xs minor-xs) (linear-tick-values x-min x-max max-ticks base divisors))
(tick-values->pre-ticks major-xs minor-xs)))
(defproc (linear-ticks-format) ticks-format/c
(λ (x-min x-max ts)
(with-exact-bounds
x-min x-max
(define digits (digits-for-range x-min x-max))
(for/list ([t (in-list ts)])
(real->plot-label (pre-tick-value t) digits)))))
(defproc (linear-ticks [#:base base (and/c exact-integer? (>=/c 2)) (linear-ticks-base)]
[#:divisors divisors (listof exact-positive-integer?) (linear-ticks-divisors)]
) ticks?
(ticks (linear-ticks-layout #:base base #:divisors divisors)
(linear-ticks-format)))
;; ===================================================================================================
;; Uniform spacing ticks
(defproc (uniform-ticks-layout [#:layout layout ticks-layout/c (linear-ticks-layout)]) ticks-layout/c
(λ (x-min x-max max-ticks transform)
(define ts (layout x-min x-max max-ticks transform))
(define xs (map pre-tick-value ts))
(define majors (map pre-tick-major? ts))
(define new-xs (map (invertible-function-finv (apply-transform transform x-min x-max)) xs))
(map pre-tick new-xs majors)))
(defproc (uniform-ticks [#:layout layout ticks-layout/c (linear-ticks-layout)]) ticks?
(ticks (uniform-ticks-layout #:layout layout)
(linear-ticks-format)))
;; ===================================================================================================
;; Exponential ticks (use for log scale)
(defparam log-ticks-base (and/c exact-integer? (>=/c 2)) 10)
(defproc (log-ticks-layout [#:base base (and/c exact-integer? (>=/c 2)) (log-ticks-base)]
) ticks-layout/c
(λ (x-min x-max max-ticks transform)
(with-exact-bounds
x-min x-max
(when ((exact->inexact x-min) . <= . 0)
(raise-type-error 'log-ticks-layout "positive real" 0 x-min x-max))
(define log-start (floor-log/base base x-min))
(define log-end (ceiling-log/base base x-max))
(define log-xs (for/list ([i (in-range log-start (add1 log-end))]) i))
(define skip (max 1 (floor (/ (+ (length log-xs) 2) 5))))
(filter (λ (t) (<= x-min (pre-tick-value t) x-max))
(append*
(for/list ([log-x (in-list log-xs)]
[m (in-cycle (in-range skip))])
(define x (expt base log-x))
(cond [(= skip 1) (for/list ([i (in-range 0 (sub1 base) skip)])
(pre-tick (+ x (* i x))
(and (zero? i) (zero? m))))]
[else (list (cond [(zero? m) (pre-tick x #t)]
[else (pre-tick x #f)]))])))))))
(defproc (log-ticks-format [#:base base (and/c exact-integer? (>=/c 2)) (log-ticks-base)]
) ticks-format/c
(define base-str (number->string base))
(λ (x-min x-max ts)
(with-exact-bounds
x-min x-max
(define epsilon (expt 10 (- (digits-for-range x-min x-max))))
(define base-digits (digits-for-range 0 base))
(for/list ([t (in-list ts)])
(define x (pre-tick-value t))
(define log-x (floor-log/base base x))
(define round? ((abs (- x (expt base log-x))) . < . epsilon))
(define major-str (format "~a~a" base-str (integer->superscript log-x)))
(cond [round? major-str]
[else (format "~a×~a"
(real->plot-label (/ x (expt base log-x)) base-digits)
major-str)])))))
(defproc (log-ticks [#:base base (and/c exact-integer? (>=/c 2)) (log-ticks-base)]) ticks?
(ticks (log-ticks-layout #:base base)
(log-ticks-format #:base base)))
;; ===================================================================================================
;; Date/time helpers
(defproc (find-linear-tick-step [x-min real?] [x-max real?] [max-ticks exact-positive-integer?]
[steps (listof real?)]) real?
(with-exact-bounds
x-min x-max
(let/ec break
(for ([step (in-list (sort steps <))])
(define-values (_start _end num) (linear-seq-args x-min x-max step))
(when (num . <= . max-ticks)
(break step)))
#f)))
(define (count-unchanging-fields formatter fmt-list xs)
(let ([fmt-list (filter symbol? fmt-list)])
(define formatted-dates (for/list ([x (in-list xs)])
(apply-formatter formatter fmt-list x)))
(count equal?* (transpose formatted-dates))))
(define (choose-format-list formatter fmt-lists xs)
(let ([fmt-lists (sort fmt-lists >
#:key (λ (fmt-list) (count symbol? fmt-list))
#:cache-keys? #t)])
(argmin (λ (fmt-list) (count-unchanging-fields formatter fmt-list xs))
fmt-lists)))
;; ===================================================================================================
;; Date ticks
(define 12h-descending-date-ticks-formats
'("~Y-~m-~d ~I:~M:~f~p"
"~Y-~m-~d ~I:~M~p"
"~Y-~m-~d ~I~p"
"~Y-~m-~d"
"~Y-~m"
"~Y"
"~m-~d ~I:~M:~f~p"
"~m-~d ~I:~M~p"
"~m-~d ~I~p"
"~m-~d"
"~I:~M:~f~p"
"~I:~M~p"
"~M:~fs"
"~fs"))
(define 24h-descending-date-ticks-formats
'("~Y-~m-~d ~H:~M:~f"
"~Y-~m-~d ~H:~M"
"~Y-~m-~d ~Hh"
"~Y-~m-~d"
"~Y-~m"
"~Y"
"~m-~d ~H:~M:~f"
"~m-~d ~H:~M"
"~m-~d ~Hh"
"~m-~d"
"~H:~M:~f"
"~H:~M"
"~M:~fs"
"~fs"))
(defparam date-ticks-formats (listof string?) 24h-descending-date-ticks-formats)
;; Tick steps to try, in seconds
(define date-steps
(list 1 2 5 10 15 20 30 40 45
seconds-per-minute
(* 2 seconds-per-minute)
(* 5 seconds-per-minute)
(* 10 seconds-per-minute)
(* 15 seconds-per-minute)
(* 20 seconds-per-minute)
(* 30 seconds-per-minute)
seconds-per-hour
(* 2 seconds-per-hour)
(* 3 seconds-per-hour)
(* 4 seconds-per-hour)
(* 6 seconds-per-hour)
(* 8 seconds-per-hour)
(* 12 seconds-per-hour)
seconds-per-day
(* 2 seconds-per-day)
(* 5 seconds-per-day)
(* 10 seconds-per-day)
seconds-per-week
(* 2 seconds-per-week)
avg-seconds-per-month
(* 2 avg-seconds-per-month)
(* 3 avg-seconds-per-month)
(* 4 avg-seconds-per-month)
(* 6 avg-seconds-per-month)
(* 8 avg-seconds-per-month)
(* 9 avg-seconds-per-month)
avg-seconds-per-year
(* 2 avg-seconds-per-year)
(* 5 avg-seconds-per-year)))
(define (date-tick-values x-min x-max max-ticks)
(with-exact-bounds
x-min x-max
(define range (- x-max x-min))
(define step
(cond [(range . < . (* max-ticks (first date-steps)))
(define-values (step _)
(linear-tick-step+divisor x-min x-max max-ticks 10 '(1 2 5)))
step]
[(range . > . (* max-ticks (last date-steps)))
(define-values (step _)
(linear-tick-step+divisor (/ x-min avg-seconds-per-year)
(/ x-max avg-seconds-per-year)
max-ticks 10 '(1 2 5)))
(* step avg-seconds-per-year)]
[else (find-linear-tick-step x-min x-max max-ticks date-steps)]))
(define date-round
(cond [(step . >= . avg-seconds-per-year) utc-seconds-round-year]
[(step . >= . avg-seconds-per-month) utc-seconds-round-month]
[else (λ (d) d)]))
(define major-xs (linear-major-values/step x-min x-max step))
(values (map date-round major-xs) empty)))
(defproc (date-ticks-layout) ticks-layout/c
(λ (x-min x-max max-ticks transform)
(define-values (major-xs minor-xs) (date-tick-values x-min x-max max-ticks))
(tick-values->pre-ticks major-xs minor-xs)))
(defproc (date-ticks-format [#:formats formats (listof string?) (date-ticks-formats)]) ticks-format/c
(define fmt-lists (map parse-format-string formats))
(λ (x-min x-max ts)
(with-exact-bounds
x-min x-max
(define formatter (plot-date-formatter x-min x-max))
(define xs (map pre-tick-value ts))
(define fmt-list (choose-format-list formatter fmt-lists xs))
(for/list ([x (in-list xs)])
(string-append* (apply-formatter formatter fmt-list x))))))
(defproc (date-ticks [#:formats formats (listof string?) (date-ticks-formats)]) ticks?
(ticks (date-ticks-layout)
(date-ticks-format #:formats formats)))
;; ===================================================================================================
;; Time ticks
(define descending-time-ticks-formats
'("~dd ~H:~M:~f"
"~dd ~H:~M"
"~dd ~Hh"
"~dd"
"~H:~M:~f"
"~H:~M"
"~Hh"
"~M:~f"
"~Mm"
"~ss"))
(defparam time-ticks-formats (listof string?) descending-time-ticks-formats)
;; Tick steps to try, in seconds
(define time-steps
(list 1 2 5 10 15 20 30 40 45
seconds-per-minute
(* 2 seconds-per-minute)
(* 5 seconds-per-minute)
(* 10 seconds-per-minute)
(* 15 seconds-per-minute)
(* 20 seconds-per-minute)
(* 30 seconds-per-minute)
(* 45 seconds-per-minute)
seconds-per-hour
(* 2 seconds-per-hour)
(* 3 seconds-per-hour)
(* 4 seconds-per-hour)
(* 6 seconds-per-hour)
(* 8 seconds-per-hour)
(* 12 seconds-per-hour)
(* 18 seconds-per-hour)
seconds-per-day
(* 2 seconds-per-day)
(* 5 seconds-per-day)
(* 10 seconds-per-day)
(* 15 seconds-per-day)
(* 30 seconds-per-day)
(* 60 seconds-per-day)
(* 90 seconds-per-day)))
(define (time-tick-values x-min x-max max-ticks)
(with-exact-bounds
x-min x-max
(define range (- x-max x-min))
(define step
(cond [(range . < . (* max-ticks (first time-steps)))
(define-values (step _)
(linear-tick-step+divisor x-min x-max max-ticks 10 '(1 2 5)))
step]
[(range . > . (* max-ticks (last time-steps)))
(define-values (step _)
(linear-tick-step+divisor (/ x-min seconds-per-day)
(/ x-max seconds-per-day)
max-ticks 10 '(1 2 5)))
(* step seconds-per-day)]
[else
(find-linear-tick-step x-min x-max max-ticks time-steps)]))
(define major-xs (linear-major-values/step x-min x-max step))
(values major-xs empty)))
(defproc (time-ticks-layout) ticks-layout/c
(λ (x-min x-max max-ticks transform)
(define-values (major-xs minor-xs) (time-tick-values x-min x-max max-ticks))
(tick-values->pre-ticks major-xs minor-xs)))
(defproc (time-ticks-format [#:formats formats (listof string?) (time-ticks-formats)]) ticks-format/c
(define fmt-lists (map parse-format-string formats))
(λ (x-min x-max ts)
(with-exact-bounds
x-min x-max
(define formatter (plot-time-formatter x-min x-max))
(define xs (map pre-tick-value ts))
(define fmt-list (choose-format-list formatter fmt-lists xs))
(for/list ([x (in-list xs)])
(string-append* (apply-formatter formatter fmt-list x))))))
(defproc (time-ticks [#:formats formats (listof string?) (time-ticks-formats)]) ticks?
(ticks (time-ticks-layout)
(time-ticks-format #:formats formats)))
;; ===================================================================================================
;; Byte and bit ticks
;; "", Kilo, Mega, Giga, Tera, Peta, Exa, Zeta, Yotta
(define byte-suffixes #("B" "KB" "MB" "GB" "TB" "PB" "EB" "ZB" "YB"))
(define bit-suffixes #("b" "Kb" "Mb" "Gb" "Tb" "Pb" "Eb" "Zb" "Yb"))
(defproc (bit/byte-ticks-format [#:size size (or/c 'byte 'bit) 'byte]
[#:kind kind (or/c 'CS 'SI) 'CS]) ticks-format/c
(λ (x-min x-max ts)
(with-exact-bounds
x-min x-max
(define suffixes (if (eq? size 'bit) bit-suffixes byte-suffixes))
(define-values (base pow) (case kind
[(SI) (values 10 3)]
[else (values 2 10)]))
(define x-largest (max* (abs x-min) (abs x-max)))
(define b (floor-log/base (expt base pow) x-largest))
(define format-str
(cond [(and (b . >= . 0) (b . < . (vector-length suffixes)))
(format "~a ~a" "~a" (vector-ref suffixes b))]
[else
(format "~a×~a~a ~a" "~a"
base (integer->superscript (* b pow)) (vector-ref suffixes 0))]))
(define unit (expt base (* b pow)))
(define digits (digits-for-range (/ x-min unit) (/ x-max unit)))
(for/list ([t (in-list ts)])
(define unit-x (/ (pre-tick-value t) unit))
(format format-str (real->plot-label unit-x digits #f))))))
(defproc (bit/byte-ticks [#:size size (or/c 'byte 'bit) 'byte]
[#:kind kind (or/c 'CS 'SI) 'CS]) ticks?
(define layout
(case kind
[(SI) (linear-ticks-layout #:base 10 #:divisors '(1 2 5))]
[else (linear-ticks-layout #:base 2 #:divisors '(1 2))]))
(ticks layout (bit/byte-ticks-format #:size size #:kind kind)))
;; ===================================================================================================
;; Currency
;; US "short scale" suffixes
(define us-currency-scale-suffixes '("" "K" "M" "B" "T"))
;; The UK officially uses the short scale now
;; Million is abbreviated "m" instead of "mn" because "mn" stands for minutes; also, the Daily
;; Telegraph Style Guide totally says to use "m"
(define uk-currency-scale-suffixes '("" "k" "m" "bn" "tr"))
;; European countries use the long scale: million, milliard, billion
(define eu-currency-scale-suffixes '("" "K" "M" "Md" "B"))
;; The larger the scale suffixes get, the less standardized they are; so we stop at trillion (short)
;; US negative amounts are in parenthesis:
(define us-currency-format-strings '("~$~w.~f~s" "(~$~w.~f~s)" "~$0"))
;; The UK is more reasonable, using a negative sign for negative amounts:
(define uk-currency-format-strings '("~$~w.~f ~s" "-~$~w.~f ~s" "~$0"))
;; The more common EU format (e.g. France, Germany, Italy, Spain):
(define eu-currency-format-strings '("~w,~f ~s~$" "-~w,~f ~s~$" "0 ~$"))
(defparam currency-scale-suffixes (listof string?) us-currency-scale-suffixes)
(defparam currency-format-strings (list/c string? string? string?) us-currency-format-strings)
(struct amount-data (sign whole fractional unit suffix) #:transparent)
(define (currency-formatter x-min x-max)
(λ (fmt data)
(case fmt
[(~$) (amount-data-sign data)]
[(~w) (number->string (amount-data-whole data))]
[(~f) (match-define (amount-data _sign _whole f unit _suffix) data)
(define digits (digits-for-range (/ x-min unit) (/ x-max unit)))
(cond [(= 1 unit) (substring (real->decimal-string* f 2 (max 2 digits)) 2)]
[(zero? f) "0"]
[else (substring (real->decimal-string* f 1 (max 1 digits)) 2)])]
[(~s) (amount-data-suffix data)]
[else #f])))
(defproc (currency-ticks-format [#:kind kind (or/c string? symbol?) 'USD]) ticks-format/c
(λ (x-min x-max ts)
(with-exact-bounds
x-min x-max
(define formatter (currency-formatter x-min x-max))
(match-define (list positive-format-string negative-format-string zero-format-string)
(currency-format-strings))
(define positive-format-list (parse-format-string positive-format-string))
(define negative-format-list (parse-format-string negative-format-string))
(define zero-format-list (parse-format-string zero-format-string))
(define suffixes (list->vector (currency-scale-suffixes)))
(define n (vector-length suffixes))
(define sign (cond [(string? kind) kind]
[else (hash-ref currency-code->sign kind (λ () (symbol->string kind)))]))
(define x-largest (max* (abs x-min) (abs x-max)))
(define b (let ([b (floor-log/base 1000 x-largest)])
(if (b . < . 0) (+ b 1) b)))
(define suffix
(cond [(and (b . >= . 0) (b . < . n)) (vector-ref suffixes b)]
[else (format "×10~a" (integer->superscript (* b 3)))]))
(define unit
(cond [(= 0 (string-length suffix)) 1]
[else (expt 1000 b)]))
(for/list ([t (in-list ts)])
(define x (pre-tick-value t))
(define format-list (cond [(positive? x) positive-format-list]
[(negative? x) negative-format-list]
[else zero-format-list]))
(define unit-x (/ (abs x) unit))
(string-append*
(apply-formatter formatter format-list
(amount-data sign (floor unit-x) (- unit-x (floor unit-x)) unit suffix)))))))
(defproc (currency-ticks-layout) ticks-layout/c
(linear-ticks-layout #:base 10 #:divisors '(1 2 4 5)))
(defproc (currency-ticks [#:kind kind (or/c string? symbol?) 'USD]) ticks?
(ticks (currency-ticks-layout)
(currency-ticks-format #:kind kind)))
;; ===================================================================================================
;; Fractions
(defparam fraction-ticks-base (and/c exact-integer? (>=/c 2)) 10)
(defparam fraction-ticks-divisors (listof exact-positive-integer?) '(1 2 3 4 5))
(define (format-fraction x)
(cond [(inexact? x) (format-fraction (inexact->exact x))]
[(x . < . 0) (format "-~a" (format-fraction (- x)))]
[(x . = . 0) "0"]
[(x . < . 1) (format "~a/~a" (numerator x) (denominator x))]
[else
(define d (denominator x))
(cond [(d . = . 1) (format "~a" (numerator x))]
[else
(define w (floor x))
(let ([x (- x w)])
(format "~a ~a/~a" w (numerator x) (denominator x)))])]))
(defproc (fraction-ticks-format) ticks-format/c
(λ (x-min x-max ts)
(for/list ([t (in-list ts)])
(format-fraction (pre-tick-value t)))))
(defproc (fraction-ticks [#:base base (and/c exact-integer? (>=/c 2)) (fraction-ticks-base)]
[#:divisors divisors (listof exact-positive-integer?)
(fraction-ticks-divisors)]) ticks?
(ticks (linear-ticks #:base base #:divisors divisors)
(fraction-ticks-format)))