Given two ranges:

   



[

a

1


,

a

2


]


{\displaystyle [a_{1},a_{2}]}

   and 
   



[

b

1


,

b

2


]


{\displaystyle [b_{1},b_{2}]}

; 
   then a value   



s


{\displaystyle s}

   in range   



[

a

1


,

a

2


]


{\displaystyle [a_{1},a_{2}]}


   is linearly mapped to a value   



t


{\displaystyle t}

   in range   



[

b

1


,

b

2


]


{\displaystyle [b_{1},b_{2}]}


   where:



   



t
=

b

1


+



(
s
−

a

1


)
(

b

2


−

b

1


)


(

a

2


−

a

1


)





{\displaystyle t=b_{1}+{(s-a_{1})(b_{2}-b_{1}) \over (a_{2}-a_{1})}}




Task

Write a function/subroutine/... that takes two ranges and a real number, and returns the mapping of the real number from the first to the second range.

Use this function to map values from the range    [0, 10]    to the range    [-1, 0]. 



Extra credit

Show additional idiomatic ways of performing the mapping, using tools available to the language.




 
(defn maprange [[a1 a2] [b1 b2] s]
	(+ b1 (/ (* (- s a1) (- b2 b1)) (- a2 a1))))
 
> (doseq [s (range 11)]
       (printf "%2s maps to %s\n" s (maprange [0 10] [-1 0] s)))
 
 0 maps to -1
 1 maps to -9/10
 2 maps to -4/5
 3 maps to -7/10
 4 maps to -3/5
 5 maps to -1/2
 6 maps to -2/5
 7 maps to -3/10
 8 maps to -1/5
 9 maps to -1/10
10 maps to 0
 