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.




>>> def maprange( a, b, s):
	(a1, a2), (b1, b2) = a, b
	return  b1 + ((s - a1) * (b2 - b1) / (a2 - a1))
 
>>> for s in range(11):
	print("%2g maps to %g" % (s, maprange( (0, 10), (-1, 0), s)))
 
 
 0 maps to -1
 1 maps to -0.9
 2 maps to -0.8
 3 maps to -0.7
 4 maps to -0.6
 5 maps to -0.5
 6 maps to -0.4
 7 maps to -0.3
 8 maps to -0.2
 9 maps to -0.1
10 maps to 0