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.




/* map s from [a, b] to [c, d] */
define m(a, b, c, d, s) {
	return (c + (s - a) * (d - c) / (b - a))
}
 
scale = 6  /* division to 6 decimal places */
"[0, 10] => [-1, 0]
"
for (i = 0; i <= 10; i += 2) {
	/*
         * If your bc(1) has a print statement, you can try
	 * print i, " => ", m(0, 10, -1, 0, i), "\n"
	 */
	i; "   => "; m(0, 10, -1, 0, i)
}
quit