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.




 
# syntax: GAWK -f MAP_RANGE.AWK
BEGIN {
    a1 = 0
    a2 = 10
    b1 = -1
    b2 = 0
    for (i=a1; i<=a2; i++) {
      printf("%g maps to %g\n",i,map_range(a1,a2,b1,b2,i))
    }
    exit(0)
}
function map_range(a1,a2,b1,b2,num) {
    return b1 + ((num-a1) * (b2-b1) / (a2-a1))
}
 