function NeumaierSum $($input$)$

var sum $=0\mathrm{.}0$

varc$=0\mathrm{.}0\frac{,}{\frac{?}{?}}$A running compensation for lost low$-$order bits.

for $i=1$ to input.length do

vart$=$ sum $+$ input$[$i$]$

if $|$ sum $||$ input$[$i$]|$ then

c sum $-$ t$)+$ input$[$i$]//$ If sum bigger, tracks low$-$order digits of input$[$i$]$

else

c $+=($input$[$i$]-$ t$)+$ sum $//$ Else tracks low$-$order digits of sum.

endif

sum $=t$

return sum $+$ c $//$ Correction only applied once in the very end.

It maintains a running sum and also a compensator $c$ that keeps track of things lost to rounding error.

This pseudocode uses modifiable state $($the vars$).$

Question $11.$ Modify the NeumaierSum pseudocode so that it does not use any modifiable state. In the HW

object, create the function $q11()$ whose input is a Seq$[$Double$]$ to do this summation. Use the case class

Neumaier $($defined at the top in scalahw.scala$)$ to keep track of the state $($sum and compensator c$).$ Use

foldLeft $($no indexing$)$ to implement the summation algorithm without any loops $($if you are stuck, examine

how we used foldLeft in class$).$ The state that foldLeft uses should be a case class Neumaier $($so you should

know how to create this thing and how to pull information out of it$).$ Remember Do not use vars!!!. Do not

use the return keyword. You must update the function definition to specify its return type.