OpenEuphoria

Re: simpson.ex: The Simpson Rule

• Posted by Hawke' <mdeland at GEOCITIES.COM> Dec 17, 1998
• 315 views

Alan Tu wrote:
> Last thing, speed does matter, so suggestions to improve speed and all
> other suggestions are welcome!

> include get.e
> include function.e

> type even(integer x)
>     return integer(0.5*x)
 at this point, i'm not sure, but, since you are calling it so often,
     return remainder(x,2) = 0
 may be considerably faster...
> end type

> atom delta, coeff, solution, real, answer, current, temp, test
> object a, b, n
> even subd
>   real = 0
>   clear_screen()
>   puts(1,"Enter A: ")
>   a = get(0)
>   a = a[2]
>   puts(1,"\nEnter B: ")
>   b = get(0)
>   b = b[2]
>   puts(1,"\nEnter N: ")
>   n = get(0)
>   subd = n[2]
>   delta = (b-a)/subd
>   coeff = (1/3)*delta
       coeff = delta/3 would be faster, one less operation and one less
set
       of () to parse...
  --add this:
    current = 0
>   puts(1,"\n")
>   for i = 0 to subd do
>     solution = f(a+i*delta)
      change this to
         solution = f(a+current)
>     if i = 0 or i = subd then
>         real = real+solution
>     elsif 0.5*i != floor(0.5*i) then
>         real = real+4*solution
>     elsif 0.5*i = floor(0.5*i) then
>         real = real+2*solution
>     end if

    --change the compound if..then to:
      if i = 0 or i = subd then
           real = real + solution
      else test = 0.5*i
           temp = solution + solution
           real = real + temp
           if test != floor(test) then
                real = real + temp
           end if
      end if
  --add this:
  current = current + delta
> end for
> answer = coeff*real
> puts(1,"The estimated integral is: ")
> print(1,answer)
> puts(1,"\nNote: Simpson's Rule often provides exact answers.")
>

a straight up typing of the newly modified function/program is thusly:

include get.e
include function.e
type even(integer x)
  return remainder(x,2) = 0
end type

atom delta, coeff, solution, real, answer, current, temp, test
object a, b, n
even subd
  real = 0
  clear_screen()
  puts(1,"Enter A: ")
  a = get(0) a = a[2]
  puts(1,"\nEnter B: ")
  b = get(0) b = b[2]
  puts(1,"\nEnter N: ")
  n = get(0) subd = n[2]
  delta = (b-a)/subd
  coeff = delta/3
  current = 0
  puts(1,"\n")
  for i = 0 to subd do
    solution = f(a+current)
    if i = 0 or i = subd then
         real = real + solution
    else test = 0.5*i
         temp = solution + solution
         real = real + temp
         if test != floor(test) then
            real = real + temp
         end if
    end if
    current = current + delta
  end for
  answer = coeff*real
  puts(1,"The estimated integral is: ")
  print(1,answer)
  puts(1,"\nNote: Simpson's Rule often provides exact answers.")

and the sample function is the 'same' of course....
hope this shows some speed improvements...
everyone knows i'm a sucker for tweaking :)
the benchmark program i posted for testing reverse() seemed
to provide everyone with a (seemingly?) stable platform for
testing functions across different processors and you are
welcome of course to use that to time the two versions :)

take care and care of,
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