ex1

From duba@aten.cs.rice.edu Thu Feb 23 15:11:18 1995
Date: Thu, 23 Feb 95 15:11:15 CST
From: duba@aten.cs.rice.edu (Bruce Duba)
To: matthias@aten.cs.rice.edu, shriram@aten.cs.rice.edu
Subject: Jam

I just took some scheme code and translated it into Jam (Shriram, you
may recognize the program). Our "inorder" expression is weird when the
return exp is also a side effect. Also, if 4k! is an id what about
4k!*x ? Is it an id or a multiplication?

rat(more, rational) = lda(more, numerator(rational), denominator(rational));

lda(more, top, bot) =
 let decimal = more-1
 in 
  do loop(top=top, more=more) =
   inorder if more=decimal then display(`.') elsefalse
   return
    if more=0 then newline()
    elseif top=0 then inorder display(0) return newline()
    else inorder display(quotient(top, bot))
         return loop(10*remainder(top, bot), more-1);

// CF for root 2
// The actual CF is [1;2,2,2,...]

root2(n) =
 do loop (top=1, bot=2, k=n) =
  if k=0 then 1 + top/bot
  else loop(bot, 2*bot + top, k-1);

a=26390;
c=396^4;

pie(n) =
 do loop(num=0, k=0, 4k=0, alpha=1103, 4k!=1, k!tothe4th=1, gamma=1) =
  if k>n then num
  else 
   let nextk = k+1
   in
    loop(num + (4k! * alpha)/(k!tothe4th * gamma),
         nextk,
	 4k+4,
         alpha+a,
	 4k! * (4k+1) * (4k+2) * (4k+3) * (4k+ 4),
	 k!tothe4th * next-k^4,
	 gamma*c);

pi(n) =
 let factor = 2*root2(100*n) / 9801
 in 1/(factor*pie(n));

py(n, k) = rat(k, pi(n));