(* Compute analytic functions as truncated sums.  Determine
  the recurrence relations of their terms. *)

MODULE recurrence;

FROM InOut     IMPORT WriteString, WriteLn;
FROM RealInOut IMPORT WriteReal, ReadReal;

VAR n: CARDINAL;
   i,x,y,s,t: REAL;

BEGIN
 WriteString(' exp'); WriteLn;
 n := 1;
 REPEAT
   ReadReal(x); y := 1.0;
   i := 0.0; t := 1.0;
   REPEAT
     i := i + 1.0;
     t := t*x/i;
     y := y+t;
   UNTIL y+t = y;
   WriteReal(x,9); WriteReal(y,9); WriteReal(i,9);
   DEC(n);
 UNTIL n = 0;

 WriteString(' sin'); WriteLn;
 n := 1;
 REPEAT
   ReadReal(x); y := x;
   i := 1.0; s := x*x;
   t := x;
   REPEAT
     i := i + 2.0;
     t := -t*s/((i-1.0)*i);
     y := y + t;
   UNTIL y + t = y;
   WriteReal(x,9); WriteReal(y,9); WriteReal(i/2.0,9);
   DEC(n);
 UNTIL n = 0;

 WriteString(' cos'); WriteLn;
 n := 1;
 REPEAT
   ReadReal(x); y := 1.0;
   i := 0.0; s := x*x;
   t := 1.0;
   REPEAT
     i := i + 2.0;
     t := -t*s/((i-1.0)*i);
     y := y + t;
   UNTIL y + t = y;
   WriteReal(x,9); WriteReal(y,9); WriteReal(i/2.0,9);
   DEC(n);
 UNTIL n = 0;

 WriteString(' arcsin'); WriteLn;
 n := 1;
 REPEAT
   ReadReal(x); y := x;
   i := 1.0; s := x*x;
   t := x;
   REPEAT
     i := i + 2.0;
     t := t*s*((i-2.0)*(i-2.0))/((i-1.0)*i);
     y := y + t;
   UNTIL y + t = y;
   WriteReal(x,9); WriteReal(y,9); WriteReal(i/2.0,9);
   DEC(n);
 UNTIL n = 0;

 WriteString(' arctan'); WriteLn;
 n := 1;
 REPEAT
   ReadReal(x); y := x;
   i := 1.0; s := x*x;
   t := x;
   REPEAT
     i := i + 2.0;
     t := -t*s*(i-2.0)/i;
     y := y + t;
   UNTIL y + t = y;
   WriteReal(x,9); WriteReal(y,9); WriteReal(i/2.0,9);
   DEC(n);
 UNTIL n = 0;

 WriteString(' ln'); WriteLn;
 n := 1;
 REPEAT
   ReadReal(x); x := x - 1.0;
   y := x; t := x; i := 1.0;
   REPEAT
     i := i + 1.0;
     t := -t*x*(i-1.0)/i;
     y := y + t;
   UNTIL y + t = y;
   WriteReal(x + 1.0,9); WriteReal(y,9); WriteReal(i,9);
   DEC(n);
 UNTIL n = 0;
END recurrence.

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