A-M baby

Task/Arithmetic-Rational/Icon/arithmetic-rational-1.icon

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+procedure main()
+   limit := 2^19
+
+   write("Perfect numbers up to ",limit," (using rational arithmetic):")
+   every write(is_perfect(c := 2 to limit))
+   write("End of perfect numbers")
+
+   # verify the rest of the implementation
+
+   zero := makerat(0)          # from integer
+   half := makerat(0.5)        # from real
+   qtr  := makerat("1/4")      # from strings ...
+   one  := makerat("1")
+   mone := makerat("-1")
+
+   verifyrat("eqrat",zero,zero)
+   verifyrat("ltrat",zero,half)
+   verifyrat("ltrat",half,zero)
+   verifyrat("gtrat",zero,half)
+   verifyrat("gtrat",half,zero)
+   verifyrat("nerat",zero,half)
+   verifyrat("nerat",zero,zero)
+   verifyrat("absrat",mone,)
+
+end
+
+procedure is_perfect(c)       #: test for perfect numbers using rational arithmetic
+   rsum := rational(1, c, 1)
+   every f := 2 to sqrt(c) do
+      if 0 = c % f then
+         rsum := addrat(rsum,addrat(rational(1,f,1),rational(1,integer(c/f),1)))
+   if rsum.numer = rsum.denom = 1 then
+      return c
+end

Task/Arithmetic-Rational/Icon/arithmetic-rational-2.icon

@@ -0,0 +1,61 @@
+procedure verifyrat(p,r1,r2)  #: verification tests for rational procedures
+return write("Testing ",p,"( ",rat2str(r1),", ",rat2str(\r2) | &null," ) ==> ","returned " || rat2str(p(r1,r2)) | "failed")
+end
+
+procedure makerat(x)          #: make rational (from integer, real, or strings)
+local n,d
+static c
+initial c := &digits++'+-'
+
+   return case type(x) of {
+             "real"    : real2rat(x)
+             "integer" : ratred(rational(x,1,1))
+             "string"  : if x ? ( n := integer(tab(many(c))), ="/", d := integer(tab(many(c))), pos(0)) then
+                            ratred(rational(n,d,1))
+                         else
+                            makerat(numeric(x))
+          }
+end
+
+procedure absrat(r1)          #: abs(rational)
+   r1 := ratred(r1)
+   r1.sign := 1
+   return r1
+end
+
+invocable all                 #  for string invocation
+
+procedure xoprat(op,r1,r2)    #: support procedure for binary operations that cross denominators
+   local numer, denom, div
+
+   r1 := ratred(r1)
+   r2 := ratred(r2)
+
+   return if op(r1.numer * r2.denom,r2.numer * r1.denom) then r2   # return right argument on success
+end
+
+procedure eqrat(r1,r2)        #: rational r1 = r2
+return xoprat("=",r1,r2)
+end
+
+procedure nerat(r1,r2)        #: rational r1 ~= r2
+return xoprat("~=",r1,r2)
+end
+
+procedure ltrat(r1,r2)        #: rational r1 < r2
+return xoprat("<",r1,r2)
+end
+
+procedure lerat(r1,r2)        #: rational r1 <= r2
+return xoprat("<=",r1,r2)
+end
+
+procedure gerat(r1,r2)        #: rational r1 >= r2
+return xoprat(">=",r1,r2)
+end
+
+procedure gtrat(r1,r2)        #: rational r1 > r2
+return xoprat(">",r1,r2)
+end
+
+link rational

Task/Arithmetic-Rational/Icon/arithmetic-rational-3.icon

@@ -0,0 +1,15 @@
+   record rational(numer, denom, sign)        # rational type
+
+   addrat(r1,r2) # Add rational numbers r1 and r2.
+   divrat(r1,r2) # Divide rational numbers r1 and r2.
+   medrat(r1,r2) # Form mediant of r1 and r2.
+   mpyrat(r1,r2) # Multiply rational numbers r1 and r2.
+   negrat(r)     # Produce negative of rational number r.
+   rat2real(r)   # Produce floating-point approximation of r
+   rat2str(r)    # Convert the rational number r to its string representation.
+   real2rat(v,p) # Convert real to rational with precision p (default 1e-10). Warning: excessive p gives ugly fractions
+   reciprat(r)   # Produce the reciprocal of rational number r.
+   str2rat(s)    # Convert the string representation (such as "3/2") to a rational number
+   subrat(r1,r2) # Subtract rational numbers r1 and r2.
+
+   gcd(i, j)     # returns greatest common divisor of i and j