Data commit

Task/Calkin-Wilf-sequence/FreeBASIC/calkin-wilf-sequence.basic

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+#include "gcd.bas"
+
+type rational
+    num as integer
+    den as integer
+end type
+
+dim shared as rational ONE, TWO
+ONE.num = 1 : ONE.den = 1
+TWO.num = 2 : TWO.den = 1
+
+function simplify( byval a as rational ) as rational
+   dim as uinteger g = gcd( a.num, a.den )
+   a.num /= g : a.den /= g
+   if a.den < 0 then
+       a.den = -a.den
+       a.num = -a.num
+   end if
+   return a
+end function
+
+operator + ( a as rational, b as rational ) as rational
+    dim as rational ret
+    ret.num = a.num * b.den + b.num*a.den
+    ret.den = a.den * b.den
+    return simplify(ret)
+end operator
+
+operator - ( a as rational, b as rational ) as rational
+    dim as rational ret
+    ret.num = a.num * b.den - b.num*a.den
+    ret.den = a.den * b.den
+    return simplify(ret)
+end operator
+
+operator * ( a as rational, b as rational ) as rational
+    dim as rational ret
+    ret.num = a.num * b.num
+    ret.den = a.den * b.den
+    return simplify(ret)
+end operator
+
+operator / ( a as rational, b as rational ) as rational
+    dim as rational ret
+    ret.num = a.num * b.den
+    ret.den = a.den * b.num
+    return simplify(ret)
+end operator
+
+function floor( a as rational ) as rational
+    dim as rational ret
+    ret.den = 1
+    ret.num = a.num \ a.den
+    return ret
+end function
+
+function cw_nextterm( q as rational ) as rational
+    dim as rational ret = (TWO*floor(q))
+    ret = ret + ONE : ret = ret - q
+    return ONE / ret
+end function
+
+function frac_to_int( byval a as rational ) as uinteger
+    redim as uinteger cfrac(-1)
+    dim as integer  lt = -1, ones = 1, ret = 0
+    do
+        lt += 1
+        redim preserve as uinteger cfrac(0 to lt)
+        cfrac(lt) = floor(a).num
+        a = a - floor(a) : a = ONE / a
+    loop until a.num = 0 or a.den = 0
+    if lt mod 2 = 1 and cfrac(lt) = 1 then
+        lt -= 1
+        cfrac(lt)+=1
+        redim preserve as uinteger cfrac(0 to lt)
+    end if
+    if lt mod 2 = 1 and cfrac(lt) > 1 then
+        cfrac(lt) -= 1
+        lt += 1
+        redim preserve as uinteger cfrac(0 to lt)
+        cfrac(lt) = 1
+    end if
+    for i as integer = lt to 0 step -1
+        for j as integer = 1 to cfrac(i)
+            ret *= 2
+            if ones = 1 then  ret += 1
+        next j
+        ones = 1 - ones
+    next i
+    return ret
+end function
+
+function disp_rational( a as rational ) as string
+    if a.den = 1 or a.num= 0 then return str(a.num)
+    return str(a.num)+"/"+str(a.den)
+end function
+
+dim as rational q
+q.num = 1
+q.den = 1
+for i as integer = 1 to 20
+    print i, disp_rational(q)
+    q = cw_nextterm(q)
+next i
+
+q.num = 83116
+q.den = 51639
+print disp_rational(q)+" is the "+str(frac_to_int(q))+"th term."