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Task/Arithmetic-Rational/Phix/arithmetic-rational.phix

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+without warning  -- (several unused routines in this code)
+
+constant NUM = 1, DEN = 2
+
+type frac(object r)
+    return sequence(r) and integer(r[NUM]) and integer(r[DEN]) and length(r)=2
+end type
+
+function normalise(object n, atom d=0)
+atom g
+    if sequence(n) then
+        {n,d} = n
+    end if
+    if d<0 then
+        n = -n
+        d = -d
+    end if
+    g = gcd(n,d)
+    return {n/g,d/g}
+end function
+
+function frac_new(integer n,d=1)
+    return normalise(n,d)
+end function
+
+function frac_abs(frac r)
+    return {abs(r[NUM]),r[DEN]}
+end function
+
+function frac_inv(frac r)
+    return reverse(r)
+end function
+
+function frac_add(frac a, frac b)
+integer {an,ad} = a,
+        {bn,bd} = b
+    return normalise(an*bd+bn*ad,ad*bd)
+end function
+
+function frac_sub(frac a, frac b)
+integer {an,ad} = a,
+        {bn,bd} = b
+    return normalise(an*bd-bn*ad,ad*bd)
+end function
+
+function frac_mul(frac a, frac b)
+integer {an,ad} = a,
+        {bn,bd} = b
+    return normalise(an*bn,ad*bd)
+end function
+
+function frac_div(frac a, frac b)
+integer {an,ad} = a,
+        {bn,bd} = b
+    return normalise(an*bd,ad*bn)
+end function
+
+function frac_eq(frac a, frac b)
+    return a==b
+end function
+
+function frac_ne(frac a, frac b)
+    return a!=b
+end function
+
+function frac_lt(frac a, frac b)
+    return frac_sub(a,b)[NUM]<0
+end function
+
+function frac_gt(frac a, frac b)
+    return frac_sub(a,b)[NUM]>0
+end function
+
+function frac_le(frac a, frac b)
+    return frac_sub(a,b)[NUM]<=0
+end function
+
+function frac_ge(frac a, frac b)
+    return frac_sub(a,b)[NUM]>=0
+end function
+
+function is_perfect(integer num)
+frac sum = frac_new(0)
+sequence f = factors(num,1)
+    for i=1 to length(f) do
+        sum = frac_add(sum,frac_new(1,f[i]))
+    end for
+    return frac_eq(sum,frac_new(2))
+end function
+
+procedure get_perfect_numbers()
+atom t0 = time()
+    for i=2 to power(2,19) do
+        if is_perfect(i) then
+            printf(1,"perfect: %d\n",i)
+        end if
+    end for
+    printf(1,"elapsed: %3.2f seconds\n",time()-t0)
+
+    integer pn5 = power(2,12)*(power(2,13)-1) -- 5th perfect number
+    if is_perfect(pn5) then
+        printf(1,"perfect: %d\n",pn5)
+    end if
+end procedure
+
+get_perfect_numbers()