Arithmetic/Rational: Difference between revisions

== Icon and Unicon ==

==={{header|Icon}}===

The IPL provides support for rational arithmetic

* The data type is called 'rational' not 'frac'.

* Use the record constructor 'rational' to create a rational. Sign must be 1 or -1.

* Neither Icon nor Unicon supports operator overloading. Augmented assignments make little sense w/o this.

* Procedures include 'negrat' (unary -), 'addrat' (+), 'subrat' (-), 'mpyrat' (*), 'divrat' (modulo /).

Additional procedures are implemented here to complete the task:

* 'makerat' (make), 'absrat' (abs), 'eqrat' (=), 'nerat' (~=), 'ltrat' (<), 'lerat' (<=), 'gerat' (>=), 'gtrat' (>)

<lang Icon>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</lang>

Sample output:<pre>Perfect numbers up to 524288 (using rational arithmetic):

6

28

496

8128

End of perfect numbers

Testing eqrat( (0/1), (0/1) ) ==> returned (0/1)

Testing ltrat( (0/1), (1/2) ) ==> returned (1/2)

Testing ltrat( (1/2), (0/1) ) ==> failed

Testing gtrat( (0/1), (1/2) ) ==> failed

Testing gtrat( (1/2), (0/1) ) ==> returned (0/1)

Testing nerat( (0/1), (1/2) ) ==> returned (1/2)

Testing nerat( (0/1), (0/1) ) ==> failed

Testing absrat( (-1/1), ) ==> returned (1/1)</pre>

The following task functions are missing from the IPL:

<lang Icon>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</lang>

The {{libheader|Icon Programming Library}} provides [http://www.cs.arizona.edu/icon/library/src/procs/rational.icn rational] and [http://www.cs.arizona.edu/icon/library/src/procs/numbers.icn gcd in numbers]. Record definition and usage is shown below:

<lang Icon> 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</lang>

==={{header|Unicon}}===

The Icon solution works in Unicon.