# Category talk:Wren-rat

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### Source code

```/* Module "rat.wren" */

import "./trait" for Comparable

/* Rat represents a rational number as an integral numerator and (non-zero) denominator
expressed in their lowest terms. Rat objects are immutable.
*/
class Rat is Comparable {
// Private helper function to check that 'o' is a suitable type and throw an error otherwise.
// Numbers and numeric strings are returned as rationals.
static check_(o) {
if (o is Rat) return o
if (o is Num) return Rat.fromFloat(o)
if (o is String) return (o.contains("_") && o.contains("/")) ? fromMixedString(o) :
o.contains("/") ? fromRationalString(o) : fromString(o)
Fiber.abort("Argument must either be a rational number, a number or a numeric string.")
}

// Private helper function which returns the greatest common divisor of 'n' and 'd'.
static gcd_(n, d) {
while (d != 0) {
var t = d
d = n % d
n = t
}
return n
}

// Private helper method which constructs a Rat object from a non-integral numeric string.
static fromDecimalString_(s) {
if (s.contains("e")) Fiber.abort("Argument is out of range.")
var ix = s.indexOf(".")
var dp = s[ix+1..-1]
var den = (10.pow(dp.count)).round
var num = Num.fromString(s[0...ix] + dp)
return Rat.new(num, den)
}

// Constants.
static minusOne { Rat.new( -1,  1) }
static zero     { Rat.new(  0,  1) }
static one      { Rat.new(  1,  1) }
static two      { Rat.new(  2,  1) }
static ten      { Rat.new( 10,  1) }
static half     { Rat.new(  1,  2) }
static tenth    { Rat.new(  1, 10) }

// Constructs a new Rat object by passing it a numerator and a denominator.
construct new(n, d) {
if (!(n is Num && n.isInteger)) Fiber.abort("Numerator must be an integer.")
if (!(d is Num && d.isInteger && d != 0)) {
Fiber.abort("Denominator must be a non-zero integer.")
}
if (n.abs > 9007199254740991) Fiber.abort("Numerator is out of range.")
if (d.abs > 9007199254740991) Fiber.abort("Denominator is out of range.")
if (n == 0) {
d = 1
} else if (d < 0) {
n = -n
d = -d
}
var g = Rat.gcd_(n, d).abs
if (g > 1) {
n = (n/g).truncate
d = (d/g).truncate
}
_n = n
_d = d
}

// Convenience method which constructs a new Rat object by passing it just a numerator.
static new(n) { Rat.new(n, 1) }

// Constructs a rational number from an integer.
static fromInt(i) { Rat.new(i, 1) }

// Constructs a rational number from a floating point number.
static fromFloat(f) {
if (!(f is Num)) Fiber.abort("Argument must be a number.")
if (f.isInteger) return Rat.new(f, 1)
var s = "%(f)"
return fromDecimalString_(s)
}

// Constructs a rational number from a numeric string.
static fromString(s) {
var n
s = s.trim()
if (!(n = Num.fromString(s))) Fiber.abort("Argument must be a numeric string.")
if (n.isInteger) return Rat.new(n, 1)
return fromDecimalString_(s.trimEnd("0"))
}

// Constructs a rational number from a string of the form "n/d".
// Improper fractions are allowed.
static fromRationalString(s) {
s = s.trim()
var nd = s.split("/")
if (nd.count != 2) Fiber.abort("Argument is not a suitable string.")
var n = Num.fromString(nd[0])
var d = Num.fromString(nd[1])
if (!n || !d) Fiber.abort("Argument is not a suitable string.")
return Rat.new(n, d)
}

// Constructs a rational number from a string of the form "i_n/d" where 'i' is an integer.
// Improper and negative fractional parts are allowed.
static fromMixedString(s) {
var ind = s.split("_")
if (ind.count != 2) Fiber.abort("Argument is not a suitable string.")
var nd = fromRationalString(ind[1])
var i = Rat.fromString(ind[0])
var neg = i.isNegative || (i.isZero && ind[0][0] == "-")
return neg ? i - nd : i + nd
}

// Returns the greater of two rational numbers.
static max(r1, r2) { (r1 < r2) ? r2 : r1 }

// Returns the smaller of two rational numbers.
static min(r1, r2) { (r1 < r2) ? r1 : r2 }

// Private helper method to compare two integers.
static compareInts_(i, j) { (i - j).sign }

// Determines whether a Rat object is always shown as such or, if integral, as an integer.
static showAsInt     { __showAsInt }
static showAsInt=(b) { __showAsInt = b }

// Basic properties.
num        { _n }                // numerator
den        { _d }                // denominator
ratio      { [_n, _d] }          // a two element list of the above
isInteger  { toFloat.isInteger } // checks if integral or not
isPositive { _n > 0 }            // checks if positive
isNegative { _n < 0 }            // checks if negative
isUnit     { _n.abs == 1 }       // checks if plus or minus one
isZero     { _n == 0 }           // checks if zero

// Rounding methods (similar to those in Num class).
ceil     { Rat.fromInt(toFloat.ceil) }      // higher integer
floor    { Rat.fromInt(toFloat.floor) }     // lower integer
truncate { Rat.fromInt(toFloat.truncate) }  // lower integer, towards zero
round    { Rat.fromInt(toFloat.round) }     // nearer integer
fraction { this - truncate }                // fractional part (same sign as this.num)

// Reciprocal
inverse  { Rat.new(_d, _n) }

// Integer division.
idiv(o)  { (this/o).truncate }

// Negation.
-{ Rat.new(-_n, _d) }

// Arithmetic operators (work with numbers and numeric strings as well as other rationals).
+(o) { (o = Rat.check_(o)) && Rat.new(_n * o.den + _d * o.num, _d * o.den) }
-(o) { (o = Rat.check_(o)) && (this + (-o)) }
*(o) { (o = Rat.check_(o)) && Rat.new(_n * o.num, _d * o.den) }
/(o) { (o = Rat.check_(o)) && Rat.new(_n * o.den, _d * o.num) }
%(o) { (o = Rat.check_(o)) && (this - idiv(o) * o) }

// Computes integral powers.
pow(i) {
if (!((i is Num) && i.isInteger)) Fiber.abort("Argument must be an integer.")
if (i == 0) return this
var np = _n.pow(i).round
var dp = _d.pow(i).round
return (i > 0) ? Rat.new(np, dp) : Rat.new(dp, np)
}

// Returns the square of the current instance.
square { Rat.new(_n * _n , _d *_d) }

// Other methods.
inc { this + Rat.one }            // increment
dec { this - Rat.one }            // decrement
abs { (_n >= 0) ? this : -this }  // absolute value
sign { _n.sign }                  // sign

// The inherited 'clone' method just returns 'this' as Rat objects are immutable.
// If you need an actual copy use this method instead.
copy() { Rat.new(_n, _d) }

// Compares this Rat with another one to enable comparison operators via Comparable trait.
compare(other) {
if ((other is Num) && other.isInfinity) return -other.sign
other = Rat.check_(other)
if (_d == other.den) return Rat.compareInts_(_n, other.num)
return Rat.compareInts_(_n * other.den, other.num * _d)
}

// As above but compares the absolute values of the BigRats.
compareAbs(other) { this.abs.compare(other.abs) }

// Converts the current instance to a Num.
toFloat { _n/_d }

// Converts the current instance to an integer with any fractional part truncated.
toInt { this.toFloat.truncate }

// Returns a string represenation of this instance in the form "i_n/d" where 'i' is an integer.
toMixedString {
var q = _n / _d
var r = _n % _d
if (r.isNegative) r = -r
return q.toString + "_" + r.toString + "/" + _d.toString
}

// Returns the string representation of this Rat object depending on 'showAsInt'.
toString { (Rat.showAsInt && _d == 1) ? "%(_n)" : "%(_n)/%(_d)" }
}

/*  Rats contains various routines applicable to lists of rational numbers */
class Rats {
static sum(a)  { a.reduce(Rat.zero) { |acc, x| acc + x } }
static mean(a) { sum(a)/a.count }
static prod(a) { a.reduce(Rat.one) { |acc, x| acc * x } }
static max(a)  { a.reduce { |acc, x| (x > acc) ? x : acc } }
static min(a)  { a.reduce { |acc, x| (x < acc) ? x : acc } }
}
```