class Rat

Rational number (limited-precision)

class Rat is Cool does Rational[Intuint64{ }

Rat objects store rational numbers as a pair of a numerator and denominator. Number literals with a dot but without exponent produce Rats.

say 3.1;          # OUTPUT: «3.1␤»      (same as: Rat.new(31, 10)) 
say 3.1.^name;    # OUTPUT: «Rat␤» 
say 3.1.nude;     # OUTPUT: «(31 10)␤» 
 
say <1/2>;        # OUTPUT: «0.5␤»      (same as: Rat.new(1, 2)) 
say <1/2>.^name;  # OUTPUT: «Rat␤» 
say <1/2>.nude;   # OUTPUT: «(1 2)␤» 

Thus arithmetic with short dotted-decimal numbers does not suffer from floating point errors.

To prevent the numerator and denominator from becoming pathologically large, the denominator is limited to 64 bit storage. On overflow of the denominator a Num (floating-point number) is returned instead.

For example this function crudely approximates a square root, and overflows the denominator quickly:

sub approx-sqrt($n$iterations{
    my $x = $n;
    $x = ($x + $n / $x/ 2 for ^$iterations;
    return $x;
}
say approx-sqrt(25).^name;     # OUTPUT: «Rat␤» 
say approx-sqrt(210).^name;    # OUTPUT: «Num␤» 

If you want arbitrary precision arithmetic with rational numbers, use the FatRat type instead.

Rat objects are immutable.

Methods

method perl

multi method perl(Rat:D: --> Str:D)

Returns an implementation-specific string that produces an equivalent object when given to EVAL.

say (1/3).perl;                # OUTPUT: «<1/3>␤» 
say (2/4).perl;                # OUTPUT: «0.5␤» 

Type Graph

Type relations for Rat
perl6-type-graph Rat Rat Cool Cool Rat->Cool Rational Rational Rat->Rational Mu Mu Any Any Any->Mu Cool->Any Numeric Numeric Real Real Real->Numeric Rational->Real Stringy Stringy Str Str Str->Cool Str->Stringy RatStr RatStr RatStr->Rat RatStr->Str

Stand-alone image: vector

Routines supplied by role Rational

Rat does role Rational, which provides the following routines:

(Rational) method new

method new(NuT:D: $numeratorDeT:D: $denominator --> Rational:D)

Creates a new rational object from numerator and denominator, which it normalizes to the lowest terms. The $denominator can be zero, in which case the numerator is normalized to -1, 0, or 1 depending on whether the original is negative, zero, or positive, respectively.

(Rational) method Bool

Defined as:

multi method Bool(Rational:D: --> Bool:D)

Returns False if numerator is 0, otherwise returns True. This applies for <0/0> zero-denominator Rational as well, despite ?<0/0>.Num being True.

(Rational) method Int

Defined as:

method Int(Rational:D: --> Int:D)

Coerces the invocant to Int by truncating non-whole portion of the represented number, if any. If the denominator is zero, will fail with X::Numeric::DivideByZero.

(Rational) method Num

Defined as:

method Num(Rational:D: --> Num:D)

Coerces the invocant to Num by dividing numerator by denominator. If denominator is 0, returns Inf, -Inf, or NaN, based on whether numerator is a positive number, negative number, or 0, respectively.

(Rational) method ceiling

Defined as:

method ceiling(Rational:D: --> Int:D)

Return the smallest integer not greater than the invocant. If denominator is zero, fails with X::Numeric::DivideByZero.

(Rational) method floor

Defined as:

method floor(Rational:D: --> Int:D)

Return the largest integer not greater than the invocant. If denominator is zero, fails with X::Numeric::DivideByZero.

(Rational) method isNaN

method isNaN(Rational:D: --> Bool:D)

Tests whether the invocant's Num value is a NaN. That is both its numerator and denominator are zero.

(Rational) method numerator

method numerator(Rational:D: --> NuT:D)

Returns the numerator.

(Rational) method denominator

method denominator(Rational:D: --> DeT:D)

Returns the denominator.

(Rational) method nude

method nude(Rational:D: --> Positional)

Returns a list of the numerator and denominator.

(Rational) method norm

method norm(Rational:D: --> Rational:D)

Returns a normalized Rational object, i.e. with positive denominator, and numerator and denominator coprime.

(Rational) method base-repeating

method base-repeating(Rational:D: Int:D() $base = 10)

Returns a list of two strings that, when concatenated, represent the number in base $base. The second element is the one that repeats. For example:

my ($non-rep$repeating= (19/3).base-repeating(10);
say $non-rep;                               # OUTPUT: «6.␤» 
say $repeating;                             # OUTPUT: «3␤» 
printf '%s(%s)'$non-rep$repeating;      # OUTPUT: «6.(3)» 

19/3 is 6.333333... with the 3 repeating indefinitely.

If no repetition occurs, the second string is empty:

say (5/2).base-repeating(10).perl;          # OUTPUT: «("2.5", "")␤» 

The precision for determining the repeating group is limited to 1000 characters, above that, the second string is ???.

$base defaults to 10.

Routines supplied by role Real

Rat does role Real, which provides the following routines:

(Real) method Bridge

Defined as:

method Bridge(Real:D:)

Default implementation coerces the invocant to Num and that's the behaviour of this method in core Real types. This method primarily exist to make it easy to implement custom Real types by users, with the Bridge method returning one of the core Real types (NOT necessarily a Num) that best represent the custom Real type. In turn, this lets all the core operators and methods obtain a usable value they can work with.

As an example, we can implement a custom Temperature type. It has a unit of measure and the value, which are given during instantiation. We can implement custom operators or conversion methods that work with this type. When it comes to regular mathematical operators, however, we can simply use the .Bridge method to convert the Temperature to Kelvin expressed in one of the core numeric types:

class Temperature is Real {
    has Str:D  $.unit  is required where any <K F C>;
    has Real:D $.value is required;
    method new ($value:$unit = 'K'{ self.bless :$value :$unit }
    # Note: implementing .new() that handles $value of type Temperature is left as an exercise 
 
    method Bridge {
        when $!unit eq 'F' { ($!value + 459.67) × 5/9 }
        when $!unit eq 'C' {  $!value + 273.15 }
        $!value
    }
    method gist { self.Str }
    method Str  { "$!value degrees $!unit" }
}
 
sub postfix:<> { Temperature.new: $^value:unit<C> }
sub postfix:<> { Temperature.new: $^value:unit<F> }
sub postfix:<K> { Temperature.new: $^value:unit<K> }
 
my $human := 36.6℃;
my $book  := 451℉;
my $sun   := 5778K;
say $human;                # OUTPUT: «36.6 degrees C␤» 
say $human + $book + $sun# OUTPUT: «6593.677777777778␤» 
say 123+ 456K;           # OUTPUT: «579␤» 

As we can see from the last two lines of the output, the type of the bridged result is not forced to be any particular core type. It is a Rat, when we instantiated Temperature with a Rat or when conversion was involved, and it is an Int when we instantiated Temperature with an Int.

(Real) method Complex

method Complex(Real:D: --> Complex:D)

Converts the number to a Complex with the number converted to a Num as its real part and 0e0 as the imaginary part.

(Real) method Rat

method Rat(Real:D: Real $epsilon = 1e-6)

Converts the number to a Rat with the precision $epsilon.

(Real) method Real

Defined as:

multi method Real(Real:D: --> Real:D)
multi method Real(Real:U: --> Real:D)

The :D variant simply returns the invocant. The :U variant issues a warning about using an uninitialized value in numeric context and then returns self.new.

(Real) routine rand

sub term:<rand> (--> Num:D)
method rand(Real:D: --> Real:D)

Returns a pseudo-random number between zero (inclusive) and the number (non-inclusive). The Bridge method is used to coerce the Real to a numeric that supports rand method.

The term form returns a pseudo-random Num between 0e0 (inclusive) and 1e0 (non-inclusive.)

(Real) method sign

method sign(Real:D:)

Returns -1 if the number is negative, 0 if it is zero and 1 otherwise.

(Real) method round

method round(Real:D: $scale = 1)

Rounds the number to scale $scale. If $scale is 1, rounds to an integer. If scale is 0.1, rounds to one digit after the comma etc.

(Real) method floor

method floor(Real:D --> Int:D)

Return the largest integer not greater than the number.

(Real) method ceiling

method ceiling(Real:D --> Int:D)

Returns the smallest integer not less than the number.

(Real) method truncate

method truncate(Real:D --> Int:D)

Rounds the number towards zero.

(Real) method polymod

method polymod(Real:D: +@mods)

Returns the remainders after applying sequentially all divisors in the @mods argument; the last element of the array will be the last remainder.

say (1e8+1).polymod(10 xx 8);# OUTPUT: «(1 0 0 0 0 0 0 0 1)␤» 

10 xx 8 is simply an array with eight number 10s; the first division by 10 will return 1 as a remainder, while the rest, up to the last, will return 0. With 8 divisors, as above, the result will have one more elements, in this case for the last remainder.

(Real) method base

method base(Real:D: Int:D $base where 2..36$digits? --> Str:D)

Converts the number to a string, using $base as base. For $base larger than ten, capital Latin letters are used.

255.base(16);            # 'FF' 

The optional $digits argument asks for that many digits of fraction (which may not be negative). If omitted, a reasonable default is chosen based on type. For Int this default is 0. For Num, the default is 8. For Rational, the number of places is scaled to the size of the denominator, with a minimum of 6.

A special value of Whatever (*) can be given as $digits, which functions the same as when $digits is not specified for all Real types except the Rationals. For Rationals, the Whatever indicates that you wish all of the possible digits of the fractional part, but use caution: since there's no detection of repeating fractional parts (the algorithm will eventually stop after generating 2**63 digits).

The final digit produced is always rounded.

say pi.base(103);      # OUTPUT: «3.142␤» 
say (1/128).base(10*); # OUTPUT: «0.0078125␤» 
say (1/100).base(10*); # OUTPUT: «0.01␤» 
say (1/3)  .base(10*); # WRONG: endlessly repeating fractional part 

For reverse operation, see parse-base

Routines supplied by role Numeric

Rat does role Numeric, which provides the following routines:

(Numeric) method Numeric

Defined as:

multi method Numeric(Numeric:D: --> Numeric:D)
multi method Numeric(Numeric:U: --> Numeric:D)

The :D variant simply returns the invocant. The :U variant issues a warning about using an uninitialized value in numeric context and then returns self.new.

(Numeric) method Int

method Int(Numeric:D: --> Int:D)

If this Numeric is equivalent to a Real, return the equivalent of calling truncate on that Real to get an Int. Fail with X::Numeric::Real otherwise.

(Numeric) method Rat

method Rat(Numeric:D: Real $epsilon = 1.0e-6 --> Rat:D)

If this Numeric is equivalent to a Real, return a Rat which is within $epsilon of that Real's value. Fail with X::Numeric::Real otherwise.

(Numeric) method Num

method Num(Numeric:D: --> Num:D)

If this Numeric is equivalent to a Real, return that Real as a Num as accurately as is possible. Fail with X::Numeric::Real otherwise.

(Numeric) method narrow

method narrow(Numeric:D --> Numeric:D)

Returns the number converted to the narrowest type that can hold it without loss of precision.

say (4.0 + 0i).narrow.perl;     # OUTPUT: «4␤» 
say (4.0 + 0i).narrow.^name;    # OUTPUT: «Int␤» 

(Numeric) method ACCEPTS

multi method ACCEPTS(Numeric:D: $other)

Returns True if $other can be coerced to Numeric and is numerically equal to the invocant (or both evaluate to NaN).

(Numeric) routine log

multi sub    log(Numeric:DNumeric $base = e --> Numeric:D)
multi method log(Numeric:D: Numeric $base = e --> Numeric:D)

Calculates the logarithm to base $base. Defaults to the natural logarithm. Returns NaN if $base is negative. Throws an exception if $base is 1.

(Numeric) routine log10

multi sub    log10(Numeric:D  --> Numeric:D)
multi method log10(Numeric:D: --> Numeric:D)

Calculates the logarithm to base 10. Returns NaN for negative arguments and -Inf for 0.

(Numeric) routine exp

multi sub    exp(Numeric:DNumeric:D $base = e --> Numeric:D)
multi method exp(Numeric:D: Numeric:D $base = e --> Numeric:D)

Returns $base to the power of the number, or e to the power of the number if called without a second argument.

(Numeric) method roots

multi method roots(Numeric:D: Int:D $n --> Positional)

Returns a list of the $n complex roots, which evaluate to the original number when raised to the $nth power.

(Numeric) routine abs

multi sub    abs(Numeric:D  --> Real:D)
multi method abs(Numeric:D: --> Real:D)

Returns the absolute value of the number.

(Numeric) routine sqrt

multi sub    sqrt(Numeric:D --> Numeric:D)
multi method sqrt(Numeric:D --> Numeric:D)

Returns a square root of the number. For real numbers the positive square root is returned.

On negative real numbers, sqrt returns NaN rather than a complex number, in order to not confuse people who are not familiar with complex arithmetic. If you want to calculate complex square roots, coerce to Complex first, or use the roots method.

(Numeric) method conj

multi method conj(Numeric:D --> Numeric:D)

Returns the complex conjugate of the number. Returns the number itself for real numbers.

(Numeric) method Bool

multi method Bool(Numeric:D:)

Returns False if the number is equivalent to zero, and True otherwise.

(Numeric) method succ

method succ(Numeric:D:)

Returns the number incremented by one (successor).

(Numeric) method pred

method pred(Numeric:D:)

Returns the number decremented by one (predecessor).

Routines supplied by class Cool

Rat inherits from class Cool, which provides the following routines:

(Cool) routine abs

Defined as:

sub abs(Numeric() $x)
method abs()

Coerces the invocant (or in the sub form, the argument) to Numeric and returns the absolute value (that is, a non-negative number).

say (-2).abs;       # OUTPUT: «2␤» 
say abs "6+8i";     # OUTPUT: «10␤» 

(Cool) method conj

Defined as:

method conj()

Coerces the invocant to Numeric and returns the complex conjugate (that is, the number with the sign of the imaginary part negated).

say (1+2i).conj;        # OUTPUT: «1-2i␤» 

(Cool) routine sqrt

Defined as:

sub sqrt(Numeric(Cool$x)
method sqrt()

Coerces the invocant to Numeric (or in the sub form, the argument) and returns the square root, that is, a non-negative number that, when multiplied with itself, produces the original number.

say 4.sqrt;             # OUTPUT: «2␤» 
say sqrt(2);            # OUTPUT: «1.4142135623731␤» 

(Cool) method sign

Defined as:

method sign()

Coerces the invocant to Numeric and returns its sign, that is, 0 if the number is 0, 1 for positive and -1 for negative values.

say 6.sign;             # OUTPUT: «1␤» 
say (-6).sign;          # OUTPUT: «-1␤» 
say "0".sign;           # OUTPUT: «0␤» 

(Cool) method rand

Defined as:

method rand()

Coerces the invocant to Num and returns a pseudo-random value between zero and the number.

say 1e5.rand;           # OUTPUT: «33128.495184283␤» 

(Cool) routine sin

Defined as:

sub sin(Numeric(Cool))
method sin()

Coerces the invocant (or in the sub form, the argument) to Numeric, interprets it as radians, returns its sine.

say sin(0);             # OUTPUT: «0␤» 
say sin(pi/4);          # OUTPUT: «0.707106781186547␤» 
say sin(pi/2);          # OUTPUT: «1␤» 

Note that Perl 6 is no computer algebra system, so sin(pi) typically does not produce an exact 0, but rather a very small floating-point number.

(Cool) routine asin

Defined as:

sub asin(Numeric(Cool))
method asin()

Coerces the invocant (or in the sub form, the argument) to Numeric, and returns its arc-sine in radians.

say 0.1.asin;               # OUTPUT: «0.10016742116156␤» 
say asin(0.1);              # OUTPUT: «0.10016742116156␤» 

(Cool) routine cos

Defined as:

sub cos(Numeric(Cool))
method cos()

Coerces the invocant (or in sub form, the argument) to Numeric, interprets it as radians, returns its cosine.

say 0.cos;                  # OUTPUT: «1␤» 
say pi.cos;                 # OUTPUT: «-1␤» 
say cos(pi/2);              # OUTPUT: «6.12323399573677e-17␤» 

(Cool) routine acos

Defined as:

sub acos(Numeric(Cool))
method acos()

Coerces the invocant (or in sub form, the argument) to Numeric, and returns its arc-cosine in radians.

say 1.acos;                 # OUTPUT: «0␤» 
say acos(-1);               # OUTPUT: «3.14159265358979␤» 

(Cool) routine tan

Defined as:

sub tan(Numeric(Cool))
method tan()

Coerces the invocant (or in sub form, the argument) to Numeric, interprets it as radians, returns its tangent.

say tan(3);                 # OUTPUT: «-0.142546543074278␤» 
say 3.tan;                  # OUTPUT: «-0.142546543074278␤» 

(Cool) routine atan

Defined as:

sub atan(Numeric(Cool))
method atan()

Coerces the invocant (or in sub form, the argument) to Numeric, and returns its arc-tangent in radians.

say atan(3);                # OUTPUT: «1.24904577239825␤» 
say 3.atan;                 # OUTPUT: «1.24904577239825␤» 

(Cool) routine atan2

Defined as:

sub atan2(Numeric() $xNumeric() $y = 1e0)
method atan2($y = 1e0)

Coerces the arguments (including the invocant in the method form) to Numeric, and returns their two-argument arc-tangent in radians.

say atan2(3);               # OUTPUT: «1.24904577239825␤» 
say 3.atan2;                # OUTPUT: «1.24904577239825␤» 

(Cool) routine sec

Defined as:

sub sec(Numeric(Cool))
method sec()

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its secant, that is, the reciprocal of its cosine.

say 45.sec;                 # OUTPUT: «1.90359440740442␤» 
say sec(45);                # OUTPUT: «1.90359440740442␤» 

(Cool) routine asec

Defined as:

sub asec(Numeric(Cool))
method asec()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its arc-secant in radians.

say 1.asec;                 # OUTPUT: «0␤» 
say sqrt(2).asec;           # OUTPUT: «0.785398163397448␤» 

(Cool) routine cosec

Defined as:

sub cosec(Numeric(Cool))
method cosec()

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its cosecant, that is, the reciprocal of its sine.

say 0.45.cosec;             # OUTPUT: «2.29903273150897␤» 
say cosec(0.45);            # OUTPUT: «2.29903273150897␤» 

(Cool) routine acosec

Defined as:

sub acosec(Numeric(Cool))
method acosec()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its arc-cosecant in radians.

say 45.acosec;              # OUTPUT: «0.0222240516182672␤» 
say acosec(45)              # OUTPUT: «0.0222240516182672␤» 

(Cool) routine cotan

Defined as:

sub cotan(Numeric(Cool))
method cotan()

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians, returns its cotangent, that is, the reciprocal of its tangent.

say 45.cotan;               # OUTPUT: «0.617369623783555␤» 
say cotan(45);              # OUTPUT: «0.617369623783555␤» 

(Cool) routine acotan

Defined as:

sub acotan(Numeric(Cool))
method acotan()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its arc-cotangent in radians.

say 45.acotan;              # OUTPUT: «0.0222185653267191␤» 
say acotan(45)              # OUTPUT: «0.0222185653267191␤» 

(Cool) routine sinh

Defined as:

sub sinh(Numeric(Cool))
method sinh()

Coerces the invocant (or in method form, its argument) to Numeric, and returns its Sine hyperbolicus.

say 1.sinh;                 # OUTPUT: «1.1752011936438␤» 
say sinh(1);                # OUTPUT: «1.1752011936438␤» 

(Cool) routine asinh

Defined as:

sub asinh(Numeric(Cool))
method asinh()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse Sine hyperbolicus.

say 1.asinh;                # OUTPUT: «0.881373587019543␤» 
say asinh(1);               # OUTPUT: «0.881373587019543␤» 

(Cool) routine cosh

Defined as:

sub cosh(Numeric(Cool))
method cosh()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Cosine hyperbolicus.

say cosh(0.5);              # OUTPUT: «1.12762596520638␤» 

(Cool) routine acosh

Defined as:

sub acosh(Numeric(Cool))
method acosh()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse Cosine hyperbolicus.

say acosh(45);              # OUTPUT: «4.4996861906715␤» 

(Cool) routine tanh

Defined as:

sub tanh(Numeric(Cool))
method tanh()

Coerces the invocant (or in sub form, its argument) to Numeric, interprets it as radians and returns its Tangent hyperbolicus.

say tanh(0.5);              # OUTPUT: «0.46211715726001␤» 
say tanh(atanh(0.5));       # OUTPUT: «0.5␤» 

(Cool) routine atanh

Defined as:

sub atanh(Numeric(Cool))
method atanh()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse tangent hyperbolicus.

say atanh(0.5);             # OUTPUT: «0.549306144334055␤» 

(Cool) routine sech

Defined as:

sub sech(Numeric(Cool))
method sech()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Secant hyperbolicus.

say 0.sech;                 # OUTPUT: «1␤» 

(Cool) routine asech

Defined as:

sub asech(Numeric(Cool))
method asech()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse hyperbolic secant.

say 0.8.asech;              # OUTPUT: «0.693147180559945␤» 

(Cool) routine cosech

Defined as:

sub cosech(Numeric(Cool))
method cosech()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Hyperbolic cosecant.

say cosech(pi/2);           # OUTPUT: «0.434537208094696␤» 

(Cool) routine acosech

Defined as:

sub acosech(Numeric(Cool))
method acosech()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse hyperbolic cosecant.

say acosech(4.5);           # OUTPUT: «0.220432720979802␤» 

(Cool) routine cotanh

Defined as:

sub cotanh(Numeric(Cool))
method cotanh()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Hyperbolic cotangent.

say cotanh(pi);             # OUTPUT: «1.00374187319732␤» 

(Cool) routine acotanh

Defined as:

sub acotanh(Numeric(Cool))
method acotanh()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns its Inverse hyperbolic cotangent.

say acotanh(2.5);           # OUTPUT: «0.423648930193602␤» 

(Cool) routine cis

Defined as:

sub cis(Numeric(Cool))
method cis()

Coerces the invocant (or in sub form, its argument) to Numeric, and returns cos(argument) + i*sin(argument).

say cis(pi/4);              # OUTPUT: «0.707106781186548+0.707106781186547i␤» 

(Cool) routine log

Defined as:

multi sub log(Numeric(Cool$numberNumeric(Cool$base?)
multi method log(Cool:D: Cool:D $base?)

Coerces the arguments (including the invocant in the method form) to Numeric, and returns its Logarithm to base $base, or to base e (Euler's Number) if no base was supplied (Natural logarithm). Returns NaN if $base is negative. Throws an exception if $base is 1.

say (e*e).log;              # OUTPUT: «2␤» 

(Cool) routine log10

Defined as:

multi sub log10(Cool(Numeric))
multi method log10()

Coerces the invocant (or in the sub form, the invocant) to Numeric, and returns its Logarithm to base 10, that is, a number that approximately produces the original number when raised to the power of 10. Returns NaN for negative arguments and -Inf for 0.

say log10(1001);            # OUTPUT: «3.00043407747932␤» 

(Cool) routine exp

Defined as:

multi sub exp(Cool:D $powCool:D $base?)
multi method exp(Cool:D: Cool:D $base?)

Coerces the arguments (including the invocant in the method from) to Numeric, and returns $base raised to the power of the first number. If no $base is supplied, e (Euler's Number) is used.

say 0.exp;      # OUTPUT: «1␤» 
say 1.exp;      # OUTPUT: «2.71828182845905␤» 
say 10.exp;     # OUTPUT: «22026.4657948067␤» 

(Cool) method unpolar

Defined as:

method unpolar(Numeric(Cool))

Coerces the arguments (including the invocant in the method form) to Numeric, and returns a complex number from the given polar coordinates. The invocant (or the first argument in sub form) is the magnitude while the argument (i.e. the second argument in sub form) is the angle. The angle is assumed to be in radians.

say sqrt(2).unpolar(pi/4);      # OUTPUT: «1+1i␤» 

(Cool) routine round

Defined as:

multi sub round(Numeric(Cool))
multi method round(Cool:D: $unit = 1)

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it to the unit of $unit. If $unit is 1, rounds to the nearest integer.

say 1.7.round;          # OUTPUT: «2␤» 
say 1.07.round(0.1);    # OUTPUT: «1.1␤» 
say 21.round(10);       # OUTPUT: «20␤» 

Always rounds up if the number is at mid-point:

say (−.5 ).round;       # OUTPUT: «0␤» 
say ( .5 ).round;       # OUTPUT: «1␤» 
say (−.55).round(.1);   # OUTPUT: «-0.5␤» 
say ( .55).round(.1);   # OUTPUT: «0.6␤» 

Pay attention to types when using this method, as ending up with the wrong type may affect the precision you seek to achieve. For Real types, the type of the result is the type of the argument (Complex argument gets coerced to Real, ending up a Num). If rounding a Complex, the result is Complex as well, regardless of the type of the argument.

9930972392403501.round(1)      .perl.say# OUTPUT: «9930972392403501␤» 
9930972392403501.round(1e0)    .perl.say# OUTPUT: «9.9309723924035e+15␤» 
9930972392403501.round(1e0).Int.perl.say# OUTPUT: «9930972392403500␤» 

(Cool) routine floor

Defined as:

multi sub floor(Numeric(Cool))
multi method floor

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it downwards to the nearest integer.

say "1.99".floor;       # OUTPUT: «1␤» 
say "-1.9".floor;       # OUTPUT: «-2␤» 
say 0.floor;            # OUTPUT: «0␤» 

(Cool) method fmt

Defined as:

method fmt($format = '%s')

Equivalent to calling sprintf with $format as format and the invocant as the second argument. The $format will be coerced to Stringy and defaults to '%s'

(Cool) routine ceiling

Defined as:

multi sub ceiling(Numeric(Cool))
multi method ceiling

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it upwards to the nearest integer.

say "1".ceiling;        # OUTPUT: «1␤» 
say "-0.9".ceiling;     # OUTPUT: «0␤» 
say "42.1".ceiling;     # OUTPUT: «43␤» 

(Cool) routine truncate

Defined as:

multi sub truncate(Numeric(Cool))
multi method truncate()

Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it towards zero.

say 1.2.truncate;       # OUTPUT: «1␤» 
say truncate -1.2;      # OUTPUT: «-1␤» 

(Cool) routine ord

Defined as:

sub ord(Str(Cool))
method ord()

Coerces the invocant (or in sub form, its argument) to Str, and returns the Unicode code point number of the first code point.

say 'a'.ord;            # OUTPUT: «97␤» 

The inverse operation is chr.

Mnemonic: returns an ordinal number

(Cool) method path

Defined as:

method path()

DEPRECATED. Existed only in the Rakudo implementation and isn't part of any language released. Will issue deprecation warnings in future language versions and eventually will be removed entirely.

Stringifies the invocant and converts it to IO::Path object. Use the .IO method instead.

(Cool) routine chr

Defined as:

sub chr(Int(Cool))
method chr()

Coerces the invocant (or in sub form, its argument) to Int, interprets it as a Unicode code points, and returns a string made of that code point.

say '65'.chr;       # OUTPUT: «A␤» 

The inverse operation is ord.

Mnemonic: turns an integer into a character.

(Cool) routine chars

Defined as:

sub chars(Str(Cool))
method chars()

Coerces the invocant (or in sub form, its argument) to Str, and returns the number of characters in the string. Please note that on the JVM, you currently get codepoints instead of graphemes.

say 'møp'.chars;    # OUTPUT: «3␤» 
say 'ã̷̠̬̊'.chars;     # OUTPUT: «1␤» 
say '👨‍👩‍👧‍👦🏿'.chars;    # OUTPUT: «1␤» 

Graphemes are user visible characters. That is, this is what the user thinks of as a “character”.

Graphemes can contain more than one codepoint. Typically the number of graphemes and codepoints differs when Prepend or Extend characters are involved (also known as Combining characters), but there are many other cases when this may happen. Another example is \c[ZWJ] (Zero-width joiner).

You can check Grapheme_Cluster_Break property of a character in order to see how it is going to behave:

say ã̷̠̬̊.uniprops(Grapheme_Cluster_Break); # OUTPUT: «(Other Extend Extend Extend Extend)␤» 
say 👨‍👩‍👧‍👦🏿.uniprops(Grapheme_Cluster_Break); # OUTPUT: «(E_Base_GAZ ZWJ E_Base_GAZ ZWJ E_Base_GAZ ZWJ E_Base_GAZ E_Modifier)␤» 

You can read more about graphemes in the Unicode Standard, which Perl 6 tightly follows, using a method called NFG, normal form graphemes for efficiently representing them.

(Cool) routine codes

Defined as:

sub codes(Str(Cool))
method codes()

Coerces the invocant (or in sub form, its argument) to Str, and returns the number of Unicode code points.

say 'møp'.codes;    # OUTPUT: «3␤» 

The same result will be obtained with

say +'møp'.ords;    # OUTPUT: «3␤» 

ords first obtains the actual codepoints, so there might be a difference in speed.

(Cool) routine flip

Defined as:

sub flip(Str(Cool))
method flip()

Coerces the invocant (or in sub form, its argument) to Str, and returns a reversed version.

say 421.flip;       # OUTPUT: «124␤» 

(Cool) routine trim

Defined as:

sub trim(Str(Cool))
method trim()

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with both leading and trailing whitespace stripped.

my $stripped = '  abc '.trim;
say "<$stripped>";          # OUTPUT: «<abc>␤» 

(Cool) routine trim-leading

Defined as:

sub trim-leading(Str(Cool))
method trim-leading()

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with leading whitespace stripped.

my $stripped = '  abc '.trim-leading;
say "<$stripped>";          # OUTPUT: «<abc >␤» 

(Cool) routine trim-trailing

Defined as:

sub trim-trailing(Str(Cool))
method trim-trailing()

Coerces the invocant (or in sub form, its argument) to Str, and returns the string with trailing whitespace stripped.

my $stripped = '  abc '.trim-trailing;
say "<$stripped>";          # OUTPUT: «<  abc>␤» 

(Cool) routine lc

Defined as:

sub lc(Str(Cool))
method lc()

Coerces the invocant (or in sub form, its argument) to Str, and returns it case-folded to lower case.

say "ABC".lc;       # OUTPUT: «abc␤» 

(Cool) routine uc

Defined as:

sub uc(Str(Cool))
method uc()

Coerces the invocant (or in sub form, its argument) to Str, and returns it case-folded to upper case (capital letters).

say "Abc".uc;       # OUTPUT: «ABC␤» 

(Cool) routine fc

Defined as:

sub fc(Str(Cool))
method fc()

Coerces the invocant (or in sub form, its argument) to Str, and returns the result a Unicode "case fold" operation suitable for doing caseless string comparisons. (In general, the returned string is unlikely to be useful for any purpose other than comparison.)

say "groß".fc;       # OUTPUT: «gross␤» 

(Cool) routine tc

Defined as:

sub tc(Str(Cool))
method tc()

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the first letter case-folded to title case (or where not available, upper case).

say "abC".tc;       # OUTPUT: «AbC␤» 

(Cool) routine tclc

Defined as:

sub tclc(Str(Cool))
method tclc()

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the first letter case-folded to title case (or where not available, upper case), and the rest of the string case-folded to lower case.

say 'abC'.tclc;     # OUTPUT: «Abc␤» 

(Cool) routine wordcase

Defined as:

sub wordcase(Str(Cool$input:&filter = &tclcMu :$where = True)
method wordcase(:&filter = &tclcMu :$where = True)

Coerces the invocant (or in sub form, the first argument) to Str, and filters each word that smartmatches against $where through the &filter. With the default filter (first character to upper case, rest to lower) and matcher (which accepts everything), this title-cases each word:

say "perl 6 programming".wordcase;      # OUTPUT: «Perl 6 Programming␤» 

With a matcher:

say "have fun working on perl".wordcase(:where({ .chars > 3 }));
                                        # Have fun Working on Perl 

With a customer filter too:

say "have fun working on perl".wordcase(:filter(&uc), :where({ .chars > 3 }));
                                        # HAVE fun WORKING on PERL 

(Cool) routine samecase

Defined as:

sub samecase(Cool $stringCool $pattern)
method samecase(Cool:D: Cool $pattern)

Coerces the invocant (or in sub form, the first argument) to Str, and returns a copy of $string with case information for each individual character changed according to $pattern. (The pattern string can contain three types of characters, i.e. uppercase, lowercase and caseless. For a given character in $pattern its case information determines the case of the corresponding character in the result.) If $string is longer than $pattern, the case information from the last character of $pattern is applied to the remaining characters of $string.

say "perL 6".samecase("A__a__"); # OUTPUT: «Perl 6␤» 
say "pERL 6".samecase("Ab");     # OUTPUT: «Perl 6␤» 

(Cool) routine uniprop

Defined as:

multi sub uniprop(Str:D|c)
multi sub uniprop(Int:D $code)
multi sub uniprop(Int:D $codeStringy:D $propname)
multi method uniprop(|c)

Returns the unicode property of the first character. If no property is specified returns the General Category. Returns a Bool for Boolean properties.

say 'a'.uniprop;               # OUTPUT: «Ll␤» 
say '1'.uniprop;               # OUTPUT: «Nd␤» 
say 'a'.uniprop('Alphabetic'); # OUTPUT: «True␤» 
say '1'.uniprop('Alphabetic'); # OUTPUT: «False␤» 

(Cool) sub uniprops

Defined as:

sub uniprops(Str:D $strStringy:D $propname = "General_Category")

Interprets the invocant as a Str, and returns the unicode property for each character as a Seq. If no property is specified returns the General Category. Returns a Bool for Boolean properties. Similar to uniprop

(Cool) routine uniname

Defined as:

sub uniname(Str(Cool--> Str)
method uniname(--> Str)

Interprets the invocant / first argument as a Str, and returns the Unicode codepoint name of the first codepoint of the first character. See uninames for a routine that works with multiple codepoints, and uniparse for the opposite direction.

# Camelia in Unicode 
say »ö«.uniname;
# OUTPUT: «"RIGHT-POINTING DOUBLE ANGLE QUOTATION MARK"␤» 
say "Ḍ̇".uniname# Note, doesn't show "COMBINING DOT ABOVE" 
# OUTPUT: «"LATIN CAPITAL LETTER D WITH DOT BELOW"␤» 
 
# Find the char with the longest Unicode name. 
say (0..0x1FFFF).sort(*.uniname.chars)[*-1].chr.uniname;
# OUTPUT: ««ARABIC LIGATURE UIGHUR KIRGHIZ YEH WITH HAMZA ABOVE WITH ALEF MAKSURA INITIAL FORM␤»␤» 

(Cool) routine uninames

Defined as:

sub uninames(Str:D)
method uninames()

Returns of a Seq of Unicode names for the all the codepoints in the Str provided.

say »ö«.uninames.perl;
# OUTPUT: «("RIGHT-POINTING DOUBLE ANGLE QUOTATION MARK", "LATIN SMALL LETTER O WITH DIAERESIS", "LEFT-POINTING DOUBLE ANGLE QUOTATION MARK").Seq␤» 

Note this example, which gets a Seq where each element is a Seq of all the codepoints in that character.

say "Ḍ̇'oh".comb>>.uninames.perl;
# OUTPUT: «(("LATIN CAPITAL LETTER D WITH DOT BELOW", "COMBINING DOT ABOVE").Seq, ("APOSTROPHE",).Seq, ("LATIN SMALL LETTER O",).Seq, ("LATIN SMALL LETTER H",).Seq)␤» 

See uniparse for the opposite direction.

(Cool) routine unimatch

Defined as:

multi sub unimatch(Str:D $str|c)
multi unimatch(Int:D $codeStringy:D $pvalnameStringy:D $propname = $pvalname)

Checks if the given integer codepoint or the first letter of the string given have a unicode property equal to the value you give. If you supply the Unicode property to be checked it will only return True if that property matches the given value.

say unimatch 'A''Latin';           # OUTPUT: «True␤» 
say unimatch 'A''Latin''Script'# OUTPUT: «True␤» 
say unimatch 'A''Ll';              # OUTPUT: «True␤» 

(Cool) routine chop

Defined as:

sub chop(Str(Cool))
method chop()

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the last character removed.

say 'perl'.chop;                        # OUTPUT: «per␤» 

(Cool) routine chomp

Defined as:

sub chomp(Str(Cool))
method chomp()

Coerces the invocant (or in sub form, its argument) to Str, and returns it with the last character removed, if it is a logical newline.

say 'ab'.chomp.chars;                   # OUTPUT: «2␤» 
say "a\n".chomp.chars;                  # OUTPUT: «1␤» 

(Cool) routine substr

Defined as:

sub substr(Str(Cool$str|c)
method substr(|c)

Coerces the invocant (or in the sub form, the first argument) to Str, and calls Str.substr with the arguments.

(Cool) routine substr-rw

Defined as:

multi method substr-rw(|) is rw
multi sub substr-rw(|) is rw

Coerces the invocant (or in the sub form, the first argument) to Str, and calls Str.substr-rw with the arguments.

(Cool) routine ords

Defined as:

sub ords(Str(Cool$str)
method ords()

Coerces the invocant (or in the sub form, the first argument) to Str, and returns a list of Unicode codepoints for each character.

say "Camelia".ords;              # OUTPUT: «67 97 109 101 108 105 97␤» 
say ords 10;                     # OUTPUT: «49 48␤» 

This is the list-returning version of ord. The inverse operation in chrs. If you are only interested in the number of codepoints, codes is a possibly faster option.

(Cool) routine chrs

Defined as:

sub chrs(*@codepoints --> Str:D)
method chrs()

Coerces the invocant (or in the sub form, the argument list) to a list of integers, and returns the string created by interpreting each integer as a Unicode codepoint, and joining the characters.

say <67 97 109 101 108 105 97>.chrs;   # OUTPUT: «Camelia␤» 

This is the list-input version of chr. The inverse operation is ords.

(Cool) routine split

Defined as:

multi sub    split(  Str:D $delimiterStr(Cool$input$limit = Inf:$k:$v:$kv:$p:$skip-empty)
multi sub    split(Regex:D $delimiterStr(Cool$input$limit = Inf:$k:$v:$kv:$p:$skip-empty)
multi sub    split(@delimitersStr(Cool$input$limit = Inf:$k:$v:$kv:$p:$skip-empty)
multi method split(  Str:D $delimiter$limit = Inf:$k:$v:$kv:$p:$skip-empty)
multi method split(Regex:D $delimiter$limit = Inf:$k:$v:$kv:$p:$skip-empty)
multi method split(@delimiters$limit = Inf:$k:$v:$kv:$p:$skip-empty)

NOTE: the comb routine is a much better choice for many tasks that in other languages are handled by the split.

Coerces the invocant (or in the sub form, the second argument) to Str, and splits it into pieces based on delimiters found in the string.

If $delimiter is a string, it is searched for literally and not treated as a regex. You can also provide multiple delimiters by specifying them as a list; mixing Cool and Regex objects is OK.

say split(';'"a;b;c").perl;               # OUTPUT: «("a", "b", "c")␤» 
say split(';'"a;b;c"2).perl;            # OUTPUT: «("a", "b;c").Seq␤» 
 
say split(';'"a;b;c,d").perl;             # OUTPUT: «("a", "b", "c,d")␤» 
say split(/\;/"a;b;c,d").perl;            # OUTPUT: «("a", "b", "c,d")␤» 
say split(/<[;,]>/"a;b;c,d").perl;        # OUTPUT: «("a", "b", "c", "d")␤» 
 
say split(['a', /b+/4], '1a2bb345').perl# OUTPUT: «("1", "2", "3", "5")␤» 

By default, split omits the matches, and returns a list of only those parts of the string that did not match. Specifying one of the :k, :v, :kv, :p adverbs changes that. Think of the matches as a list that is interleaved with the non-matching parts.

The :v interleaves the values of that list, which will be either Match objects, if a Regex was used as a matcher in the split, or Str objects, if a Cool was used as matcher. If multiple delimiters are specified, Match objects will be generated for all of them, unless all of the delimiters are Cool.

say 'abc'.split(/b/:v);               # OUTPUT: «(a 「b」 c)␤» 
say 'abc'.split('b':v);               # OUTPUT: «(a b c)␤» 

:k interleaves the keys, that is, the indexes:

say 'abc'.split(/b/:k);               # OUTPUT: «(a 0 c)␤» 

:kv adds both indexes and matches:

say 'abc'.split(/b/:kv);               # OUTPUT: «(a 0 「b」 c)␤» 

and :p adds them as Pairs, using the same types for values as :v does:

say 'abc'.split(/b/:p);               # OUTPUT: «(a 0 => 「b」 c)␤» 
say 'abc'.split('b':p);               # OUTPUT: «(a 0 => b c)␤» 

You can only use one of the :k, :v, :kv, :p adverbs in a single call to split.

Note that empty chunks are not removed from the result list. For that behavior, use the :skip-empty named argument:

say ("f,,b,c,d".split: /","/             ).perl;  # OUTPUT: «("f", "", "b", "c", "d")␤» 
say ("f,,b,c,d".split: /","/:skip-empty).perl;  # OUTPUT: «("f", "b", "c", "d")␤» 

(Cool) routine lines

Defined as:

sub lines(Str(Cool))
method lines()

Coerces the invocant (and in sub form, the argument) to Str, decomposes it into lines (with the newline characters stripped), and returns the list of lines.

say lines("a\nb\n").join('|');          # OUTPUT: «a|b␤» 
say "some\nmore\nlines".lines.elems;    # OUTPUT: «3␤» 

This method can be used as part of an IO::Path to process a file line-by-line, since IO::Path objects inherit from Cool, e.g.:

for 'huge-csv'.IO.lines -> $line {
    # Do something with $line 
}
 
# or if you'll be processing later 
my @lines = 'huge-csv'.IO.lines;

Without any arguments, sub lines operates on $*ARGFILES, which defaults to $*IN in the absence of any filenames.

To modify values in place use is copy to force a writable container.

for $*IN.lines -> $_ is copy { s/(\w+)/{$0 ~ $0}/.say }

(Cool) method words

Defined as:

method words(Int() $limit)

Coerces the invocant to Str, and returns a list of words that make up the string (and if $limit is supplied, only the first $limit words).

say 'The quick brown fox'.words.join('|');      # OUTPUT: «The|quick|brown|fox␤» 
say 'The quick brown fox'.words(2).join('|');   # OUTPUT: «The|quick␤» 

Only whitespace counts as word boundaries

say "isn't, can't".words.join('|');             # OUTPUT: «isn't,|can't␤» 

(Cool) routine comb

Defined as:

multi sub comb(Regex $matcherStr(Cool$input$limit = * --> Seq)
multi method comb(Regex $matcher$limit = * --> Seq)

Returns all (or if supplied, at most $limit) matches of the invocant (method form) or the second argument (sub form) against the Regex as a list of strings.

say "6 or 12".comb(/\d+/).join("");           # OUTPUT: «6, 12␤» 

(Cool) method contains

Defined as:

method contains(Cool:D: |c)

Coerces the invocant Str, and calls Str.contains on it. Please refer to that version of the method for arguments and general syntax.

say 123.contains("2")# OUTPUT: «True␤» 

Since Int is a subclass of Cool, 123 is coerced to a Str and then contains is called on it.

say (1,1* + * … * > 250).contains(233)# OUTPUT: «True␤» 

Seqs are also subclasses of Cool, and they are stringified to a comma-separated form. In this case we are also using an Int, which is going to be stringified also; "233" is included in that sequence, so it returns True. Please note that this sequence is not lazy; the stringification of lazy sequences does not include each and every one of their components for obvious reasons.

(Cool) routine index

Defined as:

multi sub    index(Str(Cool$sStr:D $needleInt(Cool$startpos = 0 --> Int)
multi method index(Str(Cool$needleInt(Cool$startpos = 0 --> Int)

Coerces the first two arguments (in method form, also counting the invocant) to Str, and searches for $needle in the string starting from $startpos. It returns the offset into the string where $needle was found, and an undefined value if it was not found.

See the documentation in type Str for examples.

(Cool) routine rindex

Defined as:

multi sub    rindex(Str(Cool$haystackStr(Cool$needleInt(Cool$startpos = $haystack.chars)
multi method rindex(Str(Cool$haystack: Str(Cool$needleInt(Cool$startpos = $haystack.chars)

Coerces the first two arguments (including the invocant in method form) to Str and $startpos to Int, and returns the last position of $needle in $haystack not after $startpos. Returns an undefined value if $needle wasn't found.

See the documentation in type Str for examples.

(Cool) method match

Defined as:

multi method match(Cool:D: $target*%adverbs)

Coerces the invocant to Str and calls the method match on it.

(Cool) method fmt

Defined as:

method fmt($format = '%s' --> Str:D)

Uses $format to return a formatted representation of the invocant.

For more information about formats strings, see sprintf.

say 11.fmt('This Int equals %03d');               # OUTPUT: «This Int equals 011␤» 
say '16'.fmt('Hexadecimal %x');                   # OUTPUT: «Hexadecimal 10␤» 

(Cool) routine roots

Defined as:

multi sub roots(Numeric(Cool$xInt(Cool$n)
multi method roots(Int(Cool$n)

Coerces the first argument (and in method form, the invocant) to Numeric and the second ($n) to Int, and produces a list of $n Complex $n-roots, which means numbers that, raised to the $nth power, approximately produce the original number.

For example

my $original = 16;
my @roots = $original.roots(4);
say @roots;
 
for @roots -> $r {
    say abs($r ** 4 - $original);
}
 
# OUTPUT:«2+0i 1.22464679914735e-16+2i -2+2.44929359829471e-16i -3.67394039744206e-16-2i␤» 
# OUTPUT:«1.77635683940025e-15␤» 
# OUTPUT:«4.30267170434156e-15␤» 
# OUTPUT:«8.03651692704705e-15␤» 
# OUTPUT:«1.04441561648202e-14␤» 

(Cool) method match

Defined as:

method match(|)

Coerces the invocant to Stringy and calls Str.match.

(Cool) method subst

Defined as:

method subst(|)

Coerces the invocant to Stringy and calls Str.subst.

(Cool) method trans

Defined as:

method trans(|)

Coerces the invocant to Str and calls Str.trans

(Cool) method IO

Defined as:

method IO(--> IO::Path:D)

Coerces the invocant to IO::Path.

.say for '.'.IO.dir;        # gives a directory listing 

(Cool) routine EVAL

Defined as:

method EVAL(*%_)
sub EVAL($code where Cool|Blob:$lang = 'perl6')

The method form calls subroutine form with invocant as $code, passing along named args, if any. Subroutine form coerces Cool $code to Str. If $code is a Blob, it'll be processed using the same encoding as the $lang compiler would: for perl6, uses the encoding specified via --encoding command line argument, or utf-8 if none were given; for Perl5, processes using same rules as perl.

This works as-is with a literal string parameter. More complex input, such as a variable or string with embedded code, is illegal by default. This can be overridden in any of several ways:

use MONKEY-SEE-NO-EVAL# Or... 
use MONKEY;             # shortcut that turns on all MONKEY pragmas 
use Test;
 
# any of the above allows: 
EVAL "say { 5 + 5 }";   # OUTPUT: «10␤» 

In case the MONKEY-SEE-NO-EVAL pragma is not activated, the compiler will complain with a EVAL is a very dangerous function!!! exception. And it is essentially right, since that will run arbitrary code with the same permissions as the program. You should take care of cleaning the code that is going to pass through EVAL if you activate the MONKEY-SEE-NO-EVAL pragma.

Please note that you can interpolate to create routine names using quotation, as can be seen in this example or other ways to interpolate to create identifier names. This only works, however, for already declared functions and other objects and is thus safer to use.

Symbols in the current lexical scope are visible to code in an EVAL.

my $answer = 42;
EVAL 'say $answer;';    # OUTPUT: «42␤» 

However, since the set of symbols in a lexical scope is immutable after compile time, an EVAL can never introduce symbols into the surrounding scope.

EVAL 'my $lives = 9'say $lives;   # error, $lives not declared 

Furthermore, the EVAL is evaluated in the current package:

module M {
    EVAL 'our $answer = 42'
}
say $M::answer;         # OUTPUT: «42␤» 

And also the current language, meaning any added syntax is available:

sub infix:<mean>(*@ais assoc<list> {
    @a.sum / @a.elems
}
EVAL 'say 2 mean 6 mean 4';     # OUTPUT: «4␤» 

An EVAL statement evaluates to the result of the last statement:

sub infix:<mean>(*@ais assoc<list> {
    @a.sum / @a.elems
}
say EVAL 'say 1; 2 mean 6 mean 4';         # OUTPUT: «1␤4␤» 

EVAL is also a gateway for executing code in other languages:

EVAL "use v5.20; say 'Hello from perl5!'":lang<Perl5>;

(Cool) sub EVALFILE

Defined as:

sub EVALFILE($filename where Blob|Cool:$lang = 'perl6')

Slurps the specified file and evaluates it. Behaves the same way as EVAL with regard to Blob decoding, scoping, and the $lang parameter. Evaluates to the value produced by the final statement in the file.

EVALFILE "foo.p6";

(Cool) routine unpolar

Defined as:

method unpolar(Real $angle)
multi sub unpolar(Real $magReal $angle)

Returns a Complex with the coordinates corresponding to the angle in radians and magnitude corresponding to the object value or $mag in the case it's being used as a sub

say 1.unpolar(⅓*pi);
# OUTPUT: «0.5000000000000001+0.8660254037844386i␤»