class Complex is Cool does Numeric {}

Represents a number in the complex plane.

Complex objects are immutable.

Operators

postfix i

Adding a trailing i to a number literal makes it a Complex, for example:

say 2i;     # same as Complex.new(0, 2); 
say 1-2e3i; # same as Complex.new(1, -2e3);

Methods

method new

Defined as:

multi method new(Real $re, Real $im --> Complex:D)

Creates a new Complex object from real and imaginary parts.

my $complex = Complex.new(1, 1);
say $complex;    # OUTPUT: «1+1i␤»

When created without arguments, both parts are considered to be zero.

say Complex.new; # OUTPUT: «0+0i␤»

method re

Defined as:

method re(Complex:D: --> Real:D)

Returns the real part of the complex number.

say (3+5i).re;    # OUTPUT: «3␤»

method im

Defined as:

method im(Complex:D: --> Real:D)

Returns the imaginary part of the complex number.

say (3+5i).im;    # OUTPUT: «5␤»

method reals

Defined as:

method reals(Complex:D: --> Positional:D)

Returns a two-element list containing the real and imaginary parts for this value.

say (3+5i).reals;    # OUTPUT: «(3 5)␤»

method isNaN

Defined as:

method isNaN(Complex:D: --> Bool:D)

Returns true if the real or imaginary part is NaN (not a number).

say (NaN+5i).isNaN; # OUTPUT: «True␤» 
say (7+5i).isNaN;   # OUTPUT: «False␤»

method polar

Defined as:

method polar(Complex:D: --> Positional:D)

Returns a two-element list of the polar coordinates for this value, i.e. magnitude and angle in radians.

say (10+7i).polar; # OUTPUT: «(12.2065556157337 0.610725964389209)␤»

method floor

Defined as:

method floor(Complex:D: --> Complex:D)

Returns self.re.floor + self.im.floor. That is, each of the real and imaginary parts is rounded to the highest integer not greater than the value of that part.

say (1.2-3.8i).floor;           # OUTPUT: «1-4i␤»

method ceiling

Defined as:

method ceiling(Complex:D: --> Complex:D)

Returns self.re.ceiling + self.im.ceiling. That is, each of the real and imaginary parts is rounded to the lowest integer not less than the value of that part.

say (1.2-3.8i).ceiling;         # OUTPUT: «2-3i␤»

method round

Defined as:

multi method round(Complex:D: --> Complex:D)
multi method round(Complex:D: Real() $scale --> Complex:D)

With no arguments, rounds both the real and imaginary parts to the nearest integer and returns a new Complex number. If $scale is given, rounds both parts of the invocant to the nearest multiple of $scale. Uses the same algorithm as Real.round on each part of the number.

say (1.2-3.8i).round;           # OUTPUT: «1-4i␤» 
say (1.256-3.875i).round(0.1);  # OUTPUT: «1.3-3.9i␤»

method truncate

Defined as:

method truncate(Complex:D: --> Complex:D)

Removes the fractional part of both the real and imaginary parts of the number, using Real.truncate, and returns the result as a new Complex.

say (1.2-3.8i).truncate;        # OUTPUT: «1-3i␤»

method abs

Defined as:

method abs(Complex:D: --> Num:D)
multi sub abs(Complex:D $z --> Num:D)

Returns the absolute value of the invocant (or the argument in sub form). For a given complex number $z the absolute value |$z| is defined as sqrt($z.re * $z.re + $z.im * $z.im).

say (3+4i).abs;                 # OUTPUT: «5␤» 
                                # sqrt(3*3 + 4*4) == 5

method conj

Defined as:

method conj(Complex:D: --> Complex:D)

Returns the complex conjugate of the invocant (that is, the number with the sign of the imaginary part negated).

say (1-4i).conj;                # OUTPUT: «1+4i␤»

method sqrt

Defined as:

method sqrt(Complex:D: --> Complex:D)

Returns the complex square root of the invocant, i.e. the root where the real part is ≥ 0 and the imaginary part has the same sign as the imaginary part of the invocant.

say (3-4i).sqrt;                # OUTPUT: «2-1i␤» 
say (-3+4i).sqrt;               # OUTPUT: «1+2i␤»

method gist

Defined as:

method gist(Complex:D: --> Str:D)

Returns a string representation of the form "1+2i", without internal spaces. (Str coercion also returns this.)

say (1-4i).gist;                # OUTPUT: «1-4i␤»

method perl

Defined as:

method perl(Complex:D: --> Str:D)

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

say (1-3i).perl;                # OUTPUT: «<1-3i>␤»

method Real

Defined as:

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

Coerces the invocant to Num. If the imaginary part isn't approximately zero, coercion fails with X::Numeric::Real.

The :D variant returns the result of that coercion. The :U variant issues a warning about using an uninitialized value in numeric context and then returns value 0e0.

sub infix:<**>

Declared as

multi sub infix:<**>(Complex:D \a, Complex:D \b --> Complex:D)
multi sub infix:<**>(Num(Real) \a, Complex:D \b --> Complex:D)
multi sub infix:<**>(Complex:D \a, Num(Real) \b --> Complex:D)

The exponentiation operator coerces the second argument to Complex and calculates the left-hand-side raised to the power of the right-hand side. Since 6.d, either argument can be equal to zero.

say i ** i;   # OUTPUT: «0.20787957635076193+0i␤» 
say 2 ** i;   # OUTPUT: «0.7692389013639721+0.6389612763136348i␤» 
say i ** 2;   # OUTPUT: «-1+1.2246467991473532e-16i␤» 
say 0 ** i;   # OUTPUT: «0+0i␤» 
say 0i ** 0i; # OUTPUT: «1+0i␤»

Type Graph

Expand above chart

Routines supplied by role Numeric

Complex 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:D, Numeric $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:D, Numeric: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

Complex 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 EVAL

Defined as:

method EVAL(*%_)

It calls the subroutine form with the invocant as the first argument, $code, passing along named args, if any.

(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 Raku 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:

method atan2($y = 1e0)

Coerces self and argument to Numeric, using them to compute the two-argument arc-tangent in radians.

say 3.atan2;                # OUTPUT: «1.24904577239825␤» 
say ⅔.atan2(⅓);             # OUTPUT: «1.1071487177940904␤»

The first argument defaults to 1, so in the first case the function will return the angle θ in radians between a vector that goes from origin to the point (3, 1) and the x axis.

(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) $number, Numeric(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 $pow, Cool: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')

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

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 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. It's been deprecated as of the 6.d version. Will be removed in the next ones.

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:

multi sub chars(Cool $x)
multi sub chars(Str:D $x)
multi sub chars(str $x --> int)
method chars(--> Int:D)

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␤»

If the string is native, the number of chars will be also returned as a native int.

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 Raku 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(Cool $s --> Str:D)
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) $input, :&filter = &tclc, Mu :$where = True)
method wordcase(:&filter = &tclc, Mu :$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 "raku programming".wordcase;        # OUTPUT: «Raku 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 $string, Cool $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.

Note: 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 "raKu".samecase("A_a_"); # OUTPUT: «Raku␤» 
say "rAKU".samecase("Ab");   # OUTPUT: «Raku␤»

(Cool) routine uniprop

Defined as:

multi sub uniprop(Str:D, |c)
multi sub uniprop(Int:D $code)
multi sub uniprop(Int:D $code, Stringy: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. A uniprops routine can be used to get the property for every character in a string.

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 $str, Stringy: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, but for each character in the passed string.

(Cool) routine uniname

Defined as:

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

Interprets the invocant or 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 $code, Stringy:D $pvalname, Stringy: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 $delimiter, Str(Cool) $input, $limit = Inf, :$k, :$v, :$kv, :$p, :$skip-empty)
multi sub    split(Regex:D $delimiter, Str(Cool) $input, $limit = Inf, :$k, :$v, :$kv, :$p, :$skip-empty)
multi sub    split(@delimiters, Str(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)

[1]

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(Cool:D: |c)

Coerces the invocant (or first argument, if it is called as a subroutine) to Str, and returns a list of words that make up the string. Check Str.words for additional arguments and its meaning.

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

Cool is the base class for many other classes, and some of them, like Match, can be converted to a string. This is what happens in this case:

say ( "easy come, easy goes" ~~ m:g/(ea\w+)/).words(Inf);
# OUTPUT: «(easy easy)␤» 
say words( "easy come, easy goes" ~~ m:g/(ea\w+)/ , ∞);
# OUTPUT: «(easy easy)␤»

The example above illustrates two of the ways words can be invoked, with the first argument turned into invocant by its signature. Of course, Inf is the default value of the second argument, so in both cases (and forms) it can be simply omitted.

Only whitespace (including no-break space) counts as word boundaries

say <Flying on a Boeing 747>.words.join('|');  # OUTPUT: «Flying|on|a|Boeing|747␤»

In this case, "Boeing 747" includes a (visible only in the source) no-break space; words still splits the (resulting) Str on it, even if the original array only had 4 elements:

say <Flying on a Boeing 747>.join('|');        # OUTPUT: «Flying|on|a|Boeing 747␤»

Please see Str.words for more examples and ways to invoke it.

(Cool) routine comb

Defined as:

multi sub comb(Regex $matcher, Cool $input, $limit = *)
multi sub comb(Str $matcher, Cool $input, $limit = *)
multi sub comb(Int:D $size, Cool $input, $limit = *)
multi method comb(|c)

Returns a Seq of all (or if supplied, at most $limit) matches of the invocant (method form) or the second argument (sub form) against the Regex, string or defined number.

say "6 or 12".comb(/\d+/).join(", ");           # OUTPUT: «6, 12␤» 
say comb(/\d <[1..9]> /,(11..30)).join("--");
# OUTPUT: 
# «11--12--13--14--15--16--17--18--19--21--22--23--24--25--26--27--28--29␤»

The second statement exemplifies the first form of comb, with a Regex that excludes multiples of ten, and a Range (which is Cool) as $input. comb stringifies the Range before applying .comb on the resulting string. Check Str.comb for its effect on different kind of input strings. When the first argument is an integer, it indicates the (maximum) size of the chunks the input is going to be divided in

say comb(3,[3,33,333,3333]).join("*");  # OUTPUT: «3 3*3 3*33 *333*3␤»

In this case the input is a list, which after transformation to Str (which includes the spaces) is divided in chunks of size 3.

(Cool) method contains

Defined as:

method contains(Cool:D: |c)

Coerces the invocant to a 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(Cool $s, Cool $needle, Cool $pos = 0)
method    index(Cool:D: |c)

Coerces the first two arguments (in method form, also counting the invocant) to a Str, and searches for $needle in the string $s 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) $haystack, Str(Cool) $needle, Int(Cool) $startpos = $haystack.chars)
multi method rindex(Str(Cool) $haystack: Str(Cool) $needle, Int(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) routine roots

Defined as:

multi sub roots(Numeric(Cool) $x, Int(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