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 , Real --> Complex)Creates a new Complex object from real and imaginary parts.
my = Complex.new(1, 1);say ; # 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: --> Real)Returns the real part of the complex number.
say (3+5i).re; # OUTPUT: «3»method im §
Defined as:
method im(Complex: --> Real)Returns the imaginary part of the complex number.
say (3+5i).im; # OUTPUT: «5»method reals §
Defined as:
method reals(Complex: --> Positional)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: --> Bool)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: --> Positional)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: --> Complex)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: --> Complex)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: --> Complex)multi method round(Complex: Real() --> Complex)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: --> Complex)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»routine abs §
Defined as:
method abs(Complex: --> Num)multi sub abs(Complex --> Num)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) == 5method conj §
Defined as:
method conj(Complex: --> Complex)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: --> Complex)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: --> Str)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 raku §
Defined as:
method raku(Complex: --> Str)Returns an implementation-specific string that produces an equivalent object when given to EVAL.
say (1-3i).raku; # OUTPUT: «<1-3i>»method Real §
Defined as:
multi method Real(Complex: --> Num)multi method Real(Complex: --> Num)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 \a, Complex \b --> Complex)multi sub infix:<**>(Num(Real) \a, Complex \b --> Complex)multi sub infix:<**>(Complex \a, Num(Real) \b --> Complex)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 §
Complex
Routines supplied by role Numeric §
Complex does role Numeric, which provides the following routines:
(Numeric) method Numeric §
Defined as:
multi method Numeric(Numeric: --> Numeric)multi method Numeric(Numeric: --> Numeric)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 narrow §
method narrow(Numeric --> Numeric)Returns the number converted to the narrowest type that can hold it without loss of precision.
say (4.0 + 0i).narrow.raku; # OUTPUT: «4» say (4.0 + 0i).narrow.^name; # OUTPUT: «Int»(Numeric) method ACCEPTS §
multi method ACCEPTS(Numeric: )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, Numeric = e --> Numeric)multi method log(Numeric: Numeric = e --> Numeric)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 --> Numeric)multi method log10(Numeric: --> Numeric)Calculates the logarithm to base 10. Returns NaN for negative arguments and -Inf for 0.
(Numeric) routine log2 §
multi sub log2(Numeric)multi method log2(Numeric:)Calculates the logarithm to base 2. Returns NaN for negative arguments and -Inf for 0.
(Numeric) routine exp §
multi sub exp(Numeric, Numeric = e --> Numeric)multi method exp(Numeric: Numeric = e --> Numeric)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: Int --> 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 --> Real)multi method abs(Numeric: --> Real)Returns the absolute value of the number.
(Numeric) routine sqrt §
multi sub sqrt(Numeric --> Numeric)multi method sqrt(Numeric --> Numeric)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 --> Numeric)Returns the complex conjugate of the number. Returns the number itself for real numbers.
(Numeric) method Bool §
multi method Bool(Numeric:)Returns False if the number is equivalent to zero, and True otherwise.
(Numeric) method succ §
method succ(Numeric:)Returns the number incremented by one (successor).
(Numeric) method pred §
method pred(Numeric:)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() )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) method 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) )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:
sub atan2(, = 1e0)method atan2( = 1e0)The sub should usually be written with two arguments for clarity as it is seen in other languages and in mathematical texts, but the single-argument form is available; its result will always match that of atan.
say atan2 3, 1; # OUTPUT: «1.2490457723982544» say atan2 3; # OUTPUT: «1.2490457723982544» say atan2 ⅔, ⅓; # OUTPUT: «1.1071487177940904»The method coerces self and its single 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 $x argument in either the method or the sub defaults to 1 so, in both single-argument cases, the function will return the angle θ in radians between the x-axis and a vector that goes from the origin to the point (3, 1).
(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) , Numeric(Cool) ?)multi method log(Cool: Cool ?)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 method log10()multi sub log10(Numeric )multi sub log10(Cool )Coerces the invocant (or in the sub form, the argument) to Numeric (or uses it directly if it's already in that form), and returns its Logarithm in base 10, that is, a number that approximately produces the original number when 10 is raised to its power. Returns NaN for negative arguments and -Inf for 0.
say log10(1001); # OUTPUT: «3.00043407747932»(Cool) routine log2 §
Defined as:
multi method log2()multi sub log2(Numeric )multi sub log2(Cool )Coerces the invocant to Numeric, and returns its Logarithm in base 2, that is, a number that approximately (due to computer precision limitations) produces the original number when 2 is raised to its power. Returns NaN for negative arguments and -Inf for 0.
say log2(5); # OUTPUT: «2.321928094887362» say "4".log2; # OUTPUT: «2» say 4.log2; # OUTPUT: «2»(Cool) routine exp §
Defined as:
multi sub exp(Cool , Cool ?)multi method exp(Cool: Cool ?)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), = 1)multi method round(Cool: = 1)Coerces the invocant (or in sub form, its argument) to Numeric, and rounds it to the unit of $scale. If $scale is 1, rounds to the nearest integer; an arbitrary scale will result in the closest multiple of that number.
say 1.7.round; # OUTPUT: «2» say 1.07.round(0.1); # OUTPUT: «1.1» say 21.round(10); # OUTPUT: «20» say round(1000, 23.01) # OUTPUT: «989.43»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) .raku.say; # OUTPUT: «9930972392403501» 9930972392403501.round(1e0) .raku.say; # OUTPUT: «9.9309723924035e+15» 9930972392403501.round(1e0).Int.raku.say; # OUTPUT: «9930972392403500»(Cool) routine floor §
Defined as:
multi sub floor(Numeric(Cool))multi method floorCoerces 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( = '%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 ceilingCoerces 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 )multi sub chars(Str )multi sub chars(str --> int)method chars(--> Int)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 --> Str)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 = ' 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 = ' abc '.trim-leading;say "<$stripped>"; # OUTPUT: «<abc >»(Cool) routine trim-trailing §
Defined as:
sub trim-trailing(Str(Cool))method trim-trailing()Coerces the invocant (or in sub form, its argument) to Str, and returns the string with trailing whitespace stripped.
my = ' abc '.trim-trailing;say "<$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) , : = , Mu : = True)method wordcase(: = , Mu : = 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 raku".wordcase(:where()); # Have fun Working on RakuWith a customer filter too:
say "have fun working on raku".wordcase(:filter(), :where()); # HAVE fun WORKING on RAKU(Cool) routine samecase §
Defined as:
sub samecase(Cool , Cool )method samecase(Cool: Cool )Coerces the invocant (or in sub form, the first argument) to Str, and calls Str.samecase on it.
say "raKu".samecase("A_a_"); # OUTPUT: «Raku» say "rAKU".samecase("Ab"); # OUTPUT: «Raku»(Cool) routine uniprop §
Defined as:
multi sub uniprop(Str, |c)multi sub uniprop(Int )multi sub uniprop(Int , Stringy )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 , Stringy = "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)[].chr.uniname;# OUTPUT: «BOX DRAWINGS LIGHT DIAGONAL UPPER CENTRE TO MIDDLE RIGHT AND MIDDLE LEFT TO LOWER CENTRE»(Cool) routine uninames §
Defined as:
sub uninames(Str)method uninames()Returns of a Seq of Unicode names for the all the codepoints in the Str provided.
say ‘»ö«’.uninames.raku;# 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.raku;# 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 , |c)multi sub unimatch(Int , Stringy , Stringy = )Checks if the given integer codepoint or the first letter of the given string has 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: «False»The last property corresponds to "lowercase letter", which explains why it returns false.
(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 'raku'.chop; # OUTPUT: «rak»(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) , |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 rwmulti sub substr-rw(|) is rwCoerces 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) )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(* --> Str)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 , Str(Cool) , = Inf, :, :, :, :, :)multi sub split(Regex , Str(Cool) , = Inf, :, :, :, :, :)multi sub split(, Str(Cool) , = Inf, :, :, :, :, :)multi method split( Str , = Inf, :, :, :, :, :)multi method split(Regex , = Inf, :, :, :, :, :)multi method split(, = Inf, :, :, :, :, :)Coerces the invocant (or in the sub form, the second argument) to Str, splits it into pieces based on delimiters found in the string and returns the result as a Seq.
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, which can mix Cool and Regex objects.
say split(';', "a;b;c").raku; # OUTPUT: «("a", "b", "c").Seq» say split(';', "a;b;c", 2).raku; # OUTPUT: «("a", "b;c").Seq» say split(';', "a;b;c,d").raku; # OUTPUT: «("a", "b", "c,d").Seq» say split(/\;/, "a;b;c,d").raku; # OUTPUT: «("a", "b", "c,d").Seq» say split(//, "a;b;c,d").raku; # OUTPUT: «("a", "b", "c", "d").Seq» say split(['a', /b+/, 4], '1a2bb345').raku; # OUTPUT: «("1", "2", "3", "5").Seq»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: /","/ ).raku; # OUTPUT: «("f", "", "b", "c", "d").Seq» say ("f,,b,c,d".split: /","/, :skip-empty).raku; # OUTPUT: «("f", "b", "c", "d").Seq»(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 -> # or if you'll be processing later my = 'huge-csv'.IO.lines;Without any arguments, sub lines operates on $*ARGFILES.
To modify values in place use is copy to force a writable container.
for .lines -> is copy (Cool) method words §
Defined as:
method words(Cool: |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 , Cool , = *)multi sub comb(Str , Cool , = *)multi sub comb(Int , Cool , = *)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 /,(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: |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 , Cool , :i(:), :m(:) --> Int)multi sub index(Cool , Cool , Cool , :i(:), :m(:) --> Int)multi method index(Cool: Cool --> Int)multi method index(Cool: Cool , :m(:)! --> Int)multi method index(Cool: Cool , :i(:)!, :m(:) --> Int)multi method index(Cool: Cool , Cool --> Int)multi method index(Cool: Cool , Cool , :m(:)! --> Int)multi method index(Cool: Cool , Cool , :i(:)!, :m(:) --> Int)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 $pos. It returns the offset into the string where $needle was found, and Nil if it was not found.
See the documentation in type Str for examples.
(Cool) routine rindex §
Defined as:
multi sub rindex(Cool , Cool --> Int)multi sub rindex(Cool , Cool , Cool --> Int)multi method rindex(Cool: Cool --> Int)multi method rindex(Cool: Cool , Cool --> Int)Coerces the first two arguments (including the invocant in method form) to Str and $pos to Int, and returns the last position of $needle in the string not after $pos. Returns Nil if $needle wasn't found.
See the documentation in type Str for examples.
(Cool) method match §
Defined as:
method match(Cool: , *)Coerces the invocant to Stringy and calls the method match on it.
(Cool) routine roots §
Defined as:
multi sub roots(Numeric(Cool) , Int(Cool) )multi method roots(Int(Cool) )Coerces the first argument (and in method form, the invocant) to Numeric and the second ($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 = 16;my = .roots(4);say ; for -> # 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 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)Coerces the invocant to IO::Path.
.say for '.'.IO.dir; # gives a directory listing (Cool) method sprintf §
Defined as:
method sprintf(*)Returns a string according to a series format directives that are common in many languages; the object will be the format string, while the supplied arguments will be what's going to be formatted according to it.
"% 6s".sprintf('Þor').say; # OUTPUT: « Þor» (Cool) method printf §
Defined as:
method printf(*)Uses the object, as long as it is a format string, to format and print the arguments
"%.8f".printf(now - now ); # OUTPUT: «-0.00004118» (Cool) method Complex §
Defined as:
multi method Complex()Coerces the invocant to a Numeric and calls its .Complex method. Fails if the coercion to a Numeric cannot be done.
say 1+1i.Complex; # OUTPUT: «1+1i» say π.Complex; # OUTPUT: «3.141592653589793+0i» say <1.3>.Complex; # OUTPUT: «1.3+0i» say (-4/3).Complex; # OUTPUT: «-1.3333333333333333+0i» say "foo".Complex.^name; # OUTPUT: «Failure»(Cool) method FatRat §
Defined as:
multi method FatRat()Coerces the invocant to a Numeric and calls its .FatRat method. Fails if the coercion to a Numeric cannot be done.
say 1+0i.FatRat; # OUTPUT: «1» say 2e1.FatRat; # OUTPUT: «20» say 1.3.FatRat; # OUTPUT: «1.3» say (-4/3).FatRat; # OUTPUT: «-1.333333» say "foo".FatRat.^name; # OUTPUT: «Failure»(Cool) method Int §
Defined as:
multi method Int()Coerces the invocant to a Numeric and calls its .Int method. Fails if the coercion to a Numeric cannot be done.
say 1+0i.Int; # OUTPUT: «1» say <2e1>.Int; # OUTPUT: «20» say 1.3.Int; # OUTPUT: «1» say (-4/3).Int; # OUTPUT: «-1» say "foo".Int.^name; # OUTPUT: «Failure»(Cool) method Num §
Defined as:
multi method Num()Coerces the invocant to a Numeric and calls its .Num method. Fails if the coercion to a Numeric cannot be done.
say 1+0i.Num; # OUTPUT: «1» say 2e1.Num; # OUTPUT: «20» say (16/9)².Num; # OUTPUT: «3.1604938271604937» say (-4/3).Num; # OUTPUT: «-1.3333333333333333» say "foo".Num.^name; # OUTPUT: «Failure»(Cool) method Rat §
Defined as:
multi method Rat()Coerces the invocant to a Numeric and calls its .Rat method. Fails if the coercion to a Numeric cannot be done.
say 1+0i.Rat; # OUTPUT: «1» say 2e1.Rat; # OUTPUT: «20» say (-4/3).Rat; # OUTPUT: «-1.333333» say "foo".Rat.^name; # OUTPUT: «Failure» say (.numerator, .denominator) for π.Rat; # OUTPUT: «(355 113)»(Cool) method Real §
Defined as:
multi method Real()Coerces the invocant to a Numeric and calls its .Real method. Fails if the coercion to a Numeric cannot be done.
say 1+0i.Real; # OUTPUT: «1» say 2e1.Real; # OUTPUT: «20» say 1.3.Real; # OUTPUT: «1.3» say (-4/3).Real; # OUTPUT: «-1.333333» say "foo".Real.^name; # OUTPUT: «Failure»(Cool) method UInt §
Defined as:
multi method UInt()Coerces the invocant to an Int. Fails if the coercion to an Int cannot be done or if the Int the invocant had been coerced to is negative.
say 1+0i.UInt; # OUTPUT: «1» say 2e1.UInt; # OUTPUT: «20» say 1.3.UInt; # OUTPUT: «1» say (-4/3).UInt.^name; # OUTPUT: «Failure» say "foo".UInt.^name; # OUTPUT: «Failure»