Rational number (arbitrary-precision)

class FatRat is Cool does Rational [ Int , Int ] { }

A FatRat is a rational number stored with arbitrary size numerator and denominator. Arithmetic operations involving a FatRat and optionally Int or Rat objects return a FatRat , avoiding loss of precision.

Since, unlike Rat, FatRat arithmetics do not fall back Num at some point, there is a risk that repeated arithmetic operations generate pathologically large numerators and denominators.

There are two common ways to generate FatRat objects: through the FatRat.new(Int, Int) constructor, which generates them from numerator and denominator, or by calling the .FatRat method on an Int or Rat object.

multi method perl ( FatRat : D : --> Str : D )

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

say FatRat . new ( 1 , 2 ) . perl ;

FatRat does role Rational, which provides the following routines:

method new ( NuT : D $ numerator , DeT : 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.

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 .

Defined as:

method Bridge ()

Returns the number, converted to Num .

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 .

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.

Defined as:

method ceiling ( Rational : D : --> Int : D )

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

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 .

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

Tests whether the invocant's Num value is a NaN, an acronym for Not available Number. That is both its numerator and denominator are zero.

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

Returns the numerator.

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

Returns the denominator.

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

Returns a list of the numerator and denominator.

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

DEPRECATED as of 6.d. The method is no longer needed, because as of 6.d language version, it's required for Rational type to be normalized on creation.

Returns a normalized Rational object, i.e. with positive denominator, and numerator and denominator coprime. The denominator can also by zero, but using it in any operation or a conversion to string will result in an exception.

use v6.c ; my Rational $ by-zero = 3 / 0 ; say $ by-zero . norm . raku ;

say $ by-zero ;

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 ; say $ repeating ; printf ' %s(%s) ' , $ non-rep , $ repeating ;

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 ) . raku ;

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

$base defaults to 10 .

Returns a Range object that represents the range of values supported.

FatRat does role Real, which provides the following routines:

Defined as:

method Bridge ( Real : D : )

Default implementation coerces the invocant to Num and that's the behavior 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 } 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 := 5778 K; say $ human ; say $ human + $ book + $ sun ; say 123 K + 456 K;

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.

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.

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

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

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 .

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.)

method sign ( Real : D : )

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

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 radix point (period or comma), etc.

method floor ( Real : D --> Int : D )

Return the largest integer not greater than the number.

method ceiling ( Real : D --> Int : D )

Returns the smallest integer not less than the number.

method truncate ( Real : D --> Int : D )

Rounds the number towards zero.

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 );

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.

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 );

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 ( 10 , 3 ); say ( 1 / 128 ) . base ( 10 , * ); say ( 1 / 100 ) . base ( 10 , * ); say ( 1 / 3 ) . base ( 10 , * );

For reverse operation, see parse-base

FatRat does role Numeric, which provides the following routines:

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 .

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.

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.

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.

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 + 0 i) . narrow . raku ; say ( 4.0 + 0 i) . narrow . ^ name ;

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 ).

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 .

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 .

multi sub log2 ( Numeric : D ) multi method log2 ( Numeric : D : )

Calculates the logarithm to base 2. Returns NaN for negative arguments and -Inf for 0 .

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.

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 $n th power.

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

Returns the absolute value of the number.

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.

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

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

multi method Bool ( Numeric : D : )

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

method succ ( Numeric : D : )

Returns the number incremented by one (successor).

method pred ( Numeric : D : )

Returns the number decremented by one (predecessor).

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

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 ; say abs " 6+8i " ;

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 ;

Defined as:

method EVAL ( * % _ )

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

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 ; say sqrt ( 2 );

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 ; say ( -6 ) . sign ; say " 0 " . sign ;

Defined as:

method rand ()

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

say 1e5 . rand ;

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 ); say sin ( pi / 4 ); say sin ( pi / 2 );

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.

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 ; say asin ( 0.1 );

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 ; say pi . cos ; say cos ( pi / 2 );

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 ; say acos ( -1 );

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 ); say 3 . tan ;

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 ); say 3 . atan ;

Defined as:

sub atan2 ( $ y , $ x = 1e0 ) method atan2 ( $ x = 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 ; say atan2 3 ; say atan2 ⅔, ⅓;

The method coerces self and its single argument to Numeric, using them to compute the two-argument arc-tangent in radians.

say 3 . atan2 ; say ⅔ . atan2 (⅓);

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).

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 ; say sec ( 45 );

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 ; say sqrt ( 2 ) . asec ;

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 ; say cosec ( 0.45 );

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 ; say acosec ( 45 )

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 ; say cotan ( 45 );

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 ; say acotan ( 45 )

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 ; say sinh ( 1 );

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 ; say asinh ( 1 );

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 );

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 );

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 ); say tanh ( atanh ( 0.5 ));

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 );

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 ;

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 ;

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 );

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 );

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 );

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 );

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 );

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 ;

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 );

Defined as:

multi method log2 ()

Coerces the invocant to Numeric, and returns its Logarithm to base 2, that is, a number that approximately produces the original number when raised to the power of 2. Returns NaN for negative arguments and -Inf for 0 .

say log2 ( 5 ); say " 4 " . log2 ;

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 ; say 1 . exp ; say 10 . exp ;

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 );

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 ; say 1.07 . round ( 0.1 ); say 21 . round ( 10 );

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

say ( −.5 ) . round ; say ( .5 ) . round ; say ( −.55 ) . round ( .1 ); say ( .55 ) . round ( .1 );

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 ; 9930972392403501 . round ( 1e0 ) . raku . say ; 9930972392403501 . round ( 1e0 ) . Int . raku . say ;

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 ; say " -1.9 " . floor ; say 0 . floor ;

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 ' ); say ' 16 ' . fmt ( ' Hexadecimal %x ' );

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 ; say " -0.9 " . ceiling ; say " 42.1 " . ceiling ;

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 ; say truncate -1.2 ;

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 ;

The inverse operation is chr.

Mnemonic: returns an ordinal number

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.

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 ;

The inverse operation is ord.

Mnemonic: turns an integer into a character.

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 ; say ' ã̷̠̬̊ ' . chars ; say ' 👨‍👩‍👧‍👦🏿 ' . chars ;

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 ’ ); say ‘ 👨‍👩‍👧‍👦🏿 ’ . uniprops ( ‘ Grapheme_Cluster_Break ’ );

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.

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 ;

The same result will be obtained with

say + ' møp ' . ords ;

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

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 ;

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 > " ;

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 > " ;

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 > " ;

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 ;

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 ;

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 ;

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 ;

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 ;

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 ;

With a matcher:

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

With a customer filter too:

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

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_ " ); say " rAKU " . samecase ( " Ab " );

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 ; say ' 1 ' . uniprop ; say ' a ' . uniprop ( ' Alphabetic ' ); say ' 1 ' . uniprop ( ' Alphabetic ' );

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.

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.

say ‘ »ö« ’ . uniname ; say " Ḍ̇ " . uniname ; say ( 0 .. 0x1FFFF ) . sort ( * . uniname . chars )[ * - 1 ] . chr . uniname ;

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 . raku ;

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 ;

See uniparse for the opposite direction.

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 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 ' ; say unimatch ' A ' , ' Latin ' , ' Script ' ; say unimatch ' A ' , ' Ll ' ;

The last property corresponds to "lowercase letter", which explains why it returns false.

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 ;

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 ; say " a

" . chomp . chars ;

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.

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.

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 ; say ords 10 ;

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.

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 ;

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

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 )

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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 " ) . raku ; say split ( ' ; ' , " a;b;c " , 2 ) . raku ; say split ( ' ; ' , " a;b;c,d " ) . raku ; say split ( / \; / , " a;b;c,d " ) . raku ; say split ( / < [ ;, ] > / , " a;b;c,d " ) . raku ; say split ([ ' a ' , / b + / , 4 ], ' 1a2bb345 ' ) . raku ;

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 ); say ' abc ' . split ( ' b ' , : v );

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

say ' abc ' . split ( / b / , : k );

:kv adds both indexes and matches:

say ' abc ' . split ( / b / , : kv );

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

say ' abc ' . split ( / b / , : p ); say ' abc ' . split ( ' b ' , : p );

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 ; say ( " f,,b,c,d " . split : / " , " / , : skip-empty ) . raku ;

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

b

" ) . join ( ' | ' ); say " some

more

lines " . lines . elems ;

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 { } 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 }

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 ( ' | ' ); say < The quick brown fox > . words ( 2 ) . join ( ' | ' );

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 ); say words ( " easy come, easy goes " ~~ m :g / (ea \w + ) / , ∞);

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 ( ' | ' );

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 ( ' | ' );

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

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 ( " , " ); say comb ( / \d < [ 1..9 ] > / ,( 11 .. 30 )) . join ( " -- " );

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 ( " * " );

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

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 " )

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 )

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.

Defined as:

multi sub index ( Cool : D $ s , Cool : D $ needle , : i ( : $ ignorecase ), : m ( : $ ignoremark ) --> Int : D ) multi sub index ( Cool : D $ s , Cool : D $ needle , Cool : D $ pos , : i ( : $ ignorecase ), : m ( : $ ignoremark ) --> Int : D ) multi method index ( Cool : D : Cool : D $ needle --> Int : D ) multi method index ( Cool : D : Cool : D $ needle , : m ( : $ ignoremark ) ! --> Int : D ) multi method index ( Cool : D : Cool : D $ needle , : i ( : $ ignorecase ) ! , : m ( : $ ignoremark ) --> Int : D ) multi method index ( Cool : D : Cool : D $ needle , Cool : D $ pos --> Int : D ) multi method index ( Cool : D : Cool : D $ needle , Cool : D $ pos , : m ( : $ ignoremark ) ! --> Int : D ) multi method index ( Cool : D : Cool : D $ needle , Cool : D $ pos , : i ( : $ ignorecase ) ! , : m ( : $ ignoremark ) --> Int : D )

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.

Defined as:

multi sub rindex ( Cool : D $ s , Cool : D $ needle --> Int : D ) multi sub rindex ( Cool : D $ s , Cool : D $ needle , Cool : D $ pos --> Int : D ) multi method rindex ( Cool : D : Cool : D $ needle --> Int : D ) multi method rindex ( Cool : D : Cool : D $ needle , Cool : D $ pos --> Int : D )

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.

Defined as:

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

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

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 $n th 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 ); }

Defined as:

method match (|)

Coerces the invocant to Stringy and calls Str.match.

Defined as:

method subst (|)

Coerces the invocant to Stringy and calls Str.subst.

Defined as:

method trans (|)

Coerces the invocant to Str and calls Str.trans

Defined as:

method IO ( --> IO :: Path : D )

Coerces the invocant to IO::Path.