# class FatRat

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.

# Type graph

Below you should see a clickable image showing the type relations for FatRat that links to the documentation pages for the related types. If not, try the PNG version instead.

# Routines supplied by role Rational

FatRat does role Rational, which provides the following methods:

## method new

```
method new(NuT:D $numerator, DenomT:D $denominator) returns Rational:D
```

Creates a new rational object from numerator and denominator.

## method numerator

```
method numerator(Rational:D:) returns NuT:D
```

Returns the numerator.

## method denominator

```
method denominator(Rational:D:) returns DenomT:D
```

Returns the denominator.

## method nude

```
method nude(Rational:D:) returns Positional
```

Returns a list of the numerator and denominator.

## method norm

```
method norm(Rational:D:) returns Rational:D
```

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

## method base-repeating

```
method base-repeating(Rational:D: Int:D() $base)
```

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; # 6.
say $rep; # 3
printf '%s(%s)', $non-rep, $repeating; # 6.(3)
```

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

If no repetition occurs, the second string is empty:

```
say (5/2).base-repeating(10).perl; # ("2.5", "")
```

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

.

# Routines supplied by role Real

FatRat does role Real, which provides the following methods:

## method Rat

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

Converts the number to a `Rat`

with the precision `$epsilon`

.

## routine rand

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

Returns a pseudo-random number between zero and the number.

The term form returns a pseudo-random `Num`

between 0e0 and 1e0.

## method sign

```
method sign(Real:D:)
```

Returns `-1`

if the number is negative, `0`

if it is zero and `1`

otherwise.

## method round

```
method round(Real:D: $scale = 1)
```

Rounds the number to scale `$scale`

. If `$scale`

is 1, rounds to an integer. If scale is `0.1`

, rounds to one digit after the comma etc.

## method floor

```
method floor(Real:D) returns Int:D
```

Return the largest integer not greater than the number.

## method ceiling

```
method ceiling(Real:D) returns Int:D
```

Returns the smallest integer not less than the number.

## method truncate

```
method truncate(Real:D) returns Int:D
```

Rounds the number towards zero.

## method base

```
method base(Real:D: Int:D $base where 2..36, $digits?) returns Str:D
```

Converts the number to a string, using `$base`

as base. For `$base`

larger than ten, capital Latin letters are used.

```
255.base(16) # 'FF'
```

The optional `$digits`

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

The final digit produced is always rounded.

```
say pi.base(10, 5); # 3.14159
```

# Routines supplied by role Numeric

FatRat does role Numeric, which provides the following methods:

## method Real

```
method Real(Numeric:D:) returns Real:D
```

If this `Numeric`

is equivalent to a `Real`

, return that `Real`

. Fail with `X::Numeric::Real`

otherwise.

## method Int

```
method Int(Numeric:D:) returns 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

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

```
method Num(Numeric:D:) returns 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

```
method narrow(Numeric:D) returns Numeric:D
```

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

```
say (4.0 + 0i).narrow.perl; # 4
say (4.0 + 0i).narrow.^name; # Int
```

## method ACCEPTS

```
multi method ACCEPTS(Numeric:D: $other)
```

Returns True if `$other`

is numerically the same as the invocant.

## routine log

```
multi sub log(Numeric:D, Numeric $base = e) returns Numeric:D
multi method log(Numeric:D: Numeric $base = e) returns Numeric:D
```

Calculates the logarithm to base `$base`

. Defaults to the natural logarithm.

## routine log10

```
multi sub log10(Numeric:D ) returns Numeric:D
multi method log10(Numeric:D:) returns Numeric:D
```

Calculates the logarithm to base 10.

## routine exp

```
multi sub exp(Numeric:D, Numeric:D $base = e) returns Numeric:D
multi method exp(Numeric:D: Numeric:D $base = e) returns Numeric:D
```

Returns `$base`

to the power of the number, or `e`

to the power of the number if called without a second argument.

## method roots

```
multi method roots(Numeric:D: Int:D $n) returns Positional
```

Returns a list of the `$n`

complex roots, which evaluate to the original number when raised to the `$n`

th power.

## routine abs

```
multi sub abs(Numeric:D ) returns Real:D
multi method abs(Numeric:D:) returns Real:D
```

Returns the absolute value of the number.

## routine sqrt

```
multi sub sqrt(Numeric:D) returns Numeric:D
multi method sqrt(Numeric:D) returns 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.

## method conj

```
multi method conj(Numeric:D) returns Numeric:D
```

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

## method Bool

```
multi method Bool(Numeric:D:)
```

Returns `False`

if the number is equivalent to zero, and `True`

otherwise.

## method succ

```
method succ(Numerid:D:)
```

Returns the number incremented by one (successor).

## method pred

```
method pred(Numerid:D:)
```

Returns the number decremented by one (predecessor).

# Routines supplied by class Cool

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

## routine abs

```
method abs()
sub abs(Numeric() $x)
```

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; # 2
say abs "6+8i"; # 10
```

## method conj

```
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; # 1-2i
```

## routine sqrt

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

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; # 2
say sqrt(2); # 1.4142135623731
```

## method sign

```
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; # 1
say (-6).sign; # -1
say "0".sign; # 0
```

## method rand

```
method rand()
```

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

```
say 1e5.rand; # 33128.495184283
```

## routine sin

```
method sin()
sub sin(Numeric(Cool))
```

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

```
say sin(0); # 0
say sin(pi/4); # 0.707106781186547
say sin(pi/2); # 1
```

Note that Perl 6 is no computer algebra system, so `sin(pi)`

typically does not produce an exact 0, but rather a very small floating-point number.

## routine asin

```
sub asin(Numeric(Cool))
method asin()
```

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

```
say 0.1.asin; # 0.10016742116156
```

## routine cos

```
method cos()
sub cos(Numeric(Cool))
```

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

```
say 0.cos; # 1
say pi.cos; # -1
say cos(pi/2); # 6.12323399573677e-17
```

## routine acos

```
method acos()
sub acos(Numeric(Cool))
```

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

## routine tan

```
method tan()
sub tan(Numeric(Cool))
```

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

## routine atan

```
method atan()
sub atan(Numeric(Cool))
```

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

## routine atan2

```
method atan2($y = 1e0)
sub atan2(Numeric() $x, Numeric() $y = 1e0)
```

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

## method sec

```
method sec()
sub sec(Numeric(Cool))
```

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

## routine asec

```
method asec()
sub asec(Numeric(Cool))
```

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

## routine cosec

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

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

## routine acosec

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

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

## routine cotan

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

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

## routine acotan

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

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

## routine sinh

```
method sinh()
sub sinh(Numeric(Cool))
```

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

## routine asinh

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

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

## routine cosh

```
method cosh()
sub cosh(Numeric(Cool))
```

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

## routine acosh

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

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

## routine tanh

```
method tanh()
sub tanh(Numeric(Cool))
```

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

## routine atanh

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

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

## routine log

```
multi method log(Cool:D: Cool:D $base?)
multi sub log(Numeric(Cool) $number, Numeric(Cool) $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.

```
say (e*e).log; # 2
```

## routine log10

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

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.

```
say log10(1001); # 3.00043407747932
```

## method exp

```
multi method exp(Cool:D: Cool:D $base?)
multi sub exp(Cool:D $pow, 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; # 1
say 1.exp; # 2.71828182845905
say 10.exp; # 22026.4657948067
```

## routine round

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

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; # 2
say 1.07.round(0.1); # 1.1
say 21.round(10); # 20
```

## routine floor

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

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

```
say "1.99".floor; # 1
say "-1.9".floor; # -2
say 0.floor; # 0
```

## routine ceiling

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

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

```
say "1".ceiling; # 1
say "-0.9".ceiling; # 0
say "42.1".ceiling; # 43
```

## routine truncate

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

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

```
say 1.2.truncate # 1
say truncate -1.2; # -1
```

## routine ord

```
method ord()
sub ord(Str(Cool))
```

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

```
say 'a'.ord; # 65
```

The inverse operation is chr.

Mnemonic: returns an ordinal number

## routine chr

```
method chr()
sub chr(Int(Cool))
```

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; # A
```

The inverse operation is ord.

Mnemonic: turns an integer into a *char*acter.

## routine chars

```
method chars()
sub chars(Str(Cool))
```

Coerces the invocant (or in sub form, its argument) to Str, and returns the number of characters in the string. Characters should actually be grapheme clusters, though current implementations erroneously count codepoints instead.

```
say 'møp'.chars; # 3
```

## routine codes

```
method codes()
sub codes(Str(Cool))
```

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

```
say 'møp'.codes; # 3
```

## routine flip

```
method flip()
sub flip(Str(Cool))
```

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

```
say 421.flip; # 124
```

## routine trim

```
method trim()
sub trim(Str(Cool))
```

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>"; # <abc>
```

## routine trim-leading

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

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>"; # <abc >
```

## routine trim-trailing

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

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>"; # < abc>
```

## routine lc

```
method lc()
sub lc(Str(Cool))
```

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

```
say "ABC".lc; # abc
```

## routine uc

```
method uc()
sub uc(Str(Cool))
```

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

```
say "Abc".uc; # ABC
```

## routine tc

```
method tc()
sub tc(Str(Cool))
```

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; # AbC
```

## routine tclc

```
method tclc()
sub tclc(Str(Cool))
```

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; # Abc
```

## routine wordcase

```
method wordcase(:&filter = &tclc, Mu :$where = True)
sub wordcase(Str(Cool) $input, :&filter = &tclc, Mu :$where = True)
```

Coerces the invocant (or in sub form, the first argument) to Str, and filters each word that smart-matches against `$where`

through the `&filter`

. With the default filter (first character to upper case, rest to lower) and matcher (which accepts everything), this title-cases each word:

```
say "perl 6 programming".wordcase; # Perl 6 Programming
```

With a matcher:

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

With a customer filter too:

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

## routine uniname

```
method uniname() returns Str
sub uniname(Str(Cool) returns Str
```

Interprets the invocant / first argument as a /type/Str, and returns the Unicode codepoint name of the first character.

## routine chop

```
method chop()
sub chop(Str(Cool))
```

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

```
say 'perl'.chop; # per
```

## routine chomp

```
method chomp()
sub chomp(Str(Cool))
```

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; # 2
say "a\n".chomp.chars; # 1
```

## routine substr

```
method substr($from, $chars?)
sub substr(Str(Cool) $str, $from, $chars?)
```

Coerces the invocant (or in the sub form, the first argument) to Str, and returns the string starting from offset `$from`

. If `$chars`

is supplied, at most `$chars`

characters are returned.

```
say 'zenith'.substr(2); # nith
say 'zenith'.substr(0, 3); # zen
# works on non-strings too:
say 20151224.substr(6); # 24
# sub form:
say substr "zenith", 0, 3; # zen
```

If the `$from`

parameter is a Callable, it is called with the number of chars in the string as argument. This allows easy indexing relative to the end:

```
say 20151224.substr(*-2); # 24
```

## routine ords

```
method ords()
sub ords(Str(Cool) $str)
```

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

```
say "Perl 6".ords; # 80 101 114 108 32 54
say ords 10; # 49 48
```

This is the list-returning version of ord. The inverse operation in chrs.

## routine chrs

```
method chrs()
sub chrs(*@codepoints) return Str:D
```

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 <80 101 114 108 32 54>.chrs; # Perl 6
```

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

## routine split

```
multi method split( Str:D $delimiter, $limit = Inf, :$all)
multi method split(Regex:D $delimiter, $limit = Inf, :$all)
multi sub split( Str:D $delimiter, Str(Cool) $input, $limit = Inf, :$all)
multi sub split(Regex:D $delimiter, Str(Cool) $input, $limit = Inf, :$all)
```

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.

If the named parameter `:all`

is passed, the matches from `$delimiter`

are included in the result list.

Note that unlike in Perl 5, empty chunks are not removed from the result list. If you want that behavior, consider using comb instead.

```
say split(';', "a;b;c").perl; # ("a", "b", "c").list
say split(';', "a;b;c", :all).perl; # ("a", ";", "b", ";", "c").list
say split(';', "a;b;c", 2).perl; # ("a", "b;c").list
say split(';', "a;b;c", 2, :all).perl; #("a", ";", "b;c").list
say split(';', "a;b;c,d").perl; # ("a", "b", "c,d").list
say split(/\;/, "a;b;c,d").perl; # ("a", "b", "c,d").list
say split(/<[;,]>/, "a;b;c,d").perl; # ("a", "b", "c", "d").list
```

## routine lines

```
method lines()
sub lines(Str(Cool))
```

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('|'); # a|b
say "some\nmore\nlines".lines.elems; # 3
```

## method words

```
method words(Int() $limit)
```

Coerces the invocant to Str, and returns a list of words that make up the string (and if `$limit`

is supplied, only the first `$limit`

words).

```
say 'The quick brown fox'.words.join('|'); # The|quick|brown|fox
say 'The quick brown fox'.words(2).join('|'); # The|quick
```

Only whitespace counts as word boundaries

```
say "isn't, can't".words.join('|'); # isn't,|can't
```

## routine comb

```
multi method comb(Regex $matcher, $limit = *) returns List:D
multi sub comb(Regex $matcher, Str(Cool) $input, $limit = *) returns List:D
```

Returns all (or if supplied, at most `$limit`

) matches of the invocant (method form) or the second argument (sub form) against the Regex as a list of strings.

```
say "6 or 12".comb(/\d+/).join(", "); # 6, 12
```

## routine index

```
multi sub index(Str(Cool) $s, Str:D $needle, Int(Cool) $startpos = 0) returns Int
multi method index(Str(Cool) $needle, Int(Cool) $startpos = 0) returns Int
```

Coerces the first two arguments (in method form, also counting the invocant) to Str, and searches for `$needle`

in the string starting from `$startpos`

. It returns the offset into the string where `$needle`

was found, and an undefined value if it was not found.

See the documentation in type Str for examples.

## routine rindex

```
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.

## routine roots

```
multi method roots(Int(Cool) $n)
multi sub roots(Numeric(Cool) $x, 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);
}
```

produces this output:

```
2+0i 1.22464679914735e-16+2i -2+2.44929359829471e-16i -3.67394039744206e-16-2i
1.77635683940025e-15
4.30267170434156e-15
8.03651692704705e-15
1.04441561648202e-14
```

## method IO

```
method IO() returns IO::Path:D
```

Coerces the invocant to IO::Path.

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

# Routines supplied by class Any

FatRat inherits from class Any, which provides the following methods:

## method ACCEPTS

```
multi method ACCEPTS(Any:D: Mu $other)
```

Returns `True`

if `$other === self`

(i.e. it checks object identity).

Many built-in types override this for more specific comparisons

## method any

```
method any() returns Junction:D
```

Interprets the invocant as a list and creates an `any`

-Junction from it.

```
say so 2 == <1 2 3>.any; # True
say so 5 == <1 2 3>.any; # False
```

## method all

```
method all() returns Junction:D
```

Interprets the invocant as a list and creates an `all`

-Junction from it.

```
say so 1 < <2 3 4>.all; # True
say so 3 < <2 3 4>.all; # False
```

## method one

```
method one() returns Junction:D
```

Interprets the invocant as a list and creates an `one`

-Junction from it.

```
say so 1 == (1, 2, 3).one; # True
say so 1 == (1, 2, 1).one; # False
```

## method none

```
method none() returns Junction:D
```

Interprets the invocant as a list and creates an `none`

-Junction from it.

```
say so 1 == (1, 2, 3).none; # False
say so 4 == (1, 2, 3).none; # True
```

## method list

Interprets the invocant as a list, and returns that List.

```
say so 42.list.^name; # List
say so 42.list.elems; # 1
```

## method flat

Interprets the invocant as a list, flattens it, and returns that list.

```
say ((1, 2), (3)).elems; # 2
say ((1, 2), (3)).flat.elems; # 3
```

## method eager

Interprets the invocant as a list, evaluates it eagerly, and returns that list.

```
say (1..10).eager; # 1 2 3 4 5 6 7 8 9 10
```

## method elems

Interprets the invocant as a list, and returns the number of elements in the list.

```
say 42.elems; # 1
say <a b c>.elems; # 3
```

## method end

Interprets the invocant as a list, and returns the last index of that list.

```
say 6.end; # 0
say <a b c>.end; # 2
```

## method pairup

```
method pairup() returns List
```

Interprets the invocant as a list, and constructs a list of pairs from it, in the same way that assignment to a Hash does. That is, it takes two consecutive elements and constructs a pair from them, unless the item in the key position already is a pair (in which case the pair is passed is passed through, and the next list item, if any, is considered to be a key again).

```
say (a => 1, 'b', 'c').pairup.perl; # ("a" => 1, "b" => "c").list
```

## sub exit

```
sub exit(Int() $status = 0)
```

Exits the current process with return code `$status`

.

# Routines supplied by class Mu

FatRat inherits from class Mu, which provides the following methods:

## routine defined

```
multi sub defined(Mu) returns Bool:D
multi method defined() returns Bool:D
```

Returns `False`

on the type object, and `True`

otherwise.

```
say Int.defined; # False
say 42.defined; # True
```

Very few types (like Failure) override `defined`

to return `False`

even for instances:

```
sub fails() { fail 'oh noe' };
say fails().defined; # False
```

## routine Bool

```
multi sub Bool(Mu) returns Bool:D
multi method Bool() returns Bool:D
```

Returns `False`

on the type object, and `True`

otherwise.

Many built-in types override this to be `False`

for empty collections, the empty string or numerical zeros

```
say Mu.Bool; # False
say Mu.new.Bool; # True
say [1, 2, 3].Bool; # True
say [].Bool; # False
say { 'hash' => 'full'}.Bool; # True
say {}.Bool; # False
```

## method Str

```
multi method Str() returns Str
```

Returns a string representation of the invocant, intended to be machine readable. Method `Str`

warns on type objects, and produces the empty string.

```
say Mu.Str; #!> use of uninitialized value of type Mu in string context
```

## routine gist

```
multi sub gist(Mu) returns Str
multi method gist() returns Str
```

Returns a string representation of the invocant, optimized for fast recognition by humans.

The default `gist`

method in `Mu`

re-dispatches to the perl method for defined invocants, and returns the type name in parenthesis for type object invocants. Many built-in classes override the case of instances to something more specific.

`gist`

is the method that say calls implicitly, so `say $something`

and `say $something.gist`

generally produce the same output.

```
say Mu.gist; # (Mu)
say Mu.new.gist; # Mu.new()
```

## routine perl

```
multi sub perl(Mu) returns Str
multi method perl() returns Str
```

Returns a Perlish representation of the object (i.e., can usually be re-evaluated with EVAL to regenerate the object). The exact output of `perl`

is implementation specific, since there are generally many ways to write a Perl expression that produces a particular value

## method clone

```
method clone(*%twiddles)
```

Creates a shallow clone of the invocant. If named arguments are passed to it, their values are used in every place where an attribute name matches the name of a named argument.

```
class Point2D {
has ($.x, $.y);
multi method gist(Point2D:D:) {
"Point($.x, $.y)";
}
}
my $p = Point2D.new(x => 2, y => 3);
say $p; # Point(2, 3)
say $p.clone(y => -5); # Point(2, -5)
```

## method new

```
multi method new(*%attrinit)
```

Default method for constructing (create + initialize) new objects of a class. This method expects only named arguments which are then used to initialize attributes with accessors of the same name.

Classes may provide their own `new`

method to override this default.

`new`

triggers an object construction mechanism that calls submethods named `BUILD`

in each class of an inheritance hierarchy, if they exist. See the documentation on object construction for more information.

## method bless

```
method bless(*%attrinit) returns Mu:D
```

Lower-level object construction method than `new`

.

Creates a new object of the same type as the invocant, uses the named arguments to initialize attributes, and returns the created object.

You can use this method when writing custom constructors:

```
class Point {
has $.x;
has $.y;
multi method new($x, $y) {
self.bless(:$x, :$y);
}
}
my $p = Point.new(-1, 1);
```

(Though each time you write a custom constructor, remember that it makes subclassing harder).

## method CREATE

```
method CREATE() returns Mu:D
```

Allocates a new object of the same type as the invocant, without initializing any attributes.

```
say Mu.CREATE.defined; # True
```

## method print

```
multi method print() returns Bool:D
```

Prints value to `$*OUT`

after stringification using `.Str`

method without adding a newline at end.

```
"abc\n".print; # abc
```

## method say

```
multi method say() returns Bool:D
```

Prints value to `$*OUT`

after stringification using `.gist`

method with newline at end.

```
say 42; # 42
```

## method ACCEPTS

```
multi method ACCEPTS(Mu:U: $other)
```

`ACCEPTS`

is the method that smart matching with the infix ~~ operator and given/when invokes on the right-hand side (the matcher).

The `Mu:U`

multi performs a type check. Returns `True`

if `$other`

conforms to the invocant (which is always a type object or failure).

```
say 42 ~~ Mu; # True
say 42 ~~ Int; # True
say 42 ~~ Str; # False
```

Note that there is no multi for defined invocants; this is to allow autothreading of junctions, which happens as a fallback mechanism when no direct candidate is available to dispatch to.

## method WHICH

```
multi method WHICH() returns ObjAt:D
```

Returns an object of type ObjAt which uniquely identifies the object. Value types override this method which makes sure that two equivalent objects return the same return value from `WHICH`

.

```
say 42.WHICH eq 42.WHICH; # True
```

## method WHERE

```
method WHERE() returns Int
```

Returns an `Int`

representing the memory address of the object.

## method WHY

```
multi method WHY()
```

Returns the attached Pod value. For instance,

```
sub cast(Spell $s)
#= Initiate a specified spell normally
#= (do not use for class 7 spells)
{
do-raw-magic($s);
}
say &cast.WHY;
```

prints

```
Initiate a specified spell normally (do not use for class 7 spells)
```

See the documentation specification for details about attaching Pod to variables, classes, functions, methods, etc.

## trait is export

```
multi sub trait_mod:<is>(Mu:U \type, :$export!)
```

Marks a type as being exported, that is, available to external users.

```
my class SomeClass is export { }
```

A user of a module or class automatically gets all the symbols imported that are marked as `is export`

.

## method take

```
method take()
```

Takes the given item and passes it to the enclosing `gather`

block.

```
#| randomly select numbers for lotto
my $num-selected-numbers = 6;
my $max-lotto-numbers = 49;
gather for ^$num-selected-numbers {
take (1 .. $max-lotto-numbers).pick(1);
}.say; #-> 32 22 1 17 32 9 (for example)
```

## method so

```
method so()
```

Returns a `Bool`

value representing the logical non-negation of an expression. One can use this method similarly to the English sentence: "If that is **so**, then do this thing". For instance,

```
my @args = <-a -e -b -v>;
my $verbose-selected = any(@args) eq '-v' | '-V';
if $verbose-selected.so {
say "Verbose option detected in arguments";
} #-> Verbose option detected in arguments
```

## method not

```
method not()
```

Returns a `Bool`

value representing the logical negation of an expression. Thus it is the opposite of `so`

.

```
my @args = <-a -e -b>;
my $verbose-selected = any(@args) eq '-v' | '-V';
if $verbose-selected.not {
say "Verbose option not present in arguments";
} #-> Verbose option not present in arguments
```

Since there is also a prefix version of `not`

, the above code reads better like so:

```
my @args = <-a -e -b>;
my $verbose-selected = any(@args) eq '-v' | '-V';
if not $verbose-selected {
say "Verbose option not present in arguments";
} #-> Verbose option not present in arguments
```