=begin pod :kind("Type") :subkind("class") :category("basic")

=TITLE class Int

=SUBTITLE Integer (arbitrary-precision)

=for code :skip-test<Defined in BOOTSTRAP, this definition fails>
class Int is Cool does Real { }

C<Int> objects store integral numbers of arbitrary size. C<Int>s are immutable.

There are two main syntax forms for C<Int> literals

    123;         # Int in decimal notation
    :16<BEEF>;   # Int in radix notations

For your convenience common radix forms come with a prefix shortcut.

    say so :2<11111111> == 0b11111111 == :8<377> == 0o377 == 255 == 0d255 == :16<ff> == 0xff;
    # OUTPUT: «True␤»

All forms allow underscores between any two digits which can serve as visual
separators, but don't carry any meaning:

    5_00000;       # five Lakhs
    500_000;       # five hundred thousand
    0xBEEF_CAFE;   # a strange place
    :2<1010_1010>; # 0d170

Radix notation also supports round and angle brackets which allow you to parse
a string for a given base, and putting together digits into a whole number
respectively:

    :16("9F");         # 159
    :100[99, 2, 3];    # 990203

These notations allow you to use variables, too:

    my $two = "2";
    my $ninety-nine = "99";
    :16($ninety-nine); # 153
    :100[99, $two, 3]; # 990203

=head1 Methods

=head method new

Defined as:

    multi method new(Any:U $type)
    multi method new(Any:D \value --> Int:D)
    multi method new(int   \value --> Int:D)

The first form will throw an exception; the second and third form will create
 an new Int from the actual integer value contained in the variable.


=head2 method Capture

Defined as:

    method Capture()

Throws C<X::Cannot::Capture>.

=head2 routine chr

Defined as:

    multi sub    chr(Int:D  --> Str:D)
    multi method chr(Int:D: --> Str:D)

Returns a one-character string, by interpreting the integer as a Unicode
codepoint number and converting it to the corresponding character.

Example:

    65.chr;  # returns "A"
    196.chr; # returns "Ä"

=head2 routine expmod

Defined as:

    multi sub    expmod(      $x,     $y,     $mod --> Int:D)
    multi sub    expmod(Int:D $x, Int $y, Int $mod --> Int:D)
    multi method expmod(Int:D:    Int $y, Int $mod --> Int:D)

Returns the given C<Int> raised to the C<$y> power within modulus C<$mod>,
that is gives the result of C<($x ** $y) mod $mod>. The subroutine form
can accept non-C<Int> arguments, which will be coerced to C<Int>.

    say expmod(4, 2, 5);    # OUTPUT: «1␤»
    say 7.expmod(2, 5);     # OUTPUT: «4␤»

C<$y> argument can also be negative, in which case, the result is
equivalent to C<($x ** $y)> mod $mod.

    say 7.expmod(-2, 5);     # OUTPUT: «4␤»


=head2 method polymod

Defined as:

    method polymod(Int:D: +@mods)

Returns a sequence of mod results corresponding to the divisors in C<@mods> in
the same order as they appear there. For the best effect,  the divisors should
be given from the smallest "unit" to the largest (e.g. 60 seconds per minute, 60
minutes per hour) and the results are returned in the same way: from smallest to
the largest (5 seconds, 4 minutes). The last non-zero value will be the last
remainder.

    say 120.polymod(10);    # OUTPUT: «(0 12)␤»
    say 120.polymod(10,10); # OUTPUT: «(0 2 1)␤»

In the first case, 120 is divided by 10 giving as a remainder 12, which is the
last element. In the second, 120 is C<div>ided by 10, giving 12, whose remainder
once divided by 10 is 2; the result of the integer division of 12 C<div> 10 is
the last remainder.  The number of remainders will be always one more item than
the number of given divisors. If the divisors are given as a lazy list, runs
until the remainder is 0 or the list of divisors is exhausted. All divisors must
be C<Int>s, unless the method is called on a non-C<Int> number.

    my $seconds = 1 * 60*60*24 # days
                + 3 * 60*60    # hours
                + 4 * 60       # minutes
                + 5;           # seconds

    say $seconds.polymod(60, 60);                # OUTPUT: «(5 4 27)␤»
    say $seconds.polymod(60, 60, 24);            # OUTPUT: «(5 4 3 1)␤»

    say 120.polymod:      1, 10, 10², 10³, 10⁴;  # OUTPUT: «(0 0 12 0 0 0)␤»
    say 120.polymod: lazy 1, 10, 10², 10³, 10⁴;  # OUTPUT: «(0 0 12)␤»
    say 120.polymod:      1, 10, 10² … ∞;        # OUTPUT: «(0 0 12)␤»

    say ⅔.polymod(⅓);                            # OUTPUT: «(0 2)␤»
    say 5.Rat.polymod(.3, .2);                   # OUTPUT: «(0.2 0 80)␤»

    my @digits-in-base37 = 9123607.polymod(37 xx *); # Base conversion
    say @digits-in-base37.reverse                    # OUTPUT: «[4 32 4 15 36]␤»


To illustrate how the C<Int>, non-lazy version of polymod works, consider
this code that implements it:

    my $seconds = 2 * 60*60*24 # days
                + 3 * 60*60    # hours
                + 4 * 60       # minutes
                + 5;           # seconds

    my @pieces;
    for 60, 60, 24 -> $divisor {
        @pieces.push: $seconds mod $divisor;
        $seconds div= $divisor
    }
    @pieces.push: $seconds;

    say @pieces; # OUTPUT: «[5 4 3 2]␤»

For a more detailed discussion, see
L<this blog post|http://blogs.perl.org/users/zoffix_znet/2016/05/perl-6-polymod-break-up-a-number-into-denominations.html>.

We can use lazy lists in C<polymod>, as long as they are finite:

=for code
my $some-numbers = lazy gather { take 3*$_ for 1..3 };
say 600.polymod( $some-numbers ); # OUTPUT: «(0 2 6 3)␤»


=head2 routine is-prime

Defined as:

    multi sub    is-prime (Int:D $number --> Bool:D)
    multi method is-prime (Int:D: --> Bool:D)

Returns C<True> if this C<Int> is known to be a prime, or is likely to be a
prime based on a probabilistic Miller-Rabin test.

Returns C<False> if this C<Int> is known not to be a prime.

    say 2.is-prime;         # OUTPUT: «True␤»
    say is-prime(9);        # OUTPUT: «False␤»

=head2 routine lsb

Defined as:

    multi method lsb(Int:D:)
    multi sub    lsb(Int:D)

Short for "Least Significant Bit".  Returns L<Nil|/type/Nil> if the number is
0. Otherwise returns the zero-based index from the right of the least
significant (rightmost) 1 in the binary representation of the number.

    say 0b01011.lsb;        # OUTPUT: «0␤»
    say 0b01010.lsb;        # OUTPUT: «1␤»
    say 0b10100.lsb;        # OUTPUT: «2␤»
    say 0b01000.lsb;        # OUTPUT: «3␤»
    say 0b10000.lsb;        # OUTPUT: «4␤»

=head2 routine msb

Defined as:

    multi method msb(Int:D:)
    multi sub    msb(Int:D)

Short for "Most Significant Bit".  Returns L<Nil|/type/Nil> if the number is 0.
Otherwise returns the zero-based index from the right of the most significant
(leftmost) 1 in the binary representation of the number.

    say 0b00001.msb;        # OUTPUT: «0␤»
    say 0b00011.msb;        # OUTPUT: «1␤»
    say 0b00101.msb;        # OUTPUT: «2␤»
    say 0b01010.msb;        # OUTPUT: «3␤»
    say 0b10011.msb;        # OUTPUT: «4␤»

=head2 routine unival

Defined as:

    multi sub    unival(Int:D  --> Numeric)
    multi method unival(Int:D: --> Numeric)

Returns the number represented by the Unicode codepoint with the given integer
number, or L<NaN|/type/Num#NaN> if it does not represent a number.

    say ord("¾").unival;    # OUTPUT: «0.75␤»
    say 190.unival;         # OUTPUT: «0.75␤»
    say unival(65);         # OUTPUT: «NaN␤»

=head2 method Range

Returns a L<Range object|/type/Range> that represents the range of values supported.

=head2 method Bridge

Defined as:

    method Bridge(Int:D: --> Num:D)

Returns the integer converted to C<Num>.

=head1 Operators

=head2 infix div

    multi sub infix:<div>(Int:D, Int:D --> Int:D)

Does an integer division, rounded down.

=end pod

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