DRAFT: Synopsis 32: Setting Library - Numeric
Rod Adams <firstname.lastname@example.org> Larry Wall <email@example.com> Aaron Sherman <firstname.lastname@example.org> Mark Stosberg <email@example.com> Carl Mäsak <firstname.lastname@example.org> Moritz Lenz <email@example.com> Tim Nelson <firstname.lastname@example.org>
Created: 19 Mar 2009 extracted from S29-functions.pod
Last Modified: 9 Apr 2010 Version: 6
The document is a draft.
If you read the HTML version, it is generated from the Pod in the pugs repository under /docs/Perl6/Spec/S32-setting-library/Numeric.pod so edit it there in the SVN repository if you would like to make changes.
This documents Bit, Int, Numeric, Rat, Complex, and Bool.
XXX So where are Bit, Int, and Rat
our Bool multi method succ ( Bool $b: ) is export
our Bool multi method pred ( Bool $b: ) is export
Numeric is a role for everything that's a scalar number. So
Complex and other numeric types do that role. However it is an abstract interface, so
$number.WHAT will never return
Numeric. Users who provide their own scalar numeric types are encouraged to implement the
The following are all defined in the
Numeric provides some constants in addition to the basic mathematical functions.
constant pi is export = 3.14159_26535_89793_23846_26433_83279_50288; constant e is export = 2.71828_18284_59045_23536_02874_71352_66249; constant i is export = 1i;
our Numeric multi method succ ( Numeric $x: ) is export our Int multi method succ ( Int $x: ) is export
Returns the successor of
$x. This method is used by
postfix:<++> to increment the value in a container.
our Numeric multi method pred ( Numeric $x: ) is export our Int multi method pred ( Int $x: ) is export
Returns the predecessor of
$x. This method is used by
postfix:<--> to decrement the value in a container.
our Numeric multi method abs ( Numeric $x: ) is export
our Numeric multi method exp ( Numeric $exponent: Numeric :$base = Num::e ) is export
Performs similar to
$base ** $exponent.
$base defaults to the constant e.
our Numeric multi method log ( Numeric $x: Numeric $base = Num::e ) is export
Logarithm of base
$base, default Natural. Calling with
$x == 0 is an error.
our Numeric multi method log10 (Numeric $x:) is export
10 logarithm, otherwise identical to
our Num term:<rand>
Pseudo random number in range
0 ..^ 1. That is,
0 is theoretically possible, while
1 is not. Note that there is no unary
rand function in Perl 6, so just multiply
rand by your desired multiplier. For picking a random integer you probably want to use something like
our Numeric multi method sqrt ( Numeric $x: ) is export
Returns the principle square root of the parameter.
method roots (Numeric $x: Int $n ) is export
Returns a list of all
$nth (complex) roots of
$n <= 0, itself if
$n == 0, and is free to return a single
Inf, or in case of complex numbers if one of the components is.
our Complex multi postfix:<i> ( Numeric $x )
Returns a complex number representing the parameter multiplied by the imaginary unit
i. Note that there is no
.i method. To follow a variable name with the postfix, it's necessary to use a backslash or parentheses:
our Numeric multi method to-radians ( Numeric $x: TrigBase $base ) is export
$base to radians.
our Numeric multi method from-radians ( Numeric $x: TrigBase $base ) is export
Convert from radians to
role Real does Numeric;
Numeric, is an abstract role that represents the interface of a real scalar number (i.e. neither
Complex nor vector-like). For example
Rat implement the
our Int multi method floor ( Real $x: ) is export
Returns the highest integer not greater than
our Int multi method ceiling ( Real $x: ) is export
Returns the lowest integer not less than
our Int multi method round ( Real $x: $scale = 1) is export
Returns the nearest integer to
$x. The algorithm is:
floor($x / $scale + 0.5) * $scale
(Other rounding algorithms will be given extended names beginning with "round".)
Functions that round to a particular precision may easily be created with currying:
constant &roundcents ::= &round.assuming(:scale(1/100));
our Int multi method truncate ( Real $x: ) is export
Returns the closest integer to
$x whose absolute value is not greater than the absolute value of
$x. (In other words, just chuck any fractional part.) This is the default rounding function used by implicit integer conversions.
You may also truncate using explicit integer casts, either
Int() for an arbitrarily large integers, or
int() for native integers.
our Int multi method sign ( Real $x: ) is export
Returns 1 when
$x is greater than 0, -1 when it is less than 0, 0 when it is equal to 0, or undefined when the value passed is undefined.
multi srand ( Real $seed = default_seed_algorithm())
Seed the generator
$seed defaults to some combination of various platform dependent characteristics to yield a non-deterministic seed. Note that you get one
srand() for free when you start a Perl program, so you must call
srand() yourself if you wish to specify a deterministic seed (or if you wish to be differently nondeterministic).
our Complex multi method cis (Real $angle:) is export
our Complex multi method unpolar (Real $mag: Real $angle) is export
Returns a complex number specified in polar coordinates. Angle is in radians.
class Num does Real;
Num is a machine-precision numeric real value.
Complex is an immutable type. Each
Complex object stores two numbers, the real and imaginary part. For all practical purposes a
Complex with a
NaN in real or imaginary part may be considered a
NaN itself (and
(NaN + 1i) ~~ NaN is
Coercion of a
Complex to any
Real returns the real part (coerced, if necessary) if the imaginary part is 0, and fails otherwise. Comparison between a
Real number and a
Complex must be smart enough not to coerce the
Complex to a real number blindly.
our Complex multi method new(Real $re, Real $im)
Complex number from real and imaginary part. This is the method form of
$re + ($im)i.
our Seq multi method polar (Complex $nim:) is export
Returns (magnitude, angle) corresponding to the complex number. The magnitude is non-negative, and the angle in the range
-π ..^ π.
our Real multi method re()
Returns the real part of the complex number.
our Real multi method im()
Returns the imaginary part of a complex number.
The following are also defined in
Numeric. The trig functions depend on the current (lexically scoped) trig base:
enum TrigBase is export <Radians Degrees Gradians Circles>; constant $?TRIGBASE = Radians;
Numeric multi method func ( Numeric $x: TrigBase $base = CALLER::<$?TRIGBASE> ) is export
where func is one of: sin, cos, tan, asin, acos, atan, sec, cosec, cotan, asec, acosec, acotan, sinh, cosh, tanh, asinh, acosh, atanh, sech, cosech, cotanh, asech, acosech, acotanh.
Performs the various trigonometric functions.
$base is used to declare how you measure your angles. Given the value of an arc representing a single full revolution.
$base Subdivisions of circle ---- ---------------------- Radians 2*pi Degrees 360 Gradians 400 Circles 1
To change the base within your own lexical scope, it suffices to redefine the compiler constant with the
use trigbase Degrees;
In addition to setting the new lexical
$?TRIGBASE, this also curries a new set of functions into the current lexical scope that assume the new base. (Note that methods calls cannot be curried, so methods must still look up the caller's trigbase. The optimizer may, of course, optimize these into fast function calls.)
our Numeric multi method atan2 ( Numeric $y: Numeric $x = 1 ) our Numeric multi atan2 ( Numeric $y, Numeric $x = 1 )
This second form of
atan computes the arctangent of
$y/$x, and takes the quadrant into account. Otherwise behaves as other trigonometric functions.
Int is an immutable, integral number of arbitrary size.
class Rat does Real;
An immutable rational number, represented by two
Ints, a numerator and a denominator. All interface methods return values as if the numerator and denominator were stored in a normal form: both numerator and denominator are minimal in their magnitude, and the denominator is positive. So
Rat.new(2, -4).denominator return
2, because the normal form is
multi method new(Int $num, Int $denom)
Rat object from the numerator and denominator. Fails if
$denom == 0.
our Seq[Int] multi method nude()
Seq of numerator and denominator
our Int multi method denominator()
Returns the denominator
our Int multi method numerator()
Returns the numerator
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