role Numeric
role Numeric { ... }
Common role for numbers and types that can act as numbers.
Binary numeric operations return an object of the "wider" type:
Int narrowest
Rat
FatRat
Num
Complex widest
So for example the product of a Rat and an Int is a Rat.
Unary operations that in pure math usually return an irrational number generally return Num in Raku.
Methods
method Numeric
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 narrow
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 + 0i).narrow.raku; # OUTPUT: «4»
say (4.0 + 0i).narrow.^name; # OUTPUT: «Int»
method ACCEPTS
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).
routine log
multi 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.
Throws an exception if $base is 1.
Returns NaN for negative arguments. As of 6.e language version (early
implementation exists in Rakudo compiler 2023.02+), will return a
Complex value for negative arguments.
routine log10
multi log10(Numeric:D --> Numeric:D)
multi method log10(Numeric:D: --> Numeric:D)
Calculates the logarithm to base 10. Returns -Inf for 0.
Returns NaN for negative arguments. As of 6.e language version (early
implementation exists in Rakudo compiler 2023.02+), will return a
Complex value for negative arguments.
routine log2
multi log2(Numeric:D)
multi method log2(Numeric:D:)
Calculates the logarithm to base 2. Returns -Inf for 0.
Returns NaN for negative arguments. As of 6.e language version (early
implementation exists in Rakudo compiler 2023.02+), will return a
Complex value for negative arguments.
routine exp
multi 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.
method roots
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 $nth power.
routine abs
multi abs(Numeric:D --> Real:D)
multi method abs(Numeric:D: --> Real:D)
Returns the absolute value of the number.
routine sqrt
multi 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.
As of 6.e language version (early implementation exists in Rakudo compiler 2023.02+), will return a Complex value for negative arguments.
method conj
multi method conj(Numeric:D --> 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(Numeric:D:)
Returns the number incremented by one (successor).
method pred
method pred(Numeric:D:)
Returns the number decremented by one (predecessor).