Muldis::D::Core::Integer - Muldis D integer numeric operators
This document is Muldis::D::Core::Integer version 0.138.0.
This document is part of the Muldis D language specification, whose root document is Muldis::D; you should read that root document before you read this one, which provides subservient details. Moreover, you should read the Muldis::D::Core document before this current document, as that forms its own tree beneath a root document branch.
This document describes essentially all of the core Muldis D operators that are specific to the core data type Int, essentially all the generic ones that a typical programming language should have.
Int
This documentation is pending.
function order (Order <-- topic : Int, other : Int, misc_args? : Tuple, is_reverse_order? : Bool) implements sys.std.Core.Ordered.order {...}
This is a (total) order-determination function specific to Int. Its only valid misc_args argument is Tuple:D0.
order-determination
misc_args
Tuple:D0
function pred (Int <-- topic : Int) implements sys.std.Core.Ordered.Ordinal.pred {...}
This function results in the value that precedes its argument. It is a shorthand for adding 1 to its argument.
function succ (Int <-- topic : Int) implements sys.std.Core.Ordered.Ordinal.succ {...}
This function results in the value that succeeds its argument. It is a shorthand for subtracting 1 from its argument.
function abs (NNInt <-- topic : Int) implements sys.std.Core.Numeric.abs {...}
This function results in the absolute value of its argument.
function sum (Int <-- topic? : bag_of.Int) implements sys.std.Core.Numeric.sum {...}
This function results in the sum of the N element values of its argument; it is a reduction operator that recursively takes each pair of input values and adds (which is both commutative and associative) them together until just one is left, which is the result. If topic has zero values, then sum results in the integer zero, which is the identity value for addition.
topic
sum
function diff (Int <-- minuend : Int, subtrahend : Int) implements sys.std.Core.Numeric.diff {...}
This function results in the difference when its subtrahend argument is subtracted from its minuend argument.
subtrahend
minuend
function abs_diff (Int <-- topic : Int, other : Int) implements sys.std.Core.Numeric.abs_diff {...}
This symmetric function results in the absolute difference between its 2 arguments.
function product (Int <-- topic? : bag_of.Int) implements sys.std.Core.Numeric.product {...}
This function results in the product of the N element values of its argument; it is a reduction operator that recursively takes each pair of input values and multiplies (which is both commutative and associative) them together until just one is left, which is the result. If topic has zero values, then product results in the integer 1, which is the identity value for multiplication.
product
function frac_quotient (Rat <-- dividend : Int, divisor : Int) implements sys.std.Core.Numeric.frac_quotient {...}
This function results in the rational quotient when its dividend argument is divided by its divisor argument using the semantics of real number division. This function will fail if divisor is zero. It is an alternate way to construct a Rat literal at runtime in terms of 2 Int that are its numerator and denominator possrep attributes.
dividend
divisor
Rat
numerator
denominator
function whole_quotient (Int <-- dividend : Int, divisor : Int, round_meth : RoundMeth) implements sys.std.Core.Numeric.whole_quotient {...}
This function results in the integer quotient when its dividend argument is divided by its divisor argument using the semantics of real number division, and then the latter's result is rounded to the same or nearest integer, where the nearest is determined by the rounding method specified by the round_meth argument. This function will fail if divisor is zero.
round_meth
function remainder (Int <-- dividend : Int, divisor : Int, round_meth : RoundMeth) implements sys.std.Core.Numeric.remainder {...}
This function results in the integer remainder when its dividend argument is divided by its divisor argument using the semantics of real number division, and then the latter's result is rounded to the same or nearest integer. The semantics of this function preserve the identity x mod y = x - y * (x div y) (read x as dividend and y as divisor) where the division has the same semantics as sys.std.Core.Integer.whole_quotient (rounding guided by round_meth); the sign of this function's result always matches the sign of the dividend or the divisor if round_meth is ToZero (aka truncate) or Down (aka floor), respectively. This function will fail if divisor is zero.
x mod y = x - y * (x div y)
x
y
sys.std.Core.Integer.whole_quotient
ToZero
Down
function quot_and_rem (Tuple <-- dividend : Int, divisor : Int, round_meth : RoundMeth) implements sys.std.Core.Numeric.quot_and_rem {...}
This function results in a binary tuple whose attribute names are quotient and remainder and whose respective attribute values are what sys.std.Core.Integer.whole_quotient and sys.std.Core.Integer.remainder would result in when given the same arguments. This function will fail if divisor is zero.
quotient
remainder
sys.std.Core.Integer.remainder
function range (Int <-- topic : set_of.Int) implements sys.std.Core.Numeric.range {...}
This function results in the difference between the lowest and highest element values of its argument. If topic has zero values, then this function will fail.
function frac_mean (Rat <-- topic : bag_of.Int) implements sys.std.Core.Numeric.frac_mean {...}
This function results in the rational mean or arithmetic average of the N element values of its argument. It is equivalent to first taking the sum of the input values, and dividing that sum by the count of the input values using the semantics of real number division. If topic has zero values, then this function will fail.
function median (set_of.Int <-- topic : bag_of.Int) implements sys.std.Core.Numeric.median {...}
This function results in the 1 or 2 median values of the N element values of its argument; they are returned as a set. It is equivalent to first arranging the input values from least to greatest, and then taking the single middle value, if the count of input values is odd, or taking the 2 middle values, if the count of input values is even (but if the 2 middle values are the same value, the output has one element). If topic has zero values, then the result set is empty.
function frac_mean_of_median (Rat <-- topic : bag_of.Int) implements sys.std.Core.Numeric.frac_mean_of_median {...}
This function is a wrapper over sys.std.Core.Integer.median that will result in the rational mean of its result elements; it will fail if there are zero elements.
sys.std.Core.Integer.median
function mode (set_of.Int <-- topic : bag_of.Int) implements sys.std.Core.Numeric.mode {...}
This function results in the mode of the N element values of its argument; it is the set of values that appear the most often as input elements, and all have the same count of occurrances. As a trivial case, if all input elements have the same count of occurrances, then they will all be in the output. If topic has zero values, then the result set is empty.
function power_with_whole_exp (Rat <-- radix : Int, exponent : Int) implements sys.std.Core.Numeric.power_with_whole_exp {...}
This function results in a rational number that is the result of its radix argument taken to the power of its integer exponent argument. This function will result in 1 if radix and exponent are both zero (rather than failing).
radix
exponent
These functions implement commonly used integer numeric operations.
function whole_mean (Int <-- topic : bag_of.Int, round_meth : RoundMeth) {...}
This function results in the integer mean or arithmetic average of the N element values of its argument. It is equivalent to first taking the sum of the input values, and dividing that sum by the count of the input values, where the semantics of the division are the same as those of sys.std.Core.Integer.whole_quotient (rounding the result of a real number division as per round_meth). If topic has zero values, then this function will fail.
function whole_mean_of_median (Int <-- topic : bag_of.Int, round_meth : RoundMeth) {...}
This function is a wrapper over sys.std.Core.Integer.median that will result in the integer mean of its result elements; it will fail if there are zero elements.
function power (Int <-- radix : Int, exponent : NNInt) {...}
This function results in its radix argument taken to the power of its (non-negative integer) exponent argument. This function will result in 1 if radix and exponent are both zero (rather than failing), which seems reasonable given that the Integer.power function strictly has no numeric continuity (unlike Rational.power) and that this is by far the most common practice in both pure integer math contexts and computer languages, including SQL. Note that this operation is also known as exponentiation or exp.
Integer.power
Rational.power
exp
function factorial (PInt <-- topic : NNInt) {...}
This function results in the factorial of its argument (it is defined for an argument of zero to result in 1, as per the identity value for multiplication of an empty set). Note that this operation is also known as i!.
i!
updater assign_pred (&topic : Int) implements sys.std.Core.Ordered.Ordinal.assign_pred {...}
This update operator is a short-hand for first invoking the sys.std.Core.Integer.pred function with the same argument, and then assigning the result of that function to its argument.
sys.std.Core.Integer.pred
updater assign_succ (&topic : Int) implements sys.std.Core.Ordered.Ordinal.assign_succ {...}
This update operator is a short-hand for first invoking the sys.std.Core.Integer.succ function with the same argument, and then assigning the result of that function to its argument.
sys.std.Core.Integer.succ
These system-service routines provide ways to get random numbers from the system. Where the results are in the range between truly random and pseudo-random is, for the moment, an implementation detail, but the details of these functions is subject to become more formalized later.
system-service fetch_random (&target : Int, interval : sp_interval_of.Int) [...]
This system-service routine will update the variable supplied as its target argument so that it holds a randomly generated integer value that is included within the interval defined by its interval argument. This function will fail if interval represents an empty interval.
target
interval
Go to Muldis::D for the majority of distribution-internal references, and Muldis::D::SeeAlso for the majority of distribution-external references.
Darren Duncan (darren@DarrenDuncan.net)
darren@DarrenDuncan.net
This file is part of the formal specification of the Muldis D language.
Muldis D is Copyright © 2002-2010, Muldis Data Systems, Inc.
See the LICENSE AND COPYRIGHT of Muldis::D for details.
The TRADEMARK POLICY in Muldis::D applies to this file too.
The ACKNOWLEDGEMENTS in Muldis::D apply to this file too.
To install Muldis::D, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Muldis::D
CPAN shell
perl -MCPAN -e shell install Muldis::D
For more information on module installation, please visit the detailed CPAN module installation guide.