NAME
Muldis::D::Core::Integer - Muldis D integer numeric operators
VERSION
This document is Muldis::D::Core::Integer version 0.120.0.
PREFACE
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.
DESCRIPTION
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.
This documentation is pending.
FUNCTIONS IMPLEMENTING VIRTUAL ORDERED FUNCTIONS
sys.std.Core.Integer.order
function sys.std.Core.Integer.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.
FUNCTIONS IMPLEMENTING VIRTUAL ORDINAL FUNCTIONS
sys.std.Core.Integer.pred
function sys.std.Core.Integer.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.
sys.std.Core.Integer.succ
function sys.std.Core.Integer.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.
FUNCTIONS IMPLEMENTING VIRTUAL NUMERIC FUNCTIONS
sys.std.Core.Integer.abs
function sys.std.Core.Integer.abs (NNInt <-- $topic : Int) implements sys.std.Core.Numeric.abs {...}
This function results in the absolute value of its argument.
sys.std.Core.Integer.sum
function sys.std.Core.Integer.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.
sys.std.Core.Integer.diff
function sys.std.Core.Integer.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.
sys.std.Core.Integer.abs_diff
function sys.std.Core.Integer.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.
sys.std.Core.Integer.product
function sys.std.Core.Integer.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.
sys.std.Core.Integer.frac_quotient
function sys.std.Core.Integer.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.
sys.std.Core.Integer.whole_quotient
function sys.std.Core.Integer.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.
sys.std.Core.Integer.remainder
function sys.std.Core.Integer.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.
sys.std.Core.Integer.quot_and_rem
function sys.std.Core.Integer.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.
sys.std.Core.Integer.range
function sys.std.Core.Integer.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.
sys.std.Core.Integer.frac_mean
function sys.std.Core.Integer.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.
sys.std.Core.Integer.median
function sys.std.Core.Integer.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.
sys.std.Core.Integer.frac_mean_of_median
function sys.std.Core.Integer.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.mode
function sys.std.Core.Integer.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.
sys.std.Core.Integer.power_with_whole_exp
function sys.std.Core.Integer.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).
FUNCTIONS FOR INTEGER MATH
These functions implement commonly used integer numeric operations.
sys.std.Core.Integer.whole_mean
function sys.std.Core.Integer.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.
sys.std.Core.Integer.whole_mean_of_median
function sys.std.Core.Integer.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.
sys.std.Core.Integer.power
function sys.std.Core.Integer.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.
sys.std.Core.Integer.factorial
function sys.std.Core.Integer.factorial (PInt <-- $topic : NNInt) {...}
This function results in the factorial of its argument (it is defined for an argument of zero to result in 1, as per the identity value for multiplication of an empty set). Note that this operation is also known as i!.
SYSTEM-SERVICES FOR RANDOM NUMBER GENERATORS
These system-service routines provide ways to get random numbers from the system. Where the results are in the range between truly random and pseudo-random is, for the moment, an implementation detail, but the details of these functions is subject to become more formalized later.
sys.std.Core.Integer.fetch_random
system-service sys.std.Core.Integer.fetch_random (&$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.
SEE ALSO
Go to Muldis::D for the majority of distribution-internal references, and Muldis::D::SeeAlso for the majority of distribution-external references.
AUTHOR
Darren Duncan (darren@DarrenDuncan.net)
LICENSE AND COPYRIGHT
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.
TRADEMARK POLICY
The TRADEMARK POLICY in Muldis::D applies to this file too.
ACKNOWLEDGEMENTS
The ACKNOWLEDGEMENTS in Muldis::D apply to this file too.