NAME
Muldis::D::Core::Numeric - Muldis D generic numeric operators
VERSION
This document is Muldis::D::Core::Numeric version 0.143.0.
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 numeric operators, essentially all the generic ones that a typical programming language should have.
This documentation is pending.
VIRTUAL FUNCTIONS FOR THE NUMERIC MIXIN TYPE
sys.std.Core.Numeric.abs
function abs (Numeric <-- topic@ : Numeric) {...}
This virtual function results in the absolute value of its argument. Note that this operation is also known as modulus.
sys.std.Core.Numeric.sum
function sum (Numeric <-- topic@ : bag_of.Numeric) {...}
This virtual 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. Conceptually, if topic has zero values, then sum results in the number zero, which is the identity value for addition; however, while each implementing function of sum could actually result in a type-specific value of zero, this virtual function itself will instead fail when topic has zero values, because then it would lack the necessary type information to know which type-specific implementing function to dispatch to. Note that this operation is also known as addition or plus or +.
sys.std.Core.Numeric.diff
function diff (Numeric <-- minuend@ : Numeric, subtrahend@ : Numeric) {...}
This virtual function results in the difference when its subtrahend argument is subtracted from its minuend argument. Note that this operation is also known as subtraction or minus or -.
sys.std.Core.Numeric.abs_diff
function abs_diff (Numeric <-- topic@ : Numeric, other@ : Numeric) {...}
This virtual symmetric function results in the absolute difference between its 2 arguments. Note that this operation is also known as |-|.
sys.std.Core.Numeric.product
function product (Numeric <-- topic@ : bag_of.Numeric) {...}
This virtual 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. Conceptually, if topic has zero values, then product results in the number 1, which is the identity value for multiplication; however, while each implementing function of product could actually result in a type-specific value of 1, this virtual function itself will instead fail when topic has zero values, because then it would lack the necessary type information to know which type-specific implementing function to dispatch to. Note that this operation is also known as multiply or times or *.
sys.std.Core.Numeric.frac_quotient
function frac_quotient (Numeric <-- dividend@ : Numeric, divisor@ : Numeric) {...}
This virtual function results in the possibly-fractional 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. Note that this operation is also known as divide or /.
sys.std.Core.Numeric.whole_quotient
function whole_quotient (Numeric <-- dividend@ : Numeric, divisor@ : Numeric, round_meth : RoundMeth) {...}
This virtual function results in the whole-number 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 whole number, where the nearest is determined by the rounding method specified by the round_meth argument. This function will fail if divisor is zero. Note that this operation is also known as divide or div.
sys.std.Core.Numeric.remainder
function remainder (Numeric <-- dividend@ : Numeric, divisor@ : Numeric, round_meth : RoundMeth) {...}
This virtual function results in the possibly-fractional 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 whole number. 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.Numeric.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. Note that this operation is also known as modulo or mod.
sys.std.Core.Numeric.quot_and_rem
function quot_and_rem (Tuple <-- dividend@ : Numeric, divisor@ : Numeric, round_meth : RoundMeth) {...}
This virtual function results in a binary tuple whose attribute names are quotient and remainder and whose respective attribute values are what sys.std.Core.Numeric.whole_quotient and sys.std.Core.Numeric.remainder would result in when given the same arguments. This function will fail if divisor is zero.
sys.std.Core.Numeric.range
function range (Numeric <-- topic@ : set_of.Numeric) {...}
This virtual 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.Numeric.frac_mean
function frac_mean (Numeric <-- topic@ : bag_of.Numeric) {...}
This virtual function results in the possibly-fractional 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.Numeric.median
function median (set_of.Numeric <-- topic@ : bag_of.Numeric) {...}
This virtual 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.Numeric.frac_mean_of_median
function frac_mean_of_median (Numeric <-- topic@ : bag_of.Numeric) {...}
This virtual function is a wrapper over sys.std.Core.Numeric.median that will result in the possibly-fractional mean of its result elements; it will fail if there are zero elements.
sys.std.Core.Numeric.mode
function mode (set_of.Numeric <-- topic@ : bag_of.Numeric) {...}
This virtual 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.Numeric.power_with_whole_exp
function power_with_whole_exp (Numeric <-- radix@ : Numeric, exponent@ : Numeric) {...}
This virtual function results in a possibly-fractional number that is the result of its possibly-fractional radix argument taken to the power of its whole-number exponent argument. Because this function constrains its exponent argument to being a whole number, then when its radix argument is any real or rational number at all, this function is guaranteed to have a naturally real and rational result, even when radix is a negative number. The only way that this operation could conceivably result in a naturally complex or irrational number when its radix is rational is if its exponent is a fractional number. This function will result in 1 if radix and exponent are both zero (rather than failing). Note that this operation is also known as exponentiation or ^.
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.