NAME
Muldis::D::Ext::Integer - Muldis D extension for integer data types and operators
VERSION
This document is Muldis::D::Ext::Integer version 0.85.0.
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.
DESCRIPTION
Muldis D has a mandatory core set of system-defined (eternally available) entities, which is referred to as the Muldis D core or the core; they are the minimal entities that all Muldis D implementations need to provide; they are mutually self-describing and are used to bootstrap the language; any entities outside the core, called Muldis D extensions, are non-mandatory and are defined in terms of the core or each other, but the reverse isn't true.
This current Integer document describes the system-defined Muldis D Integer Extension, which consists of integer data types and operators, essentially all the generic ones that a typical programming language should have, but for the bare minimum needed for bootstrapping Muldis D, which are defined in the language core instead.
This current document does not describe the polymorphic operators that all types, or some types including core types, have defined over them; said operators are defined once for all types in Muldis::D::Core.
This documentation is pending.
TYPE SUMMARY
Following are all the data types described in this document, arranged in a type graph according to their proper sub|supertype relationships (but that a few of them just reappear from the core set to provide a similar context, and aren't re-described here):
sys.std.Core.Type.Universal
sys.std.Core.Type.Empty
sys.std.Core.Type.Scalar
sys.std.Core.Type.DHScalar
sys.std.Core.Type.Int
sys.std.Core.Type.NNInt
sys.std.Core.Type.PInt
# These are all finite integer types.
sys.std.Integer.Type.PInt2_36This documentation is pending.
SYSTEM-DEFINED INTEGER-CONCERNING DATA TYPES
sys.std.Integer.Type.PInt2_36
This is an enumeration data type. PInt2_36 is a proper subtype of PInt where all member values are between 2 and 36. (The significance of the number 36 is 10 digits plus 26 letters.) Its default and minimum value is 2. Its maximum value is 36. The cardinality of this type is 35.
FUNCTIONS FOR INTEGER MATH
These functions implement commonly used integer numeric operations.
sys.std.Integer.inc
function sys.std.Integer.inc (Int <-- Int $topic)
This function results in its argument incremented by 1. Note that this operation is also known as ++.
sys.std.Integer.dec
function sys.std.Integer.dec (Int <-- Int $topic)
This function results in its argument decremented by 1. Note that this operation is also known as --.
sys.std.Integer.abs
function sys.std.Integer.abs (NNInt <-- Int $topic)
This function results in the absolute value of its argument. Note that this operation is also known as I||.
sys.std.Integer.sum
function sys.std.Integer.sum (Int <-- bag_of.Int $topic?)
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. Note that this operation is also known as addition or plus or I+.
sys.std.Integer.diff
function sys.std.Integer.diff (Int <-- Int $minuend, Int $subtrahend)
This 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 I-.
sys.std.Integer.abs_diff
function sys.std.Integer.abs_diff (Int <-- Int $topic, Int $other)
This symmetric function results in the absolute difference between its 2 arguments. Note that this operation is also known as I|-|.
sys.std.Integer.product
function sys.std.Integer.product (Int <-- bag_of.Int $topic?)
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. Note that this operation is also known as multiply or times or I*.
sys.std.Integer.quotient
function sys.std.Integer.quotient (Int <-- Int $dividend, Int $divisor)
This function results in the quotient when its dividend argument is divided by its divisor argument using integer division. This function will fail if divisor is zero. Note that this operation is also known as divide or I/.
sys.std.Integer.remainder
function sys.std.Integer.remainder (NNInt <-- Int $dividend, Int $divisor)
This function results in the remainder when its dividend argument is divided by its divisor argument using integer division. This function will fail if divisor is zero. Note that this operation is also known as modulus or %.
sys.std.Integer.quot_and_rem
function sys.std.Integer.quot_and_rem (Tuple <-- Int $dividend, Int $divisor)
This function results in a binary tuple whose attribute names are quotient (an Int) and remainder (a NNInt) and whose respective attribute values are what sys.std.Integer.quotient and sys.std.Integer.remainder would result in when given the same arguments. This function will fail if divisor is zero.
sys.std.Integer.maybe_quotient
function sys.std.Integer.maybe_quotient (maybe_of.Int <-- Int $dividend, Int $divisor)
This function is exactly the same as sys.std.Integer.quotient except that it results in a Maybe of what is otherwise the result, and that result has zero elements if divisor is zero.
sys.std.Integer.maybe_remainder
function sys.std.Integer.maybe_remainder (maybe_of.NNInt <-- Int $dividend, Int $divisor)
This function is exactly the same as sys.std.Integer.remainder except that it results in a Maybe of what is otherwise the result, and that result has zero elements if divisor is zero.
sys.std.Integer.maybe_quot_and_rem
function sys.std.Integer.maybe_quot_and_rem (Relation <-- Int $dividend, Int $divisor)
This function results in a binary relation whose attribute names are quotient (an Int) and remainder (a NNInt). If divisor is nonzero then the result has a single tuple whose respective attribute values are what sys.std.Integer.quotient and sys.std.Integer.remainder would result in when given the same arguments; if divisor is zero, then the result has zero tuples.
sys.std.Integer.range
function sys.std.Integer.range (Int <-- set_of.Int $topic)
This function results in the difference between the lowest and highest element values of its argument. If topic has zero values, then range results in the integer zero.
sys.std.Integer.median
function sys.std.Integer.median (set_of.Int <-- bag_of.Int $topic)
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.Integer.mode
function sys.std.Integer.mode (set_of.Int <-- bag_of.Int $topic)
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.Integer.power
function sys.std.Integer.power (Int <-- Int $radix, NNInt $exponent)
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 I^.
sys.std.Integer.factorial
function sys.std.Integer.factorial (PInt <-- NNInt $topic)
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!.
FUNCTIONS FOR INTEGER CONVERSION WITH TEXT
These functions convert between Int values and canonically formatted representations of integers as character strings.
sys.std.Integer.Int_from_Text
function sys.std.Integer.Int_from_Text (Int <-- Text $text, PInt2_36 $radix)
This selector function results in the Int value that its (not-empty) text argument maps to when the whole character string is evaluated as a base-radix integer. Extending the typical formats of [base-2, base-8, base-10, base-16], this function supports base-2 through base-36; to get the latter, the characters 0-9 and A-Z represent values in 0-35. This function will fail if text can't be mapped as specified.
sys.std.Integer.Text_from_Int
function sys.std.Integer.Text_from_Int (Text <-- Int $int, PInt2_36 $radix)
This selector function results in the (not-empty) Text value where its int argument is formatted as a base-radix integer.
FUNCTIONS FOR INTEGER CONVERSION WITH BLOB
These functions convert between Int values and canonically formatted representations of integers as binary strings. Conjecture: These may not actually be useful, and perhaps only operators that take an argument specifying a fixed-length field size, with big and little endian versions, would be appropriate instead. Or maybe both kinds are necessary.
sys.std.Integer.Int_from_Blob_S_VBE
function sys.std.Integer.Int_from_Blob_S_VBE (Int <-- Blob $blob)
This selector function results in the Int value that its blob argument maps to when the whole bit string is treated literally as a variable-length binary (two's complement) signed integer of 1 or more bits in length. The first bit is taken as the sign bit, and any other bits provide greater precision than the -1 thru 0 range. The bit string is assumed to be big-endian, since it may not be possible to use little-endian in situations where the bit length isn't a multiple of 8.
sys.std.Integer.Blob_S_VBE_from_Int
function sys.std.Integer.Blob_S_VBE_from_Int (Blob <-- Int $int)
This selector function results in the Blob value where its int argument is formatted as a variable-length binary (two's complement) signed integer of 1 or more bits in length; the smallest number of bits necessary to store int is used.
sys.std.Integer.Int_from_Blob_U_VBE
function sys.std.Integer.Int_from_Blob_U_VBE (NNInt <-- Blob $blob)
This function is the same as sys.std.Integer.Int_from_Blob_S_VBE but that it does unsigned integers.
sys.std.Integer.Blob_U_VBE_from_Int
function sys.std.Integer.Blob_U_VBE_from_Int (NNInt <-- Blob $blob)
This function is the same as sys.std.Integer.Blob_S_VBE_from_Int but that it does unsigned integers.
SYSTEM SERVICES FOR RANDOM NUMBER GENERATORS
These system service routines provide ways to get random numbers from the system. Where the results are in the range between truly random and pseudo-random is, for the moment, an implementation detail, but the details of these functions is subject to become more formalized later.
sys.std.Integer.fetch_random
system_service sys.std.Integer.fetch_random (Int &$target, Int $min, Int $max, Bool $exclude_min?, Bool $exclude_max?)
This system service routine will update the variable supplied as its target argument so that it holds a randomly generated integer value in the range whose bounds are defined by its min and max arguments. If exclude_min or exclude_max are Bool:true, then the randomly generated value will not be equal to min or max, respectively; otherwise, the generated value might be equal to min or max. This function will fail if max is before min. Each of the exclude_m[in|ax] parameters is optional and defaults to Bool:false if no explicit argument is given to it.
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 (perl@DarrenDuncan.net)
LICENSE AND COPYRIGHT
This file is part of the formal specification of the Muldis D language.
Muldis D is Copyright © 2002-2009, 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.