SortAsymptote ( ordinal )

Limits an ordinal to (-1,1), for nested sort calculations

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Jeremy Bante

https://github.com/jbante/

Sample input:

List (
SortAsymptote ( 1 );
SortAsymptote ( 2 );
SortAsymptote ( 5 );
SortAsymptote ( 10 );
SortAsymptote ( 20 );
SortAsymptote ( 50 );
SortAsymptote ( 100 );
SortAsymptote ( 1000 );
SortAsymptote ( 10000 );
SortAsymptote ( 100000 );
SortAsymptote ( 1000000 );
)

Sample output:

.4093838908503588
.5234946419594956
.6418029522161849
.7057001703361976
.752752020690265
.797235329374854
.8219094323976252
.8735578447045257
.9020610312524535
.920082701393012
.9325031743866805

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

/**
 * =====================================
 * SortAsymptote ( ordinal )
 *		http://www.briandunning.com/cf/1280
 *
 * PURPOSE:
 *		Limits the range of ordinal to fit within (-1,1). This can be useful
 *		when creating nested custom sort orders, where "child" records have a
 *		numeric sort order, but must also respect the sort order of "parent"
 *		records, so that child records with the same parent record cluster
 *		together. In these cases, this function can be used to restrict the
 *		child sort order to be smaller than the order of magnitude for the
 *		parent sort order.
 *
 * RETURNS:
 *		A number, -1 < number < 1.
 *		If a < b, then SortAsymptote ( a ) < SortAsymptote ( b ).
 *		If a > 0, then SortAsymptote ( a ) > 0.
 *
 * PARAMETERS:
 *		ordinal: The number used for within-group sorting
 *
 * DEPENDENCIES: none
 *
 * Example:
 *		Parent::sort + SortAsymptote ( Child::sort ) //= Child::sortCalc
 *
 * HISTORY:
 * CREATED on 2011-02-15 by Jeremy Bante <http://scr.im/jbantetsg>.
 * =====================================
 */

Let ( [
	~ordinal = Ln ( Abs ( ordinal ) + 1 ); //Flatten the range
	~sort = ~ordinal / ( 1 + ~ordinal ) //Confine to asymptote
];
	If ( ordinal < 0 ; 0 - ~sort ; /*else*/ ~sort )
)

Limits the range of ordinal to fit within (-1,1). This can be useful when creating nested custom sort orders, where "child" records have a numeric sort order, but must also respect the sort order of "parent" records, so that child records with the same parent record cluster together. In these cases, this function can be used to restrict the child sort order to be smaller than the order of magnitude for the parent sort order. For example, where Parent::sort is known to contain integer values:

Parent::sort + SortAsymptote ( Child::sort ) //= Child::sortCalc

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Note: these functions are not guaranteed or supported by BrianDunning.com. Please contact the individual developer with any questions or problems.

SortAsymptote ( ordinal )

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