368 lines
11 KiB
XML
368 lines
11 KiB
XML
<?xml version="1.0" encoding="utf-8"?>
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<!--
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Copyright (C) 2014-2023 Ryan Specialty, LLC.
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This file is part of tame-core.
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tame-core is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as
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published by the Free Software Foundation, either version 3 of the
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License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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-->
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<package xmlns="http://www.lovullo.com/rater"
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xmlns:c="http://www.lovullo.com/calc"
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xmlns:t="http://www.lovullo.com/rater/apply-template"
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core="true"
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desc="Percentage arithmetic">
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<import package="../base" />
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Converting between real and~percent is trivial:
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$$
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\begin{align}
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r &= p\over100;
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p &= 100r.
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\end{align}
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$$
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^[Percent difference] (also called ^[relative change]) describes
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the~change in value as a~percentage (for example: $10$~is $50%$
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of~$20$, and is~$100%$ of~$5$). ^[Percent change] recognizes the
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direction of the change (that is---$10$ is~$20$ reduced by~$50%$, so
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$p=-50$).
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Since ``change'' sounds like a~verb eclarative contexts, we use
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the~term ^[percent difference] to mean ^[relative change]; it is
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defined as:
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$$\delta \over x = {{x_\beta - x_\alpha}\over{x_\alpha}} \times 100 = p.$$
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Notice that this preserves the direction of the change. So, in the
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context of the previous example, we can say that $10$
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\emph{reduces}~$20$ by~$50%$, giving~$p=-50%$.
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<template name="_rtop_"
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desc="Rational number to percentage">
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<param name="@name@" desc="Percentage to convert" />
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<param name="@index@" desc="Index">
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<text></text>
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</param>
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<param name="@desc@" desc="Optional description">
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<text>Real number to convert into percentage</text>
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</param>
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<param name="@difference@"
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desc="Whether to interpret as a percent difference (default
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false)">
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<text>false</text>
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</param>
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<param name="@negate@" desc="Whether to negate percentage before
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conversion">
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<text>false</text>
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</param>
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<c:product>
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<if name="@negate@" eq="true">
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<c:const value="-1" desc="Negate result" />
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</if>
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<c:sum>
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<c:value-of name="@name@" index="@index@" />
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<if name="@difference@" eq="true">
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<c:const value="-1"
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desc="Percent difference is relative (1 = 100%)" />
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</if>
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</c:sum>
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<c:const value="100"
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desc="Real to percentage" />
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</c:product>
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</template>
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<template name="_ptor_" desc="Percent to rational number">
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<param name="@name@" desc="Percentage to convert" />
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<param name="@index@" desc="Index" />
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<param name="@value@" desc="Constant (instead of named value)" />
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<param name="@desc@" desc="Optional description for constant value">
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<text>Percent to convert</text>
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</param>
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<param name="@difference@" desc="Whether to perform a percent
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difference (default false)">
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<text>false</text>
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</param>
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<param name="@negate@" desc="Whether to negate percentage before
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conversion">
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<text>false</text>
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</param>
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<c:sum>
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<if name="@difference@" eq="true">
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<c:const value="1"
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desc="Perform percent difference" />
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</if>
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<c:quotient>
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<c:product>
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<if name="@negate@" eq="true">
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<c:value-of name="NEGATE" />
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</if>
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<if name="@name@">
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<c:value-of name="@name@" index="@index@" />
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</if>
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<unless name="@name@">
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<c:const value="@value@" desc="@desc@" />
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</unless>
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</c:product>
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<c:const value="100" desc="Convert to rational number" />
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</c:quotient>
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</c:sum>
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</template>
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<template name="_ptor-each_"
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desc="Each percent to real number">
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<param name="@name@" desc="Percentage to convert" />
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<param name="@generates@" desc="Value to generate into" />
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<param name="@difference@"
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desc="Whether to perform a percent difference">
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<text>false</text>
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</param>
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<param name="@negate@" desc="Whether to negate percentage before
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conversion">
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<text>false</text>
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</param>
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<rate yields="_{@generates@}">
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<c:sum of="@name@"
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generates="@generates@" index="k"
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desc="Real representation of {@name@}">
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<t:ptor difference="@difference@" negate="@negate@"
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name="@name@" index="k" />
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</c:sum>
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</rate>
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</template>
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<!--
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Yields a total percent as an integer and rational number. The
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integer is useful for displaying a total percent (e.g. for
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credits/surcharges) and the rational number is useful for using
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for multiplication in an equation.
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Example:
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<t:total-percent class="foo"
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to_int="fooPercentTotal" to_rat="fooTotal"
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index="k">
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<with-param name="@values@">
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<c:value-of name="fooA" index="k" />
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<c:value-of name="fooB" index="k" />
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</with-param>
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</t:total-percent>
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Let fooA = 5, fooB = -7
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will yield:
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- fooPercentTotal = -2
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- fooTotal = 0.98
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-->
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<template name="_total-percent_"
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desc="Generates a total percentage as an integer and a
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rational number">
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<!-- for use by @values@ -->
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<param name="@index@" desc="Index variable" />
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<param name="@class@" desc="Classification match" />
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<param name="@to_int@" desc="Integer total to yield" />
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<param name="@to_rat@" desc="Rational number to yield" />
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<param name="@values@" desc="Value nodes" />
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<param name="@yields_int@" desc="Yields for integer total">
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<text>_</text>
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<param-value name="@to_int@" />
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</param>
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<param name="@yields_rat@" desc="Yields for rational total">
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<text>_</text>
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<param-value name="@to_rat@" />
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</param>
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<!-- percent total (e.g. 7 for 7%) -->
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<rate-each class="@class@" yields="@yields_int@"
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generates="@to_int@" index="@index@">
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<c:sum>
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<param-copy name="@values@" />
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</c:sum>
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</rate-each>
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<!-- as a rational number (to multiply by; e.g. 1.07 for 7%, 0.93 for -7%) -->
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<rate-each class="@class@" yields="@yields_rat@"
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generates="@to_rat@" index="k">
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<c:sum>
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<c:const value="1" desc="Relative percent" />
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<t:ptor name="@to_int@" index="k" />
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</c:sum>
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</rate-each>
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</template>
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<!--
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This template is useful for, say, when a coverage is partially
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included, but additional coverage may be purchased. For example,
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if 10% of coverage X is included, but you can purchase more Y if
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10% is insufficient, then we can simply reduce coverage Y by 10%
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of coverage X.
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If the initial value is insufficient, then the value 0 will be
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produced.
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-->
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<template name="_percent-reduction_"
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desc="Reduces a set of values by a percentage of another set of values">
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<param name="@index@" desc="Value index" />
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<param name="@reduce@" desc="Vector to reduce values of" />
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<param name="@percentof@" desc="Vector to reduce values by a percentage of" />
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<param name="@percent@" desc="Percent reduction (as a float)" />
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<param name="@minval@" desc="Minimum value to reduce by (optional)" />
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<param name="@condition@" desc="Boolean conditions (vector for
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each index) under which reduction should be applied" />
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<param name="@desc@" desc="Optional description">
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<text>Percent to reduce by</text>
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</param>
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<param name="@label@" desc="Label for max() application">
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<text>Reduced </text>
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<param-value name="@reduce@" />
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<text> by </text>
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<param-value name="@percent@" />
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<text>*</text>
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<param-value name="@percentof@" />
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<text> (cannot fall below 0)</text>
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</param>
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<c:apply name="max" label="@label@">
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<!-- if the reduction produces a value less than 0, then simply return 0 -->
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<c:arg name="max1">
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<c:const value="0"
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desc="0 will be returned if the reduction is too great" />
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</c:arg>
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<c:arg name="max2">
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<c:sum>
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<c:value-of name="@reduce@" index="@index@"
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label="Initial value" />
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<c:let>
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<c:values>
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<c:value name="reduce" type="float"
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desc="Value to reduce by, should condition be met">
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<c:product>
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<c:const value="@percent@" desc="@desc@" />
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<c:value-of name="@percentof@" index="@index@" />
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</c:product>
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</c:value>
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</c:values>
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<t:negate>
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<c:product label="Conditional reduction">
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<if name="@condition@">
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<c:when name="@condition@" index="@index@">
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<c:eq>
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<c:value-of name="TRUE" />
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</c:eq>
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</c:when>
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</if>
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<if name="@minval@">
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<c:apply name="max" max1="reduce">
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<c:arg name="max2">
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<c:const value="@minval@"
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desc="Minimum value to reduce by" />
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</c:arg>
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</c:apply>
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</if>
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<unless name="@minval@">
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<c:value-of name="reduce" label="Value to reduce by" />
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</unless>
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</c:product>
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</t:negate>
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</c:let>
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</c:sum>
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</c:arg>
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</c:apply>
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</template>
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<template name="_percent-of-set_"
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desc="Returns the percent of a set of given values">
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<param name="@class@" desc="Class match" />
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<param name="@of@" desc="Vector of values to take the percent of" />
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<param name="@percent@" desc="Percent reduction (as a float)" />
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<param name="@generates@" desc="Value to generate" />
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<param name="@yields@" desc="Yield">
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<param-value name="@generates@" />
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<text>Total</text>
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</param>
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<rate-each class="@class@" yields="@yields@"
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generates="@generates@" index="k">
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<c:apply name="round">
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<c:arg name="roundval">
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<c:apply name="max">
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<!-- if the reduction produces a value less than 0, then simply return 0 -->
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<c:arg name="max1">
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<c:const value="0"
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desc="0 will be returned if the reduction is too great" />
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</c:arg>
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<c:arg name="max2">
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<c:product label="Percent value">
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<c:const value="@percent@" desc="Percent to reduce by" />
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<c:value-of name="@of@" index="k"
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label="Value to take percentage of" />
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</c:product>
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</c:arg>
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</c:apply>
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</c:arg>
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</c:apply>
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</rate-each>
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</template>
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</package>
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