tame/core/numeric/percent.xml

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<?xml version="1.0" encoding="utf-8"?>
<!--
Copyright (C) 2014-2022 Ryan Specialty Group, LLC.
This file is part of tame-core.
tame-core is free software: you can redistribute it and/or modify it
under the terms of the GNU General Public License as
published by the Free Software Foundation, either version 3 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
-->
<package xmlns="http://www.lovullo.com/rater"
xmlns:c="http://www.lovullo.com/calc"
xmlns:t="http://www.lovullo.com/rater/apply-template"
core="true"
desc="Percentage arithmetic">
<import package="../base" />
Converting between real and~percent is trivial:
$$
\begin{align}
r &amp;= p\over100;
p &amp;= 100r.
\end{align}
$$
^[Percent difference] (also called ^[relative change]) describes
the~change in value as a~percentage (for example: $10$~is $50%$
of~$20$, and is~$100%$ of~$5$). ^[Percent change] recognizes the
direction of the change (that is---$10$ is~$20$ reduced by~$50%$, so
$p=-50$).
Since ``change'' sounds like a~verb eclarative contexts, we use
the~term ^[percent difference] to mean ^[relative change]; it is
defined as:
$$\delta \over x = {{x_\beta - x_\alpha}\over{x_\alpha}} \times 100 = p.$$
Notice that this preserves the direction of the change. So, in the
context of the previous example, we can say that $10$
\emph{reduces}~$20$ by~$50%$, giving~$p=-50%$.
<template name="_rtop_"
desc="Rational number to percentage">
<param name="@name@" desc="Percentage to convert" />
<param name="@index@" desc="Index">
<text></text>
</param>
<param name="@desc@" desc="Optional description">
<text>Real number to convert into percentage</text>
</param>
<param name="@difference@"
desc="Whether to interpret as a percent difference (default
false)">
<text>false</text>
</param>
<param name="@negate@" desc="Whether to negate percentage before
conversion">
<text>false</text>
</param>
<c:product>
<if name="@negate@" eq="true">
<c:const value="-1" desc="Negate result" />
</if>
<c:sum>
<c:value-of name="@name@" index="@index@" />
<if name="@difference@" eq="true">
<c:const value="-1"
desc="Percent difference is relative (1 = 100%)" />
</if>
</c:sum>
<c:const value="100"
desc="Real to percentage" />
</c:product>
</template>
<template name="_ptor_" desc="Percent to rational number">
<param name="@name@" desc="Percentage to convert" />
<param name="@index@" desc="Index" />
<param name="@value@" desc="Constant (instead of named value)" />
<param name="@desc@" desc="Optional description for constant value">
<text>Percent to convert</text>
</param>
<param name="@difference@" desc="Whether to perform a percent
difference (default false)">
<text>false</text>
</param>
<param name="@negate@" desc="Whether to negate percentage before
conversion">
<text>false</text>
</param>
<c:sum>
<if name="@difference@" eq="true">
<c:const value="1"
desc="Perform percent difference" />
</if>
<c:quotient>
<c:product>
<if name="@negate@" eq="true">
<c:value-of name="NEGATE" />
</if>
<if name="@name@">
<c:value-of name="@name@" index="@index@" />
</if>
<unless name="@name@">
<c:const value="@value@" type="float" desc="@desc@" />
</unless>
</c:product>
<c:const value="100" type="integer" desc="Convert to rational number" />
</c:quotient>
</c:sum>
</template>
<template name="_ptor-each_"
desc="Each percent to real number">
<param name="@name@" desc="Percentage to convert" />
<param name="@generates@" desc="Value to generate into" />
<param name="@difference@"
desc="Whether to perform a percent difference">
<text>false</text>
</param>
<param name="@negate@" desc="Whether to negate percentage before
conversion">
<text>false</text>
</param>
<rate yields="_{@generates@}">
<c:sum of="@name@"
generates="@generates@" index="k"
desc="Real representation of {@name@}">
<t:ptor difference="@difference@" negate="@negate@"
name="@name@" index="k" />
</c:sum>
</rate>
</template>
<!--
Yields a total percent as an integer and rational number. The
integer is useful for displaying a total percent (e.g. for
credits/surcharges) and the rational number is useful for using
for multiplication in an equation.
Example:
<t:total-percent class="foo"
to_int="fooPercentTotal" to_rat="fooTotal"
index="k">
<with-param name="@values@">
<c:value-of name="fooA" index="k" />
<c:value-of name="fooB" index="k" />
</with-param>
</t:total-percent>
Let fooA = 5, fooB = -7
will yield:
- fooPercentTotal = -2
- fooTotal = 0.98
-->
<template name="_total-percent_"
desc="Generates a total percentage as an integer and a
rational number">
<!-- for use by @values@ -->
<param name="@index@" desc="Index variable" />
<param name="@class@" desc="Classification match" />
<param name="@to_int@" desc="Integer total to yield" />
<param name="@to_rat@" desc="Rational number to yield" />
<param name="@values@" desc="Value nodes" />
<param name="@yields_int@" desc="Yields for integer total">
<text>_</text>
<param-value name="@to_int@" />
</param>
<param name="@yields_rat@" desc="Yields for rational total">
<text>_</text>
<param-value name="@to_rat@" />
</param>
<!-- percent total (e.g. 7 for 7%) -->
<rate-each class="@class@" yields="@yields_int@"
generates="@to_int@" index="@index@">
<c:sum>
<param-copy name="@values@" />
</c:sum>
</rate-each>
<!-- as a rational number (to multiply by; e.g. 1.07 for 7%, 0.93 for -7%) -->
<rate-each class="@class@" yields="@yields_rat@"
generates="@to_rat@" index="k">
<c:sum>
<c:const value="1" desc="Relative percent" />
<t:ptor name="@to_int@" index="k" />
</c:sum>
</rate-each>
</template>
<!--
This template is useful for, say, when a coverage is partially
included, but additional coverage may be purchased. For example,
if 10% of coverage X is included, but you can purchase more Y if
10% is insufficient, then we can simply reduce coverage Y by 10%
of coverage X.
If the initial value is insufficient, then the value 0 will be
produced.
-->
<template name="_percent-reduction_"
desc="Reduces a set of values by a percentage of another set of values">
<param name="@index@" desc="Value index" />
<param name="@reduce@" desc="Vector to reduce values of" />
<param name="@percentof@" desc="Vector to reduce values by a percentage of" />
<param name="@percent@" desc="Percent reduction (as a float)" />
<param name="@minval@" desc="Minimum value to reduce by (optional)" />
<param name="@condition@" desc="Boolean conditions (vector for
each index) under which reduction should be applied" />
<param name="@desc@" desc="Optional description">
<text>Percent to reduce by</text>
</param>
<param name="@label@" desc="Label for max() application">
<text>Reduced </text>
<param-value name="@reduce@" />
<text> by </text>
<param-value name="@percent@" />
<text>*</text>
<param-value name="@percentof@" />
<text> (cannot fall below 0)</text>
</param>
<c:apply name="max" label="@label@">
<!-- if the reduction produces a value less than 0, then simply return 0 -->
<c:arg name="max1">
<c:const value="0"
desc="0 will be returned if the reduction is too great" />
</c:arg>
<c:arg name="max2">
<c:sum>
<c:value-of name="@reduce@" index="@index@"
label="Initial value" />
<c:let>
<c:values>
<c:value name="reduce" type="float"
desc="Value to reduce by, should condition be met">
<c:product>
<c:const value="@percent@" desc="@desc@" />
<c:value-of name="@percentof@" index="@index@" />
</c:product>
</c:value>
</c:values>
<t:negate>
<c:product label="Conditional reduction">
<if name="@condition@">
<c:when name="@condition@" index="@index@">
<c:eq>
<c:value-of name="TRUE" />
</c:eq>
</c:when>
</if>
<if name="@minval@">
<c:apply name="max" max1="reduce">
<c:arg name="max2">
<c:const value="@minval@"
desc="Minimum value to reduce by" />
</c:arg>
</c:apply>
</if>
<unless name="@minval@">
<c:value-of name="reduce" label="Value to reduce by" />
</unless>
</c:product>
</t:negate>
</c:let>
</c:sum>
</c:arg>
</c:apply>
</template>
<template name="_percent-of-set_"
desc="Returns the percent of a set of given values">
<param name="@class@" desc="Class match" />
<param name="@of@" desc="Vector of values to take the percent of" />
<param name="@percent@" desc="Percent reduction (as a float)" />
<param name="@generates@" desc="Value to generate" />
<param name="@yields@" desc="Yield">
<param-value name="@generates@" />
<text>Total</text>
</param>
<rate-each class="@class@" yields="@yields@"
generates="@generates@" index="k">
<c:apply name="round">
<c:arg name="roundval">
<c:apply name="max">
<!-- if the reduction produces a value less than 0, then simply return 0 -->
<c:arg name="max1">
<c:const value="0"
desc="0 will be returned if the reduction is too great" />
</c:arg>
<c:arg name="max2">
<c:product label="Percent value">
<c:const value="@percent@" desc="Percent to reduce by" />
<c:value-of name="@of@" index="k"
label="Value to take percentage of" />
</c:product>
</c:arg>
</c:apply>
</c:arg>
</c:apply>
</rate-each>
</template>
</package>