2021-01-21 13:40:28 +01:00
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</head><body>
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<p><span class="h1">Working With Floating Point</span>
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<br/><br/>
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Some RETRO systems include support for floating point numbers.
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When present, this is built over the system <span class="tt">libm</span> using the
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C <span class="tt">double</span> type.
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<br/><br/>
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Floating point values are typically 64 bit IEEE 754 double
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precision (1 bit for the sign, 11 bits for the exponent, and
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the remaining 52 bits for the value), i.e. 15 decimal digits
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of precision.
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<br/><br/>
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2021-03-30 13:58:25 +02:00
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<span class="h2">Sigil</span>
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2021-01-21 13:40:28 +01:00
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<br/><br/>
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Floating point numbers start with a <span class="tt">.</span>
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<br/><br/>
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Examples:
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<br/><br/>
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Token Value
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<tt class='indentedcode'>.1 1.0</tt>
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<tt class='indentedcode'>.0.5 0.5</tt>
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<tt class='indentedcode'>.-.4 -0.4</tt>
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<tt class='indentedcode'>.1.3 1.3</tt>
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<br/><br/>
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<span class="h2">Namespace</span>
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<br/><br/>
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Floating point words are in the <span class="tt">f:</span> namespace. There is also
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a related <span class="tt">e:</span> namespace for <strong>encoded values</strong>, which allows
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storing of floats in standard memory.
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<br/><br/>
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<span class="h2">Operation</span>
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<br/><br/>
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Floating point values exist on a separate stack, and are bigger
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than the standard memory cells, so can not be directly stored
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and fetched from memory.
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<br/><br/>
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The floating point system also provides an alternate stack that
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can be used to temporarily store values.
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<br/><br/>
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The following words exist for arranging values on the floating
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point stack. These are direct analogs to the non-prefiexd words
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for dealing with the data stack.
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<br/><br/>
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• <span class="tt">f:nip</span><br/>
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• <span class="tt">f:over</span><br/>
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• <span class="tt">f:depth</span><br/>
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• <span class="tt">f:drop</span><br/>
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• <span class="tt">f:drop-pair</span><br/>
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• <span class="tt">f:dup</span><br/>
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• <span class="tt">f:dup-pair</span><br/>
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• <span class="tt">f:dump-stack</span><br/>
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• <span class="tt">f:tuck</span><br/>
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• <span class="tt">f:swap</span><br/>
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• <span class="tt">f:rot</span><br/>
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<br/><br/>
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For the secondary floating point stack, the following words are
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provided:
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<br/><br/>
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• <span class="tt">f:push</span><br/>
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• <span class="tt">f:pop</span><br/>
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• <span class="tt">f:adepth</span><br/>
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• <span class="tt">f:dump-astack</span><br/>
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<br/><br/>
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<span class="h2">Constants</span>
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<br/><br/>
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<tt class='indentedcode'>| Name | Returns |</tt>
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<tt class='indentedcode'>| -------- | ----------------- |</tt>
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<tt class='indentedcode'>| `f:E` | Euler's number |</tt>
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<tt class='indentedcode'>| `f:-INF` | Negative infinity |</tt>
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<tt class='indentedcode'>| `f:INF` | Positive infinity |</tt>
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<tt class='indentedcode'>| `f:NAN` | Not a Number |</tt>
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<tt class='indentedcode'>| `f:PI` | PI |</tt>
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<br/><br/>
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<span class="h2">Comparisons</span>
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<br/><br/>
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The basic set of comparators are the same as those for
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operating on integers. These are:
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<br/><br/>
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• <span class="tt">f:-eq?</span><br/>
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• <span class="tt">f:between?</span><br/>
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• <span class="tt">f:eq?</span><br/>
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• <span class="tt">f:gt?</span><br/>
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• <span class="tt">f:lt?</span><br/>
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• <span class="tt">f:negative?</span><br/>
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• <span class="tt">f:positive?</span><br/>
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• <span class="tt">f:case</span><br/>
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<br/><br/>
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There are also a few additions for comparing to special values
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like infinity and NaN.
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<br/><br/>
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• <span class="tt">f:-inf?</span><br/>
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• <span class="tt">f:inf?</span><br/>
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• <span class="tt">f:nan?</span><br/>
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<br/><br/>
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<span class="h2">Basic Math</span>
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<br/><br/>
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• <span class="tt">f:*</span><br/>
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• <span class="tt">f:+</span><br/>
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• <span class="tt">f:-</span><br/>
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• <span class="tt">f:/</span><br/>
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• <span class="tt">f:abs</span><br/>
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• <span class="tt">f:floor</span><br/>
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• <span class="tt">f:inc</span><br/>
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• <span class="tt">f:limit</span><br/>
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• <span class="tt">f:max</span><br/>
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• <span class="tt">f:min</span><br/>
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• <span class="tt">f:negate</span><br/>
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• <span class="tt">f:power</span><br/>
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• <span class="tt">f:ceiling</span><br/>
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• <span class="tt">f:dec</span><br/>
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• <span class="tt">f:log</span><br/>
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• <span class="tt">f:sqrt</span><br/>
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• <span class="tt">f:square</span><br/>
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• <span class="tt">f:round</span><br/>
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• <span class="tt">f:sign</span><br/>
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• <span class="tt">f:signed-sqrt</span><br/>
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• <span class="tt">f:signed-square</span><br/>
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<br/><br/>
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<span class="h2">Geometry</span>
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<br/><br/>
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RETRO provides a small number of words for doing geometric
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related calculations.
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<br/><br/>
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| Word | Returns |
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| -------- | ------------ |
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| <span class="tt">f:acos</span> | arc cosine |
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| <span class="tt">f:asin</span> | arc sine |
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| <span class="tt">f:atan</span> | arc tangent |
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| <span class="tt">f:cos</span> | cosine |
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| <span class="tt">f:sin</span> | sine |
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| <span class="tt">f:tan</span> | tangent |
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<br/><br/>
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<span class="h2">Storage and Retrieval</span>
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<br/><br/>
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By leveraging the encoded value functions, RETRO is able to
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allow storage of floating point values in memory. This does
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have a tradeoff in accuracy as the memory cells are considerably
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smaller than a full floating point size.
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<br/><br/>
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You can use <span class="tt">f:fetch</span> to fetch a floating point value and
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<span class="tt">f:store</span> to store one.
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<br/><br/>
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If you need more precision, try Kiyoshi Yoneda's FloatVar
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example (<span class="tt">example/FloatVar.forth</span>), which includes words to
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store and retrieve values using multiple cells.
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<br/><br/>
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• <span class="tt">f:to-number</span><br/>
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• <span class="tt">f:to-string</span><br/>
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<br/><br/>
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<span class="h2">I/O</span>
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<br/><br/>
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The floating point vocabulary has a single I/O word, <span class="tt">f:put</span>,
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for the display of floating point numbers.
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<br/><br/>
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<span class="h2">Encoded Values</span>
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<br/><br/>
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RETRO provides a means of encoding and decoding floating point
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values into standard integer cells. This is based on the paper
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"Encoding floating point values to shorter integers" by Kiyoshi
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Yoneda and Charles Childers.
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<br/><br/>
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• <span class="tt">f:E1</span><br/>
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• <span class="tt">f:to-e</span><br/>
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• <span class="tt">e:-INF</span><br/>
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• <span class="tt">e:-inf?</span><br/>
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• <span class="tt">e:INF</span><br/>
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• <span class="tt">e:MAX</span><br/>
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• <span class="tt">e:MIN</span><br/>
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• <span class="tt">e:NAN</span><br/>
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• <span class="tt">e:clip</span><br/>
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• <span class="tt">e:inf?</span><br/>
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• <span class="tt">e:max?</span><br/>
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• <span class="tt">e:min?</span><br/>
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• <span class="tt">e:n?</span><br/>
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• <span class="tt">e:nan?</span><br/>
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• <span class="tt">e:put</span><br/>
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• <span class="tt">e:to-f</span><br/>
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• <span class="tt">e:zero?</span><br/>
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</p>
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</body></html>
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