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explain integer math sin/cos routines even better
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Irmen de Jong
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ee262f6aad
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22c9e99fa3
@ -500,11 +500,10 @@ but perhaps the provided ones can be of service too.
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Sets a new seed for the pseudo-RNG sequence (both rnd and rndw). The seed consists of two words.
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Do not use zeros for the seed!
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.. sidebar::
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.. hint::
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This is a graph showing the various ranges of values mentioned in the integer sine and cosine
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routines that follow below.
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routines that follow below. (Note that the x input value never corresponds to an exact *degree*
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around the circle 0..359 as that exceeds a byte value. There's double-degrees though; 0...179)
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Only the sine function is shown, but the cosine function follows the same pattern.
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.. image:: sinegraph.svg
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BIN
docs/source/sinegraph.odg
Normal file
BIN
docs/source/sinegraph.odg
Normal file
Binary file not shown.
@ -1,16 +1,30 @@
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<rect class="BoundingBox" stroke="none" fill="none" x="1708" y="5769" width="854" height="1001"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="1958" y="6279"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">0</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id18">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="1537" y="1218" width="1214" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="1787" y="1728"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">127</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="1495" y="3769" width="1214" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="1745" y="4279"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">127</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id19">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="2397" y="6968" width="740" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="2647" y="7478"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">0</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="2355" y="9519" width="740" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="2605" y="10029"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">0</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id20">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="2398" y="6243" width="740" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="2648" y="6753"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">0</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="2356" y="8794" width="740" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="2606" y="9304"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">0</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id21">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="6000" y="6968" width="977" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="6250" y="7478"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">90</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="5958" y="9519" width="977" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="6208" y="10029"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">90</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id22">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="9787" y="6968" width="1214" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="10037" y="7478"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">179</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="9745" y="9519" width="1214" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="9995" y="10029"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">179</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id23">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="250" y="1205" width="1214" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="500" y="1715"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">255</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="208" y="3756" width="1214" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="458" y="4266"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">255</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id24">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="269" y="3205" width="1214" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="519" y="3715"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">128</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="227" y="5756" width="1214" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="477" y="6266"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">128</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id25">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="416" y="4993" width="740" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="666" y="5503"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">0</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="374" y="7544" width="740" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-weight="400"><tspan class="TextPosition" x="624" y="8054"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">0</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id26">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="7250" y="1468" width="2230" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-style="italic" font-weight="400"><tspan class="TextPosition" x="7500" y="1978"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">y = sin(x)</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="7208" y="4019" width="2230" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-style="italic" font-weight="400"><tspan class="TextPosition" x="7458" y="4529"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">y = sin(x)</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id27">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="2498" y="250" width="715" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-style="italic" font-weight="400"><tspan class="TextPosition" x="2748" y="760"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">y</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="2500" y="2769" width="715" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-style="italic" font-weight="400"><tspan class="TextPosition" x="2750" y="3279"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">y</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id28">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="10687" y="5026" width="715" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-style="italic" font-weight="400"><tspan class="TextPosition" x="10937" y="5536"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">x</tspan></tspan></tspan></text>
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="10645" y="7577" width="715" height="726"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Liberation Sans, sans-serif" font-size="423px" font-style="italic" font-weight="400"><tspan class="TextPosition" x="10895" y="8087"><tspan fill="rgb(0,0,0)" stroke="none" style="white-space: pre">x</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id29">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="11067" y="8794" width="3297" height="748"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Droid Sans Mono, monospace" font-size="423px" font-weight="400"><tspan class="TextPosition" x="11317" y="9313"><tspan fill="rgb(42,96,153)" stroke="none" style="white-space: pre">sin8, sin8u</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id30">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="11067" y="9519" width="3805" height="748"/>
|
||||
<text class="SVGTextShape"><tspan class="TextParagraph" font-family="Droid Sans Mono, monospace" font-size="423px" font-weight="400"><tspan class="TextPosition" x="11317" y="10038"><tspan fill="rgb(42,96,153)" stroke="none" style="white-space: pre">sinr8, sinr8u</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id31">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="1372" y="533" width="2296" height="3230"/>
|
||||
<text class="SVGTextShape" transform="rotate(-60 1946 3430)"><tspan class="TextParagraph" font-family="Droid Sans Mono, monospace" font-size="423px" font-weight="400"><tspan class="TextPosition" x="1946" y="3430"><tspan fill="rgb(42,96,153)" stroke="none" style="white-space: pre">sin8, sinr8</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
<g class="TextShape">
|
||||
<g id="id32">
|
||||
<rect class="BoundingBox" stroke="none" fill="none" x="250" y="89" width="2550" height="3670"/>
|
||||
<text class="SVGTextShape" transform="rotate(-60 824 3426)"><tspan class="TextParagraph" font-family="Droid Sans Mono, monospace" font-size="423px" font-weight="400"><tspan class="TextPosition" x="824" y="3426"><tspan fill="rgb(42,96,153)" stroke="none" style="white-space: pre">sin8u, sinr8u</tspan></tspan></tspan></text>
|
||||
</g>
|
||||
</g>
|
||||
</g>
|
||||
|
||||
|
Before Width: | Height: | Size: 32 KiB After Width: | Height: | Size: 36 KiB |
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Reference in New Issue
Block a user