avr-q 1.0.0

Fixed point arithmetic for AVR
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316

<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang="">
<head>
  <meta charset="utf-8" />
  <meta name="generator" content="pandoc" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
  <title>README</title>
  <style>
    html {
      color: #1a1a1a;
      background-color: #fdfdfd;
    }
    body {
      margin: 0 auto;
      max-width: 36em;
      padding-left: 50px;
      padding-right: 50px;
      padding-top: 50px;
      padding-bottom: 50px;
      hyphens: auto;
      overflow-wrap: break-word;
      text-rendering: optimizeLegibility;
      font-kerning: normal;
    }
    @media (max-width: 600px) {
      body {
        font-size: 0.9em;
        padding: 12px;
      }
      h1 {
        font-size: 1.8em;
      }
    }
    @media print {
      html {
        background-color: white;
      }
      body {
        background-color: transparent;
        color: black;
        font-size: 12pt;
      }
      p, h2, h3 {
        orphans: 3;
        widows: 3;
      }
      h2, h3, h4 {
        page-break-after: avoid;
      }
    }
    p {
      margin: 1em 0;
    }
    a {
      color: #1a1a1a;
    }
    a:visited {
      color: #1a1a1a;
    }
    img {
      max-width: 100%;
    }
    svg {
      height: auto;
      max-width: 100%;
    }
    h1, h2, h3, h4, h5, h6 {
      margin-top: 1.4em;
    }
    h5, h6 {
      font-size: 1em;
      font-style: italic;
    }
    h6 {
      font-weight: normal;
    }
    ol, ul {
      padding-left: 1.7em;
      margin-top: 1em;
    }
    li > ol, li > ul {
      margin-top: 0;
    }
    blockquote {
      margin: 1em 0 1em 1.7em;
      padding-left: 1em;
      border-left: 2px solid #e6e6e6;
      color: #606060;
    }
    code {
      font-family: Menlo, Monaco, Consolas, 'Lucida Console', monospace;
      font-size: 85%;
      margin: 0;
      hyphens: manual;
    }
    pre {
      margin: 1em 0;
      overflow: auto;
    }
    pre code {
      padding: 0;
      overflow: visible;
      overflow-wrap: normal;
    }
    .sourceCode {
     background-color: transparent;
     overflow: visible;
    }
    hr {
      background-color: #1a1a1a;
      border: none;
      height: 1px;
      margin: 1em 0;
    }
    table {
      margin: 1em 0;
      border-collapse: collapse;
      width: 100%;
      overflow-x: auto;
      display: block;
      font-variant-numeric: lining-nums tabular-nums;
    }
    table caption {
      margin-bottom: 0.75em;
    }
    tbody {
      margin-top: 0.5em;
      border-top: 1px solid #1a1a1a;
      border-bottom: 1px solid #1a1a1a;
    }
    th {
      border-top: 1px solid #1a1a1a;
      padding: 0.25em 0.5em 0.25em 0.5em;
    }
    td {
      padding: 0.125em 0.5em 0.25em 0.5em;
    }
    header {
      margin-bottom: 4em;
      text-align: center;
    }
    #TOC li {
      list-style: none;
    }
    #TOC ul {
      padding-left: 1.3em;
    }
    #TOC > ul {
      padding-left: 0;
    }
    #TOC a:not(:hover) {
      text-decoration: none;
    }
    code{white-space: pre-wrap;}
    span.smallcaps{font-variant: small-caps;}
    div.columns{display: flex; gap: min(4vw, 1.5em);}
    div.column{flex: auto; overflow-x: auto;}
    div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
    /* The extra [class] is a hack that increases specificity enough to
       override a similar rule in reveal.js */
    ul.task-list[class]{list-style: none;}
    ul.task-list li input[type="checkbox"] {
      font-size: inherit;
      width: 0.8em;
      margin: 0 0.8em 0.2em -1.6em;
      vertical-align: middle;
    }
    .display.math{display: block; text-align: center; margin: 0.5rem auto;}
    /* CSS for syntax highlighting */
    pre > code.sourceCode { white-space: pre; position: relative; }
    pre > code.sourceCode > span { line-height: 1.25; }
    pre > code.sourceCode > span:empty { height: 1.2em; }
    .sourceCode { overflow: visible; }
    code.sourceCode > span { color: inherit; text-decoration: inherit; }
    div.sourceCode { margin: 1em 0; }
    pre.sourceCode { margin: 0; }
    @media screen {
    div.sourceCode { overflow: auto; }
    }
    @media print {
    pre > code.sourceCode { white-space: pre-wrap; }
    pre > code.sourceCode > span { display: inline-block; text-indent: -5em; padding-left: 5em; }
    }
    pre.numberSource code
      { counter-reset: source-line 0; }
    pre.numberSource code > span
      { position: relative; left: -4em; counter-increment: source-line; }
    pre.numberSource code > span > a:first-child::before
      { content: counter(source-line);
        position: relative; left: -1em; text-align: right; vertical-align: baseline;
        border: none; display: inline-block;
        -webkit-touch-callout: none; -webkit-user-select: none;
        -khtml-user-select: none; -moz-user-select: none;
        -ms-user-select: none; user-select: none;
        padding: 0 4px; width: 4em;
        color: #aaaaaa;
      }
    pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa;  padding-left: 4px; }
    div.sourceCode
      {   }
    @media screen {
    pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
    }
    code span.al { color: #ff0000; font-weight: bold; } /* Alert */
    code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
    code span.at { color: #7d9029; } /* Attribute */
    code span.bn { color: #40a070; } /* BaseN */
    code span.bu { color: #008000; } /* BuiltIn */
    code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
    code span.ch { color: #4070a0; } /* Char */
    code span.cn { color: #880000; } /* Constant */
    code span.co { color: #60a0b0; font-style: italic; } /* Comment */
    code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
    code span.do { color: #ba2121; font-style: italic; } /* Documentation */
    code span.dt { color: #902000; } /* DataType */
    code span.dv { color: #40a070; } /* DecVal */
    code span.er { color: #ff0000; font-weight: bold; } /* Error */
    code span.ex { } /* Extension */
    code span.fl { color: #40a070; } /* Float */
    code span.fu { color: #06287e; } /* Function */
    code span.im { color: #008000; font-weight: bold; } /* Import */
    code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
    code span.kw { color: #007020; font-weight: bold; } /* Keyword */
    code span.op { color: #666666; } /* Operator */
    code span.ot { color: #007020; } /* Other */
    code span.pp { color: #bc7a00; } /* Preprocessor */
    code span.sc { color: #4070a0; } /* SpecialChar */
    code span.ss { color: #bb6688; } /* SpecialString */
    code span.st { color: #4070a0; } /* String */
    code span.va { color: #19177c; } /* Variable */
    code span.vs { color: #4070a0; } /* VerbatimString */
    code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
  </style>
</head>
<body>
<header id="title-block-header">
<h1 class="title">README</h1>
</header>
<h1 id="fixed-point-arithmetic-for-avr">Fixed point arithmetic for
AVR</h1>
<p>This library provides <a
href="https://en.wikipedia.org/wiki/Q_(number_format)">fixed-point
arithmetic types</a> for AVR microcontrollers.</p>
<h2 id="the-fixed-point-formats-supported-are">The fixed point formats
supported are</h2>
<ul>
<li><strong>Q7.8 format</strong>: A 16-bit fixed-point number with 7
integer bits and 8 fractional bits (<code>Q7p8</code>).</li>
<li><strong>Q15.8 format</strong>: A 24-bit fixed-point number with 15
integer bits and 8 fractional bits (<code>Q15p8</code>).</li>
</ul>
<h2 id="the-supported-operations-are">The supported operations are</h2>
<ul>
<li>Basic arithmetic operations: addition, subtraction, multiplication,
and division.</li>
<li>Macros for easy construction of fixed-point numbers from integers or
fractions.</li>
<li>Conversions between fixed-point types and integer types.</li>
<li>Optional <code>curveipo</code> feature for curve interpolation.</li>
</ul>
<h2 id="usage">Usage</h2>
<p>Add this to your <code>Cargo.toml</code>:</p>
<div class="sourceCode" id="cb1"><pre
class="sourceCode toml"><code class="sourceCode toml"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">[dependencies]</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="dt">avr-q</span> <span class="op">=</span> <span class="st">&quot;1&quot;</span></span></code></pre></div>
<h2 id="examples">Examples</h2>
<h3 id="creating-fixed-point-numbers">Creating fixed-point numbers</h3>
<div class="sourceCode" id="cb2"><pre
class="sourceCode rust"><code class="sourceCode rust"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="kw">use</span> <span class="pp">avr_q::</span><span class="op">{</span>q7p8<span class="op">,</span> Q7p8<span class="op">};</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="co">// From an integer</span></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> a <span class="op">=</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">5</span>)<span class="op">;</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="pp">assert_eq!</span>(a<span class="op">.</span>to_int()<span class="op">,</span> <span class="dv">5</span>)<span class="op">;</span></span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a><span class="co">// From a fraction</span></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> b <span class="op">=</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">1</span> <span class="op">/</span> <span class="dv">2</span>)<span class="op">;</span> <span class="co">// 0.5</span></span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> c <span class="op">=</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">10</span> <span class="op">/</span> <span class="dv">3</span>)<span class="op">;</span> <span class="co">// 3.33...</span></span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a><span class="co">// From variables</span></span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> numerator <span class="op">=</span> <span class="dv">10_i16</span><span class="op">;</span></span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> denominator <span class="op">=</span> <span class="dv">3_i16</span><span class="op">;</span></span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> d <span class="op">=</span> <span class="pp">q7p8!</span>(numerator <span class="op">/</span> denominator)<span class="op">;</span></span></code></pre></div>
<h3 id="arithmetic-operations">Arithmetic operations</h3>
<div class="sourceCode" id="cb3"><pre
class="sourceCode rust"><code class="sourceCode rust"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="kw">use</span> <span class="pp">avr_q::</span><span class="op">{</span>q7p8<span class="op">,</span> Q7p8<span class="op">};</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> a <span class="op">=</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">1</span> <span class="op">/</span> <span class="dv">2</span>)<span class="op">;</span> <span class="co">// 0.5</span></span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> b <span class="op">=</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">1</span> <span class="op">/</span> <span class="dv">4</span>)<span class="op">;</span> <span class="co">// 0.25</span></span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> sum <span class="op">=</span> a <span class="op">+</span> b<span class="op">;</span></span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a><span class="pp">assert_eq!</span>(sum<span class="op">,</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">3</span> <span class="op">/</span> <span class="dv">4</span>))<span class="op">;</span> <span class="co">// 0.75</span></span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> diff <span class="op">=</span> a <span class="op">-</span> b<span class="op">;</span></span>
<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a><span class="pp">assert_eq!</span>(diff<span class="op">,</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">1</span> <span class="op">/</span> <span class="dv">4</span>))<span class="op">;</span> <span class="co">// 0.25</span></span>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> prod <span class="op">=</span> a <span class="op">*</span> b<span class="op">;</span></span>
<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a><span class="pp">assert_eq!</span>(prod<span class="op">,</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">1</span> <span class="op">/</span> <span class="dv">8</span>))<span class="op">;</span> <span class="co">// 0.125</span></span>
<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> quot <span class="op">=</span> a <span class="op">/</span> b<span class="op">;</span></span>
<span id="cb3-16"><a href="#cb3-16" aria-hidden="true" tabindex="-1"></a><span class="pp">assert_eq!</span>(quot<span class="op">,</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">2</span>))<span class="op">;</span> <span class="co">// 2.0</span></span>
<span id="cb3-17"><a href="#cb3-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-18"><a href="#cb3-18" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> neg <span class="op">=</span> <span class="op">-</span>a<span class="op">;</span></span>
<span id="cb3-19"><a href="#cb3-19" aria-hidden="true" tabindex="-1"></a><span class="pp">assert_eq!</span>(neg<span class="op">,</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="op">-</span><span class="dv">1</span> <span class="op">/</span> <span class="dv">2</span>))<span class="op">;</span></span>
<span id="cb3-20"><a href="#cb3-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-21"><a href="#cb3-21" aria-hidden="true" tabindex="-1"></a><span class="kw">let</span> abs <span class="op">=</span> neg<span class="op">.</span>abs()<span class="op">;</span></span>
<span id="cb3-22"><a href="#cb3-22" aria-hidden="true" tabindex="-1"></a><span class="pp">assert_eq!</span>(abs<span class="op">,</span> <span class="pp">q7p8!</span>(<span class="kw">const</span> <span class="dv">1</span> <span class="op">/</span> <span class="dv">2</span>))<span class="op">;</span></span></code></pre></div>
<h2 id="license">License</h2>
<p>This project is licensed under either of</p>
<ul>
<li>Apache License, Version 2.0, (LICENSE-APACHE or
http://www.apache.org/licenses/LICENSE-2.0)</li>
<li>MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)</li>
</ul>
<p>at your option.</p>
</body>
</html>