doc/html/ratio/users_guide.html


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
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725

<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>User's Guide</title>
<link rel="stylesheet" href="../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.76.1">
<link rel="home" href="../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset">
<link rel="up" href="../ratio.html" title="Chapter&#160;22.&#160;Boost.Ratio 1.0.1">
<link rel="prev" href="../ratio.html" title="Chapter&#160;22.&#160;Boost.Ratio 1.0.1">
<link rel="next" href="reference.html" title="Reference">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
<td align="center"><a href="../../../index.html">Home</a></td>
<td align="center"><a href="../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../ratio.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ratio.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="ratio.users_guide"></a><a class="link" href="users_guide.html" title="User's Guide">User's Guide</a>
</h2></div></div></div>
<div class="toc"><dl>
<dt><span class="section"><a href="users_guide.html#ratio.users_guide.getting_started">Getting Started</a></span></dt>
<dt><span class="section"><a href="users_guide.html#ratio.users_guide.tutorial">Tutorial</a></span></dt>
<dt><span class="section"><a href="users_guide.html#ratio.users_guide.Examples">Example</a></span></dt>
<dt><span class="section"><a href="users_guide.html#ratio.users_guide.ext_references">External Resources</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="ratio.users_guide.getting_started"></a><a class="link" href="users_guide.html#ratio.users_guide.getting_started" title="Getting Started">Getting Started</a>
</h3></div></div></div>
<div class="toc"><dl><dt><span class="section"><a href="users_guide.html#ratio.users_guide.getting_started.install">Installing
        Ratio</a></span></dt></dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="ratio.users_guide.getting_started.install"></a><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install" title="Installing Ratio">Installing
        Ratio</a>
</h4></div></div></div>
<h6>
<a name="ratio.users_guide.getting_started.install.h0"></a>
          <span><a name="ratio.users_guide.getting_started.install.getting_boost_ratio_"></a></span><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install.getting_boost_ratio_">Getting
          Boost.Ratio </a>
        </h6>
<p>
          Boost.Ratio is in the latest Boost release in the folder <code class="computeroutput"><span class="special">/</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span></code>.
          Documentation, tests and examples folder are at <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">libs</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span></code>.
        </p>
<p>
          You can also access the latest (unstable?) state from the <a href="http://svn.boost.org/svn/boost/trunk" target="_top">Boost
          trunk</a> directories <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span></code>
          and <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">ratio</span></code>.
        </p>
<p>
          Just go to <a href="http://svn.boost.org/trac/boost/wiki/BoostSubversion" target="_top">the
          wiki</a> and follow the instructions there for anonymous SVN access.
        </p>
<h6>
<a name="ratio.users_guide.getting_started.install.h1"></a>
          <span><a name="ratio.users_guide.getting_started.install.where_to_install_boost_ratio__"></a></span><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install.where_to_install_boost_ratio__">Where
          to install Boost.Ratio? </a>
        </h6>
<p>
          The simple way is to decompress (or checkout from SVN) the files in your
          BOOST_ROOT directory.
        </p>
<h6>
<a name="ratio.users_guide.getting_started.install.h2"></a>
          <span><a name="ratio.users_guide.getting_started.install.building_boost_ratio_"></a></span><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install.building_boost_ratio_">Building
          Boost.Ratio </a>
        </h6>
<p>
          <span class="bold"><strong>Boost.Ratio</strong></span> is a header only library,
          so no need to compile anything, you just need to <code class="computeroutput"><span class="identifier">include</span>
          <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>.
        </p>
<h6>
<a name="ratio.users_guide.getting_started.install.h3"></a>
          <span><a name="ratio.users_guide.getting_started.install.requirements"></a></span><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install.requirements">Requirements</a>
        </h6>
<p>
          <span class="bold"><strong>Boost.Ratio</strong></span> depends on some Boost libraries.
          For these specific parts you must use either Boost version 1.39.0 or later
          (even older versions may work).
        </p>
<p>
          In particular, <span class="bold"><strong>Boost.Ratio</strong></span> depends on:
        </p>
<div class="variablelist">
<p class="title"><b></b></p>
<dl>
<dt><span class="term"><a href="http://www.boost.org/libs/config" target="_top"><span class="bold"><strong>Boost.Config</strong></span></a></span></dt>
<dd><p>
                for configuration purposes, ...
              </p></dd>
<dt><span class="term"><a href="http://www.boost.org/libs/integer" target="_top"><span class="bold"><strong>Boost.Integer</strong></span></a></span></dt>
<dd><p>
                for cstdint conformance, and integer traits ...
              </p></dd>
<dt><span class="term"><a href="http://www.boost.org/libs/mpl" target="_top"><span class="bold"><strong>Boost.MPL</strong></span></a></span></dt>
<dd><p>
                for MPL Assert and bool, logical ...
              </p></dd>
<dt><span class="term"><a href="http://www.boost.org/libs/static_assert" target="_top"><span class="bold"><strong>Boost.StaticAssert</strong></span></a></span></dt>
<dd><p>
                for STATIC_ASSERT, ...
              </p></dd>
<dt><span class="term"><a href="http://www.boost.org/libs/type_traits" target="_top"><span class="bold"><strong>Boost.TypeTraits</strong></span></a></span></dt>
<dd><p>
                for is_base, is_convertible ...
              </p></dd>
<dt><span class="term"><a href="http://www.boost.org/libs/utility" target="_top"><span class="bold"><strong>Boost.Utility/EnableIf</strong></span></a></span></dt>
<dd><p>
                for enable_if, ...
              </p></dd>
</dl>
</div>
<h6>
<a name="ratio.users_guide.getting_started.install.h4"></a>
          <span><a name="ratio.users_guide.getting_started.install.building_an_executable_that_uses__emphasis_role__bold__boost_ratio__emphasis__"></a></span><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install.building_an_executable_that_uses__emphasis_role__bold__boost_ratio__emphasis__">Building
          an executable that uses <span class="bold"><strong>Boost.Ratio</strong></span> </a>
        </h6>
<p>
          No link is needed.
        </p>
<h6>
<a name="ratio.users_guide.getting_started.install.h5"></a>
          <span><a name="ratio.users_guide.getting_started.install.exception_safety_"></a></span><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install.exception_safety_">Exception
          safety </a>
        </h6>
<p>
          All functions in the library are exception-neutral, providing the strong
          exception safety guarantee.
        </p>
<h6>
<a name="ratio.users_guide.getting_started.install.h6"></a>
          <span><a name="ratio.users_guide.getting_started.install.thread_safety_"></a></span><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install.thread_safety_">Thread
          safety </a>
        </h6>
<p>
          All functions in the library are thread-unsafe except when noted explicitly.
        </p>
<h6>
<a name="ratio.users_guide.getting_started.install.h7"></a>
          <span><a name="ratio.users_guide.getting_started.install.tested_compilers_"></a></span><a class="link" href="users_guide.html#ratio.users_guide.getting_started.install.tested_compilers_">Tested
          compilers </a>
        </h6>
<p>
          <span class="bold"><strong>Boost.Ratio</strong></span> should work with an C++03
          conforming compiler. The current version has been tested on:
        </p>
<p>
          Windows with
        </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
              MSVC 10.0
            </li>
<li class="listitem">
              MSVC 9.0 Express
            </li>
<li class="listitem">
              MSVC 8.0
            </li>
</ul></div>
<p>
          Cygwin 1.5 with
        </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
              GCC 3.4.4
            </li></ul></div>
<p>
          Cygwin 1.7 with
        </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
              GCC 4.3.4
            </li></ul></div>
<p>
          MinGW with
        </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
              GCC 4.4.0
            </li>
<li class="listitem">
              GCC 4.5.0
            </li>
<li class="listitem">
              GCC 4.5.0 -std=c++0x
            </li>
<li class="listitem">
              GCC 4.6.0
            </li>
<li class="listitem">
              GCC 4.6.0 -std=c++0x
            </li>
</ul></div>
<p>
          Ubuntu 10.10
        </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
              GCC 4.4.5
            </li>
<li class="listitem">
              GCC 4.4.5 -std=c++0x
            </li>
<li class="listitem">
              GCC 4.5.1
            </li>
<li class="listitem">
              GCC 4.5.1 -std=c++0x
            </li>
<li class="listitem">
              clang 2.8
            </li>
</ul></div>
<p>
          Initial versions were tested on:
        </p>
<p>
          MacOS with GCC 4.2.4
        </p>
<p>
          Ubuntu Linux with GCC 4.2.4
        </p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
            Please let us know how this works on other platforms/compilers.
          </p></td></tr>
</table></div>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
            Please send any questions, comments and bug reports to boost &lt;at&gt;
            lists &lt;dot&gt; boost &lt;dot&gt; org.
          </p></td></tr>
</table></div>
</div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="ratio.users_guide.tutorial"></a><a class="link" href="users_guide.html#ratio.users_guide.tutorial" title="Tutorial">Tutorial</a>
</h3></div></div></div>
<h5>
<a name="ratio.users_guide.tutorial.h0"></a>
        <span><a name="ratio.users_guide.tutorial.ratio"></a></span><a class="link" href="users_guide.html#ratio.users_guide.tutorial.ratio">Ratio</a>
      </h5>
<p>
        <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a>
        is a general purpose utility inspired by Walter Brown allowing one to easily
        and safely compute rational values at compile-time. The <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a> class catches all errors (such
        as divide by zero and overflow) at compile time. It is used in the duration
        and <code class="computeroutput"><span class="identifier">time_point</span></code> classes to
        efficiently create units of time. It can also be used in other "quantity"
        libraries or anywhere there is a rational constant which is known at compile-time.
        The use of this utility can greatly reduce the chances of run-time overflow
        because the <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a> (and any ratios resulting
        from <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a>
        arithmetic) are always reduced to the lowest terms.
      </p>
<p>
        <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a>
        is a template taking two <code class="computeroutput"><span class="identifier">intmax_ts</span></code>,
        with the second defaulted to 1. In addition to copy constructors and assignment,
        it only has two public members, both of which are <code class="computeroutput"><span class="keyword">static</span>
        <span class="keyword">const</span> <span class="identifier">intmax_t</span></code>.
        One is the numerator of the <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a> and the other is the denominator.
        The <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a>
        is always normalized such that it is expressed in lowest terms, and the denominator
        is always positive. When the numerator is 0, the denominator is always 1.
      </p>
<p>
        <span class="bold"><strong>Example:</strong></span>
      </p>
<pre class="programlisting"><span class="keyword">typedef</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">5</span><span class="special">,</span> <span class="number">3</span><span class="special">&gt;</span>   <span class="identifier">five_thirds</span><span class="special">;</span>
<span class="comment">// five_thirds::num == 5, five_thirds::den == 3</span>

<span class="keyword">typedef</span> <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">25</span><span class="special">,</span> <span class="number">15</span><span class="special">&gt;</span> <span class="identifier">also_five_thirds</span><span class="special">;</span>
<span class="comment">// also_five_thirds::num == 5, also_five_thirds::den == 3</span>

<span class="keyword">typedef</span> <span class="identifier">ratio_divide</span><span class="special">&lt;</span><span class="identifier">five_thirds</span><span class="special">,</span> <span class="identifier">also_five_thirds</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">one</span><span class="special">;</span>
<span class="comment">// one::num == 1, one::den == 1</span>
</pre>
<p>
        This facility also includes convenience typedefs for the SI prefixes <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">atto</span></code></a>
        through <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">exa</span></code></a> corresponding to their internationally
        recognized definitions (in terms of <a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a>). This is a tremendous syntactic
        convenience. It will prevent errors in specifying constants as one no longer
        has to double count the number of zeros when trying to write millions or
        billions.
      </p>
<p>
        <span class="bold"><strong>Example:</strong></span>
      </p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">ratio_multiply</span><span class="special">&lt;</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;,</span> <span class="identifier">giga</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">_5giga</span><span class="special">;</span>
<span class="comment">// _5giga::num == 5000000000, _5giga::den == 1</span>

<span class="keyword">typedef</span> <span class="identifier">ratio_multiply</span><span class="special">&lt;</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;,</span> <span class="identifier">nano</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">_5nano</span><span class="special">;</span>
<span class="comment">// _5nano::num == 1, _5nano::den == 200000000</span>
</pre>
<h5>
<a name="ratio.users_guide.tutorial.h1"></a>
        <span><a name="ratio.users_guide.tutorial.ratio_i_o"></a></span><a class="link" href="users_guide.html#ratio.users_guide.tutorial.ratio_i_o">Ratio
        I/O</a>
      </h5>
<p>
        For each <code class="computeroutput"><span class="identifier">ratio</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span> <span class="identifier">D</span><span class="special">&gt;</span></code> there exists a <code class="computeroutput"><span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">ratio</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span>
        <span class="identifier">D</span><span class="special">&gt;,</span>
        <span class="identifier">CharT</span><span class="special">&gt;</span></code>
        for which you can query two strings: <code class="computeroutput"><span class="identifier">short_name</span></code>
        and <code class="computeroutput"><span class="identifier">long_name</span></code>. For those
        <code class="computeroutput"><span class="identifier">ratio</span></code>'s that correspond to
        an <a href="http://en.wikipedia.org/wiki/SI_prefix#List_of_SI_prefixes" target="_top">SI
        prefix</a> long_name corresponds to the internationally recognized prefix,
        stored as a <code class="computeroutput"><span class="identifier">basic_string</span><span class="special">&lt;</span><span class="identifier">CharT</span><span class="special">&gt;</span></code>. For example <code class="computeroutput"><span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">mega</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">long_name</span><span class="special">()</span></code>
        returns <code class="computeroutput"><span class="identifier">string</span><span class="special">(</span><span class="string">"mega"</span><span class="special">)</span></code>.
        For those <code class="computeroutput"><span class="identifier">ratio</span></code>s that correspond
        to an <a href="http://en.wikipedia.org/wiki/SI_prefix#List_of_SI_prefixes" target="_top">SI
        prefix</a> <code class="computeroutput"><span class="identifier">short_name</span></code>
        corresponds to the internationally recognized symbol, stored as a <code class="computeroutput"><span class="identifier">basic_string</span><span class="special">&lt;</span><span class="identifier">CharT</span><span class="special">&gt;</span></code>.
        For example, <code class="computeroutput"><span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">mega</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">short_name</span><span class="special">()</span></code>
        returns <code class="computeroutput"><span class="identifier">string</span><span class="special">(</span><span class="string">"M"</span><span class="special">)</span></code>.
        For all other <code class="computeroutput"><span class="identifier">ratio</span></code>s, both
        <code class="computeroutput"><span class="identifier">long_name</span><span class="special">()</span></code>
        and <code class="computeroutput"><span class="identifier">short_name</span><span class="special">()</span></code>
        return a <code class="computeroutput"><span class="identifier">basic_string</span></code> containing
        "[<code class="computeroutput"><span class="identifier">ratio</span><span class="special">::</span><span class="identifier">num</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">::</span><span class="identifier">den</span></code>]".
      </p>
<p>
        <code class="computeroutput"><span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">ratio</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span> <span class="identifier">D</span><span class="special">&gt;,</span> <span class="identifier">CharT</span><span class="special">&gt;</span></code> is only defined for four character types:
      </p>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
            <code class="computeroutput"><span class="keyword">char</span></code>: UTF-8
          </li>
<li class="listitem">
            <code class="computeroutput"><span class="identifier">char16_t</span></code>: UTF-16
          </li>
<li class="listitem">
            <code class="computeroutput"><span class="identifier">char32_t</span></code>: UTF-32
          </li>
<li class="listitem">
            <code class="computeroutput"><span class="keyword">wchar_t</span></code>: UTF-16 (if wchar_t
            is 16 bits) or UTF-32
          </li>
</ul></div>
<p>
        When the character is char, UTF-8 will be used to encode the names. When
        the character is <code class="computeroutput"><span class="identifier">char16_t</span></code>,
        UTF-16 will be used to encode the names. When the character is <code class="computeroutput"><span class="identifier">char32_t</span></code>, UTF-32 will be used to encode
        the names. When the character is <code class="computeroutput"><span class="keyword">wchar_t</span></code>,
        the encoding will be UTF-16 if <code class="computeroutput"><span class="keyword">wchar_t</span></code>
        is 16 bits, and otherwise UTF-32.
      </p>
<p>
        The <code class="computeroutput"><span class="identifier">short_name</span></code> (Greek mu
        or &#956;) for micro is defined by <a href="http://www.unicode.org/charts/PDF/U0080.pdf" target="_top">Unicode</a>
        to be U+00B5.
      </p>
<p>
        <span class="bold"><strong>Examples:</strong></span>
      </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">ratio</span><span class="special">/</span><span class="identifier">ratio_io</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>

<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">;</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ratio_string&lt;deca, char&gt;::long_name() = "</span>
         <span class="special">&lt;&lt;</span>  <span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">deca</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">long_name</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ratio_string&lt;deca, char&gt;::short_name() = "</span>
         <span class="special">&lt;&lt;</span>  <span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">deca</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">short_name</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ratio_string&lt;giga, char&gt;::long_name() = "</span>
         <span class="special">&lt;&lt;</span>  <span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">giga</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">long_name</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ratio_string&lt;giga, char&gt;::short_name() = "</span>
         <span class="special">&lt;&lt;</span>  <span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">giga</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">short_name</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ratio_string&lt;ratio&lt;4, 6&gt;, char&gt;::long_name() = "</span>
         <span class="special">&lt;&lt;</span>  <span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">4</span><span class="special">,</span> <span class="number">6</span><span class="special">&gt;,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">long_name</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"ratio_string&lt;ratio&lt;4, 6&gt;, char&gt;::short_name() = "</span>
         <span class="special">&lt;&lt;</span>  <span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">4</span><span class="special">,</span> <span class="number">6</span><span class="special">&gt;,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">short_name</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
        The output will be
      </p>
<pre class="programlisting"><span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">deca</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">long_name</span><span class="special">()</span> <span class="special">=</span> <span class="identifier">deca</span>
<span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">deca</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">short_name</span><span class="special">()</span> <span class="special">=</span> <span class="identifier">da</span>
<span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">giga</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">long_name</span><span class="special">()</span> <span class="special">=</span> <span class="identifier">giga</span>
<span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">giga</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">short_name</span><span class="special">()</span> <span class="special">=</span> <span class="identifier">G</span>
<span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">4</span><span class="special">,</span> <span class="number">6</span><span class="special">&gt;,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">long_name</span><span class="special">()</span> <span class="special">=</span> <span class="special">[</span><span class="number">2</span><span class="special">/</span><span class="number">3</span><span class="special">]</span>
<span class="identifier">ratio_string</span><span class="special">&lt;</span><span class="identifier">ratio</span><span class="special">&lt;</span><span class="number">4</span><span class="special">,</span> <span class="number">6</span><span class="special">&gt;,</span> <span class="keyword">char</span><span class="special">&gt;::</span><span class="identifier">short_name</span><span class="special">()</span> <span class="special">=</span> <span class="special">[</span><span class="number">2</span><span class="special">/</span><span class="number">3</span><span class="special">]</span>
</pre>
<h5>
<a name="ratio.users_guide.tutorial.h2"></a>
        <span><a name="ratio.users_guide.tutorial.ratio_mpl_numeric_metafunctions"></a></span><a class="link" href="users_guide.html#ratio.users_guide.tutorial.ratio_mpl_numeric_metafunctions">Ratio
        MPL Numeric Metafunctions</a>
      </h5>
<p>
        With the view of the _ratio class as a <a class="link" href="reference.html#ratio.reference.mpl.rational_constant" title="Rational Constant Concept">Rational
        Constant</a> we can mix _ratio&lt;&gt; and <span class="bold"><strong>Boost.MPL</strong></span>
        Integral Constants in the same expression, as in
      </p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">times</span><span class="special">&lt;</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;,</span> <span class="identifier">giga</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">_5giga</span><span class="special">;</span>
<span class="comment">// _5giga::num == 5000000000, _5giga::den == 1</span>

<span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">times</span><span class="special">&lt;</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;,</span> <span class="identifier">nano</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">_5nano</span><span class="special">;</span>
<span class="comment">// _5nano::num == 1, _5nano::den == 200000000</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="ratio.users_guide.Examples"></a><a class="link" href="users_guide.html#ratio.users_guide.Examples" title="Example">Example</a>
</h3></div></div></div>
<div class="toc"><dl><dt><span class="section"><a href="users_guide.html#ratio.users_guide.Examples.si_units">SI units</a></span></dt></dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="ratio.users_guide.Examples.si_units"></a><a class="link" href="users_guide.html#ratio.users_guide.Examples.si_units" title="SI units">SI units</a>
</h4></div></div></div>
<p>
          This example illustrates the use of type-safe physics code interoperating
          with <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><span class="identifier">duration</span></code> types, taking advantage of the
          <span class="bold"><strong>Boost.Ratio</strong></span> infrastructure and design
          philosophy.
        </p>
<p>
          Let's start by defining a <code class="computeroutput"><span class="identifier">length</span></code>
          class template that mimics <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><span class="identifier">duration</span></code>,
          which represents a time duration in various units, but restricts the representation
          to <code class="computeroutput"><span class="keyword">double</span></code> and uses <span class="bold"><strong>Boost.Ratio</strong></span> for length unit conversions:
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Ratio</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">length</span> <span class="special">{</span>
<span class="keyword">private</span><span class="special">:</span>
    <span class="keyword">double</span> <span class="identifier">len_</span><span class="special">;</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="keyword">typedef</span> <span class="identifier">Ratio</span> <span class="identifier">ratio</span><span class="special">;</span>
    <span class="identifier">length</span><span class="special">()</span> <span class="special">:</span> <span class="identifier">len_</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">{}</span>
    <span class="identifier">length</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">double</span><span class="special">&amp;</span> <span class="identifier">len</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">len_</span><span class="special">(</span><span class="identifier">len</span><span class="special">)</span> <span class="special">{}</span>

    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    <span class="identifier">length</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">length</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;&amp;</span> <span class="identifier">d</span><span class="special">)</span>
            <span class="special">:</span> <span class="identifier">len_</span><span class="special">(</span><span class="identifier">d</span><span class="special">.</span><span class="identifier">count</span><span class="special">()</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_divide</span><span class="special">&lt;</span><span class="identifier">Ratio</span><span class="special">,</span> <span class="identifier">R</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">::</span><span class="identifier">den</span> <span class="special">/</span>
                               <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_divide</span><span class="special">&lt;</span><span class="identifier">Ratio</span><span class="special">,</span> <span class="identifier">R</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">::</span><span class="identifier">num</span><span class="special">)</span> <span class="special">{}</span>

    <span class="keyword">double</span> <span class="identifier">count</span><span class="special">()</span> <span class="keyword">const</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">len_</span><span class="special">;}</span>

    <span class="identifier">length</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">length</span><span class="special">&amp;</span> <span class="identifier">d</span><span class="special">)</span> <span class="special">{</span><span class="identifier">len_</span> <span class="special">+=</span> <span class="identifier">d</span><span class="special">.</span><span class="identifier">count</span><span class="special">();</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">length</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">-=(</span><span class="keyword">const</span> <span class="identifier">length</span><span class="special">&amp;</span> <span class="identifier">d</span><span class="special">)</span> <span class="special">{</span><span class="identifier">len_</span> <span class="special">-=</span> <span class="identifier">d</span><span class="special">.</span><span class="identifier">count</span><span class="special">();</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>

    <span class="identifier">length</span> <span class="keyword">operator</span><span class="special">+()</span> <span class="keyword">const</span> <span class="special">{</span><span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">length</span> <span class="keyword">operator</span><span class="special">-()</span> <span class="keyword">const</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">length</span><span class="special">(-</span><span class="identifier">len_</span><span class="special">);}</span>

    <span class="identifier">length</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">*=(</span><span class="keyword">double</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="identifier">len_</span> <span class="special">*=</span> <span class="identifier">rhs</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">length</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">/=(</span><span class="keyword">double</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="identifier">len_</span> <span class="special">/=</span> <span class="identifier">rhs</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
<span class="special">};</span>
</pre>
<p>
          Here's a small sampling of length units:
        </p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">length</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;</span> <span class="special">&gt;</span>          <span class="identifier">meter</span><span class="special">;</span>        <span class="comment">// set meter as "unity"</span>
<span class="keyword">typedef</span> <span class="identifier">length</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">centi</span></code></a><span class="special">&gt;</span>              <span class="identifier">centimeter</span><span class="special">;</span>   <span class="comment">// 1/100 meter</span>
<span class="keyword">typedef</span> <span class="identifier">length</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">kilo</span></code></a><span class="special">&gt;</span>               <span class="identifier">kilometer</span><span class="special">;</span>    <span class="comment">// 1000  meters</span>
<span class="keyword">typedef</span> <span class="identifier">length</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">254</span><span class="special">,</span> <span class="number">10000</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">inch</span><span class="special">;</span>         <span class="comment">// 254/10000 meters</span>
</pre>
<p>
          Note that since <code class="computeroutput"><span class="identifier">length</span></code>'s
          template parameter is actually a generic ratio type, so we can use boost::ratio
          allowing for more complex length units:
        </p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">length</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_multiply</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">12</span><span class="special">&gt;,</span> <span class="identifier">inch</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>   <span class="identifier">foot</span><span class="special">;</span>  <span class="comment">// 12 inchs</span>
<span class="keyword">typedef</span> <span class="identifier">length</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_multiply</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">5280</span><span class="special">&gt;,</span> <span class="identifier">foot</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span> <span class="identifier">mile</span><span class="special">;</span>  <span class="comment">// 5280 feet</span>
</pre>
<p>
          Now we need a floating point-based definition of seconds:
        </p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><span class="identifier">duration</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">seconds</span><span class="special">;</span>                         <span class="comment">// unity</span>
</pre>
<p>
          We can even support sub-nanosecond durations:
        </p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><span class="identifier">duration</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span>  <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">pico</span></code></a><span class="special">&gt;</span> <span class="identifier">picosecond</span><span class="special">;</span>  <span class="comment">// 10^-12 seconds</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><span class="identifier">duration</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">femto</span></code></a><span class="special">&gt;</span> <span class="identifier">femtosecond</span><span class="special">;</span> <span class="comment">// 10^-15 seconds</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><span class="identifier">duration</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span>  <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio_si_typedefs" title="SI typedefs"><code class="computeroutput"><span class="identifier">atto</span></code></a><span class="special">&gt;</span> <span class="identifier">attosecond</span><span class="special">;</span>  <span class="comment">// 10^-18 seconds</span>
</pre>
<p>
          Finally, we can write a proof-of-concept of an SI units library, hard-wired
          for meters and floating point seconds, though it will accept other units:
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">quantity</span>
<span class="special">{</span>
    <span class="keyword">double</span> <span class="identifier">q_</span><span class="special">;</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="keyword">typedef</span> <span class="identifier">R1</span> <span class="identifier">time_dim</span><span class="special">;</span>
    <span class="keyword">typedef</span> <span class="identifier">R2</span> <span class="identifier">distance_dim</span><span class="special">;</span>
    <span class="identifier">quantity</span><span class="special">()</span> <span class="special">:</span> <span class="identifier">q_</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">{}</span>

    <span class="keyword">double</span> <span class="identifier">get</span><span class="special">()</span> <span class="keyword">const</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">q_</span><span class="special">;}</span>
    <span class="keyword">void</span> <span class="identifier">set</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">q</span><span class="special">)</span> <span class="special">{</span><span class="identifier">q_</span> <span class="special">=</span> <span class="identifier">q</span><span class="special">;}</span>
<span class="special">};</span>

<span class="keyword">template</span> <span class="special">&lt;&gt;</span>
<span class="keyword">class</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="special">&gt;</span>
<span class="special">{</span>
    <span class="keyword">double</span> <span class="identifier">q_</span><span class="special">;</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="identifier">quantity</span><span class="special">()</span> <span class="special">:</span> <span class="identifier">q_</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">{}</span>
    <span class="identifier">quantity</span><span class="special">(</span><span class="identifier">seconds</span> <span class="identifier">d</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">q_</span><span class="special">(</span><span class="identifier">d</span><span class="special">.</span><span class="identifier">count</span><span class="special">())</span> <span class="special">{}</span>  <span class="comment">// note:  only User1::seconds needed here</span>

    <span class="keyword">double</span> <span class="identifier">get</span><span class="special">()</span> <span class="keyword">const</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">q_</span><span class="special">;}</span>
    <span class="keyword">void</span> <span class="identifier">set</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">q</span><span class="special">)</span> <span class="special">{</span><span class="identifier">q_</span> <span class="special">=</span> <span class="identifier">q</span><span class="special">;}</span>
<span class="special">};</span>

<span class="keyword">template</span> <span class="special">&lt;&gt;</span>
<span class="keyword">class</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;</span> <span class="special">&gt;</span>
<span class="special">{</span>
    <span class="keyword">double</span> <span class="identifier">q_</span><span class="special">;</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="identifier">quantity</span><span class="special">()</span> <span class="special">:</span> <span class="identifier">q_</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">{}</span>
    <span class="identifier">quantity</span><span class="special">(</span><span class="identifier">meter</span> <span class="identifier">d</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">q_</span><span class="special">(</span><span class="identifier">d</span><span class="special">.</span><span class="identifier">count</span><span class="special">())</span> <span class="special">{}</span>  <span class="comment">// note:  only User1::meter needed here</span>

    <span class="keyword">double</span> <span class="identifier">get</span><span class="special">()</span> <span class="keyword">const</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">q_</span><span class="special">;}</span>
    <span class="keyword">void</span> <span class="identifier">set</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">q</span><span class="special">)</span> <span class="special">{</span><span class="identifier">q_</span> <span class="special">=</span> <span class="identifier">q</span><span class="special">;}</span>
<span class="special">};</span>

<span class="keyword">template</span> <span class="special">&lt;&gt;</span>
<span class="keyword">class</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="special">&gt;</span>
<span class="special">{</span>
    <span class="keyword">double</span> <span class="identifier">q_</span><span class="special">;</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="identifier">quantity</span><span class="special">()</span> <span class="special">:</span> <span class="identifier">q_</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special">{}</span>
    <span class="identifier">quantity</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">d</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">q_</span><span class="special">(</span><span class="identifier">d</span><span class="special">)</span> <span class="special">{}</span>

    <span class="keyword">double</span> <span class="identifier">get</span><span class="special">()</span> <span class="keyword">const</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">q_</span><span class="special">;}</span>
    <span class="keyword">void</span> <span class="identifier">set</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">q</span><span class="special">)</span> <span class="special">{</span><span class="identifier">q_</span> <span class="special">=</span> <span class="identifier">q</span><span class="special">;}</span>
<span class="special">};</span>
</pre>
<p>
          That allows us to create some useful SI-based unit types:
        </p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="special">&gt;</span>  <span class="identifier">Scalar</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="special">&gt;</span>  <span class="identifier">Time</span><span class="special">;</span>         <span class="comment">// second</span>
<span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;</span> <span class="special">&gt;</span>  <span class="identifier">Distance</span><span class="special">;</span>     <span class="comment">// meter</span>
<span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;-</span><span class="number">1</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">Speed</span><span class="special">;</span>        <span class="comment">// meter/second</span>
<span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;-</span><span class="number">2</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">Acceleration</span><span class="special">;</span> <span class="comment">// meter/second^2</span>
</pre>
<p>
          To make quantity useful, we need to be able to do arithmetic:
        </p>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R4</span><span class="special">&gt;</span>
<span class="identifier">quantity</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_subtract</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R3</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">,</span>
         <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_subtract</span><span class="special">&lt;</span><span class="identifier">R2</span><span class="special">,</span> <span class="identifier">R4</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>
<span class="keyword">operator</span><span class="special">/(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R3</span><span class="special">,</span> <span class="identifier">R4</span><span class="special">&gt;&amp;</span> <span class="identifier">y</span><span class="special">)</span>
<span class="special">{</span>
    <span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_subtract</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R3</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">,</span>
                    <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_subtract</span><span class="special">&lt;</span><span class="identifier">R2</span><span class="special">,</span> <span class="identifier">R4</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span> <span class="identifier">R</span><span class="special">;</span>
    <span class="identifier">R</span> <span class="identifier">r</span><span class="special">;</span>
    <span class="identifier">r</span><span class="special">.</span><span class="identifier">set</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">get</span><span class="special">()</span> <span class="special">/</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">get</span><span class="special">());</span>
    <span class="keyword">return</span> <span class="identifier">r</span><span class="special">;</span>
<span class="special">}</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R3</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R4</span><span class="special">&gt;</span>
<span class="identifier">quantity</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_add</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R3</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">,</span>
         <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_add</span><span class="special">&lt;</span><span class="identifier">R2</span><span class="special">,</span> <span class="identifier">R4</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>
<span class="keyword">operator</span><span class="special">*(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R3</span><span class="special">,</span> <span class="identifier">R4</span><span class="special">&gt;&amp;</span> <span class="identifier">y</span><span class="special">)</span>
<span class="special">{</span>
    <span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_add</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R3</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">,</span>
                    <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_add</span><span class="special">&lt;</span><span class="identifier">R2</span><span class="special">,</span> <span class="identifier">R4</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span> <span class="identifier">R</span><span class="special">;</span>
    <span class="identifier">R</span> <span class="identifier">r</span><span class="special">;</span>
    <span class="identifier">r</span><span class="special">.</span><span class="identifier">set</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">get</span><span class="special">()</span> <span class="special">*</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">get</span><span class="special">());</span>
    <span class="keyword">return</span> <span class="identifier">r</span><span class="special">;</span>
<span class="special">}</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span>
<span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;</span>
<span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;&amp;</span> <span class="identifier">y</span><span class="special">)</span>
<span class="special">{</span>
    <span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="identifier">R</span><span class="special">;</span>
    <span class="identifier">R</span> <span class="identifier">r</span><span class="special">;</span>
    <span class="identifier">r</span><span class="special">.</span><span class="identifier">set</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">get</span><span class="special">()</span> <span class="special">+</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">get</span><span class="special">());</span>
    <span class="keyword">return</span> <span class="identifier">r</span><span class="special">;</span>
<span class="special">}</span>

<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">R2</span><span class="special">&gt;</span>
<span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;</span>
<span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;&amp;</span> <span class="identifier">y</span><span class="special">)</span>
<span class="special">{</span>
    <span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;</span> <span class="identifier">R</span><span class="special">;</span>
    <span class="identifier">R</span> <span class="identifier">r</span><span class="special">;</span>
    <span class="identifier">r</span><span class="special">.</span><span class="identifier">set</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">get</span><span class="special">()</span> <span class="special">-</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">get</span><span class="special">());</span>
    <span class="keyword">return</span> <span class="identifier">r</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
          With all of the foregoing scaffolding, we can now write an exemplar of
          a type-safe physics function:
        </p>
<pre class="programlisting"><span class="identifier">Distance</span>
<span class="identifier">compute_distance</span><span class="special">(</span><span class="identifier">Speed</span> <span class="identifier">v0</span><span class="special">,</span> <span class="identifier">Time</span> <span class="identifier">t</span><span class="special">,</span> <span class="identifier">Acceleration</span> <span class="identifier">a</span><span class="special">)</span>
<span class="special">{</span>
    <span class="keyword">return</span> <span class="identifier">v0</span> <span class="special">*</span> <span class="identifier">t</span> <span class="special">+</span> <span class="identifier">Scalar</span><span class="special">(.</span><span class="number">5</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">a</span> <span class="special">*</span> <span class="identifier">t</span> <span class="special">*</span> <span class="identifier">t</span><span class="special">;</span>  <span class="comment">// if a units mistake is made here it won't compile</span>
<span class="special">}</span>
</pre>
<p>
          Finally, we can exercise what we've created, even using custom time durations
          (<code class="computeroutput"><span class="identifier">User1</span><span class="special">::</span><span class="identifier">seconds</span></code>) as well as Boost time durations
          (<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><span class="identifier">hours</span></code>). The input can be in arbitrary,
          though type-safe, units, the output is always in SI units. (A complete
          Units library would support other units, of course.)
        </p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
    <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">8</span><span class="special">,</span> <span class="identifier">BOOST_INTMAX_C</span><span class="special">(</span><span class="number">0</span><span class="identifier">x7FFFFFFFD</span><span class="special">)&gt;</span> <span class="identifier">R1</span><span class="special">;</span>
    <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">3</span><span class="special">,</span> <span class="identifier">BOOST_INTMAX_C</span><span class="special">(</span><span class="number">0</span><span class="identifier">x7FFFFFFFD</span><span class="special">)&gt;</span> <span class="identifier">R2</span><span class="special">;</span>
    <span class="keyword">typedef</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_subtract</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span><span class="special">,</span>
                             <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_subtract</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;,</span> <span class="identifier">boost</span><span class="special">::</span><a class="link" href="reference.html#ratio.reference.std.ratio_hpp.ratio" title="Class Template ratio&lt;&gt;"><code class="computeroutput"><span class="identifier">ratio</span></code></a><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span> <span class="special">&gt;</span> <span class="identifier">RR</span><span class="special">;</span>
    <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ratio_subtract</span><span class="special">&lt;</span><span class="identifier">R1</span><span class="special">,</span> <span class="identifier">R2</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">RS</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">RS</span><span class="special">::</span><span class="identifier">num</span> <span class="special">&lt;&lt;</span> <span class="char">'/'</span> <span class="special">&lt;&lt;</span> <span class="identifier">RS</span><span class="special">::</span><span class="identifier">den</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>


    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"*************\n"</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"* testUser1 *\n"</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"*************\n"</span><span class="special">;</span>
    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Distance</span> <span class="identifier">d</span><span class="special">(</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">mile</span><span class="special">(</span><span class="number">110</span><span class="special">)</span> <span class="special">);</span>
    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Time</span> <span class="identifier">t</span><span class="special">(</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">chrono</span><span class="special">::</span><code class="computeroutput"><span class="identifier">hours</span></code><span class="special">(</span><span class="number">2</span><span class="special">)</span> <span class="special">);</span>

    <span class="identifier">RR</span> <span class="identifier">r</span><span class="special">=</span><span class="identifier">d</span> <span class="special">/</span> <span class="identifier">t</span><span class="special">;</span>
    <span class="comment">//r.set(d.get() / t.get());</span>

    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Speed</span> <span class="identifier">rc</span><span class="special">=</span> <span class="identifier">r</span><span class="special">;</span>

    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Speed</span> <span class="identifier">s</span> <span class="special">=</span> <span class="identifier">d</span> <span class="special">/</span> <span class="identifier">t</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Speed = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">get</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" meters/sec\n"</span><span class="special">;</span>
    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Acceleration</span> <span class="identifier">a</span> <span class="special">=</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Distance</span><span class="special">(</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">foot</span><span class="special">(</span><span class="number">32.2</span><span class="special">)</span> <span class="special">)</span> <span class="special">/</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Time</span><span class="special">()</span> <span class="special">/</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Time</span><span class="special">();</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Acceleration = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">get</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" meters/sec^2\n"</span><span class="special">;</span>
    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Distance</span> <span class="identifier">df</span> <span class="special">=</span> <span class="identifier">compute_distance</span><span class="special">(</span><span class="identifier">s</span><span class="special">,</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">Time</span><span class="special">(</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">seconds</span><span class="special">(</span><span class="number">0.5</span><span class="special">)</span> <span class="special">),</span> <span class="identifier">a</span><span class="special">);</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Distance = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">df</span><span class="special">.</span><span class="identifier">get</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" meters\n"</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"There are "</span>
        <span class="special">&lt;&lt;</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">mile</span><span class="special">::</span><span class="identifier">ratio</span><span class="special">::</span><span class="identifier">den</span> <span class="special">&lt;&lt;</span> <span class="char">'/'</span> <span class="special">&lt;&lt;</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">mile</span><span class="special">::</span><span class="identifier">ratio</span><span class="special">::</span><span class="identifier">num</span> <span class="special">&lt;&lt;</span> <span class="string">" miles/meter"</span><span class="special">;</span>
    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">meter</span> <span class="identifier">mt</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">mile</span> <span class="identifier">mi</span> <span class="special">=</span> <span class="identifier">mt</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">" which is approximately "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mi</span><span class="special">.</span><span class="identifier">count</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"There are "</span>
        <span class="special">&lt;&lt;</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">mile</span><span class="special">::</span><span class="identifier">ratio</span><span class="special">::</span><span class="identifier">num</span> <span class="special">&lt;&lt;</span> <span class="char">'/'</span> <span class="special">&lt;&lt;</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">mile</span><span class="special">::</span><span class="identifier">ratio</span><span class="special">::</span><span class="identifier">den</span> <span class="special">&lt;&lt;</span> <span class="string">" meters/mile"</span><span class="special">;</span>
    <span class="identifier">mi</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
    <span class="identifier">mt</span> <span class="special">=</span> <span class="identifier">mi</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">" which is approximately "</span> <span class="special">&lt;&lt;</span> <span class="identifier">mt</span><span class="special">.</span><span class="identifier">count</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">'\n'</span><span class="special">;</span>
    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">attosecond</span> <span class="identifier">as</span><span class="special">(</span><span class="number">1</span><span class="special">);</span>
    <span class="identifier">User1</span><span class="special">::</span><span class="identifier">seconds</span> <span class="identifier">sec</span> <span class="special">=</span> <span class="identifier">as</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"1 attosecond is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">sec</span><span class="special">.</span><span class="identifier">count</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" seconds\n"</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"sec = as;  // compiles\n"</span><span class="special">;</span>
    <span class="identifier">sec</span> <span class="special">=</span> <span class="identifier">User1</span><span class="special">::</span><span class="identifier">seconds</span><span class="special">(</span><span class="number">1</span><span class="special">);</span>
    <span class="identifier">as</span> <span class="special">=</span> <span class="identifier">sec</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"1 second is "</span> <span class="special">&lt;&lt;</span> <span class="identifier">as</span><span class="special">.</span><span class="identifier">count</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" attoseconds\n"</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"as = sec;  // compiles\n"</span><span class="special">;</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
          <span class="emphasis"><em>See the source file <a href="../../../example/si_physics.cpp" target="_top">example/si_physics.cpp</a></em></span>
        </p>
</div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="ratio.users_guide.ext_references"></a><a class="link" href="users_guide.html#ratio.users_guide.ext_references" title="External Resources">External Resources</a>
</h3></div></div></div>
<div class="variablelist">
<p class="title"><b></b></p>
<dl>
<dt><span class="term"><a href="http://www.open-std.org/jtc1/sc22/wg21" target="_top"><span class="bold"><strong>C++
          Standards Committee's current Working Paper</strong></span></a></span></dt>
<dd><p>
              The most authoritative reference material for the library is the C++
              Standards Committee's current Working Paper (WP). 20.6 Compile-time
              rational arithmetic "ratio"
            </p></dd>
<dt><span class="term"><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2008/n2661.htm" target="_top"><span class="bold"><strong>N2661 - A Foundation to Sleep On</strong></span></a></span></dt>
<dd><p>
              From Howard E. Hinnant, Walter E. Brown, Jeff Garland and Marc Paterno.
              Is very informative and provides motivation for key design decisions
            </p></dd>
<dt><span class="term"><a href="http://lwg.github.com/issues/lwg-defects.html#1281" target="_top"><span class="bold"><strong>LWG 1281. CopyConstruction and Assignment between ratios having
          the same normalized form</strong></span></a></span></dt>
<dd><p>
              From Vicente Juan Botet Escriba.
            </p></dd>
</dl>
</div>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2008 Howard Hinnant<br>Copyright &#169; 2006, 2008 Beman Dawes<br>Copyright &#169; 2009-2011 Vicente J. Botet
      Escriba<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../ratio.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../ratio.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>