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
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
"http://www.w3.org/TR/html4/loose.dtd">
<html>
<head>
<title>perlnumber - perldoc.perl.org</title>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<meta http-equiv="Content-Language" content="en-gb">
<link href="static/css-20090810.css" rel="stylesheet" rev="stylesheet" type="text/css" media="screen">
</head>
<body onLoad="perldoc.startup();" onPageShow="if (event.persisted) perldoc.startup();">
<div id="page">
<div id="header">
<div id="homepage_link">
<a href="index.html"></a>
</div>
<div id="search_form">
<form action="search.html" method="GET" id="search">
<input type="text" name="q" id="search_box" alt="Search">
</form>
</div>
</div>
<div id="body">
<div id="left_column">
<div class="side_group">
<div class="side_panel doc_panel">
<p>Manual</p>
<ul>
<li><a href="index-overview.html">Overview</a>
<li><a href="index-tutorials.html">Tutorials</a>
<li><a href="index-faq.html">FAQs</a>
<li><a href="index-history.html">History / Changes</a>
<li><a href="index-licence.html">License</a>
</ul>
</div>
<div class="side_panel doc_panel">
<p>Reference</p>
<ul>
<li><a href="index-language.html">Language</a>
<li><a href="index-functions.html">Functions</a>
<li><a href="perlop.html">Operators</a>
<li><a href="perlvar.html">Special Variables</a>
<li><a href="index-pragmas.html">Pragmas</a>
<li><a href="index-utilities.html">Utilities</a>
<li><a href="index-internals.html">Internals</a></li>
<li><a href="index-platforms.html">Platform Specific</a>
</ul>
</div>
<div class="side_panel doc_panel">
<p>Modules</p>
<ul>
<li>
<a href="index-modules-A.html">A</a>
•
<a href="index-modules-B.html">B</a>
•
<a href="index-modules-C.html">C</a>
•
<a href="index-modules-D.html">D</a>
•
<a href="index-modules-E.html">E</a>
<li>
<a href="index-modules-F.html">F</a>
•
<a href="index-modules-G.html">G</a>
•
<a href="index-modules-H.html">H</a>
•
<a href="index-modules-I.html">I</a>
•
<a href="index-modules-L.html">L</a>
<li>
<a href="index-modules-M.html">M</a>
•
<a href="index-modules-N.html">N</a>
•
<a href="index-modules-O.html">O</a>
•
<a href="index-modules-P.html">P</a>
•
<a href="index-modules-S.html">S</a>
<li>
<a href="index-modules-T.html">T</a>
•
<a href="index-modules-U.html">U</a>
•
<a href="index-modules-X.html">X</a>
</ul>
</div>
</div>
<div class="side_group">
<div class="side_panel links_panel">
<p>News / Blogs</p>
<ul>
<li><a href="http://perlbuzz.com">Perl Buzz</a></li>
<li><a href="http://ironman.enlightenedperl.org">Perl Iron Man</a></li>
<li><a href="http://perlsphere.net">Perlsphere</a></li>
<li><a href="http://planet.perl.org">Planet Perl</a></li>
<li><a href="http://news.perlfoundation.org/">TPF news</a></li>
<li><a href="http://use.perl.org">Use Perl</a></li>
</ul>
</div>
<div class="side_panel links_panel">
<p>See also</p>
<ul>
<li><a href="http://search.cpan.org">CPAN</a></li>
<li><a href="http://www.perl.org">Perl.org</a></li>
<li><a href="http://www.perl.com">Perl.com</a></li>
<li><a href="http://www.perlfoundation.org/perl5/index.cgi">Perl 5 Wiki</a></li>
<li><a href="http://jobs.perl.org">Perl Jobs</a></li>
<li><a href="http://www.pm.org">Perl Mongers</a></li>
<li><a href="http://www.perlmonks.org">Perl Monks</a></li>
</ul>
</div>
<div class="side_panel links_panel">
<p>Contact</p>
<ul>
<li><a href="http://perl.jonallen.info">Site designed and maintained by Jon Allen (JJ)</a>
<li><a href="http://perl.jonallen.info">http://perl.jonallen.info</a>
</ul>
<ul>
<li><a href="http://perl.jonallen.info/projects/perldoc">View the project page and FAQs</a>
</ul>
</div>
</div>
</div>
<div id="centre_column">
<div id="content_header">
<div id="title_bar">
<div id="page_name">
<h1>perlnumber</h1>
</div>
<div id="perl_version">
Perl 5 version 10.1 documentation
</div>
<div id="page_links">
<a href="#" onClick="toolbar.goToTop();return false;">Go to top</a>
• <a href="#" id="page_index_toggle">Show page index</a>
</div>
</div>
<div id="breadcrumbs">
<a href="index.html">Home</a> >
<a href="index-language.html">Language reference</a> >
perlnumber
</div>
</div>
<div id="content_body">
<!--[if lt IE 7]>
<div class="noscript">
<p>
<strong>It looks like you're using Internet Explorer 6. This is a very old
browser which does not offer full support for modern websites.</strong>
</p>
<p>
Unfortunately this means that this website will not work on
your computer.
</p>
<p>
Don't miss out though! To view the site (and get a better experience from
many other websites), simply upgrade to
<a href="http://www.microsoft.com/windows/Internet-explorer/default.aspx">Internet
Explorer 8</a>
or download an alternative browser such as
<a href="http://www.mozilla.com/en-US/firefox/firefox.html">Firefox</a>,
<a href="http://www.apple.com/safari/download/">Safari</a>, or
<a href="http://www.google.co.uk/chrome">Google Chrome</a>.
</p>
<p>
All of these browsers are free. If you're using a PC at work, you may
need to contact your IT administrator.
</p>
</div>
<![endif]-->
<noscript>
<div class="noscript">
<p>
<strong>Please note: Many features of this site require JavaScript. You appear to have JavaScript disabled,
or are running a non-JavaScript capable web browser.</strong>
</p>
<p>
To get the best experience, please enable JavaScript or download a modern web browser such as <a href="http://www.microsoft.com/windows/Internet-explorer/default.aspx">Internet Explorer 8</a>, <a href="http://www.mozilla.com/en-US/firefox/firefox.html">Firefox</a>, <a href="http://www.apple.com/safari/download/">Safari</a>, or <a href="http://www.google.co.uk/chrome">Google Chrome</a>.
</p>
</div>
</noscript>
<div id="from_search"></div>
<h1>perlnumber</h1>
<!-- -->
<ul><li><a href="#NAME">NAME</a><li><a href="#SYNOPSIS">SYNOPSIS</a><li><a href="#DESCRIPTION">DESCRIPTION</a><li><a href="#Storing-numbers">Storing numbers</a><li><a href="#Numeric-operators-and-numeric-conversions">Numeric operators and numeric conversions</a><li><a href="#Flavors-of-Perl-numeric-operations">Flavors of Perl numeric operations</a><li><a href="#AUTHOR">AUTHOR</a><li><a href="#SEE-ALSO">SEE ALSO</a></ul><a name="NAME"></a><h1>NAME</h1>
<p>perlnumber - semantics of numbers and numeric operations in Perl</p>
<a name="SYNOPSIS"></a><h1>SYNOPSIS</h1>
<pre class="verbatim"><ol><li> <span class="i">$n</span> = <span class="n">1234</span><span class="sc">;</span> <span class="c"># decimal integer</span></li><li> <span class="i">$n</span> = <span class="n">0b1110011</span><span class="sc">;</span> <span class="c"># binary integer</span></li><li> <span class="i">$n</span> = <span class="n">01234</span><span class="sc">;</span> <span class="c"># octal integer</span></li><li> <span class="i">$n</span> = <span class="n">0x1234</span><span class="sc">;</span> <span class="c"># hexadecimal integer</span></li><li> <span class="i">$n</span> = <span class="n">12.34e-56</span><span class="sc">;</span> <span class="c"># exponential notation</span></li><li> <span class="i">$n</span> = <span class="q">"-12.34e56"</span><span class="sc">;</span> <span class="c"># number specified as a string</span></li><li> <span class="i">$n</span> = <span class="q">"1234"</span><span class="sc">;</span> <span class="c"># number specified as a string</span></li></ol></pre><a name="DESCRIPTION"></a><h1>DESCRIPTION</h1>
<p>This document describes how Perl internally handles numeric values.</p>
<p>Perl's operator overloading facility is completely ignored here. Operator
overloading allows user-defined behaviors for numbers, such as operations
over arbitrarily large integers, floating points numbers with arbitrary
precision, operations over "exotic" numbers such as modular arithmetic or
p-adic arithmetic, and so on. See <a href="overload.html">overload</a> for details.</p>
<a name="Storing-numbers"></a><h1>Storing numbers</h1>
<p>Perl can internally represent numbers in 3 different ways: as native
integers, as native floating point numbers, and as decimal strings.
Decimal strings may have an exponential notation part, as in <code class="inline"><span class="q">"12.34e-56"</span></code>
.
<i>Native</i> here means "a format supported by the C compiler which was used
to build perl".</p>
<p>The term "native" does not mean quite as much when we talk about native
integers, as it does when native floating point numbers are involved.
The only implication of the term "native" on integers is that the limits for
the maximal and the minimal supported true integral quantities are close to
powers of 2. However, "native" floats have a most fundamental
restriction: they may represent only those numbers which have a relatively
"short" representation when converted to a binary fraction. For example,
0.9 cannot be represented by a native float, since the binary fraction
for 0.9 is infinite:</p>
<pre class="verbatim"><ol><li> <span class="w">binary0</span><span class="n">.1110011001100</span>...</li></ol></pre><p>with the sequence <code class="inline"><span class="n">1100</span></code>
repeating again and again. In addition to this
limitation, the exponent of the binary number is also restricted when it
is represented as a floating point number. On typical hardware, floating
point values can store numbers with up to 53 binary digits, and with binary
exponents between -1024 and 1024. In decimal representation this is close
to 16 decimal digits and decimal exponents in the range of -304..304.
The upshot of all this is that Perl cannot store a number like
12345678901234567 as a floating point number on such architectures without
loss of information.</p>
<p>Similarly, decimal strings can represent only those numbers which have a
finite decimal expansion. Being strings, and thus of arbitrary length, there
is no practical limit for the exponent or number of decimal digits for these
numbers. (But realize that what we are discussing the rules for just the
<i>storage</i> of these numbers. The fact that you can store such "large" numbers
does not mean that the <i>operations</i> over these numbers will use all
of the significant digits.
See <a href="#Numeric-operators-and-numeric-conversions">"Numeric operators and numeric conversions"</a> for details.)</p>
<p>In fact numbers stored in the native integer format may be stored either
in the signed native form, or in the unsigned native form. Thus the limits
for Perl numbers stored as native integers would typically be -2**31..2**32-1,
with appropriate modifications in the case of 64-bit integers. Again, this
does not mean that Perl can do operations only over integers in this range:
it is possible to store many more integers in floating point format.</p>
<p>Summing up, Perl numeric values can store only those numbers which have
a finite decimal expansion or a "short" binary expansion.</p>
<a name="Numeric-operators-and-numeric-conversions"></a><h1>Numeric operators and numeric conversions</h1>
<p>As mentioned earlier, Perl can store a number in any one of three formats,
but most operators typically understand only one of those formats. When
a numeric value is passed as an argument to such an operator, it will be
converted to the format understood by the operator.</p>
<p>Six such conversions are possible:</p>
<pre class="verbatim"><ol><li> native integer --> native floating point (*)</li><li> native integer --> decimal string</li><li> native floating_point --> native integer (*)</li><li> native floating_point --> decimal string (*)</li><li> decimal string --> native integer</li><li> decimal string --> native floating point (*)</li></ol></pre><p>These conversions are governed by the following general rules:</p>
<ul>
<li>
<p>If the source number can be represented in the target form, that
representation is used.</p>
</li>
<li>
<p>If the source number is outside of the limits representable in the target form,
a representation of the closest limit is used. (<i>Loss of information</i>)</p>
</li>
<li>
<p>If the source number is between two numbers representable in the target form,
a representation of one of these numbers is used. (<i>Loss of information</i>)</p>
</li>
<li>
<p>In <code class="inline"><span class="w">native</span> <span class="w">floating</span> <span class="w">point</span> --> <span class="w">native</span> <span class="w">integer</span></code>
conversions the magnitude
of the result is less than or equal to the magnitude of the source.
(<i>"Rounding to zero".</i>)</p>
</li>
<li>
<p>If the <code class="inline"><span class="w">decimal</span> <span class="w">string</span> --> <span class="w">native</span> <span class="w">integer</span></code>
conversion cannot be done
without loss of information, the result is compatible with the conversion
sequence <code class="inline"><span class="w">decimal_string</span> --> <span class="w">native_floating_point</span> --> <span class="w">native_integer</span></code>
.
In particular, rounding is strongly biased to 0, though a number like
<code class="inline"><span class="q">"0.99999999999999999999"</span></code>
has a chance of being rounded to 1.</p>
</li>
</ul>
<p><b>RESTRICTION</b>: The conversions marked with <code class="inline">(*)</code> above involve steps
performed by the C compiler. In particular, bugs/features of the compiler
used may lead to breakage of some of the above rules.</p>
<a name="Flavors-of-Perl-numeric-operations"></a><h1>Flavors of Perl numeric operations</h1>
<p>Perl operations which take a numeric argument treat that argument in one
of four different ways: they may force it to one of the integer/floating/
string formats, or they may behave differently depending on the format of
the operand. Forcing a numeric value to a particular format does not
change the number stored in the value.</p>
<p>All the operators which need an argument in the integer format treat the
argument as in modular arithmetic, e.g., <code class="inline"><span class="w">mod</span> <span class="n">2</span>**<span class="n">32</span></code>
on a 32-bit
architecture. <code class="inline"><a class="l_k" href="functions/sprintf.html">sprintf</a> <span class="q">"%u"</span><span class="cm">,</span> <span class="n">-1</span></code>
therefore provides the same result as
<code class="inline"><a class="l_k" href="functions/sprintf.html">sprintf</a> <span class="q">"%u"</span><span class="cm">,</span> ~<span class="n">0</span></code>
.</p>
<ul>
<li><a name="Arithmetic-operators"></a><b>Arithmetic operators</b>
<p>The binary operators <code class="inline">+</code>
<code class="inline">-</code>
<code class="inline"><span class="i">*</span></code>
<code class="inline">/</code> <code class="inline"><span class="i">%</span></code>
<code class="inline">==</code>
<code class="inline">!=</code>
<code class="inline">></code> <code class="inline"><</code>
<code class="inline">>=</code>
<code class="inline"><=</code>
and the unary operators <code class="inline">-</code>
<code class="inline"><a class="l_k" href="functions/abs.html">abs</a></code> and <code class="inline">--</code>
will
attempt to convert arguments to integers. If both conversions are possible
without loss of precision, and the operation can be performed without
loss of precision then the integer result is used. Otherwise arguments are
converted to floating point format and the floating point result is used.
The caching of conversions (as described above) means that the integer
conversion does not throw away fractional parts on floating point numbers.</p>
</li>
<li><a name="%2b%2b"></a><b>++</b>
<p><code class="inline">++</code>
behaves as the other operators above, except that if it is a string
matching the format <code class="inline"><span class="q">/^[a-zA-Z]*[0-9]*\z/</span></code>
the string increment described
in <a href="perlop.html">perlop</a> is used.</p>
</li>
<li><a name="Arithmetic-operators-during-use-integer"></a><b>Arithmetic operators during <code class="inline"><a class="l_k" href="functions/use.html">use</a> <span class="w">integer</span></code>
</b>
<p>In scopes where <code class="inline"><a class="l_k" href="functions/use.html">use</a> <span class="w">integer</span><span class="sc">;</span></code>
is in force, nearly all the operators listed
above will force their argument(s) into integer format, and return an integer
result. The exceptions, <code class="inline"><a class="l_k" href="functions/abs.html">abs</a></code>, <code class="inline">++</code>
and <code class="inline">--</code>
, do not change their
behavior with <code class="inline"><a class="l_k" href="functions/use.html">use</a> <span class="w">integer</span><span class="sc">;</span></code>
</p>
</li>
<li><a name="Other-mathematical-operators"></a><b>Other mathematical operators</b>
<p>Operators such as <code class="inline"><span class="i">**</span></code>
, <code class="inline"><a class="l_k" href="functions/sin.html">sin</a></code> and <code class="inline"><a class="l_k" href="functions/exp.html">exp</a></code> force arguments to floating point
format.</p>
</li>
<li><a name="Bitwise-operators"></a><b>Bitwise operators</b>
<p>Arguments are forced into the integer format if not strings.</p>
</li>
<li><a name="Bitwise-operators-during-use-integer"></a><b>Bitwise operators during <code class="inline"><a class="l_k" href="functions/use.html">use</a> <span class="w">integer</span></code>
</b>
<p>forces arguments to integer format. Also shift operations internally use
signed integers rather than the default unsigned.</p>
</li>
<li><a name="Operators-which-expect-an-integer"></a><b>Operators which expect an integer</b>
<p>force the argument into the integer format. This is applicable
to the third and fourth arguments of <code class="inline"><a class="l_k" href="functions/sysread.html">sysread</a></code>, for example.</p>
</li>
<li><a name="Operators-which-expect-a-string"></a><b>Operators which expect a string</b>
<p>force the argument into the string format. For example, this is
applicable to <code class="inline"><a class="l_k" href="functions/printf.html">printf</a> <span class="q">"%s"</span><span class="cm">,</span> <span class="i">$value</span></code>
.</p>
</li>
</ul>
<p>Though forcing an argument into a particular form does not change the
stored number, Perl remembers the result of such conversions. In
particular, though the first such conversion may be time-consuming,
repeated operations will not need to redo the conversion.</p>
<a name="AUTHOR"></a><h1>AUTHOR</h1>
<p>Ilya Zakharevich <code class="inline"><span class="w">ilya</span><span class="i">@math</span>.<span class="w">ohio</span>-<span class="w">state</span>.<span class="w">edu</span></code>
</p>
<p>Editorial adjustments by Gurusamy Sarathy <gsar@ActiveState.com></p>
<p>Updates for 5.8.0 by Nicholas Clark <nick@ccl4.org></p>
<a name="SEE-ALSO"></a><h1>SEE ALSO</h1>
<p><a href="overload.html">overload</a>, <a href="perlop.html">perlop</a></p>
<div id="page_index">
<div id="page_index_header">
<div id="page_index_close"><a href="#" onClick="pageIndex.hide();return false;"></a></div>
<div id="page_index_title"><span class="page_index_top">Page index</span></div>
<div id="page_index_topright"></div>
</div>
<div id="page_index_content">
<ul><li><a href="#NAME">NAME</a><li><a href="#SYNOPSIS">SYNOPSIS</a><li><a href="#DESCRIPTION">DESCRIPTION</a><li><a href="#Storing-numbers">Storing numbers</a><li><a href="#Numeric-operators-and-numeric-conversions">Numeric operators and numeric conversions</a><li><a href="#Flavors-of-Perl-numeric-operations">Flavors of Perl numeric operations</a><li><a href="#AUTHOR">AUTHOR</a><li><a href="#SEE-ALSO">SEE ALSO</a></ul>
</div>
<div id="page_index_footer">
<div id="page_index_bottomleft"></div>
<div id="page_index_bottom"><span class="page_index_bottom"></span></div>
<div id="page_index_resize"></div>
</div>
</div>
</div>
<div id="content_footer">
</div>
</div>
<div id="right_column">
<div class="side_group">
<div class="side_panel tools_panel">
<p>Recently read</p>
<div id="recent_pages"></div>
</div>
<div class="side_panel tools_panel">
<p>Tools</p>
<ul>
<li><a href="preferences.html">Preferences</a>
</ul>
</div>
</div>
</div>
<div class="clear"></div>
</div>
<div id="footer">
<div id="footer_content">
</div>
</div>
</div>
<script language="JavaScript" src="static/combined-20090809.js" type="text/javascript"></script>
<script language="JavaScript" type="text/javascript">
perldoc.setPath(0);
perldoc.pageName = 'perlnumber';
perldoc.pageAddress = 'perlnumber.html';
perldoc.contentPage = 1;
</script>
</body>
</html>
|
