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
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html401/loose.dtd">
<html>
<!-- Created on September, 20 2006 by texi2html 1.76 -->
<!--
Written by: Lionel Cons <Lionel.Cons@cern.ch> (original author)
Karl Berry <karl@freefriends.org>
Olaf Bachmann <obachman@mathematik.uni-kl.de>
and many others.
Maintained by: Many creative people <dev@texi2html.cvshome.org>
Send bugs and suggestions to <users@texi2html.cvshome.org>
-->
<head>
<title>Maxima Manual: 10. Floating Point</title>
<meta name="description" content="Maxima Manual: 10. Floating Point">
<meta name="keywords" content="Maxima Manual: 10. Floating Point">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="texi2html 1.76">
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
pre.display {font-family: serif}
pre.format {font-family: serif}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: serif; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: serif; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.sansserif {font-family:sans-serif; font-weight:normal;}
ul.toc {list-style: none}
body
{
color: black;
background: white;
margin-left: 8%;
margin-right: 13%;
}
h1
{
margin-left: +8%;
font-size: 150%;
font-family: sans-serif
}
h2
{
font-size: 125%;
font-family: sans-serif
}
h3
{
font-size: 100%;
font-family: sans-serif
}
h2,h3,h4,h5,h6 { margin-left: +4%; }
div.textbox
{
border: solid;
border-width: thin;
/* width: 100%; */
padding-top: 1em;
padding-bottom: 1em;
padding-left: 2em;
padding-right: 2em
}
div.titlebox
{
border: none;
padding-top: 1em;
padding-bottom: 1em;
padding-left: 2em;
padding-right: 2em;
background: rgb(200,255,255);
font-family: sans-serif
}
div.synopsisbox
{
border: none;
padding-top: 1em;
padding-bottom: 1em;
padding-left: 2em;
padding-right: 2em;
background: rgb(255,220,255);
/*background: rgb(200,255,255); */
/* font-family: fixed */
}
pre.example
{
border: none;
padding-top: 1em;
padding-bottom: 1em;
padding-left: 1em;
padding-right: 1em;
background: rgb(247,242,180); /* kind of sandy */
/* background: rgb(200,255,255); */ /* sky blue */
font-family: "Lucida Console", monospace
}
div.spacerbox
{
border: none;
padding-top: 2em;
padding-bottom: 2em
}
div.image
{
margin: 0;
padding: 1em;
text-align: center;
}
-->
</style>
<link rel="icon" href="http://maxima.sourceforge.net/favicon.ico"/>
</head>
<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Floating-Point"></a>
<a name="SEC40"></a>
<table cellpadding="1" cellspacing="1" border="0">
<tr><td valign="middle" align="left">[<a href="maxima_9.html#SEC39" title="Previous section in reading order"> < </a>]</td>
<td valign="middle" align="left">[<a href="#SEC41" title="Next section in reading order"> > </a>]</td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left">[<a href="maxima_9.html#SEC35" title="Beginning of this chapter or previous chapter"> << </a>]</td>
<td valign="middle" align="left">[<a href="maxima.html#SEC_Top" title="Up section"> Up </a>]</td>
<td valign="middle" align="left">[<a href="maxima_11.html#SEC42" title="Next chapter"> >> </a>]</td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left">[<a href="maxima.html#SEC_Top" title="Cover (top) of document">Top</a>]</td>
<td valign="middle" align="left">[<a href="maxima_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>
<td valign="middle" align="left">[<a href="maxima_72.html#SEC264" title="Index">Index</a>]</td>
<td valign="middle" align="left">[<a href="maxima_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
</tr></table>
<h1 class="chapter"> 10. Floating Point </h1>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top"><a href="#SEC41">10.1 Definitions for Floating Point</a></td><td> </td><td align="left" valign="top">
</td></tr>
</table>
<hr size="6">
<a name="Definitions-for-Floating-Point"></a>
<a name="SEC41"></a>
<table cellpadding="1" cellspacing="1" border="0">
<tr><td valign="middle" align="left">[<a href="#SEC40" title="Previous section in reading order"> < </a>]</td>
<td valign="middle" align="left">[<a href="maxima_11.html#SEC42" title="Next section in reading order"> > </a>]</td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left">[<a href="#SEC40" title="Beginning of this chapter or previous chapter"> << </a>]</td>
<td valign="middle" align="left">[<a href="#SEC40" title="Up section"> Up </a>]</td>
<td valign="middle" align="left">[<a href="maxima_11.html#SEC42" title="Next chapter"> >> </a>]</td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left">[<a href="maxima.html#SEC_Top" title="Cover (top) of document">Top</a>]</td>
<td valign="middle" align="left">[<a href="maxima_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>
<td valign="middle" align="left">[<a href="maxima_72.html#SEC264" title="Index">Index</a>]</td>
<td valign="middle" align="left">[<a href="maxima_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
</tr></table>
<h2 class="section"> 10.1 Definitions for Floating Point </h2>
<dl>
<dt><u>Function:</u> <b>bffac</b><i> (<var>expr</var>, <var>n</var>)</i>
<a name="IDX346"></a>
</dt>
<dd><p>Bigfloat version of the factorial (shifted gamma)
function. The second argument is how many digits to retain and return,
it's a good idea to request a couple of extra.
</p>
<p><code>load ("bffac")</code> loads this function.
</p>
</dd></dl>
<dl>
<dt><u>Option variable:</u> <b>algepsilon</b>
<a name="IDX347"></a>
</dt>
<dd><p>Default value: 10^8
</p>
<p><code>algepsilon</code> is used by <code>algsys</code>.
</p>
</dd></dl>
<dl>
<dt><u>Function:</u> <b>bfloat</b><i> (<var>expr</var>)</i>
<a name="IDX348"></a>
</dt>
<dd><p>Converts all numbers and functions of numbers in <var>expr</var> to bigfloat numbers.
The number of significant digits in the resulting bigfloats is specified by the global variable <code>fpprec</code>.
</p>
<p>When <code>float2bf</code> is <code>false</code> a warning message is printed when
a floating point number is converted into a bigfloat number (since
this may lead to loss of precision).
</p>
</dd></dl>
<dl>
<dt><u>Function:</u> <b>bfloatp</b><i> (<var>expr</var>)</i>
<a name="IDX349"></a>
</dt>
<dd><p>Returns <code>true</code> if <var>expr</var> is a bigfloat number, otherwise <code>false</code>.
</p>
</dd></dl>
<dl>
<dt><u>Function:</u> <b>bfpsi</b><i> (<var>n</var>, <var>z</var>, <var>fpprec</var>)</i>
<a name="IDX350"></a>
</dt>
<dt><u>Function:</u> <b>bfpsi0</b><i> (<var>z</var>, <var>fpprec</var>)</i>
<a name="IDX351"></a>
</dt>
<dd><p><code>bfpsi</code> is the polygamma function of real argument <var>z</var> and integer order <var>n</var>.
<code>bfpsi0</code> is the digamma function.
<code>bfpsi0 (<var>z</var>, <var>fpprec</var>)</code> is equivalent to <code>bfpsi (0, <var>z</var>, <var>fpprec</var>)</code>.
</p>
<p>These functions return bigfloat values.
<var>fpprec</var> is the bigfloat precision of the return value.
</p>
<p><code>load ("bffac")</code> loads these functions.
</p>
</dd></dl>
<dl>
<dt><u>Option variable:</u> <b>bftorat</b>
<a name="IDX352"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p><code>bftorat</code> controls the conversion of bfloats to
rational numbers.
When <code>bftorat</code> is <code>false</code>,
<code>ratepsilon</code> will be used to
control the conversion (this results in relatively small rational
numbers).
When <code>bftorat</code> is <code>true</code>,
the rational number generated will
accurately represent the bfloat.
</p>
</dd></dl>
<dl>
<dt><u>Option variable:</u> <b>bftrunc</b>
<a name="IDX353"></a>
</dt>
<dd><p>Default value: <code>true</code>
</p>
<p><code>bftrunc</code> causes trailing zeroes in non-zero bigfloat
numbers not to be displayed. Thus, if <code>bftrunc</code> is <code>false</code>, <code>bfloat (1)</code>
displays as <code>1.000000000000000B0</code>. Otherwise, this is displayed as
<code>1.0B0</code>.
</p>
</dd></dl>
<dl>
<dt><u>Function:</u> <b>cbffac</b><i> (<var>z</var>, <var>fpprec</var>)</i>
<a name="IDX354"></a>
</dt>
<dd><p>Complex bigfloat factorial.
</p>
<p><code>load ("bffac")</code> loads this function.
</p>
</dd></dl>
<dl>
<dt><u>Function:</u> <b>float</b><i> (<var>expr</var>)</i>
<a name="IDX355"></a>
</dt>
<dd><p>Converts integers, rational numbers and bigfloats in <var>expr</var>
to floating point numbers. It is also an <code>evflag</code>, <code>float</code> causes
non-integral rational numbers and bigfloat numbers to be converted to
floating point.
</p>
</dd></dl>
<dl>
<dt><u>Option variable:</u> <b>float2bf</b>
<a name="IDX356"></a>
</dt>
<dd><p>Default value: <code>false</code>
</p>
<p>When <code>float2bf</code> is <code>false</code>, a warning message is printed when
a floating point number is converted into a bigfloat number (since
this may lead to loss of precision).
</p>
</dd></dl>
<dl>
<dt><u>Function:</u> <b>floatnump</b><i> (<var>expr</var>)</i>
<a name="IDX357"></a>
</dt>
<dd><p>Returns <code>true</code> if <var>expr</var> is a floating point number, otherwise <code>false</code>.
</p>
</dd></dl>
<dl>
<dt><u>Option variable:</u> <b>fpprec</b>
<a name="IDX358"></a>
</dt>
<dd><p>Default value: 16
</p>
<p><code>fpprec</code> is the number of significant digits for arithmetic on bigfloat numbers.
<code>fpprec</code> does not affect computations on ordinary floating point numbers.
</p>
<p>See also <code>bfloat</code> and <code>fpprintprec</code>.
</p>
</dd></dl>
<dl>
<dt><u>Option variable:</u> <b>fpprintprec</b>
<a name="IDX359"></a>
</dt>
<dd><p>Default value: 0
</p>
<p><code>fpprintprec</code> is the number of digits to print when printing an ordinary float or bigfloat number.
</p>
<p>For ordinary floating point numbers,
when <code>fpprintprec</code> has a value between 2 and 16 (inclusive),
the number of digits printed is equal to <code>fpprintprec</code>.
Otherwise, <code>fpprintprec</code> is 0, or greater than 16,
and the number of digits printed is 16.
</p>
<p>For bigfloat numbers,
when <code>fpprintprec</code> has a value between 2 and <code>fpprec</code> (inclusive),
the number of digits printed is equal to <code>fpprintprec</code>.
Otherwise, <code>fpprintprec</code> is 0, or greater than <code>fpprec</code>,
and the number of digits printed is equal to <code>fpprec</code>.
</p>
<p><code>fpprintprec</code> cannot be 1.
</p>
</dd></dl>
<dl>
<dt><u>Lisp function:</u> <b>?round</b><i> (<var>x</var>)</i>
<a name="IDX360"></a>
</dt>
<dt><u>Lisp function:</u> <b>?round</b><i> (<var>x</var>, <var>divisor</var>)</i>
<a name="IDX361"></a>
</dt>
<dd><p>Round the floating point <var>x</var> to the nearest integer. The argument
must be an ordinary float, not a bigfloat. The <code>?</code> beginning the name
indicates this is a Lisp function.
</p>
<table><tr><td> </td><td><pre class="example">(%i1) ?round (-2.8);
(%o1) - 3
</pre></td></tr></table>
</dd></dl>
<dl>
<dt><u>Lisp function:</u> <b>?truncate</b><i> (<var>x</var>)</i>
<a name="IDX362"></a>
</dt>
<dt><u>Lisp function:</u> <b>?truncate</b><i> (<var>x</var>, <var>divisor</var>)</i>
<a name="IDX363"></a>
</dt>
<dd><p>Truncate the floating point <var>x</var> towards 0, to become an integer. The argument
must be an ordinary float, not a bigfloat. The <code>?</code> beginning the name
indicates this is a Lisp function.
</p>
<table><tr><td> </td><td><pre class="example">(%i1) ?truncate (-2.8);
(%o1) - 2
(%i2) ?truncate (2.4);
(%o2) 2
(%i3) ?truncate (2.8);
(%o3) 2
</pre></td></tr></table>
</dd></dl>
<hr size="6">
<table cellpadding="1" cellspacing="1" border="0">
<tr><td valign="middle" align="left">[<a href="#SEC40" title="Beginning of this chapter or previous chapter"> << </a>]</td>
<td valign="middle" align="left">[<a href="maxima_11.html#SEC42" title="Next chapter"> >> </a>]</td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left"> </td>
<td valign="middle" align="left">[<a href="maxima.html#SEC_Top" title="Cover (top) of document">Top</a>]</td>
<td valign="middle" align="left">[<a href="maxima_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>
<td valign="middle" align="left">[<a href="maxima_72.html#SEC264" title="Index">Index</a>]</td>
<td valign="middle" align="left">[<a href="maxima_abt.html#SEC_About" title="About (help)"> ? </a>]</td>
</tr></table>
<p>
<font size="-1">
This document was generated by <em>Robert Dodier</em> on <em>September, 20 2006</em> using <a href="http://texi2html.cvshome.org/"><em>texi2html 1.76</em></a>.
</font>
<br>
</p>
</body>
</html>
|
