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
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<title>~/ntl-11.4.2/doc/xdouble.cpp.html</title>
<meta name="Generator" content="Vim/8.0">
<meta name="plugin-version" content="vim7.4_v2">
<meta name="syntax" content="cpp">
<meta name="settings" content="use_css,pre_wrap,no_foldcolumn,expand_tabs,prevent_copy=">
<meta name="colorscheme" content="macvim">
<style type="text/css">
<!--
pre { white-space: pre-wrap; font-family: monospace; color: #000000; background-color: #ffffff; }
body { font-family: monospace; color: #000000; background-color: #ffffff; }
* { font-size: 1em; }
.String { color: #4a708b; }
.PreProc { color: #1874cd; }
.Statement { color: #b03060; font-weight: bold; }
.Comment { color: #0000ee; font-style: italic; }
.Type { color: #008b00; font-weight: bold; }
-->
</style>
<script type='text/javascript'>
<!--
-->
</script>
</head>
<body>
<pre id='vimCodeElement'>
<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>
<span class="Comment">MODULE: xdouble </span>
<span class="Comment">SUMMARY:</span>
<span class="Comment">The class xdouble is used to represent floating point numbers with the</span>
<span class="Comment">same precision as a 'double', but with extended exponent range</span>
<span class="Comment">(offering a few more bits than that of a 'long' for the exponent).</span>
<span class="Comment">The programming interface for xdoubles is almost identical to that of</span>
<span class="Comment">ordinary doubles.</span>
<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>
<span class="PreProc">#include </span><span class="String"><NTL/ZZ.h></span>
<span class="Type">class</span> xdouble {
<span class="Statement">public</span>:
xdouble(); <span class="Comment">// = 0</span>
xdouble(<span class="Type">const</span> xdouble& a); <span class="Comment">// copy constructor</span>
<span class="Type">explicit</span> xdouble(<span class="Type">double</span> a); <span class="Comment">// promotion constructor</span>
xdouble& <span class="Statement">operator</span>=(<span class="Type">const</span> xdouble& a); <span class="Comment">// assignment operator</span>
xdouble& <span class="Statement">operator</span>=(<span class="Type">double</span> a);
~xdouble();
<span class="Type">double</span> mantissa() <span class="Type">const</span>; <span class="Comment">// read-only access to mantissa</span>
<span class="Type">long</span> exponent() <span class="Type">const</span>; <span class="Comment">// read-only access to exponenent</span>
<span class="Type">static</span> <span class="Type">void</span> SetOutputPrecision(<span class="Type">long</span> p);
<span class="Comment">// This sets the number of decimal digits to be output. Default is</span>
<span class="Comment">// 10.</span>
<span class="Type">static</span> <span class="Type">long</span> OutputPrecision();
<span class="Comment">// returns current output precision.</span>
};
<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>
<span class="Comment"> Arithmetic Operations</span>
<span class="Comment">The following are the standard arithmetic operators, whose meaning should </span>
<span class="Comment">be clear.</span>
<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>
xdouble <span class="Statement">operator</span>+(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
xdouble <span class="Statement">operator</span>-(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
xdouble <span class="Statement">operator</span>*(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
xdouble <span class="Statement">operator</span>/(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
<span class="Comment">// PROMOTIONS: +, -, *, / promote double to xdouble on (a, b).</span>
xdouble <span class="Statement">operator</span>-(<span class="Type">const</span> xdouble& a);
xdouble& <span class="Statement">operator</span>+=(xdouble& a, <span class="Type">const</span> xdouble& b);
xdouble& <span class="Statement">operator</span>+=(xdouble& a, <span class="Type">double</span> b);
xdouble& <span class="Statement">operator</span>-=(xdouble& a, <span class="Type">const</span> xdouble& b);
xdouble& <span class="Statement">operator</span>-=(xdouble& a, <span class="Type">double</span> b);
xdouble& <span class="Statement">operator</span>*=(xdouble& a, <span class="Type">const</span> xdouble& b);
xdouble& <span class="Statement">operator</span>*=(xdouble& a, <span class="Type">double</span> b);
xdouble& <span class="Statement">operator</span>/=(xdouble& a, <span class="Type">const</span> xdouble& b);
xdouble& <span class="Statement">operator</span>/=(xdouble& a, xdouble b);
xdouble& <span class="Statement">operator</span>++(xdouble& a); <span class="Comment">// prefix</span>
<span class="Type">void</span> <span class="Statement">operator</span>++(xdouble& a, <span class="Type">int</span>); <span class="Comment">// postfix</span>
xdouble& <span class="Statement">operator</span>--(xdouble& a); <span class="Comment">// prefix</span>
<span class="Type">void</span> <span class="Statement">operator</span>--(xdouble& a, <span class="Type">int</span>); <span class="Comment">// postfix</span>
<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>
<span class="Comment"> Comparison</span>
<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>
<span class="Type">long</span> sign(<span class="Type">const</span> xdouble& a);
<span class="Comment">// returns sign (+1, -1, 0) of a</span>
<span class="Type">long</span> compare(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
<span class="Comment">// returns sign of a - b</span>
<span class="Type">long</span> <span class="Statement">operator</span>==(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
<span class="Type">long</span> <span class="Statement">operator</span>!=(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
<span class="Type">long</span> <span class="Statement">operator</span><=(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
<span class="Type">long</span> <span class="Statement">operator</span>>=(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
<span class="Type">long</span> <span class="Statement">operator</span> <(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
<span class="Type">long</span> <span class="Statement">operator</span> >(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b);
<span class="Comment">// PROMOTIONS: compare and operators ==, ..., > promote double to xdouble</span>
<span class="Comment">// on (a, b).</span>
<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>
<span class="Comment"> Input/Output</span>
<span class="Comment">Input Syntax:</span>
<span class="Comment"><number>: [ "-" ] <unsigned-number></span>
<span class="Comment"><unsigned-number>: <dotted-number> [ <e-part> ] | <e-part></span>
<span class="Comment"><dotted-number>: <digits> | <digits> "." <digits> | "." <digits> | <digits> "."</span>
<span class="Comment"><digits>: <digit> <digits> | <digit></span>
<span class="Comment"><digit>: "0" | ... | "9"</span>
<span class="Comment"><e-part>: ( "E" | "e" ) [ "+" | "-" ] <digits></span>
<span class="Comment">Examples of valid input:</span>
<span class="Comment">17 1.5 0.5 .5 5. -.5 e10 e-10 e+10 1.5e10 .5e10 .5E10</span>
<span class="Comment">Note that the number of decimal digits of precision that are used</span>
<span class="Comment">for output can be set to any number p >= 1 by calling</span>
<span class="Comment">the routine xdouble::SetOutputPrecision(p). </span>
<span class="Comment">The default value of p is 10.</span>
<span class="Comment">The current value of p is returned by a call to xdouble::OutputPrecision().</span>
<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>
ostream& <span class="Statement">operator</span><<(ostream& s, <span class="Type">const</span> xdouble& a);
istream& <span class="Statement">operator</span>>>(istream& s, xdouble& x);
<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>
<span class="Comment"> Miscellaneous</span>
<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>
xdouble trunc(<span class="Type">const</span> xdouble& a); <span class="Comment">// returns integer obtained by truncating</span>
xdouble floor(<span class="Type">const</span> xdouble& a); <span class="Comment">// returns greatest integer <= a</span>
xdouble ceil(<span class="Type">const</span> xdouble& a); <span class="Comment">// returns smallest integer >= a</span>
xdouble fabs(<span class="Type">const</span> xdouble& a); <span class="Comment">// returns |a|</span>
xdouble sqrt(<span class="Type">const</span> xdouble& a); <span class="Comment">// returns a^{1/2}; error is raised if a < 0</span>
<span class="Type">double</span> log(<span class="Type">const</span> xdouble& a); <span class="Comment">// returns log(a) (note return val is double!)</span>
xdouble xexp(<span class="Type">double</span> a); <span class="Comment">// returns exp(a) (note argument is double!)</span>
xdouble exp(<span class="Type">const</span> <span class="Type">double</span>& a); <span class="Comment">// equivalent to xexp(to_double(a))</span>
<span class="Type">void</span> power(xdouble& z, <span class="Type">const</span> xdouble& a, <span class="Type">const</span> ZZ& e);
xdouble power(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> ZZ& e);
<span class="Type">void</span> power(xdouble& z, <span class="Type">const</span> xdouble& a, <span class="Type">long</span> e);
xdouble power(<span class="Type">const</span> xdouble& a, <span class="Type">long</span> e);
<span class="Comment">// z = a^e, e may be negative</span>
<span class="Type">void</span> power2(xdouble& z, <span class="Type">long</span> e);
xdouble power2_xdouble(<span class="Type">long</span> e);
<span class="Comment">// z = 2^e, e may be negative</span>
<span class="Type">void</span> MulAdd(xdouble& z, <span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b, <span class="Type">const</span> xdouble& c);
xdouble MulAdd(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b, <span class="Type">const</span> xdouble& c);
<span class="Comment">// z = a + b*c, but faster</span>
<span class="Type">void</span> MulSub(xdouble& z, <span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b, <span class="Type">const</span> xdouble& c);
xdouble MulSub(<span class="Type">const</span> xdouble& a, <span class="Type">const</span> xdouble& b, <span class="Type">const</span> xdouble& c);
<span class="Comment">// z = a - b*c, but faster</span>
<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>
<span class="Comment">Implementation details:</span>
<span class="Comment">An xdouble is represented as a mantissa/exponent pair (x, e), where x</span>
<span class="Comment">is a double and e is a long. The real number represented by (x, e) is</span>
<span class="Comment">x * NTL_XD_BOUND^e, where</span>
<span class="Comment"> NTL_XD_BOUND = NTL_XD_HBOUND^2, and</span>
<span class="Comment"> NTL_XD_HBOUND = 2^{(max(NTL_DOUBLE_PRECISION,NTL_BITS_PER_LONG)+4)}.</span>
<span class="Comment">Also, the mantissa x satisfies 1/NTL_XD_HBOUND <= |x| <= NTL_XD_HBOUND, except</span>
<span class="Comment">that the number 0 is always represented as (0, 0). </span>
<span class="Comment">Both NTL_XD_BOUND and NTL_XD_HBOUND are macros defined in <NTL/xdouble.h>.</span>
<span class="Comment">SIZE INVARIANT: |e| < 2^(NTL_BITS_PER_LONG-4).</span>
<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>
</pre>
</body>
</html>
<!-- vim: set foldmethod=manual : -->
|
