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amath/doc/man/man3/PositionalNumeralSystem.3
Carsten Larsen 9e2c66af53 Update documentation
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.TH "PositionalNumeralSystem" 3 "Tue Jan 24 2017" "Version 1.6.2" "amath" \" -*- nroff -*-
.ad l
.nh
.SH NAME
PositionalNumeralSystem \- Base class for all numeral systems with a positional notation\&.
.SH SYNOPSIS
.br
.PP
.PP
\fC#include <ntext\&.h>\fP
.PP
Inherits \fBNumeralSystem\fP\&.
.PP
Inherited by \fBDecimalSystem\fP\&.
.SS "Public Member Functions"
.in +1c
.ti -1c
.RI "\fBPositionalNumeralSystem\fP (unsigned int \fBbase\fP, unsigned int \fBdigits\fP, const char \fBfractionpoint\fP)"
.br
.ti -1c
.RI "\fB~PositionalNumeralSystem\fP ()"
.br
.ti -1c
.RI "virtual const char * \fBGetName\fP ()"
.br
.ti -1c
.RI "virtual const char * \fBGetPrefix\fP ()"
.br
.ti -1c
.RI "virtual unsigned int \fBGetDigits\fP ()"
.br
.ti -1c
.RI "virtual void \fBSetDigits\fP (unsigned int \fBdigits\fP)"
.br
.ti -1c
.RI "virtual const char \fBGetFractionPoint\fP ()"
.br
.ti -1c
.RI "virtual void \fBSetFractionPoint\fP (const char \fBfractionpoint\fP)"
.br
.ti -1c
.RI "virtual const char * \fBGetText\fP (\fBNumber\fP *number)"
.br
.ti -1c
.RI "virtual \fBNumber\fP * \fBParse\fP (const char *text, unsigned int *length, char **end)"
.br
.in -1c
.SS "Protected Attributes"
.in +1c
.ti -1c
.RI "double \fBbase\fP"
.br
.ti -1c
.RI "unsigned int \fBdigits\fP"
.br
.ti -1c
.RI "char \fBfractionpoint\fP"
.br
.in -1c
.SS "Private Member Functions"
.in +1c
.ti -1c
.RI "const char * \fBGetText\fP (double number)"
.br
.ti -1c
.RI "void \fBIntegerToBuffer\fP (double value, unsigned int \fBdigits\fP, int *outdigits)"
.br
.in -1c
.SH "Detailed Description"
.PP
Base class for all numeral systems with a positional notation\&.
More info on positional notation is available at Wikipedia: http://en.wikipedia.org/wiki/Positional_notation
.PP
Definition at line 74 of file ntext\&.h\&.
.SH "Constructor & Destructor Documentation"
.PP
.SS "PositionalNumeralSystem::PositionalNumeralSystem (unsigned int base, unsigned int digits, const char fractionpoint)"
.PP
Definition at line 58 of file ntext\&.cpp\&.
.PP
References base, digits, and fractionpoint\&.
.PP
Referenced by DecimalSystem::DecimalSystem(), Program::NewPositionalInput(), and Program::NewPositionalOutput()\&.
.PP
.nf
61 :
62 base(base * 1\&.0), digits(digits) {
63 this->fractionpoint = fractionpoint;
64 }
.fi
.SS "PositionalNumeralSystem::~PositionalNumeralSystem ()"
.PP
Definition at line 66 of file ntext\&.cpp\&.
.PP
.nf
67 { }
.fi
.SH "Member Function Documentation"
.PP
.SS "unsigned int PositionalNumeralSystem::GetDigits ()\fC [virtual]\fP"
.PP
Implements \fBNumeralSystem\fP\&.
.PP
Definition at line 107 of file ntext\&.cpp\&.
.PP
References digits\&.
.PP
.nf
108 {
109 return digits;
110 }
.fi
.SS "const char PositionalNumeralSystem::GetFractionPoint ()\fC [virtual]\fP"
.PP
Implements \fBNumeralSystem\fP\&.
.PP
Definition at line 117 of file ntext\&.cpp\&.
.PP
References fractionpoint\&.
.PP
.nf
118 {
119 return (const char)this->fractionpoint;
120 }
.fi
.SS "const char * PositionalNumeralSystem::GetName ()\fC [virtual]\fP"
.PP
Implements \fBNumeralSystem\fP\&.
.PP
Definition at line 69 of file ntext\&.cpp\&.
.PP
References CharBuffer::Append(), base, NumeralSystem::buf, DecimalSystem::DecimalSystem(), CharBuffer::Empty(), CharBuffer::EnsureSize(), CharBuffer::GetString(), NumeralSystem::GetText(), RealNumber::RealNumber(), and StrLen()\&.
.PP
.nf
70 {
71 switch ((int)base) {
72 case 2:
73 return "binary";
74 break;
75 case 8:
76 return "octal";
77 break;
78 case 10:
79 return "decimal";
80 break;
81 case 16:
82 return "hexadecimal";
83 break;
84 }
85
86 const char *text = "base ";
87 Number *n = new RealNumber(base);
88 NumeralSystem *ns = new DecimalSystem(2);
89 const char *numtext = ns->GetText(n);
90
91 buf->EnsureSize(StrLen(text) + StrLen(numtext) + 1);
92 buf->Empty();
93 buf->Append(text);
94 buf->Append(numtext);
95
96 delete ns;
97 delete n;
98 return buf->GetString();
99 }
.fi
.SS "const char * PositionalNumeralSystem::GetPrefix ()\fC [virtual]\fP"
.PP
Implements \fBNumeralSystem\fP\&.
.PP
Definition at line 101 of file ntext\&.cpp\&.
.PP
.nf
102 {
103 // TODO: Implement
104 return "";
105 }
.fi
.SS "const char * PositionalNumeralSystem::GetText (\fBNumber\fP * number)\fC [virtual]\fP"
.PP
Implements \fBNumeralSystem\fP\&.
.PP
Reimplemented in \fBDecimalSystem\fP\&.
.PP
Definition at line 127 of file ntext\&.cpp\&.
.PP
References CharBuffer::Append(), NumeralSystem::buf, CharBuffer::CharBuffer(), cimag(), CharBuffer::Copy(), creal(), CharBuffer::Empty(), ComplexNumber::GetComplexValue(), Number::GetRealValue(), CharBuffer::GetString(), GetText(), nsysreal, and Number::system\&.
.PP
.nf
128 {
129 if (number->system == nsysreal) {
130 return GetText(number->GetRealValue());
131 }
132
133 complex w = ((ComplexNumber*)number)->GetComplexValue();
134 double a = creal(w);
135 double b = cimag(w);
136
137 if (a == 0\&.0 && b == 0\&.0) {
138 buf->Empty();
139 buf->Append('0');
140 return buf->GetString();
141 }
142
143 CharBuffer *val = new CharBuffer(512);
144 val->Empty();
145
146 if (a != 0\&.0) {
147 const char *real = GetText(a);
148 val->Append(real);
149 }
150
151 const char *imag = GetText(b);
152 if (a != 0\&.0 && b > 0\&.0) {
153 val->Append('+');
154 }
155
156 if (b != 0\&.0) {
157 val->Append(imag);
158 val->Append('i');
159 }
160
161 buf->Copy(val);
162 delete val;
163
164 return buf->GetString();
165 }
.fi
.SS "const char * PositionalNumeralSystem::GetText (double number)\fC [private]\fP"
.PP
Definition at line 167 of file ntext\&.cpp\&.
.PP
References CharBuffer::Append(), base, NumeralSystem::buf, digits, CharBuffer::Empty(), finite(), fractionpoint, CharBuffer::GetString(), IntegerToBuffer(), CharBuffer::Is(), isnan(), pow(), CharBuffer::RemoveTrailing(), round(), and trunc()\&.
.PP
Referenced by GetText()\&.
.PP
.nf
168 {
169 if (!finite(number)) {
170 return "Inf";
171 } else if (isnan(number)) {
172 return "NaN";
173 } else if (number == 0\&.0) {
174 return "0";
175 }
176
177 buf->Empty();
178
179 double dnumber = number;
180 if (dnumber < 0\&.0) {
181 buf->Append('-');
182 dnumber = -dnumber;
183 }
184
185 double expborder = log2p(base, dnumber);
186 int exponent = 0;
187
188 // Find exponent
189 if (expborder > 6\&.0 || expborder < -5\&.0) {
190 double dexp = trunc(log2p(base, dnumber));
191
192 // Adjust to keep one digits before dot\&.
193 if (dexp < 0\&.0) {
194 dexp -= 1\&.0;
195 }
196
197 dnumber = dnumber * pow(base, -dexp);
198 exponent = (int)dexp;
199 }
200
201 int digitout;
202 int intdigits;
203
204 // NOTICE: 1\&.5\&.3 Scaled trunc
205 int intvalue = (int)(trunc(dnumber * base) / base);
206 IntegerToBuffer(intvalue, digits, &intdigits);
207
208 int fragdigits = digits - intdigits;
209 if (fragdigits > 0) {
210 buf->Append('\&.');
211
212 // TODO: Fix fraction error (try 1\&.5439)
213 double fraction = fabs(round((dnumber - round(dnumber)) * pow(base, fragdigits)));
214
215 // NOTICE: 1\&.5\&.3 Changed from trunc to round
216 double actualdigits = round(log2p(base, fraction));
217 int padding = fragdigits - (finite(actualdigits) == 1 ? (int)actualdigits : 0) - 1;
218
219 // Pad zeros if needed
220 while (padding-- > 0) {
221 buf->Append('0');
222 }
223
224 // NOTICE: 1\&.5\&.3 Scaled trunc
225 intvalue = (int)(trunc(fraction * base) / base);
226 IntegerToBuffer(intvalue, digits - intdigits, &digitout);
227
228 // Remove trailing zeros
229 while (buf->RemoveTrailing('0'))
230 ;
231
232 buf->RemoveTrailing(fractionpoint);
233 }
234
235 // Add exponent
236 if (exponent != 0) {
237 buf->Append('e');
238 buf->Append(exponent > 0 ? '+' : '-');
239 IntegerToBuffer(abs(exponent), 3, &digitout);
240 }
241
242 // Make sure no rounding error is returned
243 if (buf->Is("-0")) {
244 buf->Empty();
245 buf->Append('0');
246 }
247
248 return buf->GetString();
249 }
.fi
.SS "void PositionalNumeralSystem::IntegerToBuffer (double value, unsigned int digits, int * outdigits)\fC [private]\fP"
.PP
Definition at line 251 of file ntext\&.cpp\&.
.PP
References CharBuffer::Append(), base, NumeralSystem::buf, and trunc()\&.
.PP
Referenced by GetText()\&.
.PP
.nf
252 {
253 static const char *alphaNumerics = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
254 unsigned int count = 0;
255 char *chars = new char[128]; // TODO: Find correct size
256 char *start = chars;
257
258 do {
259 count++;
260 unsigned int intremainder = (unsigned int) trunc(fmod(value, base));
261 *chars++ = alphaNumerics[intremainder];
262 value /= base;
263 } while (value >= 1\&.0);
264
265 unsigned int n = count;
266 unsigned int q = digits;
267 chars--;
268
269 while (n-- != 0 && q-- != 0) {
270 buf->Append(*chars--);
271 }
272
273 n++;
274 while (n-- != 0) {
275 buf->Append('0');
276 }
277
278 *outdigits = count;
279 delete [] start;
280 }
.fi
.SS "\fBNumber\fP * PositionalNumeralSystem::Parse (const char * text, unsigned int * length, char ** end)\fC [virtual]\fP"
.PP
Implements \fBNumeralSystem\fP\&.
.PP
Definition at line 282 of file ntext\&.cpp\&.
.PP
References base, fractionpoint, pow(), and RealNumber::RealNumber()\&.
.PP
.nf
283 {
284 unsigned int intbase = (unsigned int)base;
285 char maxNumeric = (intbase > 10 ? 10 : intbase) + '0' - 1;
286 char maxAlpha = intbase > 10 ? intbase + 'A' - 11 : 0;
287
288 unsigned int pos = 0;
289 double integer = 0;
290 double addition;
291
292 while (*text != '\0' && ((*text >= '0' && *text <= maxNumeric) || (maxAlpha != 0 && *text >= 'A' && *text <= maxAlpha))) {
293 addition = ((*text >= '0' && *text <= maxNumeric) ? (*text - '0') : (*text - 'A' + 10)) * 1\&.0;
294 integer = integer * base + addition;
295 text++;
296 pos++;
297 }
298
299 // Digits not found
300 if (pos == 0) {
301 *length = 0;
302 *end = (char*)text;
303 return new RealNumber();
304 }
305
306 double fraction = 0\&.0;
307 double divisor = 1\&.0;
308 if (*text == fractionpoint) {
309 text++;
310 pos++;
311
312 while (*text != '\0' && ((*text >= '0' && *text <= maxNumeric) || (maxAlpha != '\0' && *text >= 'A' && *text <= maxAlpha))) {
313 addition = ((*text >= '0' && *text <= maxNumeric) ? (*text - '0') : (*text - 'A' + 10));
314 fraction = fraction * base + addition;
315 divisor *= base;
316 text++;
317 pos++;
318 }
319 }
320
321 double exp = 0;
322 if (*text == 'e' || *text == 'E') {
323 text++;
324 pos++;
325
326 double sign = *text == '+' ? 1\&.0 : *text == '-' ? -1\&.0 : 0\&.0;
327
328 if (sign != 0\&.0) {
329 text++;
330 pos++;
331
332 while (*text != '\0' && ((*text >= '0' && *text <= maxNumeric) || (maxAlpha != 0 && *text >= 'A' && *text <= maxAlpha))) {
333 addition = ((*text >= '0' && *text <= maxNumeric) ? (*text - '0') : (*text - 'A' + 10)) * 1\&.0;
334 exp = exp * base + addition;
335 text++;
336 pos++;
337 }
338
339 exp *= sign;
340 } else {
341 text--;
342 pos--;
343 }
344 }
345
346 *length = pos;
347 *end = (char*)text;
348 double dnumber = (integer + (fraction / divisor)) * pow(base, exp);
349
350 return new RealNumber(dnumber);
351 }
.fi
.SS "void PositionalNumeralSystem::SetDigits (unsigned int digits)\fC [virtual]\fP"
.PP
Implements \fBNumeralSystem\fP\&.
.PP
Definition at line 112 of file ntext\&.cpp\&.
.PP
References digits\&.
.PP
.nf
113 {
114 this->digits = digits;
115 }
.fi
.SS "void PositionalNumeralSystem::SetFractionPoint (const char fractionpoint)\fC [virtual]\fP"
.PP
Implements \fBNumeralSystem\fP\&.
.PP
Definition at line 122 of file ntext\&.cpp\&.
.PP
References fractionpoint\&.
.PP
.nf
123 {
124 this->fractionpoint = fractionpoint;
125 }
.fi
.SH "Member Data Documentation"
.PP
.SS "double PositionalNumeralSystem::base\fC [protected]\fP"
.PP
Definition at line 89 of file ntext\&.h\&.
.PP
Referenced by GetName(), GetText(), IntegerToBuffer(), Parse(), and PositionalNumeralSystem()\&.
.SS "unsigned int PositionalNumeralSystem::digits\fC [protected]\fP"
.PP
Definition at line 90 of file ntext\&.h\&.
.PP
Referenced by GetDigits(), DecimalSystem::GetRealText(), GetText(), PositionalNumeralSystem(), and SetDigits()\&.
.SS "char PositionalNumeralSystem::fractionpoint\fC [protected]\fP"
.PP
Definition at line 91 of file ntext\&.h\&.
.PP
Referenced by GetFractionPoint(), DecimalSystem::GetRealText(), GetText(), Parse(), PositionalNumeralSystem(), and SetFractionPoint()\&.
.SH "Author"
.PP
Generated automatically by Doxygen for amath from the source code\&.
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