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Constants.h
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1 //# Constants.h: Mathematical and numerical constants
2 //# Copyright (C) 1993,1994,1995,1997,1998,1999,2000,2001
3 //# Associated Universities, Inc. Washington DC, USA.
4 //#
5 //# This library is free software; you can redistribute it and/or modify it
6 //# under the terms of the GNU Library General Public License as published by
7 //# the Free Software Foundation; either version 2 of the License, or (at your
8 //# option) any later version.
9 //#
10 //# This library is distributed in the hope that it will be useful, but WITHOUT
11 //# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
12 //# FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
13 //# License for more details.
14 //#
15 //# You should have received a copy of the GNU Library General Public License
16 //# along with this library; if not, write to the Free Software Foundation,
17 //# Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA.
18 //#
19 //# Correspondence concerning AIPS++ should be addressed as follows:
20 //# Internet email: aips2-request@nrao.edu.
21 //# Postal address: AIPS++ Project Office
22 //# National Radio Astronomy Observatory
23 //# 520 Edgemont Road
24 //# Charlottesville, VA 22903-2475 USA
25 //#
26 //# $Id$
27 
28 #ifndef CASA_CONSTANTS_H
29 #define CASA_CONSTANTS_H
30 
31 #include <casacore/casa/aips.h>
32 
33 #if defined (sun) && ! defined (AIPS_SOLARIS)
34 # include <sys/limits.h>
35 #else
36 # include <limits.h>
37 #endif
38 
39 #include <float.h>
40 #if !defined(AIPS_DARWIN) && !defined(AIPS_BSD)
41 #include <values.h>
42 #endif
43 
44 #if defined (AIPS_OSF)
45 # define LN_MAXFLOAT (M_LN2 * FMAXEXP)
46 # define LN_MINFLOAT (M_LN2 * (FMINEXP -1))
47 #endif
48 
49 namespace casacore { //# NAMESPACE CASACORE - BEGIN
50 
51 // <summary>Mathematical and numerical constants.</summary>
52 
53 // <use visibility=export>
54 
55 // <reviewed reviewer="UNKNOWN" date="before2004/08/25" tests="tConstants" demos="">
56 
57 //# // <prerequisite>
58 //# // </prerequisite>
59 
60 //# // <etymology>
61 //# // </etymology>
62 
63 // <synopsis>
64 // The constants and conversion factors are defined here as double precision
65 // values. Where single precision calculations are done in a situation where
66 // processing speed is of concern, for example within the inner loop of an
67 // expensive algorithm, a separate single precision variable should be defined
68 // for use within the loop.
69 //
70 // </synopsis>
71 //
72 // <note role=warning> The following list is generated by hand, and may be incomplete.
73 // After future revision of ccx2html the real data will be displayed </note>
74 
75 // <h3>Floating point limits</h3>
76 // <srcblock>
77 // flt_min the minimum single precision floating point number,
78 // excluding denormalised numbers
79 // minfloat the minimum single precision floating point number,
80 // including denormalised numbers
81 // dbl_min the minimum double precision floating point number,
82 // excluding denormalised numbers
83 // mindouble the minimum double precision floating point number,
84 // including denormalised numbers
85 // flt_max the maximum single precision floating point number
86 // dbl_max the maximum double precision floating point number
87 // flt_epsilon Minimum single precision floating point number X
88 // such that 1+X does not equal X
89 // dbl_epsilon Minimum double precision floating point number X
90 // such that 1+X does not equal X
91 // </srcblock>
92 // <h3> Irrationals </h3>
93 // <srcblock>
94 // sqrt2 sqrt(2)
95 // sqrt3 sqrt(3)
96 // _1_sqrt2 1/sqrt(2)
97 // _1_sqrt3 1/sqrt(3)
98 // </srcblock>
99 
100 // <h3>Pi and functions thereof</h3>
101 // <srcblock>
102 // pi pi
103 // _2pi 2*pi
104 // pi_2 pi/2
105 // pi_4 pi/4
106 // _1_pi 1/pi
107 // _2_pi 2/pi
108 // _1_sqrtpi 1/sqrt(pi)
109 // _2_sqrtpi 2/sqrt(pi)
110 // </srcblock>
111 
112 // <h3>e and functions thereof</h3>
113 // <srcblock>
114 // e e
115 // ln2 ln(2)
116 // ln10 ln(10)
117 // log2e log2(e)
118 // log10e log10(e)
119 // </srcblock>
120 
121 // <h3>gamma and functions thereof</h3>
122 // <srcblock>
123 // gamma gamma
124 // lngamma ln(gamma)
125 // etogamma e**gamma
126 // </srcblock>
127 
128 // <h3>Fundamental physical constants (SI units)</h3>
129 // <note role=warning> Preserved for legacy reasons only.
130 // See <linkto class=QC>QC class</linkto> for other physical constants. </note>
131 // <srcblock>
132 // c velocity of light (m/s)
133 // </srcblock>
134 
135 // <h3>Numerical conversion factors</h3>
136 // <srcblock>
137 // yotta e+24 (Y)
138 // zetta e+21 (Z)
139 // exa e+18 (E)
140 // peta e+15 (P)
141 // tera e+12 (T)
142 // giga e+09 (G)
143 // mega e+06 (M)
144 // kilo e+03 (k)
145 // hecto e+02 (h)
146 // deka e+01 (da)
147 // deci e-01 (d)
148 // centi e-02 (c)
149 // milli e-03 (m)
150 // micro e-06 (u)
151 // nano e-09 (n)
152 // pico e-12 (p)
153 // femto e-15 (f)
154 // atto e-18 (a)
155 // zepto e-21 (z)
156 // yocto e-24 (y)
157 // </srcblock>
158 
159 // <h3>Angular measure</h3>
160 // <srcblock>
161 // radian radian
162 // circle circle
163 // degree degree
164 // arcmin arcminute
165 // arcsec arcsecond
166 // </srcblock>
167 
168 // <h3>Solid angular measure</h3>
169 // <srcblock>
170 // steradian steradian
171 // sphere sphere
172 // square_degree square degree
173 // square_arcmin square arcminute
174 // square_arcsec square arcsecond
175 // </srcblock>
176 
177 // <h3>Time interval</h3>
178 // <srcblock>
179 // second second
180 // minute minute
181 // hour hour
182 // day day
183 // </srcblock>
184 
185 // <h3> Machine constants </h3>
186 //
187 // Implementation-defined limits usually defined in <src><limits.h></src>,
188 // <src><float.h></src>, and <src><values.h></src> as preprocessor
189 // defines. They are
190 // Inclusion of <src><casa/BasicSL/Constants.h</src> is
191 // sufficient to ensure that they are defined for any particular
192 // implementation, and the correct functioning of the <src>tConstants</src>
193 // test program guarantees this.
194 //
195 // In future use will be made of the (standard) <em>numeric_limits</em>
196 // template from the <src><limits></src> include file.
197 
198 // <srcblock>
199 //
200 // Refer to Section 3.2c, pp28-30 of
201 // "The Annotated C++ Reference Manual",
202 // Ellis, M.A., and Stroustrup, B.,
203 // Addison-Wesley Publishing Company, 1990.
204 // IBSN 0-201-51459-1.
205 //
206 // and
207 //
208 // Appendix B11, pp257-8 of
209 // "The C Programming Language", 2nd ed.,
210 // Kernighan, B.W., and Ritchie, D.M.,
211 // Prentice Hall Software Series, 1988.
212 // IBSN 0-13-110362-8.
213 //
214 // </srcblock>
215 
216 // <h3> Constants defined in limits.h </h3>
217 // (these are part of the ANSI C and hence POSIX standards).
218 // Acceptable limits defined by the standard are quoted.
219 // <srcblock>
220 //
221 // CHAR_BIT 8 Maximum bits in a byte.
222 // CHAR_MIN 0 or Minimum value of 'char'.
223 // SCHAR_MIN
224 // CHAR_MAX UCHAR_MAX or Maximum value of 'char'.
225 // SCHAR_MAX
226 // SCHAR_MIN -127 Minimum value of 'signed char'.
227 // SCHAR_MAX +127 Maximum value of 'signed char'.
228 // UCHAR_MAX 255 Maximum value of 'unsigned char'.
229 // MB_LEN_MAX Maximum bytes in multibyte character.
230 //
231 // SHRT_MIN -32767 Minimum value of 'short'.
232 // SHRT_MAX +32767 Maximum value of 'short'.
233 // USHRT_MAX 65535 Maximum value of 'unsigned short'.
234 //
235 // INT_MIN -32767 Minimum value of 'int'.
236 // INT_MAX +32767 Maximum value of 'int'.
237 // UINT_MAX 65535 Maximum value of 'unsigned int'.
238 //
239 // LONG_MIN -2147483647 Minimum value of 'long'.
240 // LONG_MAX +2147483647 Maximum value of 'long'.
241 // ULONG_MAX 4294967295 Maximum value of 'unsigned long'.
242 //
243 // </srcblock>
244 
245 // <h3> Constants defined in float.h </h3>
246 // (these are part of the ANSI C and hence POSIX standards).
247 // Acceptable limits defined by the standard are quoted.
248 // <srcblock>
249 //
250 // FLT_RADIX 2 Radix of exponent representation.
251 // FLT_ROUNDS Floating point rounding mode for addition
252 // -1: indeterminate
253 // 0: towards zero
254 // 1: to nearest
255 // 2: toward +infinity
256 // 3: toward -infinity
257 //
258 // FLT_MIN_EXP Minimum negative integer N such that FLT_RADIX
259 // DBL_MIN_EXP raised to the Nth minus 1 is a normalized
260 // LDBL_MIN_EXP floating point number.
261 //
262 // FLT_MAX_EXP Maximum integer N such that FLT_RADIX raised to
263 // DBL_MAX_EXP the Nth minus 1 is representable.
264 // LDBL_MAX_EXP
265 //
266 // FLT_MIN_10_EXP -37 Minimum negative integer N such that 10 raised
267 // DBL_MIN_10_EXP -37 to the Nth is in the range of normalized
268 // LDBL_MIN_10_EXP -37 floating point numbers.
269 //
270 // FLT_MAX_10_EXP 37 Maximum integer N such that 10 raised to the
271 // DBL_MAX_10_EXP 37 Nth minus 1 is representable.
272 // LDBL_MAX_10_EXP 37
273 //
274 // FLT_MANT_DIG Number of base FLT_RADIX digits in mantissa.
275 // DBL_MANT_DIG
276 // LDBL_MANT_DIG
277 //
278 // FLT_DIG 6 Decimal digits of precision.
279 // DBL_DIG 10
280 // LDBL_DIG 10
281 //
282 // FLT_EPSILON 1E-5 Minimum floating point number X such that
283 // (use C::flt_epsilon in preference to this)
284 // DBL_EPSILON 1E-9 1.0 + X does not equal 1.0.
285 // (use C::dbl_epsilon in preference to this)
286 // LDBL_EPSILON 1E-9
287 //
288 // FLT_MIN 1E-37 Minimum normalized positive floating point
289 // (use C::flt_min in preference to this)
290 // DBL_MIN 1E-37 number
291 // (use C::dbl_min in preference to this)
292 // LDBL_MIN 1E-37
293 //
294 // FLT_MAX 1E+37 Maximum representable floating point number.
295 // (use C::flt_max in preference to this)
296 // DBL_MAX 1E+37
297 // (use C::dbl_max in preference to this)
298 // LDBL_MAX 1E+37
299 //
300 // </srcblock>
301 
302 // <h3> Constants defined in values.h </h3>
303 // (not part of the POSIX standard).
304 // <note role=warning> These constants will disappear in the near future.
305 // Do not use them in new code. </note>
306 
307 // <srcblock>
308 //
309 // HIBITS Value of a short integer with only the high-order
310 // bit set (in most implementations, 0x8000).
311 //
312 // HIBITL Value of a long integer with only the high-order
313 // bit set (in most implementations, 0x80000000).
314 //
315 // MAXSHORT Maximum value of a signed short integer (in most
316 // implementations, 0x7FFF = 32767).
317 //
318 // MAXLONG Maximum value of a signed long integer (in most
319 // implementations, 0x7FFFFFFF = 2147483647).
320 //
321 // MAXINT Maximum value of a signed regular integer (usually
322 // the same as MAXSHORT or MAXLONG).
323 //
324 // MINFLOAT Minimum positive value of a single-precision
325 // floating-point number (use C::minfloat in preference
326 // to this)
327 //
328 // MINDOUBLE Minimum positive value of a double-precision
329 // floating-point number (use C::mindouble in preference
330 // to this)
331 //
332 // MAXFLOAT Maximum value of a single-precision floating-point number
333 //
334 // MAXDOUBLE Maximum value of a double-precision floating-point number
335 //
336 // FSIGNIF Number of significant bits in the mantissa of a
337 // single-precision floating-point number.
338 //
339 // DSIGNIF Number of significant bits in the mantissa of a
340 // double-precision floating-point number.
341 // </srcblock>
342 
343 // <note role=tip>
344 // Once cxx2html accepts the namespace type, the Dummy_Constants_Class can be
345 // removed.<br>
346 // Anyway, to use a constant (e.g. pi) use the C::pi construct now and later.
347 // </note>
348 
349 
351 };
352 
353 namespace C {
354  //#--------------------------------------------------------------------
355  // Mathematical constants
356  //#--------------------------------------------------------------------
357  //# <group>
358 
359  // Irrationals:
360  // <group>
361  // sqrt(2)
362  extern const Double sqrt2;
363  // sqrt(3)
364  extern const Double sqrt3;
365  // 1/sqrt(2)
366  extern const Double _1_sqrt2;
367  // 1/sqrt(3)
368  extern const Double _1_sqrt3;
369  // </group>
370 
371  // Pi and functions thereof:
372  // <group>
373  // pi
374  extern const Double pi;
375  // 2*pi
376  extern const Double _2pi;
377  // pi/2
378  extern const Double pi_2;
379  // pi/4
380  extern const Double pi_4;
381  // 1/pi
382  extern const Double _1_pi;
383  // 2/pi
384  extern const Double _2_pi;
385  // 1/sqrt(pi)
386  extern const Double _1_sqrtpi;
387  // 2/sqrt(pi)
388  extern const Double _2_sqrtpi;
389  // </group>
390 
391  // e and functions thereof:
392  // <group>
393  // e
394  extern const Double e;
395  // ln(2)
396  extern const Double ln2;
397  // ln(10)
398  extern const Double ln10;
399  // log2(e)
400  extern const Double log2e;
401  // log10(e)
402  extern const Double log10e;
403  // </group>
404 
405  // gamma and functions thereof:
406  // <group>
407  // gamma
408  extern const Double gamma;
409  // ln(gamma)
410  extern const Double lngamma;
411  // e**gamma
412  extern const Double etogamma;
413  // </group>
414 
415  // statistics related
416  // 1/(Phi^(-1)(3/4), see https://en.wikipedia.org/wiki/Median_absolute_deviation#Relation_to_standard_deviation
417  extern const Double probit_3_4;
418 
419  //#--------------------------------------------------------------------
420  //# Mathematical constants
421  //#--------------------------------------------------------------------
422  //# </group>
423 
424 
425  //#--------------------------------------------------------------------
426  // Machine constants
427  //#--------------------------------------------------------------------
428  //# <group>
429  // floating point limits
430  // <group>
431  // the minimum single precision floating point number,
432  // excluding denormalised numbers
433  extern const Double flt_min;
434  // the minimum single precision floating point number,
435  // including denormalised numbers
436  extern const Double minfloat;
437  // the minimum double precision floating point number,
438  // excluding denormalised numbers
439  extern const Double dbl_min;
440  // the minimum double precision floating point number,
441  // including denormalised numbers
442  extern const Double mindouble;
443  // the maximum single precision floating point number
444  extern const Double flt_max;
445  // the maximum double precision floating point number
446  extern const Double dbl_max;
447  // Minimum single precision floating point number X such that 1+X does not
448  // equal X
449  extern const Double flt_epsilon;
450  // Minimum double precision floating point number X such that 1+X does not
451  // equal X
452  extern const Double dbl_epsilon;
453  // </group>
454 
455  //#--------------------------------------------------------------------
456  //# Machine constants
457  //#--------------------------------------------------------------------
458  //# </group>
459 
460  //#--------------------------------------------------------------------
461  //# Physical constants, and quantities
462  //#--------------------------------------------------------------------
463  //# <group>
464 
465  // Fundamental physical constants (SI units):
466  // <group>
467  // velocity of light -- for legacy reasons only -- refer to PC
468  extern const Double c;
469  // </group>
470 
471  //#--------------------------------------------------------------------
472  //# Physical constants, and quantities
473  //#--------------------------------------------------------------------
474  //# </group>
475 
476 
477 
478  //#--------------------------------------------------------------------
479  //# Physical units
480  //#--------------------------------------------------------------------
481  //# <group>
482 
483  //#-----------------------------
484  //# Numerical conversion factors
485  //#-----------------------------
486  //# <group>
487 
488  // Numerical conversion factors
489  // <group>
490  // e+24 (Y)
491  extern const Double yotta;
492  // e+21 (Z)
493  extern const Double zetta;
494  // e+18 (E)
495  extern const Double exa;
496  // e+15 (P)
497  extern const Double peta;
498  // e+12 (T)
499  extern const Double tera;
500  // e+09 (G)
501  extern const Double giga;
502  // e+06 (M)
503  extern const Double mega;
504  // e+03 (k)
505  extern const Double kilo;
506  // e+02 (h)
507  extern const Double hecto;
508  // e+01 (da)
509  extern const Double deka;
510  // e-01 (d)
511  extern const Double deci;
512  // e-02 (c)
513  extern const Double centi;
514  // e-03 (m)
515  extern const Double milli;
516  // e-06 (u)
517  extern const Double micro;
518  // e-09 (n)
519  extern const Double nano;
520  // e-12 (p)
521  extern const Double pico;
522  // e-15 (f)
523  extern const Double femto;
524  // e-18 (a)
525  extern const Double atto;
526  // e-21 (z)
527  extern const Double zepto;
528  // e-24 (y)
529  extern const Double yocto;
530  // </group>
531 
532  // Angular measure:
533  // <group>
534  // radian
535  extern const Double radian;
536  // circle
537  extern const Double circle;
538  // degree
539  extern const Double degree;
540  // arcminute
541  extern const Double arcmin;
542  // arcsecond
543  extern const Double arcsec;
544  // </group>
545 
546  // Solid angular measure:
547  // <group>
548  // steradian
549  extern const Double steradian;
550  // sphere
551  extern const Double sphere;
552  // square degree
553  extern const Double square_degree;
554  // square arcminute
555  extern const Double square_arcmin;
556  // square arcsecond
557  extern const Double square_arcsec;
558  // </group>
559 
560  //#-----------------------------
561  //# Numerical conversion factors
562  //#-----------------------------
563  //# </group>
564 
565 
566  //#----------------------------
567  //# Physical conversion factors
568  //#----------------------------
569  //# <group>
570 
571  // Time interval [T]:
572  // <group>
573  // second
574  extern const Double second;
575  // minute
576  extern const Double minute;
577  // hour
578  extern const Double hour;
579  // day
580  extern const Double day;
581  // Difference between Julian Day and Modified Julian Day
582  extern const Double MJD0;
583  // </group>
584 
585  //#----------------------------
586  //# Physical conversion factors
587  //#----------------------------
588  //# <group>
589 
590  //#--------------------------------------------------------------------
591  //# Physical units
592  //#--------------------------------------------------------------------
593  //# <group>
594 
595 }
596 
597 
598 } //# NAMESPACE CASACORE - END
599 
600 #endif
const Double peta
e+15 (P)
const Double flt_max
the maximum single precision floating point number
const Double flt_epsilon
Minimum single precision floating point number X such that 1+X does not equal X.
const Double micro
e-06 (u)
const Double milli
e-03 (m)
const Double ln2
ln(2)
const Double circle
circle
const Double hour
hour
const Double _1_sqrt2
1/sqrt(2)
const Double sphere
sphere
const Double nano
e-09 (n)
const Double yocto
e-24 (y)
const Double deci
e-01 (d)
Mathematical and numerical constants.
Definition: Constants.h:350
const Double giga
e+09 (G)
const Double degree
degree
const Double gamma
gamma and functions thereof:
const Double femto
e-15 (f)
const Double dbl_min
the minimum double precision floating point number, excluding denormalised numbers ...
const Double zepto
e-21 (z)
const Double pi_2
pi/2
const Double log10e
log10(e)
const Double steradian
Solid angular measure:
const Double mindouble
the minimum double precision floating point number, including denormalised numbers ...
const Double minute
minute
const Double kilo
e+03 (k)
const Double sqrt2
Mathematical constants.
const Double arcsec
arcsecond
const Double pi
Pi and functions thereof:
const Double _2pi
2*pi
const Double _1_sqrt3
1/sqrt(3)
const Double radian
Angular measure:
const Double _2_pi
2/pi
const Double probit_3_4
statistics related 1/(Phi^(-1)(3/4), see https://en.wikipedia.org/wiki/Median_absolute_deviation#Rela...
const Double _1_pi
1/pi
const Double mega
e+06 (M)
const Double deka
e+01 (da)
const Double zetta
e+21 (Z)
const Double dbl_max
the maximum double precision floating point number
const Double square_arcmin
square arcminute
const Double exa
e+18 (E)
double Double
Definition: aipstype.h:55
const Double day
day
const Double lngamma
ln(gamma)
const Double pico
e-12 (p)
const Double square_degree
square degree
const Double _1_sqrtpi
1/sqrt(pi)
const Double etogamma
e**gamma
const Double tera
e+12 (T)
const Double sqrt3
sqrt(3)
const Double hecto
e+02 (h)
const Double second
Time interval [T]:
const Double yotta
Numerical conversion factors.
const Double log2e
log2(e)
const Double atto
e-18 (a)
const Double e
e and functions thereof:
const Double _2_sqrtpi
2/sqrt(pi)
const Double flt_min
Machine constants.
const Double c
Fundamental physical constants (SI units):
const Double minfloat
the minimum single precision floating point number, including denormalised numbers ...
const Double square_arcsec
square arcsecond
const Double centi
e-02 (c)
const Double ln10
ln(10)
const Double MJD0
Difference between Julian Day and Modified Julian Day.
const Double dbl_epsilon
Minimum double precision floating point number X such that 1+X does not equal X.
const Double arcmin
arcminute
const Double pi_4
pi/4