Constants.h

Go to the documentation of this file.

// # Constants.h: Mathematical and numerical constants
// # Copyright (C) 1993,1994,1995,1997,1998,1999,2000,2001
// # Associated Universities, Inc. Washington DC, USA.
// #
// # This library is free software; you can redistribute it and/or modify it
// # under the terms of the GNU Library General Public License as published by
// # the Free Software Foundation; either version 2 of the License, or (at your
// # option) any later version.
// #
// # This library is distributed in the hope that it will be useful, but WITHOUT
// # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
// # FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public
// # License for more details.
// #
// # You should have received a copy of the GNU Library General Public License
// # along with this library; if not, write to the Free Software Foundation,
// # Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA.
// #
// # Correspondence concerning AIPS++ should be addressed as follows:
// #        Internet email: casa-feedback@nrao.edu.
// #        Postal address: AIPS++ Project Office
// #                        National Radio Astronomy Observatory
// #                        520 Edgemont Road
// #                        Charlottesville, VA 22903-2475 USA
 
#ifndef CASA_CONSTANTS_H
#define CASA_CONSTANTS_H
 
#include <casacore/casa/aips.h>
 
#if defined(sun) && !defined(AIPS_SOLARIS)
#include <sys/limits.h>
#else
#include <limits.h>
#endif
 
#include <float.h>
#if !defined(AIPS_DARWIN) && !defined(AIPS_BSD)
#include <values.h>
#endif
 
#if defined(AIPS_OSF)
#define LN_MAXFLOAT (M_LN2 * FMAXEXP)
#define LN_MINFLOAT (M_LN2 * (FMINEXP - 1))
#endif
 
namespace casacore {  // # NAMESPACE CASACORE - BEGIN
 
// <summary>Mathematical and numerical constants.</summary>
 
// <use visibility=export>
 
// <reviewed reviewer="UNKNOWN" date="before2004/08/25" tests="tConstants" demos="">
 
// <synopsis>
// The constants and conversion factors are defined here as double precision
// values.  Where single precision calculations are done in a situation where
// processing speed is of concern, for example within the inner loop of an
// expensive algorithm, a separate single precision variable should be defined
// for use within the loop.
//
// </synopsis>
//
// <note role=warning> The following list is generated by hand, and may be incomplete.
// After future revision of ccx2html the real data will be displayed </note>
 
// <h3>Floating point limits</h3>
// <srcblock>
// flt_min      the minimum single precision floating point number,
//          excluding denormalised numbers
// minfloat     the minimum single precision floating point number,
//          including denormalised numbers
// dbl_min      the minimum double precision floating point number,
//          excluding denormalised numbers
// mindouble        the minimum double precision floating point number,
//          including denormalised numbers
// flt_max      the maximum single precision floating point number
// dbl_max      the maximum double precision floating point number
// flt_epsilon      Minimum single precision floating point number X
//          such that 1+X does not equal X
// dbl_epsilon      Minimum double precision floating point number X
//          such that 1+X does not equal X
// </srcblock>
// <h3> Irrationals </h3>
// <srcblock>
// sqrt2        sqrt(2)
// sqrt3        sqrt(3)
// _1_sqrt2     1/sqrt(2)
// _1_sqrt3     1/sqrt(3)
// </srcblock>
 
// <h3>Pi and functions thereof</h3>
// <srcblock>
// pi                   pi
// _2pi                 2*pi
// pi_2                 pi/2
// pi_4                 pi/4
// _1_pi                1/pi
// _2_pi                2/pi
// _1_sqrtpi            1/sqrt(pi)
// _2_sqrtpi            2/sqrt(pi)
// </srcblock>
 
// <h3>e and functions thereof</h3>
// <srcblock>
// e                    e
// ln2                  ln(2)
// ln10                 ln(10)
// log2e                log2(e)
// log10e               log10(e)
// </srcblock>
 
// <h3>gamma and functions thereof</h3>
// <srcblock>
// gamma        gamma
// lngamma      ln(gamma)
// etogamma     e**gamma
// </srcblock>
 
// <h3>Fundamental physical constants (SI units)</h3>
// <note role=warning> Preserved for legacy reasons only.
// See <linkto class=QC>QC class</linkto> for other physical constants. </note>
// <srcblock>
// c            velocity of light (m/s)
// </srcblock>
 
// <h3>Numerical conversion factors</h3>
// <srcblock>
// quetta               e+30 (Q)
// ronna                e+27 (R)
// yotta                e+24 (Y)
// zetta                e+21 (Z)
// exa                  e+18 (E)
// peta                 e+15 (P)
// tera                 e+12 (T)
// giga                 e+09 (G)
// mega                 e+06 (M)
// kilo                 e+03 (k)
// hecto                e+02 (h)
// deka                 e+01 (da)
// deci                 e-01 (d)
// centi                e-02 (c)
// milli                e-03 (m)
// micro                e-06 (u)
// nano                 e-09 (n)
// pico                 e-12 (p)
// femto                e-15 (f)
// atto                 e-18 (a)
// zepto                e-21 (z)
// yocto                e-24 (y)
// ronto                e-27 (r)
// quecto               e-30 (q)
// </srcblock>
 
// <h3>Angular measure</h3>
// <srcblock>
// radian       radian
// circle       circle
// degree       degree
// arcmin       arcminute
// arcsec       arcsecond
// </srcblock>
 
// <h3>Solid angular measure</h3>
// <srcblock>
// steradian        steradian
// sphere       sphere
// square_degree    square degree
// square_arcmin    square arcminute
// square_arcsec    square arcsecond
// </srcblock>
 
// <h3>Time interval</h3>
// <srcblock>
// second               second
// minute               minute
// hour                 hour
// day                  day
// </srcblock>
 
// <h3> Machine constants </h3>
//
// Implementation-defined limits usually defined in <src><limits.h></src>,
// <src><float.h></src>, and <src><values.h></src> as preprocessor
// defines. They are
// Inclusion of <src><casa/BasicSL/Constants.h</src> is
// sufficient to ensure that they are defined for any particular
// implementation, and the correct functioning of the <src>tConstants</src>
// test program guarantees this.
//
// In future use will be made of the (standard) <em>numeric_limits</em>
// template from the <src><limits></src> include file.
 
// <srcblock>
//
// Refer to Section 3.2c, pp28-30 of
// "The Annotated C++ Reference Manual",
// Ellis, M.A., and Stroustrup, B.,
// Addison-Wesley Publishing Company, 1990.
// IBSN 0-201-51459-1.
//
//    and
//
// Appendix B11, pp257-8 of
// "The C Programming Language", 2nd ed.,
// Kernighan, B.W., and Ritchie, D.M.,
// Prentice Hall Software Series, 1988.
// IBSN 0-13-110362-8.
//
// </srcblock>
 
// <h3> Constants defined in limits.h </h3>
// (these are part of the ANSI C and hence POSIX standards).
// Acceptable limits defined by the standard are quoted.
// <srcblock>
//
// CHAR_BIT              8  Maximum bits in a byte.
// CHAR_MIN           0 or  Minimum value of 'char'.
//               SCHAR_MIN
// CHAR_MAX   UCHAR_MAX or  Maximum value of 'char'.
//               SCHAR_MAX
// SCHAR_MIN          -127  Minimum value of 'signed char'.
// SCHAR_MAX          +127  Maximum value of 'signed char'.
// UCHAR_MAX           255  Maximum value of 'unsigned char'.
// MB_LEN_MAX               Maximum bytes in multibyte character.
//
// SHRT_MIN         -32767  Minimum value of 'short'.
// SHRT_MAX         +32767  Maximum value of 'short'.
// USHRT_MAX         65535  Maximum value of 'unsigned short'.
//
// INT_MIN          -32767  Minimum value of 'int'.
// INT_MAX          +32767  Maximum value of 'int'.
// UINT_MAX          65535  Maximum value of 'unsigned int'.
//
// LONG_MIN    -2147483647  Minimum value of 'long'.
// LONG_MAX    +2147483647  Maximum value of 'long'.
// ULONG_MAX    4294967295  Maximum value of 'unsigned long'.
//
// </srcblock>
 
// <h3> Constants defined in float.h </h3>
// (these are part of the ANSI C and hence POSIX standards).
// Acceptable limits defined by the standard are quoted.
// <srcblock>
//
// FLT_RADIX             2  Radix of exponent representation.
// FLT_ROUNDS               Floating point rounding mode for addition
//                            -1: indeterminate
//                             0: towards zero
//                             1: to nearest
//                             2: toward +infinity
//                             3: toward -infinity
//
// FLT_MIN_EXP              Minimum negative integer N such that FLT_RADIX
// DBL_MIN_EXP              raised to the Nth minus 1 is a normalized
// LDBL_MIN_EXP             floating point number.
//
// FLT_MAX_EXP              Maximum integer N such that FLT_RADIX raised to
// DBL_MAX_EXP              the Nth minus 1 is representable.
// LDBL_MAX_EXP
//
// FLT_MIN_10_EXP      -37  Minimum negative integer N such that 10 raised
// DBL_MIN_10_EXP      -37  to the Nth is in the range of normalized
// LDBL_MIN_10_EXP     -37  floating point numbers.
//
// FLT_MAX_10_EXP       37  Maximum integer N such that 10 raised to the
// DBL_MAX_10_EXP       37  Nth minus 1 is representable.
// LDBL_MAX_10_EXP      37
//
// FLT_MANT_DIG             Number of base FLT_RADIX digits in mantissa.
// DBL_MANT_DIG
// LDBL_MANT_DIG
//
// FLT_DIG               6  Decimal digits of precision.
// DBL_DIG              10
// LDBL_DIG             10
//
// FLT_EPSILON        1E-5  Minimum floating point number X such  that
// (use C::flt_epsilon in preference to this)
// DBL_EPSILON        1E-9  1.0 + X does not equal 1.0.
// (use C::dbl_epsilon in preference to this)
// LDBL_EPSILON       1E-9
//
// FLT_MIN           1E-37  Minimum normalized positive floating point
// (use C::flt_min in preference to this)
// DBL_MIN           1E-37  number
// (use C::dbl_min in preference to this)
// LDBL_MIN          1E-37
//
// FLT_MAX           1E+37  Maximum representable floating point number.
// (use C::flt_max in preference to this)
// DBL_MAX           1E+37
// (use C::dbl_max in preference to this)
// LDBL_MAX          1E+37
//
// </srcblock>
 
// <h3> Constants defined in values.h </h3>
// (not part of the POSIX standard).
// <note role=warning> These constants will disappear in the near future.
// Do not use them in new code. </note>
 
// <srcblock>
//
// HIBITS            Value of a short integer with only the high-order
//                   bit set (in most implementations, 0x8000).
//
// HIBITL            Value of a long integer with only the high-order
//                   bit set (in most implementations, 0x80000000).
//
// MAXSHORT          Maximum value of a signed short integer (in most
//                   implementations, 0x7FFF = 32767).
//
// MAXLONG           Maximum value of a signed long integer (in most
//                   implementations, 0x7FFFFFFF = 2147483647).
//
// MAXINT            Maximum value of a signed regular integer (usually
//                   the same as MAXSHORT or MAXLONG).
//
// MINFLOAT          Minimum positive value of a single-precision
//                   floating-point number (use C::minfloat in preference
//                   to this)
//
// MINDOUBLE         Minimum positive value of a double-precision
//                   floating-point number (use C::mindouble in preference
//                   to this)
//
// MAXFLOAT          Maximum value of a single-precision floating-point number
//
// MAXDOUBLE         Maximum value of a double-precision floating-point number
//
// FSIGNIF           Number of significant bits in the mantissa of a
//                   single-precision floating-point number.
//
// DSIGNIF           Number of significant bits in the mantissa of a
//                   double-precision floating-point number.
// </srcblock>
 
namespace C {
// #--------------------------------------------------------------------
//   Mathematical constants
// #--------------------------------------------------------------------
// # <group>
 
// Irrationals:
// <group>
// sqrt(2)
[[deprecated("use M_SQRT2")]]
inline constexpr double sqrt2 = 1.4142135623730950488;
// sqrt(3)
inline constexpr double sqrt3 = 1.7320508075688772935;
// 1/sqrt(2)
[[deprecated("use M_SQRT1_2")]]
inline constexpr double _1_sqrt2 = 0.70710678118654752440;
// 1/sqrt(3)
inline constexpr double _1_sqrt3 = 0.57735026918962576451;
// </group>
 
// Pi and functions thereof:
// <group>
// pi
[[deprecated("use M_PI")]]
inline constexpr double pi = 3.141592653589793238462643;
// 2*pi
[[deprecated("use (2.0*M_PI)")]]
inline constexpr double _2pi = 6.283185307179586476925286;
// pi/2
[[deprecated("use M_PI_2")]]
inline constexpr double pi_2 = 1.570796326794896619231322;
// pi/4
[[deprecated("use M_PI_4")]]
inline constexpr double pi_4 = 0.7853981633974483096156608;
// 1/pi
[[deprecated("use M_1_PI")]]
inline constexpr double _1_pi = 0.3183098861837906715377675;
// 2/pi
[[deprecated("use M_2_PI")]]
inline constexpr double _2_pi = 0.6366197723675813430755350;
// 1/sqrt(pi)
[[deprecated("use (0.5 * M_2_SQRTPI)")]]
inline constexpr double _1_sqrtpi = 0.5641895835477562869480795;
// 2/sqrt(pi)
[[deprecated("use M_2_SQRTPI")]]
inline constexpr double _2_sqrtpi = 1.1283791670955125738961590;
// </group>
 
// e and functions thereof:
// <group>
// e
[[deprecated("use M_E")]]
inline constexpr double e = 2.718281828459045235360287;
// ln(2)
[[deprecated("use M_LN2")]]
inline constexpr double ln2 = 0.6931471805599453094172321;
// ln(10)
[[deprecated("use M_LN10")]]
inline constexpr double ln10 = 2.3025850929940456840179915;
// log2(e)
[[deprecated("use M_LOG2E")]]
inline constexpr double log2e = 1.4426950408889634074;
// log10(e)
[[deprecated("use M_LOG10E")]]
inline constexpr double log10e = 0.4342944819032518276511289;
// </group>
 
// gamma and functions thereof:
// <group>
// gamma
// With C++20, could be deprecated and use std::numbers::gamma instead
inline constexpr double gamma = 0.577215664901532860606512;
// ln(gamma)
// With C++20, could be deprecated and use std::log(std::numbers::gamma) instead
inline constexpr double lngamma = -0.549539312981644822337662;
// e**gamma
// With C++20, could be deprecated and use std::exp(std::numbers::gamma) instead
inline constexpr double etogamma = 1.7810724179901979852;
// </group>
 
// statistics related
// 1/(Phi^(-1)(3/4), see
// https://en.wikipedia.org/wiki/Median_absolute_deviation#Relation_to_standard_deviation
inline constexpr double probit_3_4 = 1.482602218505602;
 
// #--------------------------------------------------------------------
// # Mathematical constants
// #--------------------------------------------------------------------
// # </group>
 
// #--------------------------------------------------------------------
//   Machine constants
// #--------------------------------------------------------------------
// # <group>
//  floating point limits
//  <group>
//  the minimum single precision floating point number,
//  excluding denormalised numbers
[[deprecated("Use FLT_MIN")]]
inline constexpr double flt_min = FLT_MIN;
// the minimum single precision floating point number,
// including denormalised numbers
[[deprecated("Use FLT_MIN")]]
inline constexpr double minfloat = FLT_MIN;
// the minimum double precision floating point number,
// excluding denormalised numbers
[[deprecated("Use DBL_MIN")]]
inline constexpr double dbl_min = DBL_MIN;
// the minimum double precision floating point number,
// including denormalised numbers
[[deprecated("Use DBL_MIN")]]
inline constexpr double mindouble = DBL_MIN;
// the maximum single precision floating point number
[[deprecated("Use FLT_MAX")]]
inline constexpr double flt_max = FLT_MAX;
// the maximum double precision floating point number
[[deprecated("Use DBL_MAX")]]
inline constexpr double dbl_max = DBL_MAX;
// Minimum single precision floating point number X such that 1+X does not
// equal X
[[deprecated("Use FLT_EPSILON")]]
inline constexpr double flt_epsilon = FLT_EPSILON;
// Minimum double precision floating point number X such that 1+X does not
// equal X
[[deprecated("Use DBL_EPSILON")]]
inline constexpr double dbl_epsilon = DBL_EPSILON;
// </group>
 
// #--------------------------------------------------------------------
// # Machine constants
// #--------------------------------------------------------------------
// # </group>
 
// #--------------------------------------------------------------------
// #  Physical constants, and quantities
// #--------------------------------------------------------------------
// # <group>
 
// Fundamental physical constants (SI units):
// <group>
// velocity of light -- for legacy reasons only -- refer to PC
inline constexpr double c = 2.99792458e+08;
// </group>
 
// #--------------------------------------------------------------------
// # Physical constants, and quantities
// #--------------------------------------------------------------------
// # </group>
 
// #--------------------------------------------------------------------
// #  Physical units
// #--------------------------------------------------------------------
// # <group>
 
// #-----------------------------
// #  Numerical conversion factors
// #-----------------------------
// # <group>
 
//  Numerical conversion factors
// <group>
// e+30 (Q)
inline constexpr double quetta = 1.0e+30;
// e+27 (R)
inline constexpr double ronna = 1.0e+27;
// e+24 (Y)
inline constexpr double yotta = 1.0e+24;
// e+21 (Z)
inline constexpr double zetta = 1.0e+21;
// e+18 (E)
inline constexpr double exa = 1.0e+18;
// e+15 (P)
inline constexpr double peta = 1.0e+15;
// e+12 (T)
inline constexpr double tera = 1.0e+12;
// e+09 (G)
inline constexpr double giga = 1.0e+09;
// e+06 (M)
inline constexpr double mega = 1.0e+06;
// e+03 (k)
inline constexpr double kilo = 1.0e+03;
// e+02 (h)
inline constexpr double hecto = 1.0e+02;
// e+01 (da)
inline constexpr double deka = 1.0e+01;
// e-01 (d)
inline constexpr double deci = 1.0e-01;
// e-02 (c)
inline constexpr double centi = 1.0e-02;
// e-03 (m)
inline constexpr double milli = 1.0e-03;
// e-06 (u)
inline constexpr double micro = 1.0e-06;
// e-09 (n)
inline constexpr double nano = 1.0e-09;
// e-12 (p)
inline constexpr double pico = 1.0e-12;
// e-15 (f)
inline constexpr double femto = 1.0e-15;
// e-18 (a)
inline constexpr double atto = 1.0e-18;
// e-21 (z)
inline constexpr double zepto = 1.0e-21;
// e-24 (y)
inline constexpr double yocto = 1.0e-24;
// e-27 (r)
inline constexpr double ronto = 1.0e-27;
// e-30 (q)
inline constexpr double quecto = 1.0e-30;
// </group>
 
// Angular measure:
// <group>
// radian
inline constexpr double radian = 1.0;
// circle
inline constexpr double circle = 6.2831853071795864769252867;
// degree
inline constexpr double degree = 0.0174532925199432957692369;
// arcminute
inline constexpr double arcmin = 0.000290888208665721596153948459;
// arcsecond
inline constexpr double arcsec = 0.00000484813681109535993589914098765;
// </group>
 
// Solid angular measure:
// <group>
// steradian
inline constexpr double steradian = 1.0;
// sphere
inline constexpr double sphere = 12.56637061435917295385057344;
// square degree
inline constexpr double square_degree = 0.30461741978670859934674354486e-3;
// square arcminute
inline constexpr double square_arcmin = 0.8461594994075238870742876246233e-7;
// square arcsecond
inline constexpr double square_arcsec = 0.235044305390978857520635451284e-10;
// </group>
 
// #-----------------------------
// # Numerical conversion factors
// #-----------------------------
// # </group>
 
// #----------------------------
// #  Physical conversion factors
// #----------------------------
// # <group>
 
// Time interval [T]:
// <group>
// second
inline constexpr double second = 1.0;
// minute
inline constexpr double minute = 60.0;
// hour
inline constexpr double hour = 3600.0;
// day
inline constexpr double day = 86400.0;
// Difference between Julian Day and Modified Julian Day
inline constexpr double MJD0 = 2400000.5;
// </group>
 
}  // namespace C
 
}  // namespace casacore
 
#endif