casacore::Dummy_Constants_class Class Reference

Mathematical and numerical constants. More...

#include <Constants.h>

Detailed Description

Mathematical and numerical constants.

Intended use:

Public interface

Review Status

Reviewed By:: UNKNOWN
Date Reviewed:: before2004/08/25
Test programs:: tConstants

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.

Warning: The following list is generated by hand, and may be incomplete; After future revision of ccx2html the real data will be displayed

Floating point limits

 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

Irrationals

 sqrt2          sqrt(2)
 sqrt3          sqrt(3)
 _1_sqrt2               1/sqrt(2)
 _1_sqrt3               1/sqrt(3)

Pi and functions thereof

 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)

e and functions thereof

 e                    e
 ln2                  ln(2)
 ln10                 ln(10)
 log2e                log2(e)
 log10e               log10(e)

gamma and functions thereof

 gamma          gamma
 lngamma                ln(gamma)
 etogamma               e**gamma

Fundamental physical constants (SI units)

Warning: Preserved for legacy reasons only; See QC class for other physical constants;

 c                      velocity of light (m/s)

Numerical conversion factors

 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)

Angular measure

 radian         radian
 circle         circle
 degree         degree
 arcmin         arcminute
 arcsec         arcsecond

Solid angular measure

 steradian              steradian
 sphere         sphere
 square_degree  square degree
 square_arcmin  square arcminute
 square_arcsec  square arcsecond

Time interval

 second               second
 minute               minute
 hour                 hour
 day                  day

Machine constants

Implementation-defined limits usually defined in <limits.h>, <float.h>, and <values.h> as preprocessor defines. They are Inclusion of <casa/BasicSL/Constants.h is sufficient to ensure that they are defined for any particular implementation, and the correct functioning of the tConstants test program guarantees this.

In future use will be made of the (standard) numeric_limits template from the <limits> include file.

 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.

Constants defined in limits.h

(these are part of the ANSI C and hence POSIX standards). Acceptable limits defined by the standard are quoted.

 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'.

Constants defined in float.h

(these are part of the ANSI C and hence POSIX standards). Acceptable limits defined by the standard are quoted.

 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

Constants defined in values.h

(not part of the POSIX standard).
Warning: These constants will disappear in the near future; Do not use them in new code;

 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.

Tip: Once cxx2html accepts the namespace type, the Dummy_Constants_Class can be removed;
Anyway, to use a constant (e;g; pi) use the C::pi construct now and later;

Definition at line 350 of file Constants.h.

The documentation for this class was generated from the following file:

casacore/casa/BasicSL/Constants.h