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:

casa/BasicSL/Constants.h