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
const Double minfloat
the minimum single precision floating point number, including denormalised numbers
const Double flt_epsilon
Minimum single precision floating point number X such that 1+X does not equal X.
const Double flt_min
Machine constants.
const Double dbl_max
the maximum double precision floating point number
const Double flt_max
the maximum single precision floating point number
const Double dbl_epsilon
Minimum double precision floating point number X such that 1+X does not equal X.
const Double mindouble
the minimum double precision floating point number, including denormalised numbers
const Double dbl_min
the minimum double precision floating point number, excluding denormalised numbers
Irrationals
const Double sqrt2
Mathematical constants.
const Double _1_sqrt3
1/sqrt(3)
const Double _1_sqrt2
1/sqrt(2)
const Double sqrt3
sqrt(3)
LatticeExprNode sqrt(const LatticeExprNode &expr)
Pi and functions thereof
const Double pi
Pi and functions thereof:
const Double _1_sqrtpi
1/sqrt(pi)
const Double _2_sqrtpi
2/sqrt(pi)
e and functions thereof
const Double log2e
log2(e)
const Double log10e
log10(e)
const Double e
e and functions thereof:
LatticeExprNode log10(const LatticeExprNode &expr)
gamma and functions thereof
const Double gamma
gamma and functions thereof:
const Double etogamma
e**gamma
const Double lngamma
ln(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)
const Double c
Fundamental physical constants (SI units):
Numerical conversion factors
const Double deka
e+01 (da)
const Double mega
e+06 (M)
const Double micro
e-06 (u)
const Double hecto
e+02 (h)
const Double milli
e-03 (m)
const Double kilo
e+03 (k)
const Double zepto
e-21 (z)
const Double yocto
e-24 (y)
const Double centi
e-02 (c)
const Double peta
e+15 (P)
const Double tera
e+12 (T)
const Double yotta
Numerical conversion factors.
const Double zetta
e+21 (Z)
const Double femto
e-15 (f)
const Double atto
e-18 (a)
const Double pico
e-12 (p)
const Double deci
e-01 (d)
const Double nano
e-09 (n)
const Double giga
e+09 (G)
Angular measure
const Double circle
circle
const Double arcmin
arcminute
const Double degree
degree
const Double radian
Angular measure:
const Double arcsec
arcsecond
Solid angular measure
const Double steradian
Solid angular measure:
const Double square_arcsec
square arcsecond
const Double square_arcmin
square arcminute
const Double square_degree
square degree
const Double sphere
sphere
TableExprNode square(const TableExprNode &node)
Time interval
const Double minute
minute
const Double second
Time interval [T]:
TableExprNode day(const TableExprNode &node)
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 3.2
c, 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'.
LatticeExprNode value(const LatticeExprNode &expr)
This function returns the value of the expression without a mask.
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
DBL_EPSILON 1E-9 1.0 + X does not equal 1.0.
LDBL_EPSILON 1E-9
FLT_MIN 1E-37 Minimum normalized positive floating point
DBL_MIN 1E-37 number
LDBL_MIN 1E-37
FLT_MAX 1E+37 Maximum representable floating point number.
DBL_MAX 1E+37
LDBL_MAX 1E+37
TableExprNode integer(const TableExprNode &node)
Convert double, bool, or string to int (using floor).
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).
implementations, 0x7FFF = 32767).
implementations, 0x7FFFFFFF = 2147483647).
the same as MAXSHORT or MAXLONG).
MINFLOAT Minimum positive
value of a single-precision
to this)
MINDOUBLE Minimum positive
value of a
double-precision
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.
