Variables
constexpr double	sqrt2
	Mathematical constants.

constexpr double	sqrt3
	sqrt(3)

constexpr double	_1_sqrt2
	1/sqrt(2)

constexpr double	_1_sqrt3
	1/sqrt(3)

constexpr double	pi
	Pi and functions thereof:

constexpr double	_2pi
	2*pi

constexpr double	pi_2
	pi/2

constexpr double	pi_4
	pi/4

constexpr double	_1_pi
	1/pi

constexpr double	_2_pi
	2/pi

constexpr double	_1_sqrtpi
	1/sqrt(pi)

constexpr double	_2_sqrtpi
	2/sqrt(pi)

constexpr double	e
	e and functions thereof:

constexpr double	ln2
	ln(2)

constexpr double	ln10
	ln(10)

constexpr double	log2e
	log2(e)

constexpr double	log10e
	log10(e)

constexpr double	gamma
	gamma and functions thereof:

constexpr double	lngamma
	ln(gamma) With C++20, could be deprecated and use std::log(std::numbers::gamma) instead

constexpr double	etogamma
	e**gamma With C++20, could be deprecated and use std::exp(std::numbers::gamma) instead

constexpr double	probit_3_4
	statistics related 1/(Phi^(-1)(3/4), see https://en.wikipedia.org/wiki/Median_absolute_deviation#Relation_to_standard_deviation

constexpr double	flt_min
	Machine constants.

constexpr double	minfloat
	the minimum single precision floating point number, including denormalised numbers

constexpr double	dbl_min
	the minimum double precision floating point number, excluding denormalised numbers

constexpr double	mindouble
	the minimum double precision floating point number, including denormalised numbers

constexpr double	flt_max
	the maximum single precision floating point number

constexpr double	dbl_max
	the maximum double precision floating point number

constexpr double	flt_epsilon
	Minimum single precision floating point number X such that 1+X does not equal X.

constexpr double	dbl_epsilon
	Minimum double precision floating point number X such that 1+X does not equal X.

constexpr double	c
	Fundamental physical constants (SI units):

constexpr double	quetta
	Numerical conversion factors.

constexpr double	ronna
	e+27 (R)

constexpr double	yotta
	e+24 (Y)

constexpr double	zetta
	e+21 (Z)

constexpr double	exa
	e+18 (E)

constexpr double	peta
	e+15 (P)

constexpr double	tera
	e+12 (T)

constexpr double	giga
	e+09 (G)

constexpr double	mega
	e+06 (M)

constexpr double	kilo
	e+03 (k)

constexpr double	hecto
	e+02 (h)

constexpr double	deka
	e+01 (da)

constexpr double	deci
	e-01 (d)

constexpr double	centi
	e-02 (c)

constexpr double	milli
	e-03 (m)

constexpr double	micro
	e-06 (u)

constexpr double	nano
	e-09 (n)

constexpr double	pico
	e-12 (p)

constexpr double	femto
	e-15 (f)

constexpr double	atto
	e-18 (a)

constexpr double	zepto
	e-21 (z)

constexpr double	yocto
	e-24 (y)

constexpr double	ronto
	e-27 (r)

constexpr double	quecto
	e-30 (q)

constexpr double	radian
	Angular measure:

constexpr double	circle
	circle

constexpr double	degree
	degree

constexpr double	arcmin
	arcminute

constexpr double	arcsec
	arcsecond

constexpr double	steradian
	Solid angular measure:

constexpr double	sphere
	sphere

constexpr double	square_degree
	square degree

constexpr double	square_arcmin
	square arcminute

constexpr double	square_arcsec
	square arcsecond

constexpr double	second
	Time interval [T]:

constexpr double	minute
	minute

constexpr double	hour
	hour

constexpr double	day
	day

constexpr double	MJD0
	Difference between Julian Day and Modified Julian Day.

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)

casacore::C::c

constexpr double c

Fundamental physical constants (SI units):

Definition Constants.h:480

Numerical conversion factors

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)

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.

Variable Documentation

◆ _1_pi

constexpr double casacore::C::_1_pi

inlineconstexpr

1/pi

Definition at line 375 of file Constants.h.

◆ _1_sqrt2

constexpr double casacore::C::_1_sqrt2

inlineconstexpr

1/sqrt(2)

Definition at line 354 of file Constants.h.

◆ _1_sqrt3

constexpr double casacore::C::_1_sqrt3

inlineconstexpr

1/sqrt(3)

Definition at line 356 of file Constants.h.

◆ _1_sqrtpi

constexpr double casacore::C::_1_sqrtpi

inlineconstexpr

1/sqrt(pi)

Definition at line 381 of file Constants.h.

◆ _2_pi

constexpr double casacore::C::_2_pi

inlineconstexpr

2/pi

Definition at line 378 of file Constants.h.

◆ _2_sqrtpi

constexpr double casacore::C::_2_sqrtpi

inlineconstexpr

2/sqrt(pi)

Definition at line 384 of file Constants.h.

◆ _2pi

constexpr double casacore::C::_2pi

inlineconstexpr

2*pi

Definition at line 366 of file Constants.h.

◆ arcmin

constexpr double casacore::C::arcmin

inlineconstexpr

arcminute

Definition at line 561 of file Constants.h.

◆ arcsec

constexpr double casacore::C::arcsec

inlineconstexpr

arcsecond

Definition at line 563 of file Constants.h.

◆ atto

constexpr double casacore::C::atto

inlineconstexpr

e-18 (a)

Definition at line 541 of file Constants.h.

◆ c

constexpr double casacore::C::c

inlineconstexpr

Fundamental physical constants (SI units):

velocity of light – for legacy reasons only – refer to PC

Definition at line 480 of file Constants.h.

Referenced by casacore::QC::c(), and casacore::QC::epsilon0().

◆ centi

constexpr double casacore::C::centi

inlineconstexpr

e-02 (c)

Definition at line 529 of file Constants.h.

◆ circle

constexpr double casacore::C::circle

inlineconstexpr

circle

Definition at line 557 of file Constants.h.

◆ day

constexpr double casacore::C::day

inlineconstexpr

day

Definition at line 600 of file Constants.h.

◆ dbl_epsilon

constexpr double casacore::C::dbl_epsilon

inlineconstexpr

Minimum double precision floating point number X such that 1+X does not equal X.

Definition at line 464 of file Constants.h.

◆ dbl_max

constexpr double casacore::C::dbl_max

inlineconstexpr

the maximum double precision floating point number

Definition at line 456 of file Constants.h.

◆ dbl_min

constexpr double casacore::C::dbl_min

inlineconstexpr

the minimum double precision floating point number, excluding denormalised numbers

Definition at line 446 of file Constants.h.

◆ deci

constexpr double casacore::C::deci

inlineconstexpr

e-01 (d)

Definition at line 527 of file Constants.h.

◆ degree

constexpr double casacore::C::degree

inlineconstexpr

degree

Definition at line 559 of file Constants.h.

◆ deka

constexpr double casacore::C::deka

inlineconstexpr

e+01 (da)

Definition at line 525 of file Constants.h.

◆ e

constexpr double casacore::C::e

inlineconstexpr

e and functions thereof:

e

Definition at line 391 of file Constants.h.

◆ etogamma

constexpr double casacore::C::etogamma

inlineconstexpr

e**gamma With C++20, could be deprecated and use std::exp(std::numbers::gamma) instead

Definition at line 416 of file Constants.h.

◆ exa

constexpr double casacore::C::exa

inlineconstexpr

e+18 (E)

Definition at line 511 of file Constants.h.

◆ femto

constexpr double casacore::C::femto

inlineconstexpr

e-15 (f)

Definition at line 539 of file Constants.h.

◆ flt_epsilon

constexpr double casacore::C::flt_epsilon

inlineconstexpr

Minimum single precision floating point number X such that 1+X does not equal X.

Definition at line 460 of file Constants.h.

◆ flt_max

constexpr double casacore::C::flt_max

inlineconstexpr

the maximum single precision floating point number

Definition at line 453 of file Constants.h.

◆ flt_min

constexpr double casacore::C::flt_min

inlineconstexpr

Machine constants.

floating point limits

the minimum single precision floating point number, excluding denormalised numbers

Definition at line 438 of file Constants.h.

◆ gamma

constexpr double casacore::C::gamma

inlineconstexpr

gamma and functions thereof:

gamma With C++20, could be deprecated and use std::numbers::gamma instead

Definition at line 410 of file Constants.h.

◆ giga

constexpr double casacore::C::giga

inlineconstexpr

e+09 (G)

Definition at line 517 of file Constants.h.

◆ hecto

constexpr double casacore::C::hecto

inlineconstexpr

e+02 (h)

Definition at line 523 of file Constants.h.

◆ hour

constexpr double casacore::C::hour

inlineconstexpr

hour

Definition at line 598 of file Constants.h.

◆ kilo

constexpr double casacore::C::kilo

inlineconstexpr

e+03 (k)

Definition at line 521 of file Constants.h.

◆ ln10

constexpr double casacore::C::ln10

inlineconstexpr

ln(10)

Definition at line 397 of file Constants.h.

◆ ln2

constexpr double casacore::C::ln2

inlineconstexpr

ln(2)

Definition at line 394 of file Constants.h.

◆ lngamma

constexpr double casacore::C::lngamma

inlineconstexpr

ln(gamma) With C++20, could be deprecated and use std::log(std::numbers::gamma) instead

Definition at line 413 of file Constants.h.

◆ log10e

constexpr double casacore::C::log10e

inlineconstexpr

log10(e)

Definition at line 403 of file Constants.h.

◆ log2e

constexpr double casacore::C::log2e

inlineconstexpr

log2(e)

Definition at line 400 of file Constants.h.

◆ mega

constexpr double casacore::C::mega

inlineconstexpr

e+06 (M)

Definition at line 519 of file Constants.h.

◆ micro

constexpr double casacore::C::micro

inlineconstexpr

e-06 (u)

Definition at line 533 of file Constants.h.

◆ milli

constexpr double casacore::C::milli

inlineconstexpr

e-03 (m)

Definition at line 531 of file Constants.h.

◆ mindouble

constexpr double casacore::C::mindouble

inlineconstexpr

the minimum double precision floating point number, including denormalised numbers

Definition at line 450 of file Constants.h.

◆ minfloat

constexpr double casacore::C::minfloat

inlineconstexpr

the minimum single precision floating point number, including denormalised numbers

Definition at line 442 of file Constants.h.

◆ minute

constexpr double casacore::C::minute

inlineconstexpr

minute

Definition at line 596 of file Constants.h.

◆ MJD0

constexpr double casacore::C::MJD0

inlineconstexpr

Difference between Julian Day and Modified Julian Day.

Definition at line 602 of file Constants.h.

◆ nano

constexpr double casacore::C::nano

inlineconstexpr

e-09 (n)

Definition at line 535 of file Constants.h.

◆ peta

constexpr double casacore::C::peta

inlineconstexpr

e+15 (P)

Definition at line 513 of file Constants.h.

◆ pi

constexpr double casacore::C::pi

inlineconstexpr

Pi and functions thereof:

pi

Definition at line 363 of file Constants.h.

◆ pi_2

constexpr double casacore::C::pi_2

inlineconstexpr

pi/2

Definition at line 369 of file Constants.h.

Referenced by casacore::Fit2D::paFromGauss2D(), and casacore::Fit2D::paToGauss2D().

◆ pi_4

constexpr double casacore::C::pi_4

inlineconstexpr

pi/4

Definition at line 372 of file Constants.h.

◆ pico

constexpr double casacore::C::pico

inlineconstexpr

e-12 (p)

Definition at line 537 of file Constants.h.

◆ probit_3_4

constexpr double casacore::C::probit_3_4

inlineconstexpr

statistics related 1/(Phi^(-1)(3/4), see https://en.wikipedia.org/wiki/Median_absolute_deviation#Relation_to_standard_deviation

Definition at line 421 of file Constants.h.

◆ quecto

constexpr double casacore::C::quecto

inlineconstexpr

e-30 (q)

Definition at line 549 of file Constants.h.

◆ quetta

constexpr double casacore::C::quetta

inlineconstexpr

Numerical conversion factors.

e+30 (Q)

Definition at line 503 of file Constants.h.

◆ radian

constexpr double casacore::C::radian

inlineconstexpr

Angular measure:

radian

Definition at line 555 of file Constants.h.

◆ ronna

constexpr double casacore::C::ronna

inlineconstexpr

e+27 (R)

Definition at line 505 of file Constants.h.

◆ ronto

constexpr double casacore::C::ronto

inlineconstexpr

e-27 (r)

Definition at line 547 of file Constants.h.

◆ second

constexpr double casacore::C::second

inlineconstexpr

Time interval [T]:

second

Definition at line 594 of file Constants.h.

◆ sphere

constexpr double casacore::C::sphere

inlineconstexpr

sphere

Definition at line 571 of file Constants.h.

◆ sqrt2

constexpr double casacore::C::sqrt2

inlineconstexpr

Mathematical constants.

Irrationals:

sqrt(2)

Definition at line 349 of file Constants.h.

◆ sqrt3

constexpr double casacore::C::sqrt3

inlineconstexpr

sqrt(3)

Definition at line 351 of file Constants.h.

◆ square_arcmin

constexpr double casacore::C::square_arcmin

inlineconstexpr

square arcminute

Definition at line 575 of file Constants.h.

◆ square_arcsec

constexpr double casacore::C::square_arcsec

inlineconstexpr

square arcsecond

Definition at line 577 of file Constants.h.

◆ square_degree

constexpr double casacore::C::square_degree

inlineconstexpr

square degree

Definition at line 573 of file Constants.h.

◆ steradian

constexpr double casacore::C::steradian

inlineconstexpr

Solid angular measure:

steradian

Definition at line 569 of file Constants.h.

◆ tera

constexpr double casacore::C::tera

inlineconstexpr

e+12 (T)

Definition at line 515 of file Constants.h.

◆ yocto

constexpr double casacore::C::yocto

inlineconstexpr

e-24 (y)

Definition at line 545 of file Constants.h.

◆ yotta

constexpr double casacore::C::yotta

inlineconstexpr

e+24 (Y)

Definition at line 507 of file Constants.h.

◆ zepto

constexpr double casacore::C::zepto

inlineconstexpr

e-21 (z)

Definition at line 543 of file Constants.h.

◆ zetta

constexpr double casacore::C::zetta

inlineconstexpr

e+21 (Z)

Definition at line 509 of file Constants.h.

Variables

Detailed Description

Intended use:

Review Status

Synopsis

Floating point limits

Irrationals

Pi and functions thereof

e and functions thereof

gamma and functions thereof

Fundamental physical constants (SI units)

Numerical conversion factors

Angular measure

Solid angular measure

Time interval

Machine constants

Constants defined in limits.h

Constants defined in float.h

Constants defined in values.h

Variable Documentation

◆ _1_pi

◆ _1_sqrt2

◆ _1_sqrt3

◆ _1_sqrtpi

◆ _2_pi

◆ _2_sqrtpi

◆ _2pi

◆ arcmin

◆ arcsec

◆ atto

◆ c

◆ centi

◆ circle

◆ day

◆ dbl_epsilon

◆ dbl_max

◆ dbl_min

◆ deci

◆ degree

◆ deka

◆ e

◆ etogamma

◆ exa

◆ femto

◆ flt_epsilon

◆ flt_max

◆ flt_min

◆ gamma

◆ giga

◆ hecto

◆ hour

◆ kilo

◆ ln10

◆ ln2

◆ lngamma

◆ log10e

◆ log2e

◆ mega

◆ micro

◆ milli

◆ mindouble

◆ minfloat

◆ minute

◆ MJD0

◆ nano

◆ peta

◆ pi

◆ pi_2

◆ pi_4

◆ pico

◆ probit_3_4

◆ quecto

◆ quetta

◆ radian

◆ ronna

◆ ronto

◆ second

◆ sphere

◆ sqrt2

◆ sqrt3