Common Pipeline Library Reference Manual 6.0
Defines

Fundamental math functionality

Defines

#define CPL_MATH_1_PI   0.3183098861837906715377675267450287240689192914809129
 1/pi
#define CPL_MATH_2_PI   0.6366197723675813430755350534900574481378385829618258
 2/pi
#define CPL_MATH_2_SQRTPI   1.1283791670955125738961589031215451716881012586579977
 2/sqrt(pi)
#define CPL_MATH_2PI   6.2831853071795864769252867665590057683943387987502116
 2 pi
#define CPL_MATH_4_PI   1.2732395447351626861510701069801148962756771659236516
 4/pi
#define CPL_MATH_DEG_RAD   57.295779513082320876798154814105170332405472466564322
 180/pi
#define CPL_MATH_E   2.7182818284590452353602874713526624977572470936999595
 The base of the exponential function.
#define CPL_MATH_FWHM_SIG   2.3548200450309493820231386529193992754947713787716411
 FWHM per Sigma, 2.0*sqrt(2.0*log(2.0))
#define CPL_MATH_LN10   2.3025850929940456840179914546843642076011014886287730
 The natural logarithm of 10.
#define CPL_MATH_LN2   0.6931471805599453094172321214581765680755001343602553
 The natural logarithm of 2.
#define CPL_MATH_LOG10E   0.4342944819032518276511289189166050822943970058036666
 log10(e)
#define CPL_MATH_LOG2E   1.4426950408889634073599246810018921374266459541529859
 log2(e)
#define CPL_MATH_PI   3.1415926535897932384626433832795028841971693993751058
 The ratio of a circles circumference to its diameter.
#define CPL_MATH_PI_2   1.5707963267948966192313216916397514420985846996875529
 pi/2
#define CPL_MATH_PI_4   0.7853981633974483096156608458198757210492923498437765
 pi/4
#define CPL_MATH_RAD_DEG   0.0174532925199432957692369076848861271344287188854173
 pi/180
#define CPL_MATH_SIG_FWHM   0.4246609001440095213607514170514448098575705468921770
 Sigma per FWHM, 0.5/sqrt(2.0*log(2.0))
#define CPL_MATH_SQRT1_2   0.7071067811865475244008443621048490392848359376884740
 sqrt(1/2)
#define CPL_MATH_SQRT2   1.4142135623730950488016887242096980785696718753769481
 The square root of 2.
#define CPL_MATH_SQRT2PI   2.5066282746310005024157652848110452530069867406099383
 sqrt(2pi)
#define CPL_MATH_SQRT3   1.7320508075688772935274463415058723669428052538103806
 The square root of 3.

Detailed Description

This module provides fundamental math constants.

Source: On-Line Encyclopedia of Integer Sequences (OEIS)

pi: http://www.research.att.com/~njas/sequences/A000796

e: http://www.research.att.com/~njas/sequences/A001113

ln(2): http://www.research.att.com/~njas/sequences/A002162

ln(10): http://www.research.att.com/~njas/sequences/A002392

sqrt(2): http://www.research.att.com/~njas/sequences/A002193

sqrt(3): http://www.research.att.com/~njas/sequences/A002194

The derived constants have been computed with the GNU Multiple-Precision Library v. 4.2.2.

The constants are listed with a precision that allows a one-line definition.

Synopsis:
   #include <cpl_math_const.h>

Define Documentation

#define CPL_MATH_1_PI   0.3183098861837906715377675267450287240689192914809129

1/pi

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_2_PI   0.6366197723675813430755350534900574481378385829618258

2/pi

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_2_SQRTPI   1.1283791670955125738961589031215451716881012586579977

2/sqrt(pi)

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_2PI   6.2831853071795864769252867665590057683943387987502116

2 pi

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_4_PI   1.2732395447351626861510701069801148962756771659236516

4/pi

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_DEG_RAD   57.295779513082320876798154814105170332405472466564322

180/pi

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_E   2.7182818284590452353602874713526624977572470936999595

The base of the exponential function.

See also:
On-Line Encyclopedia of Integer Sequences (OEIS), http://www.research.att.com/~njas/sequences/A001113
#define CPL_MATH_FWHM_SIG   2.3548200450309493820231386529193992754947713787716411

FWHM per Sigma, 2.0*sqrt(2.0*log(2.0))

See also:
CPL_MATH_LN2
Note:
Derived from a fundamental constant
#define CPL_MATH_LN10   2.3025850929940456840179914546843642076011014886287730

The natural logarithm of 10.

See also:
On-Line Encyclopedia of Integer Sequences (OEIS), http://www.research.att.com/~njas/sequences/A002392
#define CPL_MATH_LN2   0.6931471805599453094172321214581765680755001343602553

The natural logarithm of 2.

See also:
On-Line Encyclopedia of Integer Sequences (OEIS), http://www.research.att.com/~njas/sequences/A002162
#define CPL_MATH_LOG10E   0.4342944819032518276511289189166050822943970058036666

log10(e)

See also:
CPL_MATH_LN10
Note:
Derived from a fundamental constant
#define CPL_MATH_LOG2E   1.4426950408889634073599246810018921374266459541529859

log2(e)

See also:
CPL_MATH_LN2
Note:
Derived from a fundamental constant
#define CPL_MATH_PI   3.1415926535897932384626433832795028841971693993751058

The ratio of a circles circumference to its diameter.

See also:
On-Line Encyclopedia of Integer Sequences (OEIS), http://www.research.att.com/~njas/sequences/A000796
#define CPL_MATH_PI_2   1.5707963267948966192313216916397514420985846996875529

pi/2

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_PI_4   0.7853981633974483096156608458198757210492923498437765

pi/4

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_RAD_DEG   0.0174532925199432957692369076848861271344287188854173

pi/180

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_SIG_FWHM   0.4246609001440095213607514170514448098575705468921770

Sigma per FWHM, 0.5/sqrt(2.0*log(2.0))

See also:
CPL_MATH_LN2
Note:
Derived from a fundamental constant
#define CPL_MATH_SQRT1_2   0.7071067811865475244008443621048490392848359376884740

sqrt(1/2)

See also:
CPL_MATH_SQRT2
Note:
Derived from a fundamental constant
#define CPL_MATH_SQRT2   1.4142135623730950488016887242096980785696718753769481

The square root of 2.

See also:
On-Line Encyclopedia of Integer Sequences (OEIS), http://www.research.att.com/~njas/sequences/A002193
#define CPL_MATH_SQRT2PI   2.5066282746310005024157652848110452530069867406099383

sqrt(2pi)

See also:
CPL_MATH_PI
Note:
Derived from a fundamental constant
#define CPL_MATH_SQRT3   1.7320508075688772935274463415058723669428052538103806

The square root of 3.

See also:
On-Line Encyclopedia of Integer Sequences (OEIS), http://www.research.att.com/~njas/sequences/A002194