Mathematical constants

[Constant]LAL_REAL4_MANT [Constant]LAL_REAL4_MAX [Constant]LAL_REAL4_MIN [Constant]LAL_REAL4_EPS [Constant]LAL_REAL8_MANT [Constant]LAL_REAL8_MAX [Constant]LAL_REAL8_MIN [Constant]LAL_REAL8_EPS [Constant]LAL_E [Constant]LAL_LOG2E [Constant]LAL_LOG10E [Constant]LAL_LN2 [Constant]LAL_LN10 [Constant]LAL_SQRT2 [Constant]LAL_SQRT1_2 [Constant]LAL_GAMMA [Constant]LAL_PI [Constant]LAL_TWOPI [Constant]LAL_PI_2 [Constant]LAL_PI_4 [Constant]LAL_1_PI [Constant]LAL_2_PI [Constant]LAL_2_SQRTPI [Constant]LAL_PI_180 [Constant]LAL_180_PI

The following constants define the precision and range of floating-point arithmetic in LAL. They are taken from the IEEE standard 754 for binary arithmetic. All numbers are dimensionless.

Name	Value	Description
LAL_REAL4_MANT	24	Bits in REAL4 mantissa
LAL_REAL4_MAX	$3.40282347\times10^{38}$	Largest REAL4
LAL_REAL4_MIN	$1.17549435\times10^{-38}$	Smallest positive REAL4
LAL_REAL4_EPS	$1.19209290\times10^{-7}$	$2^{-(\mathtt{LAL\_REAL4\_MANT}-1)}$
LAL_REAL8_MANT	53	Bits in REAL8 mantissa
LAL_REAL8_MAX	$1.7976931348623157\times10^{308}$	Largest REAL8
LAL_REAL8_MIN	$2.2250738585072014\times10^{-308}$	Smallest positive REAL8
LAL_REAL8_EPS	$2.2204460492503131\times10^{-16}$	$2^{-(\mathtt{LAL\_REAL8\_MANT}-1)}$

LAL_REAL4_EPS and LAL_REAL8_EPS can be thought of as the difference between 1 and the next representable REAL4 or REAL8 number.

The following are fundamental mathematical constants. They are mostly taken from the GNU C math.h header (with the exception of LAL_TWOPI, which was computed using Maple). All numbers are dimensionless.

Name	Value	Expression
LAL_E	2.7182818284590452353602874713526625	$e$
LAL_LOG2E	1.4426950408889634073599246810018922	$\log_2 e$
LAL_LOG10E	0.4342944819032518276511289189166051	$\log_{10} e$
LAL_LN2	0.6931471805599453094172321214581766	$\log_e 2$
LAL_LN10	2.3025850929940456840179914546843642	$\log_e 10$
LAL_SQRT2	1.4142135623730950488016887242096981	$\sqrt{2}$
LAL_SQRT1_2	0.7071067811865475244008443621048490	$1/\sqrt{2}$
LAL_GAMMA	0.5772156649015328606065120900824024	$\gamma$
LAL_PI	3.1415926535897932384626433832795029	$\pi$
LAL_TWOPI	6.2831853071795864769252867665590058	$2\pi$
LAL_PI_2	1.5707963267948966192313216916397514	$\pi/2$
LAL_PI_4	0.7853981633974483096156608458198757	$\pi/4$
LAL_1_PI	0.3183098861837906715377675267450287	$1/\pi$
LAL_2_PI	0.6366197723675813430755350534900574	$2/\pi$
LAL_2_SQRTPI	1.1283791670955125738961589031215452	$2/\sqrt{\pi}$
LAL_PI_180	1.7453292519943295769236907684886127$\times10^{-2}$	$\pi/180$
LAL_180_PI	57.295779513082320876798154814105170	$180/\pi$