internal API

The internal package holds the machine constants that the other packages use to choose step sizes and to bound roundoff error. It contains no functions. The constants are those of gsl_machine.h in the GNU Scientific Library.

Machine constants

Every constant is a Double named machine_<prefix><quantity>. The quantity names a limit of a floating-point format:

Quantity	Meaning
dbl_epsilon	The machine epsilon of double precision, $2^{-52} \approx 2.22 \cdot 10^{-16}$.
dbl_min	The smallest positive normal double, $\approx 2.23 \cdot 10^{-308}$.
dbl_max	The largest finite double, $\approx 1.80 \cdot 10^{308}$.
flt_epsilon	The machine epsilon of single precision, $2^{-23}$.
flt_min	The smallest positive normal single-precision value.
flt_max	The largest finite single-precision value.
sflt_epsilon	The machine epsilon of the short float format of GSL, $2^{-11}$.
eps	The rounded machine tolerances of GSL_MACH_EPS, which exist only with a prefix.

The prefix names a function of that quantity:

Prefix	Value	Available for
none	the quantity itself	dbl_*, flt_*, sflt_epsilon
sqrt_	its square root	all quantities
root_3_ to root_6_	its third to sixth root	all quantities
log_	its natural logarithm	all quantities

For example, machine_sqrt_dbl_epsilon is $\sqrt{\varepsilon} \approx 1.49 \cdot 10^{-8}$ and machine_log_dbl_max is $\ln(\text{dbl\_max}) \approx 709.78$. The rounded eps values are machine_sqrt_eps ($3.2 \cdot 10^{-8}$), machine_root_3_eps ($10^{-5}$), machine_root_4_eps ($1.78 \cdot 10^{-4}$), machine_root_5_eps ($10^{-3}$), machine_root_6_eps ($3.16 \cdot 10^{-3}$) and machine_log_eps ($-34.54$).