NAME

HPL_dlamch - determines machine-specific arithmetic constants.

SYNOPSIS

#include "hpl.h"

double HPL_dlamch( const HPL_T_MACH CMACH );

DESCRIPTION

HPL_dlamch determines machine-specific arithmetic constants such as the relative machine precision (eps), the safe minimum (sfmin) such that 1 / sfmin does not overflow, the base of the machine (base), the precision (prec), the number of (base) digits in the mantissa (t), whether rounding occurs in addition (rnd=1.0 and 0.0 otherwise), the minimum exponent before (gradual) underflow (emin), the underflow threshold (rmin) base**(emin-1), the largest exponent before overflow (emax), the overflow threshold (rmax) (base**emax)*(1-eps).

ARGUMENTS

CMACH (local input) const HPL_T_MACH

Specifies the value to be returned by HPL_dlamch = HPL_MACH_EPS, HPL_dlamch := eps (default) = HPL_MACH_SFMIN, HPL_dlamch := sfmin = HPL_MACH_BASE, HPL_dlamch := base = HPL_MACH_PREC, HPL_dlamch := eps*base = HPL_MACH_MLEN, HPL_dlamch := t = HPL_MACH_RND, HPL_dlamch := rnd = HPL_MACH_EMIN, HPL_dlamch := emin = HPL_MACH_RMIN, HPL_dlamch := rmin = HPL_MACH_EMAX, HPL_dlamch := emax = HPL_MACH_RMAX, HPL_dlamch := rmax

where

eps = relative machine precision, sfmin = safe minimum, base = base of the machine, prec = eps*base, t = number of digits in the mantissa, rnd = 1.0 if rounding occurs in addition, emin = minimum exponent before underflow, rmin = underflow threshold, emax = largest exponent before overflow, rmax = overflow threshold.

EXAMPLE

#include "hpl.h"

int main(int argc, char *argv[])
{ double eps; eps = HPL_dlamch( HPL_MACH_EPS ); printf("eps=%18.8e\n", eps); exit(0); return(0);
}

REFERENCES

This function has been manually translated from the Fortran 77 LAPACK auxiliary function dlamch.f (version 2.0 -- 1992), that was itself based on the function ENVRON by Malcolm and incorporated suggestions by Gentleman and Marovich. See

Malcolm M. A., Algorithms to reveal properties of floating-point arithmetic., Comms. of the ACM, 15, 949-951 (1972).

Gentleman W. M. and Marovich S. B., More on algorithms that reveal properties of floating point arithmetic units., Comms. of the ACM, 17, 276-277 (1974).