HPL_dlamch(3)

💖 HPL_dlamch — it's giving machine-constants energy 💖

okay bestie, welcome to HPL_dlamch(3), straight out of the HPL Library Functions collection. this one's a little diva that pulls machine-specific arithmetic constants out of thin air (well, out of your hardware). let's get into it 🫶

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✨ NAME ✨

HPL_dlamch — determines machine-specific arithmetic constants. that's it, that's the job, and she does it flawlessly 💅

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🌸 SYNOPSIS 🌸

#include "hpl.h"

double HPL_dlamch( const HPL_T_MACH CMACH );

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🦋 DESCRIPTION 🦋

so like, HPL_dlamch determines machine-specific arithmetic constants. we're talking the relative machine precision (eps), the safe minimum (sfmin) — and bestie, the whole point of sfmin is that 1 / sfmin does not overflow, iconic — 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, no in-between, we don't do nuance), the minimum exponent before (gradual) underflow (emin), the underflow threshold (rmin) which is base**(emin-1), the largest exponent before overflow (emax), and the overflow threshold (rmax) which is (base**emax)*(1-eps).

literally a whole glow-up for your floating-point math 🌈

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👑 ARGUMENTS 👑

• CMACH — (local input) const HPL_T_MACH. this lil parameter specifies the value to be returned by HPL_dlamch, and honestly she's the main character:
  • = HPL_MACH_EPS, HPL_dlamch := eps (default — the vibe when you don't specify)
  • = 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, for the girlies keeping score at home:

• 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.

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🎀 EXAMPLE 🎀

look at her go, a whole working program, periodt:

#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);
}

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📚 REFERENCES 📚

ngl this function has lore. it was manually translated from the Fortran 77 LAPACK auxiliary function dlamch.f (version 2.0 -- 1992), which was itself based on the function ENVRON by Malcolm, and it 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).

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fr fr, the math here is real and the translation is faithful — treat these constants with the respect they deserve 💀

HPL 2.2 · February 24, 2016 — okay that's the whole page bestie, go forth and compute your machine constants, slay ✨💖🦋🌸💅🫶