Inferring array index type from array object
in [ADA]
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From: Warren on 30 Jun 2010 12:43 Adam Beneschan expounded in news:102a43e8-21ea-4606-8b0d-6d492f9e07f8 @v13g2000prn.googlegroups.com: > On Jun 29, 2:00�pm, Warren <ve3...(a)gmail.com> wrote: >> Warren expounded >> > Adam Beneschan expounded >> > @b4g2000pra.googlegroups.com: ... >> >> Isn't that just 1.0 / X? � >> >> > Ok, it seems to be, as the GSL (Gnu Scientific Library) >> > defines it as: >> >> > gsl_complex >> > gsl_complex_inverse (gsl_complex a) >> > { � � � � � � � � � � � � � � � /* z=1/ > a */ >> > � double s = 1.0 / gsl_complex_abs (a); >> >> > � gsl_complex z; >> > � GSL_SET_COMPLEX (&z, (GSL_REAL (a) * s) * s, -(GSL_IMAG (a) * s) * >> s); >> > � return z; >> > } >> >> gsl_complex >> gsl_complex_div (gsl_complex a, gsl_complex b) >> { � � � � � � � � � � � � � � � /* z=a/b > */ >> � double ar = GSL_REAL (a), ai = GSL_IMAG (a); >> � double br = GSL_REAL (b), bi = GSL_IMAG (b); >> >> � double s = 1.0 / gsl_complex_abs (b); >> >> � double sbr = s * br; >> � double sbi = s * bi; >> >> � double zr = (ar * sbr + ai * sbi) * s; >> � double zi = (ai * sbr - ar * sbi) * s; >> >> � gsl_complex z; >> � GSL_SET_COMPLEX (&z, zr, zi); >> � return z; >> >> } >> >> Given a=1.0, the inverse function is definitely >> higher performance. �It's simpler calculation >> probably implies more accuracy as well. > > That last makes no sense to me. The code to compute A / Z for real A > has got to be essentially the same as computing 1.0 / Z and then > multiplying the real and imaginary parts of the result by A---how else > would it be done? So while you might gain slightly in efficiency by > not performing an extra step, I don't see how you can gain in > accuracy---I've never heard of accuracy ever getting lost by > multiplying a floating-point number by 1.0. I'll concede your accuracy point. Efficiency however is still important for some applications, like realtime signal processing. Warren |