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From: Michael S <already5chosen@yahoo.com>
Newsgroups: comp.lang.c,comp.arch
Subject: Re: Radians Or Degrees?
Date: Sun, 17 Mar 2024 11:34:58 +0200
Organization: A noiseless patient Spider
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On Sun, 17 Mar 2024 11:06:21 +0200
Michael S <already5chosen@yahoo.com> wrote:

> On Sat, 16 Mar 2024 16:19:11 -0700
> Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote:
>=20
> > mitchalsup@aol.com (MitchAlsup1) writes: =20
> > > Michael S wrote:   =20
> > >> On Sat, 16 Mar 2024 01:16:25 +0000
> > >> mitchalsup@aol.com (MitchAlsup1) wrote:   =20
> > >>> Keith Thompson wrote:   =20
> > >>> > I can see how computing sin(x) with high precision for
> > >>> > "reasonable" values of x would be useful, but does any of that
> > >>> > benefit from being able to compute sin(2^53) accurately?   =20
> > >>> Because accurate argument reduction reduces the burden on the
> > >>> programmer to remain within his sandbox.   =20
> > >   =20
> > >> Not really.   =20
> > >
> > > Say you are a programmer and you receive a value like 2^53 from an
> > > Input read and you wan the most accurate possible SIN( of that ).
> > >   =20
> >=20
> > I can't think of a scenario where that would be useful (other than
> > just doing it for the sake of doing it).
> >=20
> > If 2^53 represents a physical quantity, how likely is the actual
> > value to be known within =C2=B1=CF=80 (+/i pi for those who prefer ASCI=
I)?
> >=20
> > If you can get better precision without too much extra cost, that's
> > great.  I don't know enough to have an opinion about what the best
> > tradeoff is, but I presume it's going to be different depending on
> > the application.
> >=20
> > Here's a C program that shows how precise sin(2^53) can be for types
> > float, double, and long double (I used gcc and glibc).  The
> > nextafter functions are used to compute the nearest representable
> > number.  For long double, the value of sin() changes by about 1
> > part in 1600, which seems decent, but it's not nearly as precise as
> > for values around 1.0. For float and double, the imprecision of the
> > argument is enough to make the result practically meaningless.
> >=20

<snip>

> >  =20
>=20
> As written, your example does not emphasize that the problem has
> nothing to do with implementation of sinX() library routine.
> It's best illustrated by followup conversation with bart, IMHO 100%
> O.T.
> To make the point more clear I'd rather change it to following form:
>=20
<snip>
>=20


BTW, personally I'd prefer to illustrate futility of Payne-Hanek or
equivalent reduction with following example:

#include <math.h>
#include <stdio.h>
#include <limits.h>
#include <float.h>

void foo(long double x)
{
  const double y =3D (double)sinl(x);
  printf("%.20Le %25.16La %.17f\n", x, x, y);
}

int main(void) {
  const float a0 =3D 0x1p56;
  const float b0 =3D 11;
  {
    printf("%-12s (%3zu bits, %d mantissa bits) ",
     "float", CHAR_BIT * sizeof (float), FLT_MANT_DIG);=20
    const float a =3D a0;
    const float b =3D b0;
    const float x =3D a / b;
    foo(x);
  }
  {
    printf("%-12s (%3zu bits, %d mantissa bits) ",=20
     "double", CHAR_BIT * sizeof (double), DBL_MANT_DIG);=20
    const double a =3D a0;
    const double b =3D b0;
    const double x =3D a / b;
    foo(x);
  }
  {
    printf("%-12s (%3zu bits, %d mantissa bits) ",
     "long double", CHAR_BIT * sizeof (long double), LDBL_MANT_DIG);
    const long double a =3D a0;=20
    const long double b =3D b0;
    const long double x =3D a / b;
    foo(x);
  }
}