Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Michael S <already5chosen@yahoo.com>
Newsgroups: comp.lang.c,comp.arch
Subject: Re: Radians Or Degrees?
Date: Sun, 17 Mar 2024 11:06:21 +0200
Organization: A noiseless patient Spider
Lines: 126
Message-ID: <20240317110621.00005b30@yahoo.com>
References: <ur5trn$3d64t$1@dont-email.me>
	<ur5v05$3ccut$1@dont-email.me>
	<20240222015920.00000260@yahoo.com>
	<ur69j9$3ftgj$3@dont-email.me>
	<ur86eg$1aip$1@dont-email.me>
	<ur88e4$1rr1$5@dont-email.me>
	<ur8a2p$2446$1@dont-email.me>
	<ur8ctk$2vbd$2@dont-email.me>
	<20240222233838.0000572f@yahoo.com>
	<3b2e86cdb0ee8785b4405ab10871c5ca@www.novabbs.org>
	<ur8nud$4n1r$1@dont-email.me>
	<936a852388e7e4414cb7e529da7095ea@www.novabbs.org>
	<ur9qtp$fnm9$1@dont-email.me>
	<20240314112655.000011f8@yahoo.com>
	<ut17ji$27n6b$1@dont-email.me>
	<ut2csb$2fe4u$1@dont-email.me>
	<87wmq32o26.fsf@nosuchdomain.example.com>
	<8de6385435bbdb0695a7ff213653f345@www.novabbs.org>
	<20240316190815.000005a2@yahoo.com>
	<dbfb682bf2abb9b84ce04c257a85c6d1@www.novabbs.org>
	<87o7bd3guo.fsf@nosuchdomain.example.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
Injection-Info: dont-email.me; posting-host="fd62a22e31fcf9828d4eedf77229489a";
	logging-data="3610420"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX1+umJXZUvEfJIlsxkJ95KUoblO5a/X+18o="
Cancel-Lock: sha1:X3zIjhlTrqcKat/kX9jHPA5IdxA=
X-Newsreader: Claws Mail 3.19.1 (GTK+ 2.24.33; x86_64-w64-mingw32)
Bytes: 6268

On Sat, 16 Mar 2024 16:19:11 -0700
Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote:

> mitchalsup@aol.com (MitchAlsup1) writes:
> > 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 ASCII)?
>=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
> #include <math.h>
> #include <stdio.h>
> #include <limits.h>
> #include <float.h>
> int main(void) {
>     {
>         printf("float (%zu bits, %d mantissa bits)\n", CHAR_BIT *
> sizeof (float), FLT_MANT_DIG); const float x =3D (float)(1LL<<53);
>         const float y =3D nextafterf(x, x*2);
>         printf("%.8f %.8f\n", x, sinf(x));
>         printf("%.8f %.8f\n", y, sinf(y));
>     }
>     putchar('\n');
>     {
>         printf("double (%zu bits, %d mantissa bits)\n", CHAR_BIT *
> sizeof (double), DBL_MANT_DIG); const double x =3D (double)(1LL<<53);
>         const double y =3D nextafter(x, x*2);
>         printf("%.8f %.8f\n", x, sin(x));
>         printf("%.8f %.8f\n", y, sin(y));
>     }
>     putchar('\n');
>     {
>         printf("long double (%zu bits, %d mantissa bits)\n", CHAR_BIT
> * sizeof (long double), LDBL_MANT_DIG); const long double x =3D (long
> double)(1LL<<53); const long double y =3D nextafterl(x, x*2);
>         printf("%.8Lf %.8Lf\n", x, sinl(x));
>         printf("%.8Lf %.8Lf\n", y, sinl(y));
>     }
> }
>=20
> Output:
>=20
> float (32 bits, 24 mantissa bits)
> 9007199254740992.00000000 -0.84892595
> 9007200328482816.00000000 -0.34159181
>=20
> double (64 bits, 53 mantissa bits)
> 9007199254740992.00000000 -0.84892596
> 9007199254740994.00000000 -0.12729655
>=20
> long double (128 bits, 64 mantissa bits)
> 9007199254740992.00000000 -0.84892596
> 9007199254740992.00097656 -0.84944168
>=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:

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

void foo(long double x1, long double x2)
{
  const double y1 =3D (double)sinl(x1);
  const double y2 =3D (double)sinl(x2);
  printf("%.20Le %.17f\n", x1, y1);
  printf("%.20Le %.17f\n", x2, y2);
}

int main(void) {
  const float x0 =3D (float)(1LL<<53);
  {
    printf("float (%zu bits, %d mantissa bits)\n", CHAR_BIT * sizeof
(float), FLT_MANT_DIG); const float x1 =3D x0;
    const float x2 =3D nextafterf(x1, FLT_MAX);
    foo(x1, x2);
  }
  putchar('\n');
  {
    printf("double (%zu bits, %d mantissa bits)\n", CHAR_BIT * sizeof
(double), DBL_MANT_DIG); const double x1 =3D x0;
    const double x2 =3D nextafter(x1, FLT_MAX);
    foo(x1, x2);
  }
  putchar('\n');
  {
    printf("long double (%zu bits, %d mantissa bits)\n", CHAR_BIT *
sizeof (long double), LDBL_MANT_DIG); const long double x1 =3D x0;
    const long double x2 =3D nextafterl(x1, FLT_MAX);
    foo(x1, x2);
  }
}