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Re: Radians Or Degrees?

Cross-posted to 2 groups.

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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:
> 
> > mitchalsup@aol.com (MitchAlsup1) writes:  
> > > Michael S wrote:    
> > >> On Sat, 16 Mar 2024 01:16:25 +0000
> > >> mitchalsup@aol.com (MitchAlsup1) wrote:    
> > >>> Keith Thompson wrote:    
> > >>> > 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?    
> > >>> Because accurate argument reduction reduces the burden on the
> > >>> programmer to remain within his sandbox.    
> > >    
> > >> Not really.    
> > >
> > > 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 ).
> > >    
> > 
> > I can't think of a scenario where that would be useful (other than
> > just doing it for the sake of doing it).
> > 
> > If 2^53 represents a physical quantity, how likely is the actual
> > value to be known within ±π (+/i pi for those who prefer ASCII)?
> > 
> > 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.
> > 
> > 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.
> > 

<snip>

> >   
> 
> 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:
> 
<snip>
> 


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 = (double)sinl(x);
  printf("%.20Le %25.16La %.17f\n", x, x, y);
}

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

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Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-14 11:26 +0200
  Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 17:34 +0000
    Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 19:48 +0000
      Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-15 12:16 +0100
    Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-03-14 20:30 +0000
      Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:12 -0700
      Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 22:19 +0000
        Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:21 -0700
          Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:22 -0700
    Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-15 13:49 +0200
  Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-15 11:23 +0100
    Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-15 14:15 +0200
      Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 01:23 +0000
        Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-16 16:59 +0100
    Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 13:59 -0700
      Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:13 -0700
        Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-16 13:23 -0700
      Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-15 14:16 -0700
        Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:26 -0700
          Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:30 -0700
            Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-15 15:48 -0700
              Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-17 13:41 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-17 21:49 -0700
        Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 01:16 +0000
          Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-16 19:08 +0200
            Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 17:22 +0000
              Re: Radians Or Degrees? scott@slp53.sl.home (Scott Lurndal) - 2024-03-16 18:32 +0000
              Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-16 20:49 +0200
              Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 16:19 -0700
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 00:00 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 18:38 -0700
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 01:57 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 19:57 -0700
                Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-03-17 13:10 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 11:06 +0200
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 11:34 +0200
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 10:59 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 14:15 +0200
      Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 15:13 -0700
  Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-18 15:18 -0400
    Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-18 22:19 +0000
      Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 09:54 -0400
        Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-20 18:21 +0200
          Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 12:59 -0400
            Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:40 +0000
              Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-21 08:52 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-21 14:51 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-21 16:37 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-23 09:11 +0100
          Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-03-20 17:02 +0000
            Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:47 +0000
          Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:33 +0000
            Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-21 00:03 +0200
        Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:26 +0000
          Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 16:34 -0400
        Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-21 08:38 +0100

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