Re: why is there not a ipow version of pow?

From	Michael S <already5chosen@yahoo.com>
Newsgroups	comp.lang.c++, comp.lang.c
Subject	Re: why is there not a ipow version of pow?
Date	2026-08-13 00:24 +0300
Organization	A noiseless patient Spider
Message-ID	<20260813002409.00003f1d@yahoo.com> (permalink)
References	(11 earlier) <115g94d$2pb62$1@paganini.bofh.team> <115h9mb$kpdk$1@dont-email.me> <115hjka$o7k2$1@kst.eternal-september.org> <20260812224333.000065c4@yahoo.com> <115im0c$136js$1@kst.eternal-september.org>

Cross-posted to 2 groups.

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On Wed, 12 Aug 2026 13:44:50 -0700
Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote:

> Michael S <already5chosen@yahoo.com> writes:
> > On Wed, 12 Aug 2026 03:58:16 -0700
> > Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote:  
> >> David Brown <david.brown@hesbynett.no> writes:
> >> [...]  
> >> > And I thought it is entirely obvious that when you are actually
> >> > implementing a floating point power function on a binary computer
> >> > using floating point formats specified in binary, it is most
> >> > efficient to use base 2 for the log and anti-log.  If you had a
> >> > floating point format that used base 10, you'd probably want to
> >> > use base 10 for the log and anti-log.    
> >> 
> >> Is it obvious?  It had never occurred to me.
> >> 
> >> log and exp are certainly more mathematically straightforward in
> >> base e than in other bases.   
> >
> > Only near x=1 for log(x) and near x=0 for exp(x).  
> 
> Can you explain what you mean by that?
> 
> Mathematically, exp(x) (base e) is described by the Taylor series.
> In clumsy ASCII notation, it's:
> 
>     1 + x + x**2/2! + x**3/3! + x**4/4! + ...
> 
> b**x, were b is a base other than e (often 2 or 10) is
> exp(x * log(base)), where exp() and log() are base e.  In other
> words, exp and log for bases other than e are most straightforwardly
> defined on top of exp and log for base e.
> 
> That's what I meant by "more mathematically straightforward".
> 
> If you say there are computational reasons why exp2 and log2 are
> advantageous when using binary floating-point, I can believe that.
> I just don't understand the reasons (and to be honest, I'm not sure
> I'd understand an explanation without more effort than I'm willing
> to expend, unless somebody wants to pay me to work on this stuff).
> 

It's late here and I want to sleep, so very briefly:
The best computational way to calculate a**x for constant a on
relatively big interval of x, like [0:1] or [-0.5:0.5] is not through
evaluation of polynomial of very high degree, but by splitting
interval into sub ranges and calculating y = Yi * a**(x-Xi) where
Yi is tabulated and may be Xi tabulated too, or may be Xi just regularly
spaced. For double precision and for speed/space/precision requirements
of C math library you will probably want many dozen of intervals, or
low hundreds. That allows much lower degree of poly for a**(x-Xi).
And to lower degree even further you use Chebyshev series or may be
even series derived by Remez exchange algorithm rather than Taylor
series. It means that even for a=e the second coefficient is not 1 and
likely the 1st coefficient is also not 1. So, a=e has no advantage vs
a=2. Of course, in this part of calculation a=2 also holds no
advantages vs any other base, but it has advantages in other parts of
of solution.
Different but ideologically similar reasoning applies to natural
log vs log2.

Thread

why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 03:01 -0500
  Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 13:11 +0200
    Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 12:45 +0100
      Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 14:34 +0200
      Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 14:55 +0200
        Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 15:19 +0200
          Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 15:27 +0200
            Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 16:08 +0200
              Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 16:18 +0200
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:11 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:20 +0200
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:32 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:39 +0200
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 18:33 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 18:39 +0200
                Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-11 23:31 +0300
                Re: why is there not a ipow version of pow? James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-08-11 11:46 -0400
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 18:35 +0200
                Re: why is there not a ipow version of pow? antispam@fricas.org (Waldek Hebisch) - 2026-08-11 22:53 +0000
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-12 10:08 +0200
                Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-12 03:58 -0700
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-12 13:31 +0200
                Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-12 22:43 +0300
                Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-12 13:44 -0700
                Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-13 00:24 +0300
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-12 16:49 -0500
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-13 08:38 +0200
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-13 18:59 -0500
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-13 18:51 -0700
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 00:58 -0500
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:08 -0700
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 15:48 -0500
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 13:51 -0700
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 16:40 -0500
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 19:24 -0700
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 22:51 -0500
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 22:33 -0700
                Re: why is there not a ipow version of pow? Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-15 10:40 -0700
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-15 11:41 -0700
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-17 14:48 -0500
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-16 14:58 -0700
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-14 08:57 +0200
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:46 -0700
                Re: why is there not a ipow version of pow? James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-08-13 12:59 -0400
                Re: why is there not a ipow version of pow? antispam@fricas.org (Waldek Hebisch) - 2026-08-12 20:23 +0000
                Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-11 18:19 +0000
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 20:21 +0200
                Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-11 21:10 +0000
                Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-12 00:42 +0300
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 06:41 +0200
                Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-12 14:19 +0000
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 16:56 +0200
                Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-12 15:32 +0000
                Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-12 22:05 +0300
                Re: why is there not a ipow version of pow? Paul <nospam@needed.invalid> - 2026-08-12 19:09 -0400
                Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-11 21:58 +0300
                Re: why is there not a ipow version of pow? Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-11 21:44 -0700
              Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 15:45 +0100
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 16:56 +0200
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:23 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:24 +0200
                Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 16:23 +0100
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:26 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:54 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 18:40 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 08:49 +0200
                Re: why is there not a ipow version of pow? Paul <nospam@needed.invalid> - 2026-08-12 09:11 -0400
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 16:05 +0200
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-12 12:40 -0700
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-13 15:46 +0200
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-13 14:28 -0700
                Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-11 16:20 -0700
                Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 18:43 +0100
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 19:56 +0200
                Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 20:41 +0100
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 06:42 +0200
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-12 10:23 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 20:24 +0200
                Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 20:27 +0100
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 06:45 +0200
                Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:16 +0200
      Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 15:17 +0200
        Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 15:28 +0200
          Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 16:43 +0200
            Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 16:47 +0200
              Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:24 +0200
    Re: why is there not a ipow version of pow? Paul <nospam@needed.invalid> - 2026-08-11 09:36 -0400
      Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 16:42 -0500
  Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-11 19:15 +0200
    Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 16:41 -0500
      Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 16:49 -0500
        Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 23:28 +0100
          Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 17:51 -0500
      Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-11 15:33 -0700
        Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 17:49 -0500
          Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-11 16:19 -0700
            Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-12 00:32 -0500
              Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 14:08 +0200
                Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 18:40 +0200
                Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-14 02:50 +0000
  Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-12 04:26 +0000
    Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-12 01:37 -0500
      Re: why is there not a ipow version of pow? Paul <nospam@needed.invalid> - 2026-08-13 00:12 -0400
      Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-14 11:22 +0800
        Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 01:00 -0500
          Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-14 14:47 +0800
            Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 13:54 -0500
              Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-16 22:49 +0000
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-17 14:56 -0500
                Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-17 23:53 +0000
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-17 19:59 -0500
                Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-18 02:47 +0000
                Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-17 15:17 -0500
            Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:03 -0700
              Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-15 03:51 +0800
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:52 -0700
                Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-15 04:01 +0800
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 13:27 -0700
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 13:29 -0700
                Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-15 04:49 +0800
                Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 20:32 -0700
    Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-12 11:28 +0100
      Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-12 23:52 +0000
  Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-13 17:19 +0800
    Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-13 19:07 -0500
      Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-14 10:58 +0800
        Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 01:14 -0500
      Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-17 06:40 +0000
        Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-17 21:40 +0800
  Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-18 00:42 -0500
    Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-18 09:34 +0200
    Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-18 11:32 +0200

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