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Groups > comp.lang.c++ > #124609 > unrolled thread
| Started by | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| First post | 2026-08-11 03:01 -0500 |
| Last post | 2026-08-18 11:32 +0200 |
| Articles | 20 on this page of 132 — 15 participants |
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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
Page 2 of 7 — ← Prev page 1 [2] 3 4 5 6 7 Next page →
| From | Keith Thompson <Keith.S.Thompson+u@gmail.com> |
|---|---|
| Date | 2026-08-12 03:58 -0700 |
| Message-ID | <115hjka$o7k2$1@kst.eternal-september.org> |
| In reply to | #124671 |
David Brown <david.brown@hesbynett.no> writes:
[...]
> And I thought it is entirely obvious that when you are actually
> implementing a floating point power function on a binary computer
> using floating point formats specified in binary, it is most efficient
> to use base 2 for the log and anti-log. If you had a floating point
> format that used base 10, you'd probably want to use base 10 for the
> log and anti-log.
Is it obvious? It had never occurred to me.
log and exp are certainly more mathematically straightforward in
base e than in other bases. Of course floating-point is typically
binary, but I didn't know that would imply that log(x) base 2 is
easier to compute that log(x) base e. I've always assumed that
base e is more efficient than other bases.
Also, I vaguely recall that though x**y is mathematically equivalent
to exp(y * log(x)), that's not the most efficient and/or accurate
way to compute it.
--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2026-08-12 13:31 +0200 |
| Message-ID | <115hlii$nov9$1@dont-email.me> |
| In reply to | #124674 |
On 12/08/2026 12:58, Keith Thompson 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. Of course floating-point is typically > binary, but I didn't know that would imply that log(x) base 2 is > easier to compute that log(x) base e. I've always assumed that > base e is more efficient than other bases. Maybe I have been too quick to jump to conclusions. I have not done much work with implementing such floating point functions - when I have implementing things like trig functions it is because I needed a very different balance of speed and precision than standard library functions, and where I have a clear knowledge of the range needed. There's a lot of detail in making a good "pow" function that I don't know. However, when dealing with logs and anti-logs of floating point numbers, you are going to use base 2 for at least part of the job. Your float f is already in the form m * (2 ** p), so log_n(f) will be log_n(m) + log_n(2 ** p), the later part being p * log_n(2). If you can keep that part as the simple integer "p" for the rest of your calculations - using base n = 2 for that part at least, then you would probably want to do that. Similarly, anti-logs of integer parts are easiest in base 2 and turn into an addition or subtraction on the exponent part of the floating point format. In general, I don't think logs or exponents are likely to be much difference to calculate in different bases. Clearly base "e" is nicer mathematically, but I expect you'd be doing numerical calculations using range reductions, then approximation polynomials, and different bases just mean different factors in the polynomials. The biggest factor, I expect, is how this all fits with instruction sets on the target processor. I've been thinking in terms of doing it all in software - particular instructions might make a big change to the best tactics. > > Also, I vaguely recall that though x**y is mathematically equivalent > to exp(y * log(x)), that's not the most efficient and/or accurate > way to compute it. > Certainly there are complications involved to keep the accuracy. You would not want to use this expression as-is. At the very least, I would expect you would handle the mantissa and exponent of the float separately.
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| From | Michael S <already5chosen@yahoo.com> |
|---|---|
| Date | 2026-08-12 22:43 +0300 |
| Message-ID | <20260812224333.000065c4@yahoo.com> |
| In reply to | #124674 |
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). > Of course floating-point is typically > binary, but I didn't know that would imply that log(x) base 2 is > easier to compute that log(x) base e. I've always assumed that > base e is more efficient than other bases. You are mostly wrong. David is mostly correct. > > Also, I vaguely recall that though x**y is mathematically equivalent > to exp(y * log(x)), that's not the most efficient and/or accurate > way to compute it. > Apart from corner cases, it is the most efficient. And I am pretty sure that it's sufficiently accurate for most uses, including you typical C library. I did no deep numeric analysis, but my intuition suggest that as long as underlaying primitives, i.e. log2 and 2**x, are well implemented, i.e. their maximal error is under 0.6 ULP, then the worst case error of combined calculation should be below 2.5 ULP and most likely even lower than that. Which is good enough. For more than 50% of inputs you will end within 1 ULP. Of course, you don't do it stupidly. You start by splitting a with frexp() and splitting b to integer and fractional, probably with fractional in range [-0.5:0.5]. Then you take away trivial parts, i.e integer power of two. But then you come to the main part and this part is as David suggested.
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| From | Keith Thompson <Keith.S.Thompson+u@gmail.com> |
|---|---|
| Date | 2026-08-12 13:44 -0700 |
| Message-ID | <115im0c$136js$1@kst.eternal-september.org> |
| In reply to | #124686 |
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).
>> Of course floating-point is typically
>> binary, but I didn't know that would imply that log(x) base 2 is
>> easier to compute that log(x) base e. I've always assumed that
>> base e is more efficient than other bases.
>
> You are mostly wrong. David is mostly correct.
Quite possibly.
>> Also, I vaguely recall that though x**y is mathematically equivalent
>> to exp(y * log(x)), that's not the most efficient and/or accurate
>> way to compute it.
>
> Apart from corner cases, it is the most efficient.
> And I am pretty sure that it's sufficiently accurate for most uses,
> including you typical C library. I did no deep numeric analysis, but my
> intuition suggest that as long as underlaying primitives, i.e. log2 and
> 2**x, are well implemented, i.e. their maximal error is under 0.6 ULP,
2**x is provided in <math.h> as exp2(), since C99.
> then the worst case error of combined calculation should be below 2.5
> ULP and most likely even lower than that. Which is good enough.
> For more than 50% of inputs you will end within 1 ULP.
>
> Of course, you don't do it stupidly. You start by splitting a with
> frexp() and splitting b to integer and fractional, probably with
> fractional in range [-0.5:0.5]. Then you take away trivial parts, i.e
> integer power of two. But then you come to the main part and this part
> is as David suggested.
--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */
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| From | Michael S <already5chosen@yahoo.com> |
|---|---|
| Date | 2026-08-13 00:24 +0300 |
| Message-ID | <20260813002409.00003f1d@yahoo.com> |
| In reply to | #124688 |
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.
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-12 16:49 -0500 |
| Message-ID | <115ippl$15jbt$1@dont-email.me> |
| In reply to | #124689 |
On 8/12/2026 4:24 PM, Michael S wrote: > 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. I have found over the years that 200 points seems to be best when performing a numerical integration of a curve. For me, 200 points is the point where diminishing returns has set in. Of course, YMMV. Lynn
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2026-08-13 08:38 +0200 |
| Message-ID | <115jopi$1dak6$1@dont-email.me> |
| In reply to | #124690 |
On 12/08/2026 23:49, Lynn McGuire wrote: > On 8/12/2026 4:24 PM, Michael S wrote: >> 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. > > I have found over the years that 200 points seems to be best when > performing a numerical integration of a curve. For me, 200 points is > the point where diminishing returns has set in. Of course, YMMV. > Your mileage may very much vary. The best number of points depends on many factors, such as the type of curve (how "wiggly" it is, whether it has additional characteristics like monoticity that you can use, etc.), whether you are using linearly separated points or free points, how your interpolation works, what characteristics you need for the generated results, your required precision, etc. Characteristics of the target architecture can influence the best choice of points - bigger tables may let you use simpler calculations, but calculations may be cheaper than more complicated table lookup schemes. There is no single guideline for the number of points in such tables that can be useful in any general sense. I don't quite understand the use of the table Michael is describing here, but it does not at all surprise me that practical implementations of "pow" (and no doubt many other irrational functions) combine range-splitting and tables so that the polynomial approximations are efficient. My own understanding here is probably on a similar level to Keith's - I know the theoretical maths (Taylor series and all), know the difference between the theoretical infinite precision infinite series and limited precision numerical analysis, know about error analysis, basis polynomials like Chebyshev, etc. But I also know there's a lot of detail that I would have to learn or look up, that real-world speed can have surprising differences from what you expect, that people have figured out smart tricks to get good results faster, and that you need a great deal of experience working on this kind of code to write it well. I don't have that experience or practical knowledge - I have to trust those that do (like Michael). For my own uses, I typically need things like sin functions for motor control and other such applications. Tables of perhaps 16 or 32 evenly spaced points, with cubic interpolation, are often fine to get the accuracy I need in a few clock cycles on a microcontroller. (I don't think I have ever needed a floating point "pow" on a microcontroller.)
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-13 18:59 -0500 |
| Message-ID | <115llou$23b6g$1@dont-email.me> |
| In reply to | #124694 |
On 8/13/2026 1:38 AM, David Brown wrote:
> On 12/08/2026 23:49, Lynn McGuire wrote:
>> On 8/12/2026 4:24 PM, Michael S wrote:
>>> 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.
>>
>> I have found over the years that 200 points seems to be best when
>> performing a numerical integration of a curve. For me, 200 points is
>> the point where diminishing returns has set in. Of course, YMMV.
>>
>
> Your mileage may very much vary. The best number of points depends on
> many factors, such as the type of curve (how "wiggly" it is, whether it
> has additional characteristics like monoticity that you can use, etc.),
> whether you are using linearly separated points or free points, how your
> interpolation works, what characteristics you need for the generated
> results, your required precision, etc. Characteristics of the target
> architecture can influence the best choice of points - bigger tables may
> let you use simpler calculations, but calculations may be cheaper than
> more complicated table lookup schemes. There is no single guideline for
> the number of points in such tables that can be useful in any general
> sense.
>
> I don't quite understand the use of the table Michael is describing
> here, but it does not at all surprise me that practical implementations
> of "pow" (and no doubt many other irrational functions) combine range-
> splitting and tables so that the polynomial approximations are efficient.
>
> My own understanding here is probably on a similar level to Keith's - I
> know the theoretical maths (Taylor series and all), know the difference
> between the theoretical infinite precision infinite series and limited
> precision numerical analysis, know about error analysis, basis
> polynomials like Chebyshev, etc. But I also know there's a lot of
> detail that I would have to learn or look up, that real-world speed can
> have surprising differences from what you expect, that people have
> figured out smart tricks to get good results faster, and that you need a
> great deal of experience working on this kind of code to write it well.
> I don't have that experience or practical knowledge - I have to trust
> those that do (like Michael).
>
>
> For my own uses, I typically need things like sin functions for motor
> control and other such applications. Tables of perhaps 16 or 32 evenly
> spaced points, with cubic interpolation, are often fine to get the
> accuracy I need in a few clock cycles on a microcontroller. (I don't
> think I have ever needed a floating point "pow" on a microcontroller.)
Mine is coming from a chemical process simulator where chemicals are
moving between the four phases of matter that we support: vapor,
hydrocarbon liquid, aqueous liquid, and solids, based on temperature and
pressure. The tables are incredibly non-linear.
This is my people and I:
https://www.winsim.com/
Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-13 18:51 -0700 |
| Message-ID | <115lsa8$25dmf$2@dont-email.me> |
| In reply to | #124701 |
On 8/13/2026 4:59 PM, Lynn McGuire wrote: [...] > Mine is coming from a chemical process simulator where chemicals are > moving between the four phases of matter that we support: vapor, > hydrocarbon liquid, aqueous liquid, and solids, based on temperature and > pressure. The tables are incredibly non-linear. > > This is my people and I: > https://www.winsim.com/ Notice any fractal growth in there?
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-14 00:58 -0500 |
| Message-ID | <115maqt$295ib$1@dont-email.me> |
| In reply to | #124703 |
On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: > On 8/13/2026 4:59 PM, Lynn McGuire wrote: > [...] >> Mine is coming from a chemical process simulator where chemicals are >> moving between the four phases of matter that we support: vapor, >> hydrocarbon liquid, aqueous liquid, and solids, based on temperature >> and pressure. The tables are incredibly non-linear. >> >> This is my people and I: >> https://www.winsim.com/ > > Notice any fractal growth in there? We don't do that. Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-14 12:08 -0700 |
| Message-ID | <115np2q$2pjt6$1@dont-email.me> |
| In reply to | #124707 |
On 8/13/2026 10:58 PM, Lynn McGuire wrote: > On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >> [...] >>> Mine is coming from a chemical process simulator where chemicals are >>> moving between the four phases of matter that we support: vapor, >>> hydrocarbon liquid, aqueous liquid, and solids, based on temperature >>> and pressure. The tables are incredibly non-linear. >>> >>> This is my people and I: >>> https://www.winsim.com/ >> >> Notice any fractal growth in there? > > We don't do that. Let me clarify... Do you make renders of a simulation? If so, do some of them look fractal?
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-14 15:48 -0500 |
| Message-ID | <115nuvq$2rkd3$1@dont-email.me> |
| In reply to | #124714 |
On 8/14/2026 2:08 PM, Chris M. Thomasson wrote:
> On 8/13/2026 10:58 PM, Lynn McGuire wrote:
>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote:
>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote:
>>> [...]
>>>> Mine is coming from a chemical process simulator where chemicals are
>>>> moving between the four phases of matter that we support: vapor,
>>>> hydrocarbon liquid, aqueous liquid, and solids, based on temperature
>>>> and pressure. The tables are incredibly non-linear.
>>>>
>>>> This is my people and I:
>>>> https://www.winsim.com/
>>>
>>> Notice any fractal growth in there?
>>
>> We don't do that.
> Let me clarify... Do you make renders of a simulation? If so, do some of
> them look fractal?
In short, no. We have a diagrammatic user interface that allows our
users to build a diagram of a chemical process flow diagram such as a
refinery, a natural gas plan, a pipeline with compressor stations, or a
chemical plant.
https://www.winsim.com/screenshots.html
And we have a calculation engine that takes a textual version of that
diagram and solves it thermodynamically. If, it can be solved as not
all chemical processes can be solved due to constraints or violation of
the laws of thermodynamics.
Thanks,
Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-14 13:51 -0700 |
| Message-ID | <115nv50$2rkpr$1@dont-email.me> |
| In reply to | #124721 |
On 8/14/2026 1:48 PM, Lynn McGuire wrote: > On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>> [...] >>>>> Mine is coming from a chemical process simulator where chemicals >>>>> are moving between the four phases of matter that we support: >>>>> vapor, hydrocarbon liquid, aqueous liquid, and solids, based on >>>>> temperature and pressure. The tables are incredibly non-linear. >>>>> >>>>> This is my people and I: >>>>> https://www.winsim.com/ >>>> >>>> Notice any fractal growth in there? >>> >>> We don't do that. >> Let me clarify... Do you make renders of a simulation? If so, do some >> of them look fractal? > > In short, no. We have a diagrammatic user interface that allows our > users to build a diagram of a chemical process flow diagram such as a > refinery, a natural gas plan, a pipeline with compressor stations, or a > chemical plant. > https://www.winsim.com/screenshots.html > > And we have a calculation engine that takes a textual version of that > diagram and solves it thermodynamically. If, it can be solved as not > all chemical processes can be solved due to constraints or violation of > the laws of thermodynamics. Ahhhh! So, you are not making any animations of the processes. Okay. But you have the data to do so... Fwiw, I bet you already have the data to make one of my 2d examples here: https://youtu.be/YS-tyDJVy4M
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-14 16:40 -0500 |
| Message-ID | <115o20c$2sj52$1@dont-email.me> |
| In reply to | #124723 |
On 8/14/2026 3:51 PM, Chris M. Thomasson wrote: > On 8/14/2026 1:48 PM, Lynn McGuire wrote: >> On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >>> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>>> [...] >>>>>> Mine is coming from a chemical process simulator where chemicals >>>>>> are moving between the four phases of matter that we support: >>>>>> vapor, hydrocarbon liquid, aqueous liquid, and solids, based on >>>>>> temperature and pressure. The tables are incredibly non-linear. >>>>>> >>>>>> This is my people and I: >>>>>> https://www.winsim.com/ >>>>> >>>>> Notice any fractal growth in there? >>>> >>>> We don't do that. >>> Let me clarify... Do you make renders of a simulation? If so, do some >>> of them look fractal? >> >> In short, no. We have a diagrammatic user interface that allows our >> users to build a diagram of a chemical process flow diagram such as a >> refinery, a natural gas plan, a pipeline with compressor stations, or >> a chemical plant. >> https://www.winsim.com/screenshots.html >> >> And we have a calculation engine that takes a textual version of that >> diagram and solves it thermodynamically. If, it can be solved as not >> all chemical processes can be solved due to constraints or violation >> of the laws of thermodynamics. > Ahhhh! So, you are not making any animations of the processes. Okay. But > you have the data to do so... > > Fwiw, I bet you already have the data to make one of my 2d examples here: > > https://youtu.be/YS-tyDJVy4M Actually, I do make an animation of the process simulation diagram (PSD). If the users run a dynamic (time sensitive) version of the simulation, the user can roll through their displayed results on the various sheets of the PSD using their time breaks. Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-14 19:24 -0700 |
| Message-ID | <115oiku$314lo$1@dont-email.me> |
| In reply to | #124724 |
On 8/14/2026 2:40 PM, Lynn McGuire wrote: > On 8/14/2026 3:51 PM, Chris M. Thomasson wrote: >> On 8/14/2026 1:48 PM, Lynn McGuire wrote: >>> On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >>>> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>>>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>>>> [...] >>>>>>> Mine is coming from a chemical process simulator where chemicals >>>>>>> are moving between the four phases of matter that we support: >>>>>>> vapor, hydrocarbon liquid, aqueous liquid, and solids, based on >>>>>>> temperature and pressure. The tables are incredibly non-linear. >>>>>>> >>>>>>> This is my people and I: >>>>>>> https://www.winsim.com/ >>>>>> >>>>>> Notice any fractal growth in there? >>>>> >>>>> We don't do that. >>>> Let me clarify... Do you make renders of a simulation? If so, do >>>> some of them look fractal? >>> >>> In short, no. We have a diagrammatic user interface that allows our >>> users to build a diagram of a chemical process flow diagram such as a >>> refinery, a natural gas plan, a pipeline with compressor stations, or >>> a chemical plant. >>> https://www.winsim.com/screenshots.html >>> >>> And we have a calculation engine that takes a textual version of that >>> diagram and solves it thermodynamically. If, it can be solved as not >>> all chemical processes can be solved due to constraints or violation >>> of the laws of thermodynamics. >> Ahhhh! So, you are not making any animations of the processes. Okay. >> But you have the data to do so... >> >> Fwiw, I bet you already have the data to make one of my 2d examples here: >> >> https://youtu.be/YS-tyDJVy4M > > Actually, I do make an animation of the process simulation diagram > (PSD). Can you give me a link to some screenshots so I can get on the same page? Thanks. Are you almost done with your Fortran port? > If the users run a dynamic (time sensitive) version of the > simulation, the user can roll through their displayed results on the > various sheets of the PSD using their time breaks. Cool. Fwiw, check this shit out: https://youtu.be/poXeq5V0dso A simulation for the field of one of my circle intersection fractals.
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-14 22:51 -0500 |
| Message-ID | <115onn9$32bb8$1@dont-email.me> |
| In reply to | #124725 |
On 8/14/2026 9:24 PM, Chris M. Thomasson wrote: > On 8/14/2026 2:40 PM, Lynn McGuire wrote: >> On 8/14/2026 3:51 PM, Chris M. Thomasson wrote: >>> On 8/14/2026 1:48 PM, Lynn McGuire wrote: >>>> On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >>>>> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>>>>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>>>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>>>>> [...] >>>>>>>> Mine is coming from a chemical process simulator where chemicals >>>>>>>> are moving between the four phases of matter that we support: >>>>>>>> vapor, hydrocarbon liquid, aqueous liquid, and solids, based on >>>>>>>> temperature and pressure. The tables are incredibly non-linear. >>>>>>>> >>>>>>>> This is my people and I: >>>>>>>> https://www.winsim.com/ >>>>>>> >>>>>>> Notice any fractal growth in there? >>>>>> >>>>>> We don't do that. >>>>> Let me clarify... Do you make renders of a simulation? If so, do >>>>> some of them look fractal? >>>> >>>> In short, no. We have a diagrammatic user interface that allows our >>>> users to build a diagram of a chemical process flow diagram such as >>>> a refinery, a natural gas plan, a pipeline with compressor stations, >>>> or a chemical plant. >>>> https://www.winsim.com/screenshots.html >>>> >>>> And we have a calculation engine that takes a textual version of >>>> that diagram and solves it thermodynamically. If, it can be solved >>>> as not all chemical processes can be solved due to constraints or >>>> violation of the laws of thermodynamics. >>> Ahhhh! So, you are not making any animations of the processes. Okay. >>> But you have the data to do so... >>> >>> Fwiw, I bet you already have the data to make one of my 2d examples >>> here: >>> >>> https://youtu.be/YS-tyDJVy4M >> >> Actually, I do make an animation of the process simulation diagram (PSD). > > Can you give me a link to some screenshots so I can get on the same > page? Thanks. Are you almost done with your Fortran port? ... https://www.winsim.com/screenshots.html I am about 1/3rd of the way done with my 800,000 lines of F77 code to C++ code. My custom version of F2C is doing about 60 to 70% of the work. I am equating the task as equivalent to translating about ten long engineering books from German to French. Lots of idioms and basic incompatibilities that have to be ironed out. I was shooting for the end of 2026 but that ship has sailed. Maybe middle of 2027. Then I have to port to x64 but the port should be easy (he says with the ship sitting in ten feet of mud in the harbor). Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-14 22:33 -0700 |
| Message-ID | <115otme$33pc0$1@dont-email.me> |
| In reply to | #124727 |
On 8/14/2026 8:51 PM, Lynn McGuire wrote: > On 8/14/2026 9:24 PM, Chris M. Thomasson wrote: >> On 8/14/2026 2:40 PM, Lynn McGuire wrote: >>> On 8/14/2026 3:51 PM, Chris M. Thomasson wrote: >>>> On 8/14/2026 1:48 PM, Lynn McGuire wrote: >>>>> On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >>>>>> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>>>>>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>>>>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>>>>>> [...] >>>>>>>>> Mine is coming from a chemical process simulator where >>>>>>>>> chemicals are moving between the four phases of matter that we >>>>>>>>> support: vapor, hydrocarbon liquid, aqueous liquid, and solids, >>>>>>>>> based on temperature and pressure. The tables are incredibly >>>>>>>>> non-linear. >>>>>>>>> >>>>>>>>> This is my people and I: >>>>>>>>> https://www.winsim.com/ >>>>>>>> >>>>>>>> Notice any fractal growth in there? >>>>>>> >>>>>>> We don't do that. >>>>>> Let me clarify... Do you make renders of a simulation? If so, do >>>>>> some of them look fractal? >>>>> >>>>> In short, no. We have a diagrammatic user interface that allows >>>>> our users to build a diagram of a chemical process flow diagram >>>>> such as a refinery, a natural gas plan, a pipeline with compressor >>>>> stations, or a chemical plant. >>>>> https://www.winsim.com/screenshots.html >>>>> >>>>> And we have a calculation engine that takes a textual version of >>>>> that diagram and solves it thermodynamically. If, it can be solved >>>>> as not all chemical processes can be solved due to constraints or >>>>> violation of the laws of thermodynamics. >>>> Ahhhh! So, you are not making any animations of the processes. Okay. >>>> But you have the data to do so... >>>> >>>> Fwiw, I bet you already have the data to make one of my 2d examples >>>> here: >>>> >>>> https://youtu.be/YS-tyDJVy4M >>> >>> Actually, I do make an animation of the process simulation diagram >>> (PSD). >> >> Can you give me a link to some screenshots so I can get on the same >> page? Thanks. Are you almost done with your Fortran port? > ... > > https://www.winsim.com/screenshots.html > > I am about 1/3rd of the way done with my 800,000 lines of F77 code to C+ > + code. My custom version of F2C is doing about 60 to 70% of the work. > I am equating the task as equivalent to translating about ten long > engineering books from German to French. Lots of idioms and basic > incompatibilities that have to be ironed out. > > I was shooting for the end of 2026 but that ship has sailed. Maybe > middle of 2027. Then I have to port to x64 but the port should be easy > (he says with the ship sitting in ten feet of mud in the harbor). > > Lynn > Love the flow sheet. Now from there, can you create a vector field?
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-08-15 10:40 -0700 |
| Message-ID | <p8ydnaRNrf8_OR33nZ2dnZfqn_idnZ2d@giganews.com> |
| In reply to | #124727 |
On 08/14/2026 08:51 PM, Lynn McGuire wrote: > On 8/14/2026 9:24 PM, Chris M. Thomasson wrote: >> On 8/14/2026 2:40 PM, Lynn McGuire wrote: >>> On 8/14/2026 3:51 PM, Chris M. Thomasson wrote: >>>> On 8/14/2026 1:48 PM, Lynn McGuire wrote: >>>>> On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >>>>>> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>>>>>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>>>>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>>>>>> [...] >>>>>>>>> Mine is coming from a chemical process simulator where >>>>>>>>> chemicals are moving between the four phases of matter that we >>>>>>>>> support: vapor, hydrocarbon liquid, aqueous liquid, and solids, >>>>>>>>> based on temperature and pressure. The tables are incredibly >>>>>>>>> non-linear. >>>>>>>>> >>>>>>>>> This is my people and I: >>>>>>>>> https://www.winsim.com/ >>>>>>>> >>>>>>>> Notice any fractal growth in there? >>>>>>> >>>>>>> We don't do that. >>>>>> Let me clarify... Do you make renders of a simulation? If so, do >>>>>> some of them look fractal? >>>>> >>>>> In short, no. We have a diagrammatic user interface that allows >>>>> our users to build a diagram of a chemical process flow diagram >>>>> such as a refinery, a natural gas plan, a pipeline with compressor >>>>> stations, or a chemical plant. >>>>> https://www.winsim.com/screenshots.html >>>>> >>>>> And we have a calculation engine that takes a textual version of >>>>> that diagram and solves it thermodynamically. If, it can be solved >>>>> as not all chemical processes can be solved due to constraints or >>>>> violation of the laws of thermodynamics. >>>> Ahhhh! So, you are not making any animations of the processes. Okay. >>>> But you have the data to do so... >>>> >>>> Fwiw, I bet you already have the data to make one of my 2d examples >>>> here: >>>> >>>> https://youtu.be/YS-tyDJVy4M >>> >>> Actually, I do make an animation of the process simulation diagram >>> (PSD). >> >> Can you give me a link to some screenshots so I can get on the same >> page? Thanks. Are you almost done with your Fortran port? > ... > > https://www.winsim.com/screenshots.html > > I am about 1/3rd of the way done with my 800,000 lines of F77 code to > C++ code. My custom version of F2C is doing about 60 to 70% of the > work. I am equating the task as equivalent to translating about ten > long engineering books from German to French. Lots of idioms and basic > incompatibilities that have to be ironed out. > > I was shooting for the end of 2026 but that ship has sailed. Maybe > middle of 2027. Then I have to port to x64 but the port should be easy > (he says with the ship sitting in ten feet of mud in the harbor). > > Lynn > Translating the idioms right makes for "naturals" alignment and storage, and so on. Then the numerical methods one imagines are involved in solving linearities for invariants and process control, then that's involved itself, and the relevance of the compatibility of the numerical methods, for their mathematical guarantees, for their physical estimates, about how many traincars and truckloads of feeder stock under what conditions and augury make diapers or galoshes or legos or condoms or pipe or contact lenses or lacquer or petrochemicals or drugs or otherwise usually enough more refined materials from more raw materials. Here it's like "measure-twice cut-once" the old "build a fence a mile, could you move it a foot?" If the great difference for FORTRAN and C is the account of the column-major or row-major and that of arrays and loops, then besides a simplest sort of transpose, or organization and alignment and storage, then is for the model of computation the entry-points and the state & scope, the modules, point being here it's perceived as a quite impressive and thoroughgoing sort of account of quite very much the value the algorithms and numerical methods express as models of control theory. The Bessemer furnace, .... https://en.wikipedia.org/wiki/Bessemer_process Then, there was mentioned "violations of the thermo second law", or rather, "accommodations to effects of resonance theory", these sorts acconts of "effects", which are basically anything outside otherwise the theory, or "exceptions", yes one imagines that those make for the accounts of state & scope the quite complicated, which for example "exception specification" provides in higher-level languages with exception specification as a critical component of safety in the modules of software, quite invokes the deliberations of "why" instead of merely "because". The, "term-rewriting", or a bit more holistically the "term-graph-rewriting", is definitely a thing in software since that "generative programming" is a term from the 1960's, and "program translation" is is quite usual, then for "models of computation" and "modules of computation". Long story short such an endeavor is perceived to be a store of great _value_, and such porting effort is quite a study of both the numerical methods, which as usually approximations need their error-bounds modeled, like Runge-Kutta for example after Gregory & Coates as Newton's, or about Leontief and so on, numerical methods and linear systems and linear solvers, then with regards to standard and empirical units, which are not necessarily the same and where regimes of effect are according to their own units, good luck with that, it sounds like something vital to the real-world economy.
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-15 11:41 -0700 |
| Message-ID | <115qbs8$3k7td$1@dont-email.me> |
| In reply to | #124731 |
On 8/15/2026 10:40 AM, Ross Finlayson wrote: [...] > Long story short such an endeavor is perceived to be a store of > great _value_, and such porting effort is quite a study of both > the numerical methods, which as usually approximations need > their error-bounds modeled, like Runge-Kutta for example after > Gregory & Coates as Newton's, or about Leontief and so on, > numerical methods and linear systems and linear solvers, > then with regards to standard and empirical units, which are > not necessarily the same and where regimes of effect are > according to their own units, good luck with that, it sounds > like something vital to the real-world economy. Long story short... I am not using RK for the intermediate vector field integration points, but its still pretty good. Example: https://youtu.be/Doeci7xBYh0
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-17 14:48 -0500 |
| Message-ID | <115voif$19c26$1@dont-email.me> |
| In reply to | #124731 |
On 8/15/2026 12:40 PM, Ross Finlayson wrote: > On 08/14/2026 08:51 PM, Lynn McGuire wrote: >> On 8/14/2026 9:24 PM, Chris M. Thomasson wrote: >>> On 8/14/2026 2:40 PM, Lynn McGuire wrote: >>>> On 8/14/2026 3:51 PM, Chris M. Thomasson wrote: >>>>> On 8/14/2026 1:48 PM, Lynn McGuire wrote: >>>>>> On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >>>>>>> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>>>>>>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>>>>>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>>>>>>> [...] >>>>>>>>>> Mine is coming from a chemical process simulator where >>>>>>>>>> chemicals are moving between the four phases of matter that we >>>>>>>>>> support: vapor, hydrocarbon liquid, aqueous liquid, and solids, >>>>>>>>>> based on temperature and pressure. The tables are incredibly >>>>>>>>>> non-linear. >>>>>>>>>> >>>>>>>>>> This is my people and I: >>>>>>>>>> https://www.winsim.com/ >>>>>>>>> >>>>>>>>> Notice any fractal growth in there? >>>>>>>> >>>>>>>> We don't do that. >>>>>>> Let me clarify... Do you make renders of a simulation? If so, do >>>>>>> some of them look fractal? >>>>>> >>>>>> In short, no. We have a diagrammatic user interface that allows >>>>>> our users to build a diagram of a chemical process flow diagram >>>>>> such as a refinery, a natural gas plan, a pipeline with compressor >>>>>> stations, or a chemical plant. >>>>>> https://www.winsim.com/screenshots.html >>>>>> >>>>>> And we have a calculation engine that takes a textual version of >>>>>> that diagram and solves it thermodynamically. If, it can be solved >>>>>> as not all chemical processes can be solved due to constraints or >>>>>> violation of the laws of thermodynamics. >>>>> Ahhhh! So, you are not making any animations of the processes. Okay. >>>>> But you have the data to do so... >>>>> >>>>> Fwiw, I bet you already have the data to make one of my 2d examples >>>>> here: >>>>> >>>>> https://youtu.be/YS-tyDJVy4M >>>> >>>> Actually, I do make an animation of the process simulation diagram >>>> (PSD). >>> >>> Can you give me a link to some screenshots so I can get on the same >>> page? Thanks. Are you almost done with your Fortran port? >> ... >> >> https://www.winsim.com/screenshots.html >> >> I am about 1/3rd of the way done with my 800,000 lines of F77 code to >> C++ code. My custom version of F2C is doing about 60 to 70% of the >> work. I am equating the task as equivalent to translating about ten >> long engineering books from German to French. Lots of idioms and basic >> incompatibilities that have to be ironed out. >> >> I was shooting for the end of 2026 but that ship has sailed. Maybe >> middle of 2027. Then I have to port to x64 but the port should be easy >> (he says with the ship sitting in ten feet of mud in the harbor). >> >> Lynn >> > > Translating the idioms right makes for "naturals" alignment and storage, > and so on. Then the numerical methods one imagines are > involved in solving linearities for invariants and process control, > then that's involved itself, and the relevance of the compatibility > of the numerical methods, for their mathematical guarantees, for > their physical estimates, about how many traincars and truckloads > of feeder stock under what conditions and augury make diapers or > galoshes or legos or condoms or pipe or contact lenses or lacquer > or petrochemicals or drugs or otherwise usually enough more refined > materials from more raw materials. > > Here it's like "measure-twice cut-once" the old "build a fence > a mile, could you move it a foot?" > > If the great difference for FORTRAN and C is the account of > the column-major or row-major and that of arrays and loops, > then besides a simplest sort of transpose, or organization > and alignment and storage, then is for the model of computation > the entry-points and the state & scope, the modules, point being here > it's perceived as a quite impressive and thoroughgoing sort of > account of quite very much the value the algorithms and numerical > methods express as models of control theory. > > The Bessemer furnace, .... > > https://en.wikipedia.org/wiki/Bessemer_process > > Then, there was mentioned "violations of the thermo second law", > or rather, "accommodations to effects of resonance theory", > these sorts acconts of "effects", which are basically anything > outside otherwise the theory, or "exceptions", yes one imagines > that those make for the accounts of state & scope the quite > complicated, which for example "exception specification" provides > in higher-level languages with exception specification as a critical > component of safety in the modules of software, quite invokes the > deliberations of "why" instead of merely "because". > > > The, "term-rewriting", or a bit more holistically the > "term-graph-rewriting", is definitely a thing in software since that > "generative programming" is a term from the 1960's, and "program > translation" is is quite usual, then for "models of computation" > and "modules of computation". > > > Long story short such an endeavor is perceived to be a store of > great _value_, and such porting effort is quite a study of both > the numerical methods, which as usually approximations need > their error-bounds modeled, like Runge-Kutta for example after > Gregory & Coates as Newton's, or about Leontief and so on, > numerical methods and linear systems and linear solvers, > then with regards to standard and empirical units, which are > not necessarily the same and where regimes of effect are > according to their own units, good luck with that, it sounds > like something vital to the real-world economy. Sorry, I lost you in the first part of your reply. If you are saying that it is a tough translation, yes it is. Especially since much of our Fortran was written back in the middle 1960s with Fortran II and Fortran IV (66). We did not convert to Fortran 77 until 1995 or so due to the 2X cost to compile code on the mainframes using the F77 compiler instead of the F66 compiler. And the source code is mostly uncommented since we paid a penny a line / time period (day ? month ? year?) to store the source code on the Univac 1108. The worst part of the translation is converting from arrays starting at one to arrays starting at zero. My translation tool is converting all of the multiple dimensioned arrays to single dimensioned arrays for me to get out of the array ordering issues. I am equating the translation to converting a dozen highly technical books written in German to French. Lynn
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