math.ldexp gives incorrect results on Windows #132876
Comments
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For a context: mpmath/mpmath#942 |
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Hi! 👋 This issue appears to be caused by platform-specific differences in floating-point handling, particularly on Windows. For consistency across platforms, a workaround is to use arbitrary-precision libraries such as from mpmath import mp
mp.dps = 50
x = mp.mpf(6993274598585239)
y = -1126
print(mp.ldexp(x, y))Of course, since Hope this helps! 😊 |
Just a bug in the platform libc. @tkreuzer, could you please describe your system (OS, hardware)?
It's not a real workaround, because OP want native CPython floats, not mpmath's numbers. In fact, math.ldexp() is used in the mpmath to provide the It's possible to use gmpy2: >>> import gmpy2
>>> gmpy2.set_context(gmpy2.ieee(64))
>>> gmpy2.mpfr(6993274598585239)/gmpy2.mpfr(2)**1126
mpfr('0.0')
>>> gmpy2.set_context(gmpy2.ieee(128))
>>> gmpy2.mpfr(6993274598585239)/gmpy2.mpfr(2)**1126
mpfr('7.67194470417997883016474037150491012e-324',113)
>>> float(_)
1e-323Though, it's not an option for the mpmath itself. |
Windows 10 on an Intel i/-1065G7. I implemented a workaround myself now. |
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On mpmath's master: With your patch (I doubt it's correct): |
It's slower, I get it. Would not be an issue, if it was implemented in C 🙂 Alternatively you can probably use ldexp for anything that is not a denormal (would need to test that). Then you can simplify the code a bit. And you can replace the shift loop with something like |
From quoted issue: Python 3.10.11 (tags/v3.10.11:7d4cc5a, Apr 5 2023, 00:38:17) [MSC v.1929 64 bit (AMD64)] on win32 I would like to see if someone else can reproduce this on same platform.
This can be mitigated coding in C, but that's not for the mpmath. It's also incorrect. Besides raising OverflowError in an appropriate place, you probably should remove FYI: mpmath/mpmath#945
You meant "for anything, that not produces a denormal"? Because CC @tim-one |
Patch by Timo Kreuzer: python/cpython#132876 (comment) Closes mpmath#942
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The Windows ldexp doesn't round - it chops (truncates: "round to 0"). Whether that's "a bug" is arguable, but Microsoft hasn't budged on this at all. To make this easier to follow, here's the simplest "failing" case: >>> import math
>>> tiny = math.nextafter(0, 1)
>>> tiny # smallest non-zero positive float
5e-324
>>> _.hex()
'0x0.0000000000001p-1022'
>>> math.frexp(tiny)
(0.5, -1073) # easier than counting by hand
>>> math.ldexp(0.5, -1073) # ldexp is frexp's inverse
5e-324
>>> math.ldexp(0.75, -1073) # doesn't round up
5e-324
>>> math.ldexp(0.8, -1073) # still doesn't
5e-324
>>> math.ldexp(0.9, -1073) # and still not
5e-324
>>> math.ldexp(0.9999, -1073) # nope!
5e-324
>>> math.ldexp(1.0, -1073) # finally - but not via rounding
1e-323
>>> _.hex()
'0x0.0000000000002p-1022'So long as the result isn't subnormal, no problem. The original intent of ldexp was to give a fast way to change the exponent without changing the mantissa bits at all. Subnormals don't play nice with that view, though. Python's math module generally intends to reproduce the platform's C library results for functions of the same name. There's no clear win to be had here. It's impossible for ldexp to both round and to match C programmers' expectations of how ldexp works on Windows. If you want the same semantics as multiplying by a power of 2, multiply by a power of 2. The days when ldexp was faster than float multiplication are now ancient history. Not that it's trivial. In the above, e.g., 2.0**1073 isn't representable as an IEEE double. In bad cases it can take two stages: first use ldexp to shift the input to the smallest normal binade. No information is lost. Then multiply by the appropriate negative power of 2 to finish the job. Let the hardware take care of rounding. There's no need to pick apart - or do arithmetic on - the bits yourself. |
Ah, that explains things for me. Does it happens on all M$ systems or rather limited (e.g. to win32)? (Disclaimer: I had windows box nearby 10+ years ago.) Sorry, but it seems to be a bug. Standard says: "If a range error due to underflow occurs, the correct result (after rounding) is returned." Rounding mode could be ignored only if no range error occurs.
Are you argue to get rid of CPython's versions of tgamma()/lgamma() and switch to libm's versions? ;-) So, sometimes we have workarounds for buggy libm functions. This might be the case. |
I'm not a Windows expert. It's something I've learned from the systems I personally use. It was true under DOS from the start, and is still so under my current 64-bit Windows 10 Pro.
The great thing about standards is that there are so many of them 😉. You need to identify the exact standard you have in mind. The accepted answer here: lets Microsoft off the hook because their C implementation may not define Which isn't the final word either. Hence it's "arguable", but it's not an argument I want to engage in.
If platform libms have since improved to be better than horrid on those functions, yes, it would be best if we did lose ours. You already recently discovered that, on the platform you used, its gamma is better than ours, We're not doing users on that platform much good by hiding their platform's better implementation. But since we took them over, we have our own backward compatibility worries now. Microsoft has decades of backward compatibility to worry about with
It might be. But if we do take it over on Windows, our docs need to be clear that Python's It's a fight I don't want to take part in. But I'd be +1 on leaving When I care, I multiply by a negative power of 2. It's cheap to compute 2**-n via ldexp(1.0, -n). But n has to be <= 1074, else that underflows to 0. >>> math.ldexp(0.75, -1073) # truncates
5e-324
>>> 0.75 * math.ldexp(1, -1073) # rounds
1e-323So that's the core "trick" to implementing a rounded variant of ldexp on Windows without tedious, slow, and error-prone bit fiddling. >>> math.ldexp(6993274598585239, -1126)
5e-324
>>> 6993274598585239 * math.ldexp(1, -1074) * math.ldexp(1., -1126 + 1074)
1e-323 |
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Here's a very lightly tested workaround for Windows, which defers to the platform function unless rounding may be needed. Rounding (if any is needed) is done by the multiply at the end. Details
from math import frexp, isfinite, ldexp, nextafter
BITS = 53 # number of mantissa bits
TINY_EXP = frexp(nextafter(0.0, 1.0))[1] # exp of smllest denorm
SMALLEST_NORM_EXP = TINY_EXP + BITS - 1
def ldexpr(x, n):
if not isfinite(x) or not x:
# NsNs, infs, and zeros are unchanged.
return x
# Non-zero finite.
if n >= 0:
# Left shifts may overflow, but don't round.
return ldexp(x, n)
# Right shift of non-zero finite.
original_exp = frexp(x)[1]
target_exp = original_exp + n
if target_exp >= SMALLEST_NORM_EXP:
# No bits are shifted off - no rounding involved.
return ldexp(x, n)
# Shifting into denorm-land - trailing bits may be lost.
if original_exp > SMALLEST_NORM_EXP:
# Shift down to the smallest normal binade. No bits lost,
x = ldexp(x, SMALLEST_NORM_EXP - original_exp)
assert frexp(x)[1] == SMALLEST_NORM_EXP
n += original_exp - SMALLEST_NORM_EXP
# Multiplying by 2**n finishes the job, and the HW will round as
# appropriate, Note; if n < -BITS, all of x is shifted to be <
# 1/2 ULP of TINY, so should be thrown away. If n is so very
# negative that ldexp underflows to 0, that's fine; no need to
# check in advance.
return x * ldexp(1.0, n)Note that it's important to do no more than one multiply. lest subtle "double rounding" bugs be introduced. The intent is that no information of any kind is lost before the single multiply. |
Sorry, of course I meant the C standard. It says that "Whether the functions honor the rounding direction mode is implementation-defined, unless explicitly specified otherwise." But IIUIC, that means that default rounding mode will play game, i.e. rounding to nearest. Of course, if the implementation doesn't define
What about mvsc? @tkreuzer ?
Well, in same sense our gamma() and few other functions differ from the platform versions. I would say, if MVSC defines
Thanks, seems correct and much faster, of course. Though, not a priceless: On the master: I think C-coded version of that will run almost as fast as current ldexp(), but it's not acceptable as pure-Python workaround in the mpmath. |
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MSVC does not even define into |
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Hmm, thanks, Chris. On another hand, we have in tree C99+ fix for M$: Lines 2385 to 2393 in 8a4d4f3 The C99+ "says this" in Annex F. |
I also (in addition to @chris-eibl) confirmed that MS's most recent compiler knows nothing about It's not really surprising, though - it's Microsoft 😉.
It's deeper than just that, though. The workaround I gave doesn't comply with STDC_IEC_559 either: to do so, it would have to respect the current rounding mode, not just nearest/even. Now the multiplication at the end would do so in almost all real-life cases. But, e.g., under to-plus-infinity rounding, this would give a wrong result There is a bug here on MS's side, but I've never seen them acknowledge it. Their own docs have never said anything about this, and certainly imply I expect (but don't know) they'd call it a "doc bug". |
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For However, unfortunately, +-0 do pass those tests. and those are probably common outputs. So add another if not x: # the _input_, not the result `r`
return xtest to spare the expense. Then the workaround knows up-front that it's getting a non-zero finite, and can skip testing for NaNs, infs, and zeros. Why can't you just return a 0 result? Because it's not always right. It's possible for >>> ldexp(0.5000001, -1074) # input a little over ulp(TINY)/2
0.0
>>> ldexpr(0.5000001, -1074) # which my workaround realizes
5e-324 |
I understand and it's fine. So far, CPython has no interface to change current rounding mode - thus we probably can assume default rounding. off-topic on rounding mode supportSome such interface might be interesting: then the fp context of mpmath can take into account "rounding" context settings. Currently it's doable but I don't know how to make this in a cross-platform safe way (this is on Linux with Glibc 2.36): >>> mp_d = MPContext(53, 'd')
>>> mp_u = MPContext(53, 'u')
>>> mp_d.mpf(libmp.mpf_exp(mpf(3)._mpf_, 53, 'd'))
mpf('20.085536923187664')
>>> mp_u.mpf(libmp.mpf_exp(mpf(3)._mpf_, 53, 'u'))
mpf('20.085536923187668')
>>> import ctypes
>>> libm = ctypes.CDLL('libm.so.6
I suspect same for Also, saying "not a bug" - means that MSVC will never support Annex F. They claims that "Microsoft C++ (MSVC) is consistent with the IEEE numeric standards".
Thanks, I'm already experimenting with such approach. This doesn't seems much better than current mpmath/mpmath#942. |
CPython internals do assume nearest/even. and it's deliberate that Python offers no portable way to change HW mode. Doing so would be a bottomless rat hole,. If rounding mode can change, CPYthon internals that rely on nearest/even would have to change/restore rounding mode on the fly. Besides being endlessly tedious, it's also expensive.
No idea, and no interest in finding out 😉.
I absolutely say this case is different: we document up front what we're doing. And in real life almost nobody ever cares about the sign of a zero anyway 😉. I could certainly live with CPython taking over ldexp on Windows too, provided that the docs clearly say we're doing so. Indeed, while barely anyone in real life cares about denorms for 8-byte floats (they do care for 4-byte floats, which have such relatively low precision), it would be of more real value than the tiny change to
In context, that page is talking about "IEEE Floating-Point Representation". They do fully conform with the standards in how floats are represented. Which is trivial on most boxes, because they're using the native HW representations. which themselves follow the standards for how floats are represented. |
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A possible improvement for my workaround function (which has now survived more substantial testing): the "shift down to the smallest normal binade" part is needed to ensure that if n >= -1074 # hardcoded TINY_EXP-1
# Close enough to +inf than 2**n can't underflow.
factor = ldexp(1.0, n)
assert factor
return x * factorOf course Note about the "-1": literature about the fp standards usually views the mantissa as being in the range |
I'm not sure if there are too many places to do this. Formatting, integer division, did I miss something else? The rest is a free lunch (assuming that platform libm supports custom rounding modes correctly). Though, it's not the current issue.
Well, we can say that the rounding direction mode for the math's functions is rounding to nearest, i.e. default for C99+. As CPython implementation detail, like for special values. |
Certainly, but I'm not spending time doing exhaustive code review for something I have no interest in. The intent of rounding mode is to round the final result in the specified direction. On the way to that end, internal algorithms generally want the best rounding (nearest-even) they can get for intermediate results. So review all the internal algorithms in EDIT: the very useful Veltkamp and Dekker techniques don't care about the "even" part of "nearest/even", but do rely on the "nearest" part. Alternative splitting methods can be contrived that work with other rounding modes, but that's another level of the rat hole I'm not diving into 😉.
As noted before, switching rounding modes is expensive. so I expect most libm authors also assume nearest/even for their internal algorithms.
No, it certainly isn't 😉. |
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Tested on my own machine: We're going to need more information. Specifically, we need the exact Windows version, and if it's easy enough, find the exact version of It's very likely that any fix here is going to be "update your OS to a working one". As a general rule, we prefer to expose native functionality directly, so that we aren't responsible for providing bug fixes for issues that belong to the OS. |
Actually, it is easy enough. Grab this script from our repo and run it with For reference, mine is |
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@zooba you might miss in the thread: |
I didn't, but it's irrelevant. The implementation of this function is part of the OS, not part of the compiler, so updating the OS will fix it and Python doesn't have to do a thing. |
Are you sure? I first installed Win10 some years ago, but I've applied every update Windows Update ever offered, at least twice almost every month since. Most recently last week, updates to the OS and to .NET. Never a word about being out of support. I can't install Win11, in part because I don't have a TPM, and more infuriatingly because it complains about my CPU. Which is a fast 4-core Intel CPU far more powerful than Windows needs (and 16 GB of RAM, terabytes of free disk space. both hard drive and SSD - it's a substantial box). I could buy a new box ... but the prospect of spending days in all reinstalling apps is utterly depressing ☹ Luckily, I don't personally care about whether |
The TPM requirement is what was later removed, but if it has decided it doesn't like your CPU (which seems weird... Intel CPUs should basically all be fine - motherboard would be more likely). Unfortunately, Windows does this thing where when it decides your machine can't handle an update, it never actually tells you. I assumed one of mine was up to date, but it turns out they'd blocked major updates for a year because of an audio driver (which I only found out after I bricked it...) I wouldn't tell you to buy a new box, but it's possible that if you get the installation assistant from https://www.microsoft.com/software-download/windows11/ it'll tell you that you can now get the update, or point at exactly what the issue is. I don't particularly want to fill Python up with OS version-specific workarounds for bugs that have been resolved (but not necessarily installed), but if this particular case is upsetting people and we can special-case the inputs (rather than the OS), then sure, why not. |
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Now I got curious :) I have old and new hardware. All are updated regularily, last Windows update this morning. Old desktop:
New laptop:
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I am pretty sure, Tim is on 22H2, too. Seems one cannot conclude from ucrtbase version to Windows version? BTW:
Quote from PEP 745 – Python 3.14 Release Schedule
OOI: just a few days before Windows 10 EOL. According to https://peps.python.org/pep-0011/#microsoft-windows it should be supported? Is there already a decision, whether 3.14 will drop Win10 support? |
So am I 😉. That's what So appears to be the same as yours. We also have the same
Alas, following the link you gave just ended up downloading the "PC Health Check" app, which I've tried all along over the last year. The output is always the same: That shows up with a yellow circle around an exclamation mark. I understand there are "unadvertised" ways to install Win11 anyway, but there's another: That shows up with a red circle around an X. @chris-eibl said "MS requires at least 8th gen", so that could be it. I'm hosed 😉. Thanks for the eyeballs! I appreciate the effort. |
Windows runs a daily build and caches entire binaries, so if the sources are unchanged it won't be rebuilt, and will eventually be shipped. This is what broke our old version detection for the OS - we were reading it from
I was skeptical, but I just checked my 8 year old laptop and it's 8th gen, so I guess that may be it. Sorry! That would, however, put the bug without our supported range of versions. We don't get to detect it at compile-time, unfortunately, and I'd rather not add a (relatively slow) version check for all Windows users for all time because of this. If it's just this one set of inputs that's affected, then special-casing that case would be fine, though that seems unlikely. Do we have a numeric stability policy for this module? In general, I'd expect "do what the OS does" to be our policy, like elsewhere, and would need a very compelling reason to bypass that. |
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@zooba, t's a puzzle. What should happen: MS should push a fix into a Win10 update before support ends. Since they did fix it for Win11, there's no plausible "but we can't!" argument to be made. It's a standard C library function, and the bug isn't really subtle: it's plainly wrong by all relevant standards. doesn't match MS's own docs, and is implemented correctly on all other known platforms. I'm told Win10 still has outright majority share across all desktop OSes. Since I can't upgrade to Win11, I'll probably stick with Win10 until my HW dies (I've already, e.g., replaced two failing drives, a failed SSD "accelerator", and a dead cooling fan). Hard to believe I won't be joined by millions in that. Win10 will be with us for years yet in reality. It's not so much that end users care about If MS won't fix it, I don't believe CPython should ignore it. As @skirpichev pointed out, we took over part of |
We have (as CPython implementation detail): "The math module consists mostly of thin wrappers around the platform C math library functions. Behavior in exceptional cases follows Annex F of the C99 standard where appropriate." So, fixes for exceptional cases (zeros, infinities, nans) are expected (you can see modf() workaround for Windows). Technically, this issue not fits into it. Though, a long time after this remark was added (by Mark Dickinson) - CPython had (til fa26245) own implementations for a number of libm's functions (e.g. acosh). So, I would interpret "follows to Annex F" in a more wide sense: not just for special values, but for the rest of Annex F as well, i.e. rounding.
It isn't that helpful. Much better if people can expect if module functions will follow to some known standard, like the decimal module does. I think that pure-Python modules like the mpmath aren't the right place to fix OS-specific quirks. BTW, we already require support for IEEE 754 floating- point numbers for CPython building. While platforms may not declare support for Annex F (does Windows 11 does this?), I think it's reasonable to believe that things will evolve toward better support. So, as long as Windows 10 is supported by CPython - I think we should put in a workaround (included conditionally for all Windows systems, like that for fmod()). I'll come with a patch, based on @tim-one code, after more benchmarks. |
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Here are my result (1st case corresponds to "normal" situation, when workaround not triggered):
I'll appreciate if someone repeat these tests on less noisy system, but it seems that we have some slowdown only for denormal results, as expected. BTW, nowadays we can use PyLong_AsInt() in ldexp(). That will simplify function and remove need for type-cast of the exp. Does it make sense? If so, I'll include this refactoring to final patch - it can be backported to 3.13 too. A patch (tested on Linux, of course): diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 11d9b7418a..dfee7865e6 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -2163,6 +2163,23 @@ math_ldexp_impl(PyObject *module, double x, PyObject *i)
} else {
errno = 0;
r = ldexp(x, (int)exp);
+#if 1 // _MSC_VER
+ if (r && r > -DBL_MIN && r < DBL_MIN) {
+ int original_exp;
+ frexp(x, &original_exp);
+ if (original_exp > DBL_MIN_EXP) {
+ /* Shift down to the smallest normal binade. No bits lost. */
+ x = ldexp(x, DBL_MIN_EXP - original_exp);
+ exp += original_exp - DBL_MIN_EXP;
+ }
+ /* Multiplying by 2**exp finishes the job, and the HW will round as
+ appropriate. Note: if exp < -DBL_MANT_DIG, all of x is shifted to
+ be < 1/2 ULP of smallest denorm, so should be thrown away. If exp
+ is so very negative that ldexp underflows to 0, that's fine; no
+ need to check in advance. */
+ r = x*ldexp(1.0, (int)exp);
+ }
+#endif
if (isinf(r))
errno = ERANGE;
}A benchmark: # bench.py
import pyperf
from math import ldexp
tiny = float.fromhex('0x1p-1022')
runner = pyperf.Runner()
for x, i in [(1.0, 1),
(float.fromhex('0x1p-1022'), -1),
(6993274598585239.0, -1126)]:
s = f"ldexp({x.hex()}, {i})"
runner.bench_func(s, ldexp, x, i) |
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Okay, sure, but at least include a comment clarifying that it's a known issue in some older versions of the C runtime, and it's not worth trying to identify the version being used at runtime. I know the process involved in getting non-security fixes applied to Windows 10 at this stage, it's very unlikely anyone is going to consider this worthwhile for servicing (unless we can show it's actually impacting some big paid piece of software). Pragmatism beats purity in this area. |
Co-authored-by: Tim Peters <tim.peters@gmail.com>
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PR is ready for review: #133135 |
…3135) * pythongh-132876: workaround broken ldexp() on Windows 10 ldexp() fails to round subnormal results before Windows 11, so hide their bug. (cherry picked from commit cf8941c) Co-authored-by: Sergey B Kirpichev <skirpichev@gmail.com> Co-authored-by: Tim Peters <tim.peters@gmail.com>
…#134684) gh-132876: workaround broken ldexp() on Windows 10 (GH-133135) * gh-132876: workaround broken ldexp() on Windows 10 ldexp() fails to round subnormal results before Windows 11, so hide their bug. (cherry picked from commit cf8941c) Co-authored-by: Sergey B Kirpichev <skirpichev@gmail.com> Co-authored-by: Tim Peters <tim.peters@gmail.com>
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Fixed and backported. |
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Bug report
Bug description:
The correct result would be 1e-323. This is obviously a bug in the Windows ldexp implementation (it works fine on Linux). But it would be good, if it could be fixed on the CPython side with a workaround.
math.ldexp is used by mpmath to round from multiprecision to float, leading to incorrect rounding on Windows.
CPython versions tested on:
3.13
Operating systems tested on:
Windows
Linked PRs
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