| msg57088 - (view) |
Author: Andreas Kloeckner (inducer) |
Date: 2007-11-03 18:58 |
| This here basically says it all: >>> import cmath;[cmath.asinh(i*1e-17).real for i in range(0,20)] [4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16, 4.4408920985006257e-16] The boost.math toolkit at [2] is an implementation that does better in the above (real-only) aspect. [2] http://freespace.virgin.net/boost.regex/toolkit/html/index.html Tim Peters remarks in [1] that basically all of cmath is unsound. http://mail.python.org/pipermail/python-bugs-list/2001-February/004126.html I just wanted to make sure that this issue remains on the radar. |
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| msg57089 - (view) |
Author: Martin v. Löwis (loewis) *  |
Date: 2007-11-03 19:17 |
| Can you propose a patch? |
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| msg57090 - (view) |
Author: Andreas Kloeckner (inducer) |
Date: 2007-11-03 19:42 |
| On Samstag 03 November 2007, Martin v. Löwis wrote: > Martin v. Löwis added the comment: > > Can you propose a patch? Other than point at how boost.math does things, I don't have the time to work on this right now, sorry. Andreas |
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| msg57092 - (view) |
Author: Alan McIntyre (alanmcintyre) * |
Date: 2007-11-04 05:46 |
| I have to review a few complex math topics for some of my current course work, so I wouldn't mind taking a look into this. I can't promise I'll have the time required to make all of cmath correct (assuming it's as unsound as claimed), but I'll do what I can. |
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| msg57098 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2007-11-04 15:16 |
| I took a look at this a while back, and got as far as writing a pure Python drop-in replacement for cmath, based on Kahan's "branch cuts for elementary functions" paper. This fixes a variety of problems in cmath, including the buggy branch cuts for asinh. File attached, in case it's of any use. As Tim Peters pointed out, the real problem here is a lack of decent unit tests for these functions. I have tests for the file above, but they assume IEEE754 floats, which is probably not an acceptable assumption in general. |
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| msg57104 - (view) |
Author: Martin v. Löwis (loewis) * |
Date: 2007-11-04 18:38 |
| It would be ok if a test is only run on a system with IEEE floats, and skipped elsewhere. For all practical purposes, Python assumes that all systems have IEEE float. |
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| msg57835 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2007-11-26 02:18 |
| Here is (quite a large) patch, cmath.patch, that fixes a variety of problems in the current cmath module. A summary of the changes: * sqrt, log, acos, acosh, asin, asinh, atan, atanh no longer produce overflow errors for very large inputs * exp, cos, sin, tan, cosh, sinh, tanh produce valid answers in some cases where they incorrectly overflowed before. * sqrt and log are more accurate for tiny numbers * numeric problems in some functions (especially asinh and asin) should have been fixed * the branch cuts for asinh have been moved to the standard positions * the direction of continuity for the branch cuts of tan, tanh have been fixed * on systems with full hardware and system support for signed zeros (most modern systems), functions with a branch cut are continuous on both sides of the branch cut. (As recommended by the C99 standard, amongst others.) The patch includes documentation updates, but there are still no tests. (My current tests make heavy use of the MPFR library, and assume IEEE-754 format doubles, so need to be seriously reworked.) The tests are on my to- do list, but I'm unlikely to find time for them before the new year. In the meantime, I'd very much appreciate any feedback on this patch, if anyone has the time/energy/inclination to look at it. (Andreas: are you in a position to give this a test-run?) |
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| msg59268 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2008-01-05 00:25 |
| Here's an updated patch for cmath, complete with tests and documentation changes. There's an extra file, Lib/test/cmath.ctest, containing test values for the various functions; these test values were obtained using MPFR and interval arithmetic, and (modulo bugs) should all be correctly rounded. Any feedback would be much appreciated. |
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| msg59557 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2008-01-08 20:55 |
| A note to any potential reviewers for this patch (cmath3.patch): I'm especially looking for non-mathematical feedback here, so please don't be put off by the mathematics. Some questions: - there's a new file cmath.ctest containing testcases; should this be put directly into Lib/test (where it is right now), or is there a better place. Is the name of this file reasonable? - is the new stuff in pyport.h (checks for _copysign and copysign, and automatic renaming of _copysign to copysign) okay? Should it be in cmathmodule.c instead? - is the code in test_cmath that looks for the testcase file okay? And it would be really great if someone with access to a Windows box could just verify that the tests pass with this patch applied; I've only tested it on OS X and Linux. |
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| msg59568 - (view) |
Author: Christian Heimes (christian.heimes) * |
Date: 2008-01-08 22:42 |
| * I've added a configure test for copysign a while ago. I'm using this constructor for Windows compatibility in mathmodule.c: #ifdef MS_WINDOWS # define copysign _copysign # define HAVE_COPYSIGN 1 #endif #ifdef HAVE_COPYSIGN #endif I know no platform besides Windows with a _copysign method. You don't have to add tests for _copysign for Windows. You may want to add the code to PC/pyconfig.h and define HAVE_COPYSIGN there. * test_file = testdir + os.sep + 'cmath.ctest make that: test_file = os.path.join(testdir, 'cmath.ctest') * Windows doesn't have log1p, the hyperbolic area functions (asinh) and some other functions, too. IIRC Windows does only implement the Bessel functions of 1st and 2nd kind but non of the other C99 math functions. |
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| msg59570 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2008-01-08 22:54 |
| Okay: would it be okay for me to move the #ifdef MS_WINDOWS sequence somewhere where it can be used by both mathmodule.c and cmathmodule.c, then? There are replacements for log1p and asinh in the patch, so it shouldn't matter than they're missing on Windows---it might mean that the accuracy of some of the functions is slightly reduced on Windows, though. |
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| msg59572 - (view) |
Author: Christian Heimes (christian.heimes) * |
Date: 2008-01-08 23:16 |
| It may even be a good idea to move asinh, copysign and log1p to a new file Python/pymath.c and add compensatory implementations of acosh, atanh and expm1, too. The math related code in pyport.h could then be moved to Include/pymath.h. In the past some people have asked me to implement the reverse hyperbolic functions for the math module. This is beyond a simple fix for the cmath module and should be discussed on the python-dev list first. |
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| msg59637 - (view) |
Author: Christian Heimes (christian.heimes) * |
Date: 2008-01-10 00:20 |
| Guido, how do you like the idea of Include/pymath.h and Python/pymath.c containing supplementary mathematical functions and mathematical constants? Mark's patch for cmath is rather large, can it still be applied to 2.5? |
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| msg59638 - (view) |
Author: Guido van Rossum (gvanrossum) * |
Date: 2008-01-10 00:29 |
| Are you crazy? Adding new features to 2.5? No way! |
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| msg61499 - (view) |
Author: Christian Heimes (christian.heimes) * |
Date: 2008-01-22 11:16 |
| See #1640 and svn+ssh://pythondev@svn.python.org/python/branches/trunk-math |
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| msg65703 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2008-04-23 17:08 |
| Substantial fixes for the cmath module went into the trunk and the py3k branches as part of the merge of the trunk-math branch. These fixes address the asinh problems in this issue, amongst other things. See r62380 (trunk) and r62384 (py3k). |
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| msg105510 - (view) |
Author: Sebastien Binet (bins) |
Date: 2010-05-11 13:29 |
| hi there, it seems there is still a problem, at least with asinh(-2j) see: $ python Python 2.6.5 (r265:79063, Apr 1 2010, 05:28:39) [GCC 4.4.3 20100316 (prerelease)] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>> import numpy as np >>> np.__version__ '1.4.0' >>> import cmath >>> cmath.asinh(-2j) (1.3169578969248166-1.5707963267948966j) >>> np.arcsinh(-2j) (-1.3169578969248164-1.5707963267948966j) same behaviour for python3.1: $ python3 Python 3.1.2 (r312:79147, Apr 1 2010, 09:12:21) [GCC 4.4.3 20100316 (prerelease)] on linux2 Type "help", "copyright", "credits" or "license" for more information. >>> import cmath >>> cmath.asinh(-2j) (1.3169578969248166-1.5707963267948966j) cheers, sebastien. |
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| msg105512 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2010-05-11 13:39 |
| Python's result looks fine to me, as does numpy's: they're both giving a valid inverse hyperbolic sine: >>> from cmath import sinh >>> sinh(1.3169578969248166-1.5707963267948966j) (1.0605752387249067e-16-1.9999999999999998j) >>> sinh(-1.3169578969248164-1.5707963267948966j) (-1.0605752387249064e-16-1.9999999999999993j) Perhaps numpy is using different branch cuts? |
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| msg105515 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2010-05-11 14:00 |
| A bit more explanation: Python takes account of the sign of zero when deciding which side of the branch cut a value lies, which is the proper thing to do when you have signed zeros available (according to the likes of Kahan, anyway); I suspect that numpy isn't doing that, but is treating all values that lie directly on a branch in the same way. In this case there's a branch cut from -1j down to -1j*inf. Values just to the right of that branch cut (i.e., with positive real part) should have a result with positive real part; values just to the left of it should have negative real part: Some results (using complex() to create the values, since other ways of creating complex numbers are prone to changing the sign of a zero): >>> asinh(complex(0.0, -2.0)) (1.3169578969248166-1.5707963267948966j) >>> asinh(complex(1e-10, -2.0)) (1.3169578969248166-1.5707963267371616j) >>> asinh(complex(-0.0, -2.0)) (-1.3169578969248166-1.5707963267948966j) >>> asinh(complex(-1e-10, -2.0)) (-1.3169578969248166-1.5707963267371616j) So the cmath module is working as intended here. numpy may or may not be working as intended: I don't know how much they care about branch cut continuity. |
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| msg105517 - (view) |
Author: Sebastien Binet (bins) |
Date: 2010-05-11 14:05 |
| hi Mark, that may very well be so, but I'd naively standardize on C/Fortran behaviour (but that's probably my physicist bias) on my platform, the following piece of C-code: $ cat test_cmath.c #include <complex.h> #include <stdio.h> int main(int argc, char** argv) { complex c = casinh(-2*I); printf("asinh(-2j) = %g + %gi\n", creal(c), cimag(c)); return 0; } /* EOF */ gives: $ ./a.out asinh(-2j) = -1.31696 + -1.5708i cheers, sebastien. |
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| msg105519 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2010-05-11 14:08 |
| > that may very well be so, but I'd naively standardize on C/Fortran > behaviour (but that's probably my physicist bias) Yep, that's exactly what Python does. :) (Also follows the LISP standard). Note that in your program, you're feeding complex(-0.0, -2.0) to asinh, not complex(0.0, 2.0). |
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| msg105521 - (view) |
Author: Mark Dickinson (mark.dickinson) * |
Date: 2010-05-11 14:11 |
| > Note that in your program, you're feeding complex(-0.0, -2.0) to asinh, > not complex(0.0, 2.0). Bah; that should be complex(0.0, -2.0) in the second line, of course. Anyway, try passing conj(2*I) to asinh in your C program and see what happens. :) |
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| msg105522 - (view) |
Author: Sebastien Binet (bins) |
Date: 2010-05-11 15:01 |
| > Note that in your program, you're feeding complex(-0.0, -2.0) to asinh, > not complex(0.0, -2.0). ah! (ducking) |
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