Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Sturla Molden]

"Thomas Baruchel"  wrote:

> While this is obviously the most relevant answer for many users because
> it will allow them to use Numpy arrays exactly
> as they would have used them with native types, the wrong thing is that
> from some point of view "true" vectorization
> will be lost.

What does "true vectorization" mean anyway?


Sturla

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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Elliot Hallmark]

> What does "true vectorization" mean anyway?

Calling python functions on python objects in a for loop is not really
vectorized.  It's much slower than people intend when they use numpy.

Elliot
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Marten van Kerkwijk]

Hi All,

astropy `Time` indeed using two doubles internally, but is very limited in
the operations it allows: essentially only addition/subtraction, and
multiplication with/division by a normal double.

It would be great to have better support within numpy; it is a pity to have
a float128 type that does not provide the full associated precision.

All the best,

Marten



On Sat, Dec 12, 2015 at 1:02 PM, Sturla Molden 
wrote:

> "Thomas Baruchel"  wrote:
>
> > While this is obviously the most relevant answer for many users because
> > it will allow them to use Numpy arrays exactly
> > as they would have used them with native types, the wrong thing is that
> > from some point of view "true" vectorization
> > will be lost.
>
> What does "true vectorization" mean anyway?
>
>
> Sturla
>
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Anne Archibald]

On Fri, Dec 11, 2015, 18:04 David Cournapeau  wrote:

On Fri, Dec 11, 2015 at 4:22 PM, Anne Archibald  wrote:

Actually, GCC implements 128-bit floats in software and provides them as
__float128; there are also quad-precision versions of the usual functions.
The Intel compiler provides this as well, I think, but I don't think
Microsoft compilers do. A portable quad-precision library might be less
painful.

The cleanest way to add extended precision to numpy is by adding a
C-implemented dtype. This can be done in an extension module; see the
quaternion and half-precision modules online.

We actually used __float128 dtype as an example of how to create a custom
dtype for a numpy C tutorial we did w/ Stefan Van der Walt a few years ago
at SciPy.

IIRC, one of the issue to make it more than a PoC was that numpy hardcoded
things like long double being the higest precision, etc... But that may has
been fixed since then.

I did some work on numpy's long-double support, partly to better understand
what would be needed to make quads work. The main obstacle is, I think, the
same: python floats are only 64-bit, and many functions are stuck passing
through them. It takes a lot of fiddling to make string conversions work
without passing through python floats, for example, and it takes some care
to produce scalars of the appropriate type. There are a few places where
you'd want to modify the guts of numpy if you had a higher precision
available than long doubles.

Anne
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[josef.pktd]

On Fri, Dec 11, 2015 at 11:22 AM, Anne Archibald  wrote:
> Actually, GCC implements 128-bit floats in software and provides them as
> __float128; there are also quad-precision versions of the usual functions.
> The Intel compiler provides this as well, I think, but I don't think
> Microsoft compilers do. A portable quad-precision library might be less
> painful.
>
> The cleanest way to add extended precision to numpy is by adding a
> C-implemented dtype. This can be done in an extension module; see the
> quaternion and half-precision modules online.
>
> Anne
>
>
> On Fri, Dec 11, 2015, 16:46 Charles R Harris 
> wrote:
>>
>> On Fri, Dec 11, 2015 at 6:25 AM, Thomas Baruchel  wrote:
>>>
>>> From time to time it is asked on forums how to extend precision of
>>> computation on Numpy array. The most common answer
>>> given to this question is: use the dtype=object with some arbitrary
>>> precision module like mpmath or gmpy.
>>> See
>>> http://stackoverflow.com/questions/6876377/numpy-arbitrary-precision-linear-algebra
>>> or http://stackoverflow.com/questions/21165745/precision-loss-numpy-mpmath
>>> or
>>> http://stackoverflow.com/questions/15307589/numpy-array-with-mpz-mpfr-values
>>>
>>> While this is obviously the most relevant answer for many users because
>>> it will allow them to use Numpy arrays exactly
>>> as they would have used them with native types, the wrong thing is that
>>> from some point of view "true" vectorization
>>> will be lost.
>>>
>>> With years I got very familiar with the extended double-double type which
>>> has (for usual architectures) about 32 accurate
>>> digits with faster arithmetic than "arbitrary precision types". I even
>>> used it for research purpose in number theory and
>>> I got convinced that it is a very wonderful type as long as such
>>> precision is suitable.
>>>
>>> I often implemented it partially under Numpy, most of the time by trying
>>> to vectorize at a low-level the libqd library.
>>>
>>> But I recently thought that a very nice and portable way of implementing
>>> it under Numpy would be to use the existing layer
>>> of vectorization on floats for computing the arithmetic operations by
>>> "columns containing half of the numbers" rather than
>>> by "full numbers". As a proof of concept I wrote the following file:
>>> https://gist.github.com/baruchel/c86ed748939534d8910d
>>>
>>> I converted and vectorized the Algol 60 codes from
>>> http://szmoore.net/ipdf/documents/references/dekker1971afloating.pdf
>>> (Dekker, 1971).
>>>
>>> A test is provided at the end; for inverting 100,000 numbers, my type is
>>> about 3 or 4 times faster than GMPY and almost
>>> 50 times faster than MPmath. It should be even faster for some other
>>> operations since I had to create another np.ones
>>> array for testing this type because inversion isn't implemented here
>>> (which could of course be done). You can run this file by yourself
>>> (maybe you will have to discard mpmath or gmpy if you don't have it).
>>>
>>> I would like to discuss about the way to make available something related
>>> to that.
>>>
>>> a) Would it be relevant to include that in Numpy ? (I would think to some
>>> "contribution"-tool rather than including it in
>>> the core of Numpy because it would be painful to code all ufuncs; on the
>>> other hand I am pretty sure that many would be happy
>>> to perform several arithmetic operations by knowing that they can't use
>>> cos/sin/etc. on this type; in other words, I am not
>>> sure it would be a good idea to embed it as an every-day type but I think
>>> it would be nice to have it quickly available
>>> in some way). If you agree with that, in which way should I code it (the
>>> current link only is a "proof of concept"; I would
>>> be very happy to code it in some cleaner way)?
>>>
>>> b) Do you think such attempt should remain something external to Numpy
>>> itself and be released on my Github account without being
>>> integrated to Numpy?
>>
>>
>> I think astropy does something similar for time and dates. There has also
>> been some talk of adding a user type for ieee 128 bit doubles. I've looked
>> once for relevant code for the latter and, IIRC, the available packages were
>> GPL :(.

This might be the same as or similar to a recent announcement for Julia

https://groups.google.com/d/msg/julia-users/iHTaxRVj1yM/M-WtZCedCQAJ


It would be useful to get this in a consistent way across platforms
and compilers.
I can think of several applications where higher precision reduce
operations would be
useful in statistics.
As Windows user, I never even saw a higher precision float.

Josef


>>
>> Chuck
>> ___
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Anne Archibald]

Actually, GCC implements 128-bit floats in software and provides them as
__float128; there are also quad-precision versions of the usual functions.
The Intel compiler provides this as well, I think, but I don't think
Microsoft compilers do. A portable quad-precision library might be less
painful.

The cleanest way to add extended precision to numpy is by adding a
C-implemented dtype. This can be done in an extension module; see the
quaternion and half-precision modules online.

Anne

On Fri, Dec 11, 2015, 16:46 Charles R Harris 
wrote:

> On Fri, Dec 11, 2015 at 6:25 AM, Thomas Baruchel  wrote:
>
>> From time to time it is asked on forums how to extend precision of
>> computation on Numpy array. The most common answer
>> given to this question is: use the dtype=object with some arbitrary
>> precision module like mpmath or gmpy.
>> See
>> http://stackoverflow.com/questions/6876377/numpy-arbitrary-precision-linear-algebra
>> or
>> http://stackoverflow.com/questions/21165745/precision-loss-numpy-mpmath
>> or
>> http://stackoverflow.com/questions/15307589/numpy-array-with-mpz-mpfr-values
>>
>> While this is obviously the most relevant answer for many users because
>> it will allow them to use Numpy arrays exactly
>> as they would have used them with native types, the wrong thing is that
>> from some point of view "true" vectorization
>> will be lost.
>>
>> With years I got very familiar with the extended double-double type which
>> has (for usual architectures) about 32 accurate
>> digits with faster arithmetic than "arbitrary precision types". I even
>> used it for research purpose in number theory and
>> I got convinced that it is a very wonderful type as long as such
>> precision is suitable.
>>
>> I often implemented it partially under Numpy, most of the time by trying
>> to vectorize at a low-level the libqd library.
>>
>> But I recently thought that a very nice and portable way of implementing
>> it under Numpy would be to use the existing layer
>> of vectorization on floats for computing the arithmetic operations by
>> "columns containing half of the numbers" rather than
>> by "full numbers". As a proof of concept I wrote the following file:
>> https://gist.github.com/baruchel/c86ed748939534d8910d
>>
>> I converted and vectorized the Algol 60 codes from
>> http://szmoore.net/ipdf/documents/references/dekker1971afloating.pdf
>> (Dekker, 1971).
>>
>> A test is provided at the end; for inverting 100,000 numbers, my type is
>> about 3 or 4 times faster than GMPY and almost
>> 50 times faster than MPmath. It should be even faster for some other
>> operations since I had to create another np.ones
>> array for testing this type because inversion isn't implemented here
>> (which could of course be done). You can run this file by yourself
>> (maybe you will have to discard mpmath or gmpy if you don't have it).
>>
>> I would like to discuss about the way to make available something related
>> to that.
>>
>> a) Would it be relevant to include that in Numpy ? (I would think to some
>> "contribution"-tool rather than including it in
>> the core of Numpy because it would be painful to code all ufuncs; on the
>> other hand I am pretty sure that many would be happy
>> to perform several arithmetic operations by knowing that they can't use
>> cos/sin/etc. on this type; in other words, I am not
>> sure it would be a good idea to embed it as an every-day type but I think
>> it would be nice to have it quickly available
>> in some way). If you agree with that, in which way should I code it (the
>> current link only is a "proof of concept"; I would
>> be very happy to code it in some cleaner way)?
>>
>> b) Do you think such attempt should remain something external to Numpy
>> itself and be released on my Github account without being
>> integrated to Numpy?
>>
>
> I think astropy does something similar for time and dates. There has also
> been some talk of adding a user type for ieee 128 bit doubles. I've looked
> once for relevant code for the latter and, IIRC, the available packages
> were GPL :(.
>
> Chuck
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[David Cournapeau]

On Fri, Dec 11, 2015 at 4:22 PM, Anne Archibald  wrote:

> Actually, GCC implements 128-bit floats in software and provides them as
> __float128; there are also quad-precision versions of the usual functions.
> The Intel compiler provides this as well, I think, but I don't think
> Microsoft compilers do. A portable quad-precision library might be less
> painful.
>
> The cleanest way to add extended precision to numpy is by adding a
> C-implemented dtype. This can be done in an extension module; see the
> quaternion and half-precision modules online.
>

We actually used __float128 dtype as an example of how to create a custom
dtype for a numpy C tutorial we did w/ Stefan Van der Walt a few years ago
at SciPy.

IIRC, one of the issue to make it more than a PoC was that numpy hardcoded
things like long double being the higest precision, etc... But that may has
been fixed since then.

David

> Anne
>
> On Fri, Dec 11, 2015, 16:46 Charles R Harris 
> wrote:
>
>> On Fri, Dec 11, 2015 at 6:25 AM, Thomas Baruchel 
>> wrote:
>>
>>> From time to time it is asked on forums how to extend precision of
>>> computation on Numpy array. The most common answer
>>> given to this question is: use the dtype=object with some arbitrary
>>> precision module like mpmath or gmpy.
>>> See
>>> http://stackoverflow.com/questions/6876377/numpy-arbitrary-precision-linear-algebra
>>> or
>>> http://stackoverflow.com/questions/21165745/precision-loss-numpy-mpmath
>>> or
>>> http://stackoverflow.com/questions/15307589/numpy-array-with-mpz-mpfr-values
>>>
>>> While this is obviously the most relevant answer for many users because
>>> it will allow them to use Numpy arrays exactly
>>> as they would have used them with native types, the wrong thing is that
>>> from some point of view "true" vectorization
>>> will be lost.
>>>
>>> With years I got very familiar with the extended double-double type
>>> which has (for usual architectures) about 32 accurate
>>> digits with faster arithmetic than "arbitrary precision types". I even
>>> used it for research purpose in number theory and
>>> I got convinced that it is a very wonderful type as long as such
>>> precision is suitable.
>>>
>>> I often implemented it partially under Numpy, most of the time by trying
>>> to vectorize at a low-level the libqd library.
>>>
>>> But I recently thought that a very nice and portable way of implementing
>>> it under Numpy would be to use the existing layer
>>> of vectorization on floats for computing the arithmetic operations by
>>> "columns containing half of the numbers" rather than
>>> by "full numbers". As a proof of concept I wrote the following file:
>>> https://gist.github.com/baruchel/c86ed748939534d8910d
>>>
>>> I converted and vectorized the Algol 60 codes from
>>> http://szmoore.net/ipdf/documents/references/dekker1971afloating.pdf
>>> (Dekker, 1971).
>>>
>>> A test is provided at the end; for inverting 100,000 numbers, my type is
>>> about 3 or 4 times faster than GMPY and almost
>>> 50 times faster than MPmath. It should be even faster for some other
>>> operations since I had to create another np.ones
>>> array for testing this type because inversion isn't implemented here
>>> (which could of course be done). You can run this file by yourself
>>> (maybe you will have to discard mpmath or gmpy if you don't have it).
>>>
>>> I would like to discuss about the way to make available something
>>> related to that.
>>>
>>> a) Would it be relevant to include that in Numpy ? (I would think to
>>> some "contribution"-tool rather than including it in
>>> the core of Numpy because it would be painful to code all ufuncs; on the
>>> other hand I am pretty sure that many would be happy
>>> to perform several arithmetic operations by knowing that they can't use
>>> cos/sin/etc. on this type; in other words, I am not
>>> sure it would be a good idea to embed it as an every-day type but I
>>> think it would be nice to have it quickly available
>>> in some way). If you agree with that, in which way should I code it (the
>>> current link only is a "proof of concept"; I would
>>> be very happy to code it in some cleaner way)?
>>>
>>> b) Do you think such attempt should remain something external to Numpy
>>> itself and be released on my Github account without being
>>> integrated to Numpy?
>>>
>>
>> I think astropy does something similar for time and dates. There has also
>> been some talk of adding a user type for ieee 128 bit doubles. I've looked
>> once for relevant code for the latter and, IIRC, the available packages
>> were GPL :(.
>>
>> Chuck
>> ___
>> NumPy-Discussion mailing list
>> NumPy-Discussion@scipy.org
>> https://mail.scipy.org/mailman/listinfo/numpy-discussion
>>
>
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>

Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Chris Barker - NOAA Federal]

> There has also been some talk of adding a user type for ieee 128 bit doubles. 
> I've looked once for relevant code for the latter and, IIRC, the available 
> packages were GPL :(.


This looks like it's BSD-Ish:

http://www.jhauser.us/arithmetic/SoftFloat.html

Don't know if it's any good

CHB


>
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Charles R Harris]

On Fri, Dec 11, 2015 at 6:25 AM, Thomas Baruchel  wrote:

> From time to time it is asked on forums how to extend precision of
> computation on Numpy array. The most common answer
> given to this question is: use the dtype=object with some arbitrary
> precision module like mpmath or gmpy.
> See
> http://stackoverflow.com/questions/6876377/numpy-arbitrary-precision-linear-algebra
> or http://stackoverflow.com/questions/21165745/precision-loss-numpy-mpmath
> or
> http://stackoverflow.com/questions/15307589/numpy-array-with-mpz-mpfr-values
>
> While this is obviously the most relevant answer for many users because it
> will allow them to use Numpy arrays exactly
> as they would have used them with native types, the wrong thing is that
> from some point of view "true" vectorization
> will be lost.
>
> With years I got very familiar with the extended double-double type which
> has (for usual architectures) about 32 accurate
> digits with faster arithmetic than "arbitrary precision types". I even
> used it for research purpose in number theory and
> I got convinced that it is a very wonderful type as long as such precision
> is suitable.
>
> I often implemented it partially under Numpy, most of the time by trying
> to vectorize at a low-level the libqd library.
>
> But I recently thought that a very nice and portable way of implementing
> it under Numpy would be to use the existing layer
> of vectorization on floats for computing the arithmetic operations by
> "columns containing half of the numbers" rather than
> by "full numbers". As a proof of concept I wrote the following file:
> https://gist.github.com/baruchel/c86ed748939534d8910d
>
> I converted and vectorized the Algol 60 codes from
> http://szmoore.net/ipdf/documents/references/dekker1971afloating.pdf
> (Dekker, 1971).
>
> A test is provided at the end; for inverting 100,000 numbers, my type is
> about 3 or 4 times faster than GMPY and almost
> 50 times faster than MPmath. It should be even faster for some other
> operations since I had to create another np.ones
> array for testing this type because inversion isn't implemented here
> (which could of course be done). You can run this file by yourself
> (maybe you will have to discard mpmath or gmpy if you don't have it).
>
> I would like to discuss about the way to make available something related
> to that.
>
> a) Would it be relevant to include that in Numpy ? (I would think to some
> "contribution"-tool rather than including it in
> the core of Numpy because it would be painful to code all ufuncs; on the
> other hand I am pretty sure that many would be happy
> to perform several arithmetic operations by knowing that they can't use
> cos/sin/etc. on this type; in other words, I am not
> sure it would be a good idea to embed it as an every-day type but I think
> it would be nice to have it quickly available
> in some way). If you agree with that, in which way should I code it (the
> current link only is a "proof of concept"; I would
> be very happy to code it in some cleaner way)?
>
> b) Do you think such attempt should remain something external to Numpy
> itself and be released on my Github account without being
> integrated to Numpy?
>

I think astropy does something similar for time and dates. There has also
been some talk of adding a user type for ieee 128 bit doubles. I've looked
once for relevant code for the latter and, IIRC, the available packages
were GPL :(.

Chuck
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Nathaniel Smith]

On Dec 11, 2015 7:46 AM, "Charles R Harris" 
wrote:
>
>
>
> On Fri, Dec 11, 2015 at 6:25 AM, Thomas Baruchel  wrote:
>>
>> From time to time it is asked on forums how to extend precision of
computation on Numpy array. The most common answer
>> given to this question is: use the dtype=object with some arbitrary
precision module like mpmath or gmpy.
>> See
http://stackoverflow.com/questions/6876377/numpy-arbitrary-precision-linear-algebra
or http://stackoverflow.com/questions/21165745/precision-loss-numpy-mpmath
or
http://stackoverflow.com/questions/15307589/numpy-array-with-mpz-mpfr-values
>>
>> While this is obviously the most relevant answer for many users because
it will allow them to use Numpy arrays exactly
>> as they would have used them with native types, the wrong thing is that
from some point of view "true" vectorization
>> will be lost.
>>
>> With years I got very familiar with the extended double-double type
which has (for usual architectures) about 32 accurate
>> digits with faster arithmetic than "arbitrary precision types". I even
used it for research purpose in number theory and
>> I got convinced that it is a very wonderful type as long as such
precision is suitable.
>>
>> I often implemented it partially under Numpy, most of the time by trying
to vectorize at a low-level the libqd library.
>>
>> But I recently thought that a very nice and portable way of implementing
it under Numpy would be to use the existing layer
>> of vectorization on floats for computing the arithmetic operations by
"columns containing half of the numbers" rather than
>> by "full numbers". As a proof of concept I wrote the following file:
https://gist.github.com/baruchel/c86ed748939534d8910d
>>
>> I converted and vectorized the Algol 60 codes from
http://szmoore.net/ipdf/documents/references/dekker1971afloating.pdf
>> (Dekker, 1971).
>>
>> A test is provided at the end; for inverting 100,000 numbers, my type is
about 3 or 4 times faster than GMPY and almost
>> 50 times faster than MPmath. It should be even faster for some other
operations since I had to create another np.ones
>> array for testing this type because inversion isn't implemented here
(which could of course be done). You can run this file by yourself
>> (maybe you will have to discard mpmath or gmpy if you don't have it).
>>
>> I would like to discuss about the way to make available something
related to that.
>>
>> a) Would it be relevant to include that in Numpy ? (I would think to
some "contribution"-tool rather than including it in
>> the core of Numpy because it would be painful to code all ufuncs; on the
other hand I am pretty sure that many would be happy
>> to perform several arithmetic operations by knowing that they can't use
cos/sin/etc. on this type; in other words, I am not
>> sure it would be a good idea to embed it as an every-day type but I
think it would be nice to have it quickly available
>> in some way). If you agree with that, in which way should I code it (the
current link only is a "proof of concept"; I would
>> be very happy to code it in some cleaner way)?
>>
>> b) Do you think such attempt should remain something external to Numpy
itself and be released on my Github account without being
>> integrated to Numpy?
>
>
> I think astropy does something similar for time and dates. There has also
been some talk of adding a user type for ieee 128 bit doubles. I've looked
once for relevant code for the latter and, IIRC, the available packages
were GPL :(.

You're probably thinking of the __float128 support in gcc, which relies on
a LGPL (not GPL) runtime support library. (LGPL = any patches to the
support library itself need to remain open source, but no restrictions are
imposed on code that merely uses it.)

Still, probably something that should be done outside of numpy itself for
now.

-n
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Charles R Harris]

On Fri, Dec 11, 2015 at 10:45 AM, Nathaniel Smith  wrote:

> On Dec 11, 2015 7:46 AM, "Charles R Harris" 
> wrote:
> >
> >
> >
> > On Fri, Dec 11, 2015 at 6:25 AM, Thomas Baruchel 
> wrote:
> >>
> >> From time to time it is asked on forums how to extend precision of
> computation on Numpy array. The most common answer
> >> given to this question is: use the dtype=object with some arbitrary
> precision module like mpmath or gmpy.
> >> See
> http://stackoverflow.com/questions/6876377/numpy-arbitrary-precision-linear-algebra
> or http://stackoverflow.com/questions/21165745/precision-loss-numpy-mpmath
> or
> http://stackoverflow.com/questions/15307589/numpy-array-with-mpz-mpfr-values
> >>
> >> While this is obviously the most relevant answer for many users because
> it will allow them to use Numpy arrays exactly
> >> as they would have used them with native types, the wrong thing is that
> from some point of view "true" vectorization
> >> will be lost.
> >>
> >> With years I got very familiar with the extended double-double type
> which has (for usual architectures) about 32 accurate
> >> digits with faster arithmetic than "arbitrary precision types". I even
> used it for research purpose in number theory and
> >> I got convinced that it is a very wonderful type as long as such
> precision is suitable.
> >>
> >> I often implemented it partially under Numpy, most of the time by
> trying to vectorize at a low-level the libqd library.
> >>
> >> But I recently thought that a very nice and portable way of
> implementing it under Numpy would be to use the existing layer
> >> of vectorization on floats for computing the arithmetic operations by
> "columns containing half of the numbers" rather than
> >> by "full numbers". As a proof of concept I wrote the following file:
> https://gist.github.com/baruchel/c86ed748939534d8910d
> >>
> >> I converted and vectorized the Algol 60 codes from
> http://szmoore.net/ipdf/documents/references/dekker1971afloating.pdf
> >> (Dekker, 1971).
> >>
> >> A test is provided at the end; for inverting 100,000 numbers, my type
> is about 3 or 4 times faster than GMPY and almost
> >> 50 times faster than MPmath. It should be even faster for some other
> operations since I had to create another np.ones
> >> array for testing this type because inversion isn't implemented here
> (which could of course be done). You can run this file by yourself
> >> (maybe you will have to discard mpmath or gmpy if you don't have it).
> >>
> >> I would like to discuss about the way to make available something
> related to that.
> >>
> >> a) Would it be relevant to include that in Numpy ? (I would think to
> some "contribution"-tool rather than including it in
> >> the core of Numpy because it would be painful to code all ufuncs; on
> the other hand I am pretty sure that many would be happy
> >> to perform several arithmetic operations by knowing that they can't use
> cos/sin/etc. on this type; in other words, I am not
> >> sure it would be a good idea to embed it as an every-day type but I
> think it would be nice to have it quickly available
> >> in some way). If you agree with that, in which way should I code it
> (the current link only is a "proof of concept"; I would
> >> be very happy to code it in some cleaner way)?
> >>
> >> b) Do you think such attempt should remain something external to Numpy
> itself and be released on my Github account without being
> >> integrated to Numpy?
> >
> >
> > I think astropy does something similar for time and dates. There has
> also been some talk of adding a user type for ieee 128 bit doubles. I've
> looked once for relevant code for the latter and, IIRC, the available
> packages were GPL :(.
>
> You're probably thinking of the __float128 support in gcc, which relies on
> a LGPL (not GPL) runtime support library. (LGPL = any patches to the
> support library itself need to remain open source, but no restrictions are
> imposed on code that merely uses it.)
>
> Still, probably something that should be done outside of numpy itself for
> now.
>

No, there are several other software packages out there. I know of the gcc
version, but was looking for something more portable.

Chuck
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Re: [Numpy-discussion] Fast vectorized arithmetic with ~32 significant digits under Numpy

[Eric Moore]

I have a mostly complete wrapping of the double-double type from the QD
library (http://crd-legacy.lbl.gov/~dhbailey/mpdist/) into a numpy dtype.
The real problem is, as david pointed out, user dtypes aren't quite full
equivalents of the builtin dtypes.  I can post the code if there is
interest.

Something along the lines of what's being discussed here would be nice,
since the extended type is subject to such variation.

Eric

On Fri, Dec 11, 2015 at 12:51 PM, Charles R Harris <
charlesr.har...@gmail.com> wrote:

>
>
> On Fri, Dec 11, 2015 at 10:45 AM, Nathaniel Smith  wrote:
>
>> On Dec 11, 2015 7:46 AM, "Charles R Harris" 
>> wrote:
>> >
>> >
>> >
>> > On Fri, Dec 11, 2015 at 6:25 AM, Thomas Baruchel 
>> wrote:
>> >>
>> >> From time to time it is asked on forums how to extend precision of
>> computation on Numpy array. The most common answer
>> >> given to this question is: use the dtype=object with some arbitrary
>> precision module like mpmath or gmpy.
>> >> See
>> http://stackoverflow.com/questions/6876377/numpy-arbitrary-precision-linear-algebra
>> or
>> http://stackoverflow.com/questions/21165745/precision-loss-numpy-mpmath
>> or
>> http://stackoverflow.com/questions/15307589/numpy-array-with-mpz-mpfr-values
>> >>
>> >> While this is obviously the most relevant answer for many users
>> because it will allow them to use Numpy arrays exactly
>> >> as they would have used them with native types, the wrong thing is
>> that from some point of view "true" vectorization
>> >> will be lost.
>> >>
>> >> With years I got very familiar with the extended double-double type
>> which has (for usual architectures) about 32 accurate
>> >> digits with faster arithmetic than "arbitrary precision types". I even
>> used it for research purpose in number theory and
>> >> I got convinced that it is a very wonderful type as long as such
>> precision is suitable.
>> >>
>> >> I often implemented it partially under Numpy, most of the time by
>> trying to vectorize at a low-level the libqd library.
>> >>
>> >> But I recently thought that a very nice and portable way of
>> implementing it under Numpy would be to use the existing layer
>> >> of vectorization on floats for computing the arithmetic operations by
>> "columns containing half of the numbers" rather than
>> >> by "full numbers". As a proof of concept I wrote the following file:
>> https://gist.github.com/baruchel/c86ed748939534d8910d
>> >>
>> >> I converted and vectorized the Algol 60 codes from
>> http://szmoore.net/ipdf/documents/references/dekker1971afloating.pdf
>> >> (Dekker, 1971).
>> >>
>> >> A test is provided at the end; for inverting 100,000 numbers, my type
>> is about 3 or 4 times faster than GMPY and almost
>> >> 50 times faster than MPmath. It should be even faster for some other
>> operations since I had to create another np.ones
>> >> array for testing this type because inversion isn't implemented here
>> (which could of course be done). You can run this file by yourself
>> >> (maybe you will have to discard mpmath or gmpy if you don't have it).
>> >>
>> >> I would like to discuss about the way to make available something
>> related to that.
>> >>
>> >> a) Would it be relevant to include that in Numpy ? (I would think to
>> some "contribution"-tool rather than including it in
>> >> the core of Numpy because it would be painful to code all ufuncs; on
>> the other hand I am pretty sure that many would be happy
>> >> to perform several arithmetic operations by knowing that they can't
>> use cos/sin/etc. on this type; in other words, I am not
>> >> sure it would be a good idea to embed it as an every-day type but I
>> think it would be nice to have it quickly available
>> >> in some way). If you agree with that, in which way should I code it
>> (the current link only is a "proof of concept"; I would
>> >> be very happy to code it in some cleaner way)?
>> >>
>> >> b) Do you think such attempt should remain something external to Numpy
>> itself and be released on my Github account without being
>> >> integrated to Numpy?
>> >
>> >
>> > I think astropy does something similar for time and dates. There has
>> also been some talk of adding a user type for ieee 128 bit doubles. I've
>> looked once for relevant code for the latter and, IIRC, the available
>> packages were GPL :(.
>>
>> You're probably thinking of the __float128 support in gcc, which relies
>> on a LGPL (not GPL) runtime support library. (LGPL = any patches to the
>> support library itself need to remain open source, but no restrictions are
>> imposed on code that merely uses it.)
>>
>> Still, probably something that should be done outside of numpy itself for
>> now.
>>
>
> No, there are several other software packages out there. I know of the gcc
> version, but was looking for something more portable.
>
> Chuck
>
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