[Numpy-discussion] Moving forward with value based casting

[Tyler Reddy]

A few thoughts:

- We're not trying to achieve systematic guards against integer overflow /
wrapping in ufunc inner loops, right? The performance tradeoffs for a
"result-based" casting / exception handling addition would presumably be
controversial? I know there was some discussion about having an "overflow
detection mode"  (toggle) of some sort that could be activated for ufunc
loops, but don't think that gained much traction/ priority. I think for
floats we have an awkward way to propagate something back to the user if
there's an issue.
- It sounds like the objective is instead primarily to achieve pure
dtype-based promotion, which is then effectively just a casting table,
which is what I think you mean by "cache?"
- Is it a safe assumption that for a cache (dtype-only casting table), the
main tradeoff is that we'd likely tend towards conservative upcasting and
using more memory in output types in many cases vs. NumPy at the moment?
Stephan seems concerned about that, presumably because x + 1 suddenly
changes output dtype in an overwhelming number of current code lines and
future simple examples for end users.
- If np.array + 1 absolutely has to stay the same output dtype moving
forward, then "Keeping Value based casting only for python types" is the
one that looks most promising to me initially, with a few further concerns:

1) Would that give you enough refactoring "wiggle room" to achieve the
simplifications you need? If value-based promotion still happens for a
non-NumPy operand, can you abstract that logic cleanly from the "pure dtype
cache / table" that is planned for NumPy operands?
2) Is the "out" argument to ufuncs a satisfactory alternative to the "power
users" who want to "override" default output casting type? We suggest that
they pre-allocate an output array of the desired type if they want to save
memory and if they overflow or wrap integers that is their problem. Can we
reasonably ask people who currently depend on the memory-conservation they
might get from value-based behavior to adjust in this way?
3) Presumably "out" does / will circumvent the "cache / dtype casting
table?"

Tyler

On Wed, 5 Jun 2019 at 15:37, Sebastian Berg <sebastian at sipsolutions.net>
wrote:

> Hi all,
>
> Maybe to clarify this at least a little, here are some examples for
> what currently happen and what I could imagine we can go to (all in
> terms of output dtype).
>
> float32_arr = np.ones(10, dtype=np.float32)
> int8_arr = np.ones(10, dtype=np.int8)
> uint8_arr = np.ones(10, dtype=np.uint8)
>
>
> Current behaviour:
> ------------------
>
> float32_arr + 12.  # float32
> float32_arr + 2**200  # float64 (because np.float32(2**200) == np.inf)
>
> int8_arr + 127     # int8
> int8_arr + 128     # int16
> int8_arr + 2**20   # int32
> uint8_arr + -1     # uint16
>
> # But only for arrays that are not 0d:
> int8_arr + np.array(1, dtype=np.int32)  # int8
> int8_arr + np.array([1], dtype=np.int32)  # int32
>
> # When the actual typing is given, this does not change:
>
> float32_arr + np.float64(12.)                  # float32
> float32_arr + np.array(12., dtype=np.float64)  # float32
>
> # Except for inexact types, or complex:
> int8_arr + np.float16(3)  # float16  (same as array behaviour)
>
> # The exact same happens with all ufuncs:
> np.add(float32_arr, 1)                               # float32
> np.add(float32_arr, np.array(12., dtype=np.float64)  # float32
>
>
> Keeping Value based casting only for python types
> -------------------------------------------------
>
> In this case, most examples above stay unchanged, because they use
> plain python integers or floats, such as 2, 127, 12., 3, ... without
> any type information attached, such as `np.float64(12.)`.
>
> These change for example:
>
> float32_arr + np.float64(12.)                        # float64
> float32_arr + np.array(12., dtype=np.float64)        # float64
> np.add(float32_arr, np.array(12., dtype=np.float64)  # float64
>
> # so if you use `np.int32` it will be the same as np.uint64(10000)
>
> int8_arr + np.int32(1)      # int32
> int8_arr + np.int32(2**20)  # int32
>
>
> Remove Value based casting completely
> -------------------------------------
>
> We could simply abolish it completely, a python `1` would always behave
> the same as `np.int_(1)`. The downside of this is that:
>
> int8_arr + 1  # int64 (or int32)
>
> uses much more memory suddenly. Or, we remove it from ufuncs, but not
> from operators:
>
> int8_arr + 1  # int8 dtype
>
> but:
>
> np.add(int8_arr, 1)  # int64
> # same as:
> np.add(int8_arr, np.array(1))  # int16
>
> The main reason why I was wondering about that is that for operators
> the logic seems fairly simple, but for general ufuncs it seems more
> complex.
>
> Best,
>
> Sebastian
>
>
>
> On Wed, 2019-06-05 at 15:41 -0500, Sebastian Berg wrote:
> > Hi all,
> >
> > TL;DR:
> >
> > Value based promotion seems complex both for users and ufunc-
> > dispatching/promotion logic. Is there any way we can move forward
> > here,
> > and if we do, could we just risk some possible (maybe not-existing)
> > corner cases to break early to get on the way?
> >
> > -----------
> >
> > Currently when you write code such as:
> >
> > arr = np.array([1, 43, 23], dtype=np.uint16)
> > res = arr + 1
> >
> > Numpy uses fairly sophisticated logic to decide that `1` can be
> > represented as a uint16, and thus for all unary functions (and most
> > others as well), the output will have a `res.dtype` of uint16.
> >
> > Similar logic also exists for floating point types, where a lower
> > precision floating point can be used:
> >
> > arr = np.array([1, 43, 23], dtype=np.float32)
> > (arr + np.float64(2.)).dtype  # will be float32
> >
> > Currently, this value based logic is enforced by checking whether the
> > cast is possible: "4" can be cast to int8, uint8. So the first call
> > above will at some point check if "uint16 + uint16 -> uint16" is a
> > valid operation, find that it is, and thus stop searching. (There is
> > the additional logic, that when both/all operands are scalars, it is
> > not applied).
> >
> > Note that while it is defined in terms of casting "1" to uint8 safely
> > being possible even though 1 may be typed as int64. This logic thus
> > affects all promotion rules as well (i.e. what should the output
> > dtype
> > be).
> >
> >
> > There 2 main discussion points/issues about it:
> >
> > 1. Should value based casting/promotion logic exist at all?
> >
> > Arguably an `np.int32(3)` has type information attached to it, so why
> > should we ignore it. It can also be tricky for users, because a small
> > change in values can change the result data type.
> > Because 0-D arrays and scalars are too close inside numpy (you will
> > often not know which one you get). There is not much option but to
> > handle them identically. However, it seems pretty odd that:
> >  * `np.array(3, dtype=np.int32)` + np.arange(10, dtype=int8)
> >  * `np.array([3], dtype=np.int32)` + np.arange(10, dtype=int8)
> >
> > give a different result.
> >
> > This is a bit different for python scalars, which do not have a type
> > attached already.
> >
> >
> > 2. Promotion and type resolution in Ufuncs:
> >
> > What is currently bothering me is that the decision what the output
> > dtypes should be currently depends on the values in complicated ways.
> > It would be nice if we can decide which type signature to use without
> > actually looking at values (or at least only very early on).
> >
> > One reason here is caching and simplicity. I would like to be able to
> > cache which loop should be used for what input. Having value based
> > casting in there bloats up the problem.
> > Of course it currently works OK, but especially when user dtypes come
> > into play, caching would seem like a nice optimization option.
> >
> > Because `uint8(127)` can also be a `int8`, but uint8(128) it is not
> > as
> > simple as finding the "minimal" dtype once and working with that."
> > Of course Eric and I discussed this a bit before, and you could
> > create
> > an internal "uint7" dtype which has the only purpose of flagging that
> > a
> > cast to int8 is safe.
> >
> > I suppose it is possible I am barking up the wrong tree here, and
> > this
> > caching/predictability is not vital (or can be solved with such an
> > internal dtype easily, although I am not sure it seems elegant).
> >
> >
> > Possible options to move forward
> > --------------------------------
> >
> > I have to still see a bit how trick things are. But there are a few
> > possible options. I would like to move the scalar logic to the
> > beginning of ufunc calls:
> >   * The uint7 idea would be one solution
> >   * Simply implement something that works for numpy and all except
> >     strange external ufuncs (I can only think of numba as a plausible
> >     candidate for creating such).
> >
> > My current plan is to see where the second thing leaves me.
> >
> > We also should see if we cannot move the whole thing forward, in
> > which
> > case the main decision would have to be forward to where. My opinion
> > is
> > currently that when a type has a dtype associated with it clearly, we
> > should always use that dtype in the future. This mostly means that
> > numpy dtypes such as `np.int64` will always be treated like an int64,
> > and never like a `uint8` because they happen to be castable to that.
> >
> > For values without a dtype attached (read python integers, floats), I
> > see three options, from more complex to simpler:
> >
> > 1. Keep the current logic in place as much as possible
> > 2. Only support value based promotion for operators, e.g.:
> >    `arr + scalar` may do it, but `np.add(arr, scalar)` will not.
> >    The upside is that it limits the complexity to a much simpler
> >    problem, the downside is that the ufunc call and operator match
> >    less clearly.
> > 3. Just associate python float with float64 and python integers with
> >    long/int64 and force users to always type them explicitly if they
> >    need to.
> >
> > The downside of 1. is that it doesn't help with simplifying the
> > current
> > situation all that much, because we still have the special casting
> > around...
> >
> >
> > I have realized that this got much too long, so I hope it makes
> > sense.
> > I will continue to dabble along on these things a bit, so if nothing
> > else maybe writing it helps me to get a bit clearer on things...
> >
> > Best,
> >
> > Sebastian
> >
> >
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