Moving forward with value based casting
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 notexisting) 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 0D 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
On Wed, Jun 5, 2019 at 1:43 PM Sebastian Berg sebastian@sipsolutions.net 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 notexisting) 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:
 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 0D 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.
 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.
Does NumPy actually have an logic that does these sort of checks currently? If so, it would be interesting to see what it is.
My experiments suggest that we currently have this logic of finding the "minimal" dtype that can hold the scalar value:
np.array([127], dtype=np.int8) + 127 # silent overflow!
array([2], dtype=int8)
np.array([127], dtype=np.int8) + 128 # correct result
array([255], dtype=int16)
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:
 Keep the current logic in place as much as possible
 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.
 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 think it would be fine to special case operators, but NEP13 means that the ufuncs corresponding to operators really do need to work exactly the same way. So we should also specialcase those ufuncs.
I don't think Option (3) is viable. Too many users rely upon arithmetic like "x + 1" having a predictable dtype.
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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On Wed, 20190605 at 14:14 0700, Stephan Hoyer wrote:
On Wed, Jun 5, 2019 at 1:43 PM Sebastian Berg < sebastian@sipsolutions.net> wrote:
Hi all,
<snip>
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.
Does NumPy actually have an logic that does these sort of checks currently? If so, it would be interesting to see what it is.
My experiments suggest that we currently have this logic of finding the "minimal" dtype that can hold the scalar value:
np.array([127], dtype=np.int8) + 127 # silent overflow!
array([2], dtype=int8)
np.array([127], dtype=np.int8) + 128 # correct result
array([255], dtype=int16)
The current checks all come down to `np.can_cast` (on the C side this is `PyArray_CanCastArray()`), answering True. The actual result value is not taken into account of course. So 127 can be represented as int8 and since the "int8,int8>int8" loop is checked first (and "can cast" correctly) it is used. Alternatively, you can think of it as using `np.result_type()` which will, for all practical purposes, give the same dtype (but result type may or may not be actually used, and there are some subtle differences in principle).
Effectively, in your example you could reduce it to a minimal dtype of uint7 for 127, since a uint7 can be cast safely to an int8 and also to a uint8. (If you would just say the minimal dtype is uint8, you could not distinguish the two examples).
Does that answer the question?
Best,
Sebastian
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:
 Keep the current logic in place as much as possible
 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.
 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 think it would be fine to special case operators, but NEP13 means that the ufuncs corresponding to operators really do need to work exactly the same way. So we should also specialcase those ufuncs.
I don't think Option (3) is viable. Too many users rely upon arithmetic like "x + 1" having a predictable dtype.
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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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, 20190605 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 notexisting) 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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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.
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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 "resultbased" 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 dtypebased 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 (dtypeonly 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 valuebased promotion still happens for a nonNumPy 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 preallocate 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 memoryconservation they might get from valuebased 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@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, 20190605 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 notexisting) 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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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.
 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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Hi Sebastian,
Tricky! It seems a balance between unexpected memory blowup and unexpected wrapping (the latter mostly for integers).
Some comments specifically on your message first, then some more general related ones.
1. I'm very much against letting `a + b` do anything else than `np.add(a, b)`. 2. For python values, an argument for casting by value is that a python int can be arbitrarily long; the only reasonable course of action for those seems to make them float, and once you do that one might as well cast to whatever type can hold the value (at least approximately). 3. Not necessarily preferred, but for casting of scalars, one can get more consistent behaviour also by extending the casting by value to any array that has size=1.
Overall, just on the narrow question, I'd be quite happy with your suggestion of using type information if available, i.e., only cast python values to a minimal dtype.If one uses numpy types, those mostly will have come from previous calculations with the same arrays, so things will work as expected. And in most memorylimited applications, one would do calculations inplace anyway (or, as Tyler noted, for power users one can assume awareness of memory and thus the incentive to tell explicitly what dtype is wanted  just `np.add(a, b, dtype=...)`, no need to create `out`).
More generally, I guess what I don't like about the casting rules generally is that there is a presumption that if the value can be cast, the operation will generally succeed. For `np.add` and `np.subtract`, this perhaps is somewhat reasonable (though for unsigned a bit more dubious), but for `np.multiply` or `np.power` it is much less so. (Indeed, we had a long discussion about what to do with `int ** power`  now specialcasing negative integer powers.) Changing this, however, probably really is a bridge too far!
Finally, somewhat related: I think the largest confusing actually results from the `uint64+in64 > float64` casting. Should this cast to int64 instead?
All the best,
Marten
On Wed, 20190605 at 21:35 0400, Marten van Kerkwijk wrote:
Hi Sebastian,
Tricky! It seems a balance between unexpected memory blowup and unexpected wrapping (the latter mostly for integers).
Some comments specifically on your message first, then some more general related ones.
 I'm very much against letting `a + b` do anything else than
`np.add(a, b)`.
Well, I tend to agree. But just to put it out there:
[1] + [2] == [1, 2] np.add([1], [2]) == 3
So that is already far from true, since coercion has to occur. Of course it is true that:
arr + something_else
will at some point force coercion of `something_else`, so that point is only half valid if either `a` or `b` is already a numpy array/scalar.
 For python values, an argument for casting by value is that a
python int can be arbitrarily long; the only reasonable course of action for those seems to make them float, and once you do that one might as well cast to whatever type can hold the value (at least approximately).
To be honest, the "arbitrary long" thing is another issue, which is the silent conversion to "object" dtype. Something that is also on the not done list of: Maybe we should deprecate it.
In other words, we would freeze python int to one clear type, if you have an arbitrarily large int, you would need to use `object` dtype (or preferably a new `pyint/arbitrary_precision_int` dtype) explicitly.
 Not necessarily preferred, but for casting of scalars, one can get
more consistent behaviour also by extending the casting by value to any array that has size=1.
That sounds just as horrible as the current mismatch to me, to be honest.
Overall, just on the narrow question, I'd be quite happy with your suggestion of using type information if available, i.e., only cast python values to a minimal dtype.If one uses numpy types, those mostly will have come from previous calculations with the same arrays, so things will work as expected. And in most memorylimited applications, one would do calculations inplace anyway (or, as Tyler noted, for power users one can assume awareness of memory and thus the incentive to tell explicitly what dtype is wanted  just `np.add(a, b, dtype=...)`, no need to create `out`).
More generally, I guess what I don't like about the casting rules generally is that there is a presumption that if the value can be cast, the operation will generally succeed. For `np.add` and `np.subtract`, this perhaps is somewhat reasonable (though for unsigned a bit more dubious), but for `np.multiply` or `np.power` it is much less so. (Indeed, we had a long discussion about what to do with `int ** power`  now specialcasing negative integer powers.) Changing this, however, probably really is a bridge too far!
Indeed that is right. But that is a different point. E.g. there is nothing wrong for example that `np.power` shouldn't decide that `int**power` should always _promote_ (not cast) `int` to some larger integer type if available. The only point where we seriously have such logic right now is for np.add.reduce (sum) and np.multiply.reduce (prod), which always use at least `long` precision (and actually upcast bool>int, although np.add(True, True) does not. Another difference to True + True...)
Finally, somewhat related: I think the largest confusing actually results from the `uint64+in64 > float64` casting. Should this cast to int64 instead?
Not sure, but yes, it is the other quirk in our casting that should be discussed….
 Sebastian
All the best,
Marten
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On Wed, 20190605 at 21:35 0400, Marten van Kerkwijk wrote:
Hi Sebastian,
Tricky! It seems a balance between unexpected memory blowup and unexpected wrapping (the latter mostly for integers).
Some comments specifically on your message first, then some more general related ones.
 I'm very much against letting `a + b` do anything else than
`np.add(a, b)`. 2. For python values, an argument for casting by value is that a python int can be arbitrarily long; the only reasonable course of action for those seems to make them float, and once you do that one might as well cast to whatever type can hold the value (at least approximately).
Just to throw it in, in the long run, instead of trying to find a minimal dtype (which is a bit random), simply ignoring the value of the scalar may actually be the better option.
The reason for this would be code like: ``` arr = np.zeros(5, dtype=np.int8)
for i in range(200): res = arr + i print(res.dtype) # switches from int8 to int16! ``` Instead, try `np.int8(i)` in the loop, and if it fails raise an error. Or, if that is a bit nasty – especially for interactive usage – we would go with a warning.
This is nothing we need to decide soon, since I think some of the complexity will remain (i.e. you still need to know that the scalar is a floating point number or an integer and change the logic).
Best,
Sebastian
 Not necessarily preferred, but for casting of scalars, one can get
more consistent behaviour also by extending the casting by value to any array that has size=1.
Overall, just on the narrow question, I'd be quite happy with your suggestion of using type information if available, i.e., only cast python values to a minimal dtype.If one uses numpy types, those mostly will have come from previous calculations with the same arrays, so things will work as expected. And in most memorylimited applications, one would do calculations inplace anyway (or, as Tyler noted, for power users one can assume awareness of memory and thus the incentive to tell explicitly what dtype is wanted  just `np.add(a, b, dtype=...)`, no need to create `out`).
More generally, I guess what I don't like about the casting rules generally is that there is a presumption that if the value can be cast, the operation will generally succeed. For `np.add` and `np.subtract`, this perhaps is somewhat reasonable (though for unsigned a bit more dubious), but for `np.multiply` or `np.power` it is much less so. (Indeed, we had a long discussion about what to do with `int ** power`  now specialcasing negative integer powers.) Changing this, however, probably really is a bridge too far!
Finally, somewhat related: I think the largest confusing actually results from the `uint64+in64 > float64` casting. Should this cast to int64 instead?
All the best,
Marten
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On Wed, 20190605 at 17:14 0700, Tyler Reddy wrote:
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 "resultbased" 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.
No, that is indeed a different issue. It would be nice to provide the option of integer overflow warnings/errors, but it is different since it should not affect the dtypes in use (i.e. we would never upcast to avoid the error).
 It sounds like the objective is instead primarily to achieve pure
dtypebased promotion, which is then effectively just a casting table, which is what I think you mean by "cache?"
Yes, the cache was a bad word, I used it thinking of user types where a large table would probably not be created on the fly.
 Is it a safe assumption that for a cache (dtypeonly 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.
Yes. That is at least what we currently have. For x + 1 there is a good point with sudden memory blow up. Maybe an even nicer example is `float32_arr + 1`, which would have to go to float64 if 1 is interpreted as `int32(1)`.
 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:
Well, while it is annoying me. I think we should base that decision of what we want the user API to be only. And because of that, it seems like the most likely option. At least my gut feeling is, if it is typed, we should honor the type (also for scalars), but code like x + 1 suddenly blowing up memory is not a good idea. I just realized that one (anti?)pattern that is common is the:
arr + 0. # make sure its "inexact/float"
is exactly an example of where you do not want to upcast unnecessarily.
 Would that give you enough refactoring "wiggle room" to achieve
the simplifications you need? If valuebased promotion still happens for a nonNumPy operand, can you abstract that logic cleanly from the "pure dtype cache / table" that is planned for NumPy operands?
It is tricky. There is always the slightly strange solution of making dtypes such as uint7, which "fixes" the type hierarchy as a minimal dtype for promotion purpose, but would never be exposed to users. (You probably need more strange dtypes for float and int combinations.)
To give me some wiggle room, what I was now doing is to simply decide on the correct dtype before lookup. I am pretty sure that works for all, except possibly one ufunc within numpy. The reason that this works is that almost all of our ufuncs are typed as "ii>i" (identical types). Maybe that is OK to start working, and the strange dtype hierarchy can be thought of later.
 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 preallocate 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 memoryconservation they might get from valuebased behavior to adjust in this way?
The can also use `dtype=...` (or at least we can fix that part to be reliable). Or they can cast type the input. Especially if we want to use it only for python integers/floats, adding the `np.int8(3)` is not much effort.
 Presumably "out" does / will circumvent the "cache / dtype casting
table?"
Well, out fixes one of the types, if we look at the general machinery, it would be possible to have:
ff>d df>d dd>d
loops. So if such loops are defined we cannot quite circumvent the whole lookup. If we know that all loops are of the `ff>f` all same dtype kind (which is true for almost all functions inside numpy), lookup could be simplified. For those loops with all the same dtype, the issue is fairly straight forward anyway, because I can just decide how to handle the scalar before hand.
Best,
Sebastian
Tyler
On Wed, 5 Jun 2019 at 15:37, Sebastian Berg < sebastian@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, 20190605 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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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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On Wed, Jun 5, 2019 at 10:42 PM Sebastian Berg sebastian@sipsolutions.net 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 notexisting) corner cases to break early to get on the way? ... 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...
Your email was long but very clear. The part I'm missing is "why are things the way they are?". Before diving into casting rules and all other wishes people may have, can you please try to answer that? Because there's more to it than "(maybe notexisting) corner cases".
Marten's first sentence ("a balance between unexpected memory blowup and unexpected wrapping") is in the right direction. As is Stephan's "Too many users rely upon arithmetic like "x + 1" having a predictable dtype."
The problem is clear, however you need to figure out the constraints first, then decide within the wiggle room you have what the options are.
Cheers, Ralf
I think dtypebased casting makes a lot of sense, the problem is backward compatibility.
Numpy casting is weird in a number of ways: The array + array casting is unexpected to many users (eg, uint64 + int64 > float64), and the casting of array + scalar is different from that, and value based. Personally I wouldn't want to try change it unless we make a backwardincompatible release (numpy 2.0), based on my experience trying to change much more minor things. We already put "casting" on the list of desired backwardincompatible changes on the list here: https://github.com/numpy/numpy/wiki/Backwardsincompatibleideasforamajor...
Relatedly, I've previously dreamed about a different "Cstyle" way casting might behave: https://gist.github.com/ahaldane/0f5ade49730e1a5d16ff6df4303f2e76
The proposal there is that array + array casting, array + scalar, and array + python casting would all work in the same dtypebased way, which mimics the familiar "C" casting rules.
See also: https://github.com/numpy/numpy/issues/12525
Allan
On 6/5/19 4:41 PM, 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 notexisting) 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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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.
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On Thu, 20190606 at 11:57 0400, Allan Haldane wrote:
I think dtypebased casting makes a lot of sense, the problem is backward compatibility.
Numpy casting is weird in a number of ways: The array + array casting is unexpected to many users (eg, uint64 + int64 > float64), and the casting of array + scalar is different from that, and value based. Personally I wouldn't want to try change it unless we make a backwardincompatible release (numpy 2.0), based on my experience trying to change much more minor things. We already put "casting" on the list of desired backwardincompatible changes on the list here: https://github.com/numpy/numpy/wiki/Backwardsincompatibleideasforamajor...
Relatedly, I've previously dreamed about a different "Cstyle" way casting might behave: https://gist.github.com/ahaldane/0f5ade49730e1a5d16ff6df4303f2e76
The proposal there is that array + array casting, array + scalar, and array + python casting would all work in the same dtypebased way, which mimics the familiar "C" casting rules.
If I read it right, you do propose that array + python would cast in a "minimal type" way for python.
In your write up, you describe that if you mix array + scalar, the scalar uses a minimal dtype compared to the array's dtype. What we instead have is that in principle you could have loops such as:
"ifi>f" "idi>d"
and I think we should chose the first for a scalar, because it "fits" into f just fine. (if the input is) `ufunc(int_arr, 12., int_arr)`.
I do not mind keeping the "simple" two (or even more) operand "lets assume we have uniform types" logic around. For those it is easy to find a "minimum type" even before actual loop lookup. For the above example it would work in any case well, but it would get complicating, if for example the last integer is an unsigned integer, that happens to be small enough to fit also into an integer.
That might give some wiggle room, possibly also to attach warnings to it, or at least make things easier. But I would also like to figure out as well if we shouldn't try to move in any case. Sure, attach a major version to it, but hopefully not a "big step type".
One thing that I had not thought about is, that if we create FutureWarnings, we will need to provide a way to optin to the new/old behaviour. The old behaviour can be achieved by just using the python types (which probably is what most code that wants this behaviour does already), but the behaviour is tricky. Users can pass `dtype` explicitly, but that is a huge kludge... Will think about if there is a solution to that, because if there is not, you are right. It has to be a "big step" kind of release. Although, even then it would be nice to have warnings that can be enabled to ease the transition!
 Sebastian
See also: https://github.com/numpy/numpy/issues/12525
Allan
On 6/5/19 4:41 PM, 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 notexisting) 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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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.
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On 6/6/19 12:46 PM, Sebastian Berg wrote:
On Thu, 20190606 at 11:57 0400, Allan Haldane wrote:
I think dtypebased casting makes a lot of sense, the problem is backward compatibility.
Numpy casting is weird in a number of ways: The array + array casting is unexpected to many users (eg, uint64 + int64 > float64), and the casting of array + scalar is different from that, and value based. Personally I wouldn't want to try change it unless we make a backwardincompatible release (numpy 2.0), based on my experience trying to change much more minor things. We already put "casting" on the list of desired backwardincompatible changes on the list here: https://github.com/numpy/numpy/wiki/Backwardsincompatibleideasforamajor...
Relatedly, I've previously dreamed about a different "Cstyle" way casting might behave: https://gist.github.com/ahaldane/0f5ade49730e1a5d16ff6df4303f2e76
The proposal there is that array + array casting, array + scalar, and array + python casting would all work in the same dtypebased way, which mimics the familiar "C" casting rules.
If I read it right, you do propose that array + python would cast in a "minimal type" way for python.
I'm a little unclear what you mean by "minimal type" way. By "minimal type", I thought you and others are talking about the rule numpy currently uses that "the output dtype is the minimal dtype capable of representing the value of both input dtypes", right? But in that gist I am instead proposing that outputdtype is determined by Clike rules.
For array+py_scalar I was less certain what to do than for array+array and array+npy_scalar. But I proposed the three "ranks" of 1. bool, 2. int, and 3. float/complex. My rule for array+py_scalar is that if the python scalar's rank is less than the numpy operand dtype's rank, use the numpy dtype. If the pythonscalar's rank is greater, use the "default" types of bool_, int64, float64 respectively. Eg:
np.bool_(1) + 1 > int64 (default int wins) np.int8(1) + 1 > int8 (numpy wins) np.uint8(1) + (1) > uint8 (numpy wins) np.int64(1) + 1 > int64 (numpy wins) np.int64(1) + 1.0 > float64 (default float wins) np.float32(1.0) + 1.0 > float32 (numpy wins)
Note it does not depend on the numerical value of the scalar, only its type.
In your write up, you describe that if you mix array + scalar, the scalar uses a minimal dtype compared to the array's dtype.
Sorry if I'm nitpicking/misunderstanding, but in my rules np.uint64(1) + 1 > uint64 but in numpy's "minimal dtype" rules it is > float64. So I don't think I am using the minimal rule.
What we instead have is that in principle you could have loops such as:
"ifi>f" "idi>d"
and I think we should chose the first for a scalar, because it "fits" into f just fine. (if the input is) `ufunc(int_arr, 12., int_arr)`.
I feel I'm not understanding you, but the casting rules in my gist follow those two rules if i, f are the numpy types int32 and float32.
If instead you mean (np.int64, py_float, np.int64) my rules would cast to float64, since py_float has the highest rank and so is converted to the default numpytype for that rank, float64.
I would also add that unlike current numpy, my Ccasting rules are associative (if all operands are numpy types, see note below), so it does not matter in which order you promote the types: (if)i and i(fi) give the same result. In current numpy this is not always the case:
p = np.promote_types p(p('u2', 'i1'), 'f4') # > f8 p( 'u2', p('i1', 'f4')) # > f4
(However, my casting rules are not associative if you include python scalars.. eg np.float32(1) + 1.0 + np.int64(1) . Maybe I should try to fix that...)
Best, Allan
I do not mind keeping the "simple" two (or even more) operand "lets assume we have uniform types" logic around. For those it is easy to find a "minimum type" even before actual loop lookup. For the above example it would work in any case well, but it would get complicating, if for example the last integer is an unsigned integer, that happens to be small enough to fit also into an integer.
That might give some wiggle room, possibly also to attach warnings to it, or at least make things easier. But I would also like to figure out as well if we shouldn't try to move in any case. Sure, attach a major version to it, but hopefully not a "big step type".
One thing that I had not thought about is, that if we create FutureWarnings, we will need to provide a way to optin to the new/old behaviour. The old behaviour can be achieved by just using the python types (which probably is what most code that wants this behaviour does already), but the behaviour is tricky. Users can pass `dtype` explicitly, but that is a huge kludge... Will think about if there is a solution to that, because if there is not, you are right. It has to be a "big step" kind of release. Although, even then it would be nice to have warnings that can be enabled to ease the transition!
 Sebastian
See also: https://github.com/numpy/numpy/issues/12525
Allan
On 6/5/19 4:41 PM, 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 notexisting) 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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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.
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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On Thu, 20190606 at 19:34 0400, Allan Haldane wrote:
On 6/6/19 12:46 PM, Sebastian Berg wrote:
On Thu, 20190606 at 11:57 0400, Allan Haldane wrote:
I think dtypebased casting makes a lot of sense, the problem is backward compatibility.
Numpy casting is weird in a number of ways: The array + array casting is unexpected to many users (eg, uint64 + int64 > float64), and the casting of array + scalar is different from that, and value based. Personally I wouldn't want to try change it unless we make a backwardincompatible release (numpy 2.0), based on my experience trying to change much more minor things. We already put "casting" on the list of desired backwardincompatible changes on the list here: https://github.com/numpy/numpy/wiki/Backwardsincompatibleideasforamajor...
Relatedly, I've previously dreamed about a different "Cstyle" way casting might behave: https://gist.github.com/ahaldane/0f5ade49730e1a5d16ff6df4303f2e76
The proposal there is that array + array casting, array + scalar, and array + python casting would all work in the same dtypebased way, which mimics the familiar "C" casting rules.
If I read it right, you do propose that array + python would cast in a "minimal type" way for python.
I'm a little unclear what you mean by "minimal type" way. By "minimal type", I thought you and others are talking about the rule numpy currently uses that "the output dtype is the minimal dtype capable of representing the value of both input dtypes", right? But in that gist I am instead proposing that outputdtype is determined by Clike rules.
For array+py_scalar I was less certain what to do than for array+array and array+npy_scalar. But I proposed the three "ranks" of 1. bool, 2. int, and 3. float/complex. My rule for array+py_scalar is that if the python scalar's rank is less than the numpy operand dtype's rank, use the numpy dtype. If the pythonscalar's rank is greater, use the "default" types of bool_, int64, float64 respectively. Eg:
np.bool_(1) + 1 > int64 (default int wins) np.int8(1) + 1 > int8 (numpy wins) np.uint8(1) + (1) > uint8 (numpy wins) np.int64(1) + 1 > int64 (numpy wins) np.int64(1) + 1.0 > float64 (default float wins) np.float32(1.0) + 1.0 > float32 (numpy wins)
Note it does not depend on the numerical value of the scalar, only its type.
In your write up, you describe that if you mix array + scalar, the scalar uses a minimal dtype compared to the array's dtype.
Sorry if I'm nitpicking/misunderstanding, but in my rules np.uint64(1) + 1 > uint64 but in numpy's "minimal dtype" rules it is > float64. So I don't think I am using the minimal rule.
What we instead have is that in principle you could have loops such as:
"ifi>f" "idi>d"
and I think we should chose the first for a scalar, because it "fits" into f just fine. (if the input is) `ufunc(int_arr, 12., int_arr)`.
I feel I'm not understanding you, but the casting rules in my gist follow those two rules if i, f are the numpy types int32 and float32.
If instead you mean (np.int64, py_float, np.int64) my rules would cast to float64, since py_float has the highest rank and so is converted to the default numpytype for that rank, float64.
Yes, you are right. I should look at them a bit more carefully in any case. Actually, numpy would also choose the second one, because it python float has the higher "category". The example should rather have been:
int8, float32 > float32 int64, float32 > float64
With `python_int(12) + np.array([1., 2.], dtype=float64)`. Numpy would currently choose the int8 loop here, because the scalar is of a lower or equal "category" and thus it is OK to demote it even further.
This is fairly irrelevant for most users. But for ufunc dispatching, I think it is where it gets ugly. In nonuniform ufunc dtype signatures, and no, I doubt that this is very relevant in practice or that numpy is even very consistent here.
I have a branch now which basically moves the "ResultType" logic before choosing the loop (it thus is unable to capture some of the stranger, probably nonexisting corner cases).
On a different note: The ranking you are suggesting for python types seems very much the same as what we have, with the exception that it would not look at the value (I suppose what we would do instead is to simply raise a casting error):
int8_arr + 87345 # ouput should always be int8, so crash on cast?
Which may be a viable approach. Although, signed/unsigned may be tricky:
uint8_arr + py_int # do we look at the py_int's sign?
 Sebastian
I would also add that unlike current numpy, my Ccasting rules are associative (if all operands are numpy types, see note below), so it does not matter in which order you promote the types: (if)i and i(fi) give the same result. In current numpy this is not always the case:
p = np.promote_types p(p('u2', 'i1'), 'f4') # > f8 p( 'u2', p('i1', 'f4')) # > f4
(However, my casting rules are not associative if you include python scalars.. eg np.float32(1) + 1.0 + np.int64(1) . Maybe I should try to fix that...)
Best, Allan
I do not mind keeping the "simple" two (or even more) operand "lets assume we have uniform types" logic around. For those it is easy to find a "minimum type" even before actual loop lookup. For the above example it would work in any case well, but it would get complicating, if for example the last integer is an unsigned integer, that happens to be small enough to fit also into an integer.
That might give some wiggle room, possibly also to attach warnings to it, or at least make things easier. But I would also like to figure out as well if we shouldn't try to move in any case. Sure, attach a major version to it, but hopefully not a "big step type".
One thing that I had not thought about is, that if we create FutureWarnings, we will need to provide a way to optin to the new/old behaviour. The old behaviour can be achieved by just using the python types (which probably is what most code that wants this behaviour does already), but the behaviour is tricky. Users can pass `dtype` explicitly, but that is a huge kludge... Will think about if there is a solution to that, because if there is not, you are right. It has to be a "big step" kind of release. Although, even then it would be nice to have warnings that can be enabled to ease the transition!
 Sebastian
See also: https://github.com/numpy/numpy/issues/12525
Allan
On 6/5/19 4:41 PM, 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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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I haven't read all the thread super carefully, so I might have missed something, but I think we might want to look at this together with the special rule for scalar casting.
IIUC, the basic enduser problem that motivates all thi sis: when you have a simple Python constant whose exact dtype is unspecified, people don't want numpy to first automatically pick a dtype for it, and then use that automatically chosen dtype to override the explicit dtypes that the user specified. That's that "x + 1" problem. (This also comes up a ton for languages trying to figure out how to type manifest constants.)
Numpy's original solution for this was the special casting rule for scalars. I don't understand the exact semantics, but it's something like: in any operation involving a mix of nonzerodim arrays and zerodim arrays, we throw out the exact dtype information for the scalar ("float64", "int32") and replace it with just the "kind" ("float", "int").
This has several surprising consequences:
 The output dtype depends on not just the input dtypes, but also the input shapes:
In [19]: (np.array([1, 2], dtype=np.int8) + 1).dtype Out[19]: dtype('int8')
In [20]: (np.array([1, 2], dtype=np.int8) + [1]).dtype Out[20]: dtype('int64')
 It doesn't just affect Python scalars with vague dtypes, but also scalars where the user has specifically set the dtype:
In [21]: (np.array([1, 2], dtype=np.int8) + np.int64(1)).dtype Out[21]: dtype('int8')
 I'm not sure the "kind" rule even does the right thing, especially for mixedkind operations. float16array + int8scalar has to do the same thing as float16array + int64scalar, but that feels weird? I think this is why valuebased casting got added (at around the same time as float16, in fact).
(Kinds are kinda problematic in general... the SAME_KIND casting rule is very weird – casting int32>int64 is radically different from casting float64>float32, which is radically different than casting int64>int32, but SAME_KIND treats them all the same. And it's really unclear how to generalize the 'kind' concept to new dtypes.)
My intuition is that what users actually want is for *native Python types* to be treated as having 'underspecified' dtypes, e.g. int is happy to coerce to int8/int32/int64/whatever, float is happy to coerce to float32/float64/whatever, but once you have a fullyspecified numpy dtype, it should stay.
Some cases to think about:
np.array([1, 2], dtype=int8) + [1, 1] > maybe this should have dtype int8, because there's no type info on the right side to contradict that?
np.array([1, 2], dtype=int8) + 2**40 > maybe this should be an error, because you can't cast 2**40 to int8 (under default casting safety rules)? That would introduce some valuedependence, but it would only affect whether you get an error or not, and there's precedent for that (e.g. division by zero).
In any case, it would probably be helpful to start by just writing down the whole set of rules we have now, because I'm not sure anyone understands all the details...
n
On Wed, Jun 5, 2019 at 1:42 PM Sebastian Berg sebastian@sipsolutions.net 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 notexisting) 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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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.
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On Fri, Jun 7, 2019 at 1:37 AM Nathaniel Smith njs@pobox.com wrote:
My intuition is that what users actually want is for *native Python types* to be treated as having 'underspecified' dtypes, e.g. int is happy to coerce to int8/int32/int64/whatever, float is happy to coerce to float32/float64/whatever, but once you have a fullyspecified numpy dtype, it should stay.
Thanks Nathaniel, I think this expresses a possible solution better than anything I've seen on this list before. An explicit "underspecified types" concept could make casting understandable.
In any case, it would probably be helpful to start by just writing down the whole set of rules we have now, because I'm not sure anyone understands all the details...
+1
Ralf
On Fri, Jun 7, 2019 at 1:19 AM Ralf Gommers ralf.gommers@gmail.com wrote:
On Fri, Jun 7, 2019 at 1:37 AM Nathaniel Smith njs@pobox.com wrote:
My intuition is that what users actually want is for *native Python types* to be treated as having 'underspecified' dtypes, e.g. int is happy to coerce to int8/int32/int64/whatever, float is happy to coerce to float32/float64/whatever, but once you have a fullyspecified numpy dtype, it should stay.
Thanks Nathaniel, I think this expresses a possible solution better than anything I've seen on this list before. An explicit "underspecified types" concept could make casting understandable.
I think the current model is that this holds for all scalars, but changing that to be just for not already explicitly typed types makes sense.
In the context of a mental picture, one could think in terms of coercion, of numpy having not just a `numpy.array` but also a `numpy.scalar` function, which takes some input and tries to make a numpy scalar of it. For python int, float, complex, etc., it uses the minimal numpy type.
Of course, this is slightly inconsistent with the `np.array` function which converts things to `ndarray` using a default type for int, float, complex, etc., but my sense is that that is explainable, e.g.,imagining both `np.scalar` and `np.array` to have dtype attributes, one could say that the default for one would be `'minimal'` and the other `'64bit'` (well, that doesn't work for complex, but anyway).
 Marten
On Fri, 20190607 at 07:18 +0200, Ralf Gommers wrote:
On Fri, Jun 7, 2019 at 1:37 AM Nathaniel Smith njs@pobox.com wrote:
My intuition is that what users actually want is for *native Python types* to be treated as having 'underspecified' dtypes, e.g. int is happy to coerce to int8/int32/int64/whatever, float is happy to coerce to float32/float64/whatever, but once you have a fullyspecified numpy dtype, it should stay.
Thanks Nathaniel, I think this expresses a possible solution better than anything I've seen on this list before. An explicit "underspecified types" concept could make casting understandable.
Yes, there is one small additional annoyance (but maybe it is just that). In that 127 is the 'underspecified' dtype `uint7` (it can be safely cast both to uint8 and int8).
In any case, it would probably be helpful to start by just writing down the whole set of rules we have now, because I'm not sure anyone understands all the details...
+1
OK, let me try to sketch the details below:
0. "Scalars" means scalars or 0D arrays here.
1. The logic below will only be used if we have a mix of arrays and scalars. If all are scalars, the logic is never used. (Plus one additional tricky case within ufuncs, which is more hypothetical [0])
2. Scalars will only be demoted within their category. The categories and casting rules within the category are as follows:
Boolean: Casts safely to all (nothing surprising).
Integers: Casting is possible if output can hold the value. This includes uint8(127) casting to an int8. (unsigned and signed integers are the same "category")
Floats: Scalars can be demoted based on value, roughly this avoids overflows: float16: 65000 < value < 65000 float32: 3.4e38 < value < 3.4e38 float64: 1.7e308 < value < 1.7e308 float128 (largest type, does not apply).
Complex: Same logic as floats (applied to .real and .imag).
Others: Anything else.

Ufunc, as well as `result_type` will use this liberally, which basically means finding the smallest type for each category and using that. Of course for floats we cannot do the actual cast until later, since initially we do not know if the cast will actually be performed.
This is only tricky for uint vs. int, because uint8(127) is a "small unsigned". I.e. with our current dtypes there is no strict type hierarchy uint8(x) may or may not cast to int8.

We could think of doing:
arr, min_dtype = np.asarray_and_min_dtype(pyobject)
which could even fix the list example Nathaniel had. Which would work if you would do the dtype hierarchy.
This is where the `uint7` came from a hypothetical `uint7` would fix the integer dtype hierarchy, by representing the numbers `0127` which can be cast to uint8 and int8.
Best,
Sebastian
[0] Amendment for point 1:
There is one detail (bug?) here in the logic though, that I missed before. If a ufunc (or result_type) sees a mix of scalars and arrays, it will try to decide whether or not to use value based logic. Value based logic will be skipped if the scalars are in a higher category (based on the ones above) then the highest array – for optimization I assume. Plausibly, this could cause incorrect logic when the dtype signature of a ufunc is mixed: float32, int8 > float32 float32, int64 > float64
May choose the second loop unnecessarily. Or for example if we have a datetime64 in the inputs, there would be no way for value based casting to be used.
Ralf
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On Fri, 20190607 at 13:19 0500, Sebastian Berg wrote:
On Fri, 20190607 at 07:18 +0200, Ralf Gommers wrote:
On Fri, Jun 7, 2019 at 1:37 AM Nathaniel Smith njs@pobox.com wrote:
My intuition is that what users actually want is for *native Python types* to be treated as having 'underspecified' dtypes, e.g. int is happy to coerce to int8/int32/int64/whatever, float is happy to coerce to float32/float64/whatever, but once you have a fullyspecified numpy dtype, it should stay.
Thanks Nathaniel, I think this expresses a possible solution better than anything I've seen on this list before. An explicit "underspecified types" concept could make casting understandable.
Yes, there is one small additional annoyance (but maybe it is just that). In that 127 is the 'underspecified' dtype `uint7` (it can be safely cast both to uint8 and int8).
In any case, it would probably be helpful to start by just writing down the whole set of rules we have now, because I'm not sure anyone understands all the details...
+1
OK, let me try to sketch the details below:
"Scalars" means scalars or 0D arrays here.
The logic below will only be used if we have a mix of arrays and
scalars. If all are scalars, the logic is never used. (Plus one additional tricky case within ufuncs, which is more hypothetical [0])
And of course I just realized that, trying to be simple, I forgot an important point there:
The logic in 2. is only used when there is a mix of scalars and arrays, and the arrays are in the same or higher category. As an example:
np.array([1, 2, 3], dtype=np.uint8) + np.float64(12.)
will not demote the float64, because the scalars "float" is a higher category than the arrays "integer".
 Sebastian
 Scalars will only be demoted within their category. The categories
and casting rules within the category are as follows:
Boolean: Casts safely to all (nothing surprising).
Integers: Casting is possible if output can hold the value. This includes uint8(127) casting to an int8. (unsigned and signed integers are the same "category")
Floats: Scalars can be demoted based on value, roughly this avoids overflows: float16: 65000 < value < 65000 float32: 3.4e38 < value < 3.4e38 float64: 1.7e308 < value < 1.7e308 float128 (largest type, does not apply).
Complex: Same logic as floats (applied to .real and .imag).
Others: Anything else.
Ufunc, as well as `result_type` will use this liberally, which basically means finding the smallest type for each category and using that. Of course for floats we cannot do the actual cast until later, since initially we do not know if the cast will actually be performed.
This is only tricky for uint vs. int, because uint8(127) is a "small unsigned". I.e. with our current dtypes there is no strict type hierarchy uint8(x) may or may not cast to int8.
We could think of doing:
arr, min_dtype = np.asarray_and_min_dtype(pyobject)
which could even fix the list example Nathaniel had. Which would work if you would do the dtype hierarchy.
This is where the `uint7` came from a hypothetical `uint7` would fix the integer dtype hierarchy, by representing the numbers `0127` which can be cast to uint8 and int8.
Best,
Sebastian
[0] Amendment for point 1:
There is one detail (bug?) here in the logic though, that I missed before. If a ufunc (or result_type) sees a mix of scalars and arrays, it will try to decide whether or not to use value based logic. Value based logic will be skipped if the scalars are in a higher category (based on the ones above) then the highest array – for optimization I assume. Plausibly, this could cause incorrect logic when the dtype signature of a ufunc is mixed: float32, int8 > float32 float32, int64 > float64
May choose the second loop unnecessarily. Or for example if we have a datetime64 in the inputs, there would be no way for value based casting to be used.
Ralf
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On Wed, Jun 5, 2019 at 4:42 PM Sebastian Berg sebastian@sipsolutions.net wrote:
I think the best approach is that if the user gave unambiguous types as inputs to operators then the output should be the same dtype, or type corresponding to the common promotion type of the inputs.
If the input type is not specified, I agree with the suggestion here:
 Just associate python float with float64 and python integers with long/int64 and force users to always type them explicitly if they need to.
Explicit is better than implicit
On Wed, 20190605 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 notexisting) corner cases to break early to get on the way?
Hi all,
just to note. I think I will go forward trying to fill the hole in the hierarchy with a nonexisting uint7 dtype. That seemed like it may be ugly, but if it does not escalate too much, it is probably fairly straight forward. And it would allow to simplify dispatching without any logic change at all. After that we could still decide to change the logic.
Best,
Sebastian
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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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.
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On Wed, 20190612 at 12:55 0500, Sebastian Berg wrote:
On Wed, 20190605 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 notexisting) corner cases to break early to get on the way?
Hi all,
just to note. I think I will go forward trying to fill the hole in the hierarchy with a nonexisting uint7 dtype. That seemed like it may be ugly, but if it does not escalate too much, it is probably fairly straight forward. And it would allow to simplify dispatching without any logic change at all. After that we could still decide to change the logic.
Hi Sebastian!
This seems like the right approach to me as well, I would just add one additional comment. Earlier on, you mentioned that a lot of "strange" dtypes will pop up when dealing with floats/ints. E.g. int15, int31, int63, int52 (for checking doublecompat), int23 (single compat), int10 (half compat) and so on and so forth. The lookup table would get tricky to populate by hand  It might be worth it to use the logic I suggested to autogenerate it in some way, or to "determine" the temporary underspecified type, as Nathaniel proposed in his email to the list. That is, we store the number of:
* flag (0 for numeric, 1 for nonnumeric) * sign bits (0 for unsigned ints, 1 else) * integer/fraction bits (selfexplanatory) * exponent bits (selfexplanatory) * LogNumber of items (0 for real, 1 for complex, 2 for quarternion, etc.) (I propose log because the CayleyDickson algebras [1] require a power of two)
A type is safely castable to another if all of these numbers are exceeded or met.
This would give us a clean way for registering new numeric types, while also cleanly hooking into the type system, and solving the casting scenario. Of course, I'm not proposing we generate the loops for or provide all these types ourselves, but simply that we allow people to define dtypes using such a schema. I do worry that we're specialcasing numbers here, but it is "Num"Py, so I'm also not too worried.
This flexibility would, for example, allow us to easily define a bfloat16/bcomplex32 type with all the "can_cast" logic in place, even if people have to register their own casts or loops (and just to be clear, we error if they are not). It also makes it easy to define loops for int128 and so on if they come along.
The only open question left here is: What to do with a case like int64 + uint64. And what I propose is we abandon purity for pragmatism here and tell ourselves that losing one sign bit is tolerable 90% of the time, and going to floatingpoint is probably worse. It's more of a rangeversusaccuracy question, and I would argue that people using integers expect exactness. Of course, I doubt anyone is actually relying on the fact that adding two integers produces floatingpoint results, and it has been the cause of at least one bug, which highlights that integers can be used in places where floats cannot. [0]
Hameer Abbasi
[0] https://github.com/numpy/numpy/issues/9982 [1] https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction
Best,
Sebastian
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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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.
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
On Tue, 20190618 at 04:28 +0200, Hameer Abbasi wrote:
On Wed, 20190612 at 12:55 0500, Sebastian Berg wrote:
On Wed, 20190605 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?
Hi all,
just to note. I think I will go forward trying to fill the hole in the hierarchy with a nonexisting uint7 dtype. That seemed like it may be ugly, but if it does not escalate too much, it is probably fairly straight forward. And it would allow to simplify dispatching without any logic change at all. After that we could still decide to change the logic.
Hi Sebastian!
This seems like the right approach to me as well, I would just add one additional comment. Earlier on, you mentioned that a lot of "strange" dtypes will pop up when dealing with floats/ints. E.g. int15, int31, int63, int52 (for checking doublecompat), int23 (single compat), int10 (half compat) and so on and so forth. The lookup table would get tricky to populate by hand  It might be worth it to use the logic I suggested to autogenerate it in some way, or to "determine" the temporary underspecified type, as Nathaniel proposed in his email to the list. That is, we store the number of:
 flag (0 for numeric, 1 for nonnumeric)
 sign bits (0 for unsigned ints, 1 else)
 integer/fraction bits (selfexplanatory)
 exponent bits (selfexplanatory)
 LogNumber of items (0 for real, 1 for complex, 2 for quarternion,
etc.) (I propose log because the CayleyDickson algebras [1] require a power of two)
A type is safely castable to another if all of these numbers are exceeded or met.
This would give us a clean way for registering new numeric types, while also cleanly hooking into the type system, and solving the casting scenario. Of course, I'm not proposing we generate the loops for or provide all these types ourselves, but simply that we allow people to define dtypes using such a schema. I do worry that we're special casing numbers here, but it is "Num"Py, so I'm also not too worried.
This flexibility would, for example, allow us to easily define a bfloat16/bcomplex32 type with all the "can_cast" logic in place, even if people have to register their own casts or loops (and just to be clear, we error if they are not). It also makes it easy to define loops for int128 and so on if they come along.
The only open question left here is: What to do with a case like int64
 uint64. And what I propose is we abandon purity for pragmatism here
and tell ourselves that losing one sign bit is tolerable 90% of the time, and going to floatingpoint is probably worse. It's more of a rangeversusaccuracy question, and I would argue that people using integers expect exactness. Of course, I doubt anyone is actually relying on the fact that adding two integers produces floatingpoint results, and it has been the cause of at least one bug, which highlights that integers can be used in places where floats cannot. [0]
P.S. Someone collected a list of issues where the automatic float conversion breaks things, it's old but it does highlight the importance of the issue: [0]
https://github.com/numpy/numpy/issues/12525#issuecomment457727726
Hameer Abbasi
Hameer Abbasi
[0] https://github.com/numpy/numpy/issues/9982 [1] https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction
Best,
Sebastian
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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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Hi Hameer,
On Tue, 20190618 at 04:28 +0200, Hameer Abbasi wrote:
On Wed, 20190612 at 12:55 0500, Sebastian Berg wrote:
On Wed, 20190605 at 15:41 0500, Sebastian Berg wrote:
Hi all,
<snip>
A type is safely castable to another if all of these numbers are exceeded or met.
This would give us a clean way for registering new numeric types, while also cleanly hooking into the type system, and solving the casting scenario. Of course, I'm not proposing we generate the loops for or provide all these types ourselves, but simply that we allow people to define dtypes using such a schema. I do worry that we're special casing numbers here, but it is "Num"Py, so I'm also not too worried.
This flexibility would, for example, allow us to easily define a bfloat16/bcomplex32 type with all the "can_cast" logic in place, even if people have to register their own casts or loops (and just to be clear, we error if they are not). It also makes it easy to define loops for int128 and so on if they come along.
The only open question left here is: What to do with a case like int64
 uint64. And what I propose is we abandon purity for pragmatism here
and tell ourselves that losing one sign bit is tolerable 90% of the time, and going to floatingpoint is probably worse. It's more of a rangeversusaccuracy question, and I would argue that people using integers expect exactness. Of course, I doubt anyone is actually relying on the fact that adding two integers produces floatingpoint results, and it has been the cause of at least one bug, which highlights that integers can be used in places where floats cannot. [0]
TL;DR: I started a prototype for a possible approach on casting/promotion and ufunc dispatching, any comments appreciated, especially if I took a wrong turn! I will look into writing a bit more about it more in an NEP style and not in code.
(About uint64 + int64 see below [0])
Thanks for the input, Hameer! Sorry for not following up here with some of the thoughts that I had after writing that. You are right that the bit counting is a way to handle this (and maybe keep it limited enough that caching is possible). I had started prototyping a bit with the thought that maybe caching for scalars is just not so important (just type if you need the speed). But using this method, it might be fine. Although, e.g. an int8NA type using 128 to signal an NA value would be yet another issue with "binning" the values.
I have followed a bit of an older thought of mine right now and started to do a python mockup prototyping for that. It is probably still a lot in flux, but the basic idea is to start of with using slots on a dtype objects (I realize that during the meeting we had a slight tendency towards a registration approach for casting, this seemed a bit simpler to me though).
For the sake of discussion, I posted the start at: https://github.com/seberg/numpy_dtype_prototype
On the ufunc side, it just mocks up a simple UfuncImpl model (for add/multiply, but only add semi supports units right now).
There is a mock up array object using a numpy array + new dtype (it does support `array.astype(new_dtype)`.
I have basically considered dtypes to be instances of "DType". The classes of dtypes could be thought of dtype categories (if you so will, right now these categories are not clean with respect to ufunc dispatching).
There are basically two different kinds of dtypes in this mock up:
1. Descriptor instances which are "finalized", i.e. they are proper dtypes with an itemsize and can be attached to arrays. 2. Descriptor instances which are not "finalized". These could be just abstract dtype. The simplest notion here are flexible dtypes such as "S" which cannot be attached to an array, but we still call it a dtype.
This way 1. are basically more specific versions of 2. So both groups have all the machinery for type casting/promotion/discovery, but only the first group can actually describe real data.
So how to handle casting? In this mockup, I opted for slots on the DType object (the Cside would look similar, not sure how exactly), one reason is that casting in general needs function calls in any case, because we cannot decide if one string can be cast to another without looking at its length, etc (or meters cast to seconds). For casting purposes these are:
methods:
* get_cast_func_to(...), get_cast_func_from(...) * (optionally: can_cast_to, can_cast_from) * common_type(self, other) # allow to override common type operation. * default_type() # for nonfinalized types to ask them for a real type
classmethods:
* discover_type(python_scalar) # falls back to discovering from class: * discover_type_from_class(python_type)
Of course some other information needs to be attached/registered, e.g. which python classes to associate with a certain dtype category.
To handle python integers, what I did now is that I discover them as their own dtype (a class 2. one, not a real one). Which remembers the value and knows how to cast to normal dtypes. It will do so very slowly by trying all possibilities, but user provided dtypes can handle it for better speed.
One small nice thing about this is that it should support dtypes such as `np.blasable` to mean "float32" or "float64", they may not be super fast, but it should work.
One side effect of this approach for the common type operation is that, there is no way for a user int24 to say that uint16 + int16 > int24 (or similar).
On the side of ufunc dispatching it is probably a bit hacky, but basically the idea is that it is based on the "dtypes category" (usually class). It could be extended later, but for starters makes the dispatching very simple, since we ignore type hierarchy.
Best,
Sebastian
[0] One of the additional things with uint64+int64 is that it jumps kinds/category (whatever you want to call it) between ints and floats right now. There is a more general problem with that. Our casting logic is not strictly ordered according to these categories (int < float), i.e. a large int will cause a float16 to upcast to float64. This is problematic because it is the reason why our common type/promotion is not associative, while C and Julia's is associative.
The only thing I can think of would be to find common types within the same categories kinds first, but I bet that just opens a huge can of worms (and makes dtype discovery much more complex).
Hameer Abbasi
[0] https://github.com/numpy/numpy/issues/9982 [1] https://en.wikipedia.org/wiki/Cayley%E2%80%93Dickson_construction
Best,
Sebastian
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:
 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 0D 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.
 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:
 Keep the current logic in place as much as possible
 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
NumPyDiscussion mailing list NumPyDiscussion@python.org https://mail.python.org/mailman/listinfo/numpydiscussion
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participants (9)

Allan Haldane

Hameer Abbasi

Marten van Kerkwijk

Nathaniel Smith

Neal Becker

Ralf Gommers

Sebastian Berg

Stephan Hoyer

Tyler Reddy