MasterJH5574 commented on code in PR #16575:
URL: https://github.com/apache/tvm/pull/16575#discussion_r1491924777
##########
python/tvm/relax/frontend/nn/op.py:
##########
@@ -1825,3 +1826,260 @@ def print_(tensor: Tensor):
filename, line_number =
inspect.getframeinfo(inspect.currentframe().f_back)[:2]
line_info = f"{filename}:{line_number}"
debug_func("vm.builtin.debug_print", tensor, _line_info=line_info)
+
+
+def less(a: Tensor, b: Tensor, name: str = "less") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs < rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.less(a._expr, b._expr), name)
+
+
+def less_equal(a: Tensor, b: Tensor, name: str = "less_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs <= rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.less_equal(a._expr, b._expr), name)
+
+
+def greater(a: Tensor, b: Tensor, name: str = "greater") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs > rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.greater(a._expr, b._expr), name)
+
+
+def greater_equal(a: Tensor, b: Tensor, name: str = "greater_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs >= rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.greater_equal(a._expr, b._expr), name)
+
+
+def equal(a: Tensor, b: Tensor, name: str = "equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs == rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.equal(a._expr, b._expr), name)
+
+
+def not_equal(a: Tensor, b: Tensor, name: str = "not_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs != rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.not_equal(a._expr, b._expr), name)
+
+
+def cumsum(
+ data: Tensor,
+ axis: Optional[int] = None,
+ dtype: Optional[str] = None,
+ exclusive: Optional[bool] = None,
+ name: str = "cumsum",
+) -> Tensor:
+ """Numpy style cumsum op. Return the cumulative inclusive sum of the
elements along
+ a given axis.
+
+ Parameters
+ ----------
+ data : Tensor
+ The input data to the operator.
+
+ axis : Optional[int]
+ Axis along which the cumulative sum is computed. The default (None) is
to compute
+ the cumsum over the flattened array.
+
+ dtype : Optional[str]
+ Type of the returned array and of the accumulator in which the
elements are summed.
+ If dtype is not specified, it defaults to the dtype of data.
+
+ exclusive : Optional[bool]
+ If true will return exclusive sum in which the first element is not
+ included.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The result has the same size as data, and the same shape as data if
axis is not None.
+ If axis is None, the result is a 1-d array.
+
+ Examples
+ --------
+ .. code-block:: python
+
+ a = [[1, 2, 3], [4, 5, 6]]
+
+ cumsum(a) # if axis is not provided, cumsum is done over the
flattened input.
+ -> [ 1, 3, 6, 10, 15, 21]
+
+ cumsum(a, dtype="float32")
+ -> [ 1., 3., 6., 10., 15., 21.]
+
+ cumsum(a, axis=0) # sum over rows for each of the 3 columns
+ -> [[1, 2, 3],
+ [5, 7, 9]]
+
+ cumsum(a, axis=1)
+ -> [[ 1, 3, 6],
+ [ 4, 9, 15]]
+
+ a = [1, 0, 1, 0, 1, 1, 0] # a is a boolean array
+ cumsum(a, dtype=int32) # dtype should be provided to get the expected
results
+ -> [1, 1, 2, 2, 3, 4, 4]
+ """
+ return wrap_nested(_op.cumsum(data._expr, axis, dtype, exclusive), name)
+
+
+def multinomial_from_uniform(prob: Tensor, uniform_sample: Tensor):
+ """Returns a tensor where each row contains the index sampled from the
multinomial
+ probability distribution located in the corresponding row of tensor prob.
+
+ Notes
+ -----
+ For better cpu performance, use 'vm.builtin.multinomial_from_uniform'.
+
+ Parameters
+ ----------
+ prob : Tensor
+ The probability tensor.
Review Comment:
The TIR function does not require the input prob distribution to have a sum
of 1 for each row and also does not hard require the samples to be in range
`[0, 1]`. Shall we add these notes in the docstring? It might be good to just
say the behavior is undefined when the prob distributions do not sum to 1 and
samples not in range [0, 1].
##########
python/tvm/relax/frontend/nn/op.py:
##########
@@ -1825,3 +1826,260 @@ def print_(tensor: Tensor):
filename, line_number =
inspect.getframeinfo(inspect.currentframe().f_back)[:2]
line_info = f"{filename}:{line_number}"
debug_func("vm.builtin.debug_print", tensor, _line_info=line_info)
+
+
+def less(a: Tensor, b: Tensor, name: str = "less") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs < rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.less(a._expr, b._expr), name)
+
+
+def less_equal(a: Tensor, b: Tensor, name: str = "less_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs <= rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.less_equal(a._expr, b._expr), name)
+
+
+def greater(a: Tensor, b: Tensor, name: str = "greater") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs > rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.greater(a._expr, b._expr), name)
+
+
+def greater_equal(a: Tensor, b: Tensor, name: str = "greater_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs >= rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.greater_equal(a._expr, b._expr), name)
+
+
+def equal(a: Tensor, b: Tensor, name: str = "equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs == rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.equal(a._expr, b._expr), name)
+
+
+def not_equal(a: Tensor, b: Tensor, name: str = "not_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs != rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.not_equal(a._expr, b._expr), name)
+
+
+def cumsum(
+ data: Tensor,
+ axis: Optional[int] = None,
+ dtype: Optional[str] = None,
+ exclusive: Optional[bool] = None,
+ name: str = "cumsum",
+) -> Tensor:
+ """Numpy style cumsum op. Return the cumulative inclusive sum of the
elements along
+ a given axis.
+
+ Parameters
+ ----------
+ data : Tensor
+ The input data to the operator.
+
+ axis : Optional[int]
+ Axis along which the cumulative sum is computed. The default (None) is
to compute
+ the cumsum over the flattened array.
+
+ dtype : Optional[str]
+ Type of the returned array and of the accumulator in which the
elements are summed.
+ If dtype is not specified, it defaults to the dtype of data.
+
+ exclusive : Optional[bool]
+ If true will return exclusive sum in which the first element is not
+ included.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The result has the same size as data, and the same shape as data if
axis is not None.
+ If axis is None, the result is a 1-d array.
+
+ Examples
+ --------
+ .. code-block:: python
+
+ a = [[1, 2, 3], [4, 5, 6]]
+
+ cumsum(a) # if axis is not provided, cumsum is done over the
flattened input.
+ -> [ 1, 3, 6, 10, 15, 21]
+
+ cumsum(a, dtype="float32")
+ -> [ 1., 3., 6., 10., 15., 21.]
+
+ cumsum(a, axis=0) # sum over rows for each of the 3 columns
+ -> [[1, 2, 3],
+ [5, 7, 9]]
+
+ cumsum(a, axis=1)
+ -> [[ 1, 3, 6],
+ [ 4, 9, 15]]
+
+ a = [1, 0, 1, 0, 1, 1, 0] # a is a boolean array
+ cumsum(a, dtype=int32) # dtype should be provided to get the expected
results
+ -> [1, 1, 2, 2, 3, 4, 4]
+ """
+ return wrap_nested(_op.cumsum(data._expr, axis, dtype, exclusive), name)
+
+
+def multinomial_from_uniform(prob: Tensor, uniform_sample: Tensor):
+ """Returns a tensor where each row contains the index sampled from the
multinomial
+ probability distribution located in the corresponding row of tensor prob.
+
+ Notes
+ -----
+ For better cpu performance, use 'vm.builtin.multinomial_from_uniform'.
+
+ Parameters
+ ----------
+ prob : Tensor
+ The probability tensor.
+
+ uniform_sample : Tensor
+ The uniform sample.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
Review Comment:
Shall we note the shapes of these tensors in the docstring? For example wen
can say `prob` has shape `(b, n)`, `uniform_sample` has shape `(b, 1)`, and
`result` has shape `(b, 1)`.
##########
python/tvm/relax/frontend/nn/op.py:
##########
@@ -1825,3 +1826,260 @@ def print_(tensor: Tensor):
filename, line_number =
inspect.getframeinfo(inspect.currentframe().f_back)[:2]
line_info = f"{filename}:{line_number}"
debug_func("vm.builtin.debug_print", tensor, _line_info=line_info)
+
+
+def less(a: Tensor, b: Tensor, name: str = "less") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs < rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.less(a._expr, b._expr), name)
+
+
+def less_equal(a: Tensor, b: Tensor, name: str = "less_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs <= rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.less_equal(a._expr, b._expr), name)
+
+
+def greater(a: Tensor, b: Tensor, name: str = "greater") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs > rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.greater(a._expr, b._expr), name)
+
+
+def greater_equal(a: Tensor, b: Tensor, name: str = "greater_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs >= rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.greater_equal(a._expr, b._expr), name)
+
+
+def equal(a: Tensor, b: Tensor, name: str = "equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs == rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.equal(a._expr, b._expr), name)
+
+
+def not_equal(a: Tensor, b: Tensor, name: str = "not_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs != rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.not_equal(a._expr, b._expr), name)
+
+
+def cumsum(
+ data: Tensor,
+ axis: Optional[int] = None,
+ dtype: Optional[str] = None,
+ exclusive: Optional[bool] = None,
+ name: str = "cumsum",
+) -> Tensor:
+ """Numpy style cumsum op. Return the cumulative inclusive sum of the
elements along
+ a given axis.
+
+ Parameters
+ ----------
+ data : Tensor
+ The input data to the operator.
+
+ axis : Optional[int]
+ Axis along which the cumulative sum is computed. The default (None) is
to compute
+ the cumsum over the flattened array.
+
+ dtype : Optional[str]
+ Type of the returned array and of the accumulator in which the
elements are summed.
+ If dtype is not specified, it defaults to the dtype of data.
+
+ exclusive : Optional[bool]
+ If true will return exclusive sum in which the first element is not
+ included.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The result has the same size as data, and the same shape as data if
axis is not None.
+ If axis is None, the result is a 1-d array.
+
+ Examples
+ --------
+ .. code-block:: python
+
+ a = [[1, 2, 3], [4, 5, 6]]
+
+ cumsum(a) # if axis is not provided, cumsum is done over the
flattened input.
+ -> [ 1, 3, 6, 10, 15, 21]
+
+ cumsum(a, dtype="float32")
+ -> [ 1., 3., 6., 10., 15., 21.]
+
+ cumsum(a, axis=0) # sum over rows for each of the 3 columns
+ -> [[1, 2, 3],
+ [5, 7, 9]]
+
+ cumsum(a, axis=1)
+ -> [[ 1, 3, 6],
+ [ 4, 9, 15]]
+
+ a = [1, 0, 1, 0, 1, 1, 0] # a is a boolean array
+ cumsum(a, dtype=int32) # dtype should be provided to get the expected
results
+ -> [1, 1, 2, 2, 3, 4, 4]
+ """
+ return wrap_nested(_op.cumsum(data._expr, axis, dtype, exclusive), name)
+
+
+def multinomial_from_uniform(prob: Tensor, uniform_sample: Tensor):
Review Comment:
Do we have tests showing this op can build and correctly run on GPU?
##########
python/tvm/relax/frontend/nn/op.py:
##########
@@ -1825,3 +1826,260 @@ def print_(tensor: Tensor):
filename, line_number =
inspect.getframeinfo(inspect.currentframe().f_back)[:2]
line_info = f"{filename}:{line_number}"
debug_func("vm.builtin.debug_print", tensor, _line_info=line_info)
+
+
+def less(a: Tensor, b: Tensor, name: str = "less") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs < rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.less(a._expr, b._expr), name)
+
+
+def less_equal(a: Tensor, b: Tensor, name: str = "less_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs <= rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.less_equal(a._expr, b._expr), name)
+
+
+def greater(a: Tensor, b: Tensor, name: str = "greater") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs > rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.greater(a._expr, b._expr), name)
+
+
+def greater_equal(a: Tensor, b: Tensor, name: str = "greater_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs >= rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.greater_equal(a._expr, b._expr), name)
+
+
+def equal(a: Tensor, b: Tensor, name: str = "equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs == rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.equal(a._expr, b._expr), name)
+
+
+def not_equal(a: Tensor, b: Tensor, name: str = "not_equal") -> Tensor:
+ """Broadcasted element-wise comparison for (lhs != rhs).
+
+ Parameters
+ ----------
+ a : Tensor
+ The first input tensor.
+
+ b : Tensor
+ The second input tensor.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+ """
+ return wrap_nested(_op.not_equal(a._expr, b._expr), name)
+
+
+def cumsum(
+ data: Tensor,
+ axis: Optional[int] = None,
+ dtype: Optional[str] = None,
+ exclusive: Optional[bool] = None,
+ name: str = "cumsum",
+) -> Tensor:
+ """Numpy style cumsum op. Return the cumulative inclusive sum of the
elements along
+ a given axis.
+
+ Parameters
+ ----------
+ data : Tensor
+ The input data to the operator.
+
+ axis : Optional[int]
+ Axis along which the cumulative sum is computed. The default (None) is
to compute
+ the cumsum over the flattened array.
+
+ dtype : Optional[str]
+ Type of the returned array and of the accumulator in which the
elements are summed.
+ If dtype is not specified, it defaults to the dtype of data.
+
+ exclusive : Optional[bool]
+ If true will return exclusive sum in which the first element is not
+ included.
+
+ name : str
+ Name hint.
+
+ Returns
+ -------
+ result : Tensor
+ The result has the same size as data, and the same shape as data if
axis is not None.
+ If axis is None, the result is a 1-d array.
+
+ Examples
+ --------
+ .. code-block:: python
+
+ a = [[1, 2, 3], [4, 5, 6]]
+
+ cumsum(a) # if axis is not provided, cumsum is done over the
flattened input.
+ -> [ 1, 3, 6, 10, 15, 21]
+
+ cumsum(a, dtype="float32")
+ -> [ 1., 3., 6., 10., 15., 21.]
+
+ cumsum(a, axis=0) # sum over rows for each of the 3 columns
+ -> [[1, 2, 3],
+ [5, 7, 9]]
+
+ cumsum(a, axis=1)
+ -> [[ 1, 3, 6],
+ [ 4, 9, 15]]
+
+ a = [1, 0, 1, 0, 1, 1, 0] # a is a boolean array
+ cumsum(a, dtype=int32) # dtype should be provided to get the expected
results
+ -> [1, 1, 2, 2, 3, 4, 4]
+ """
+ return wrap_nested(_op.cumsum(data._expr, axis, dtype, exclusive), name)
+
+
+def multinomial_from_uniform(prob: Tensor, uniform_sample: Tensor):
+ """Returns a tensor where each row contains the index sampled from the
multinomial
+ probability distribution located in the corresponding row of tensor prob.
+
+ Notes
+ -----
+ For better cpu performance, use 'vm.builtin.multinomial_from_uniform'.
+
+ Parameters
+ ----------
+ prob : Tensor
+ The probability tensor.
+
+ uniform_sample : Tensor
+ The uniform sample.
+
+ Returns
+ -------
+ result : Tensor
+ The computed result.
+
+ Examples
+ --------
+ .. code-block:: python
+
+ prob = [[0.2, 0.3, 0.5], [0.3, 0.4, 0.3]]
+ usample = [[0.4], [0.9]]
+
+ multinomial_from_uniform(a)
+ -> [[1], [2]]
+ """
+
+ batch = prob.shape[0]
+ cumsum_prob = cumsum(prob, axis=1, exclusive=False)
+
+ @T.prim_func(private=True)
+ def _get_sample_index(A: T.handle, B: T.handle, C: T.handle):
+ batch, vocab_size = T.int64(), T.int64()
+ prob = T.match_buffer(A, (batch, vocab_size), "float32")
+ usample = T.match_buffer(B, (batch, 1), "float32")
+ output_index = T.match_buffer(C, (batch, 1), "int64")
+
+ for ax0 in T.parallel(batch):
+ for ax1 in T.parallel(vocab_size):
+ with T.block("T_get_sample_index"):
+ v_ax0, v_ax1 = T.axis.remap("SS", [ax0, ax1])
+ T.writes(output_index[v_ax0, 0])
+ if usample[v_ax0, T.int64(0)] < prob[v_ax0, v_ax1] or
v_ax1 + 1 == vocab_size:
+ if v_ax1 == 0:
+ output_index[v_ax0, 0] = 0
+ else:
+ if not (usample[v_ax0, T.int64(0)] < prob[v_ax0,
v_ax1 - 1]):
Review Comment:
Just curious: is there any difference between using `not (xxx < yyy)` and
`xxx >= yyy` here?
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