[core] codegen/irrt: Add IRRT functions for strided-ndarray

This commit is contained in:
David Mak 2024-11-25 15:46:56 +08:00
parent 63a036bf08
commit fff7b597ec
7 changed files with 671 additions and 0 deletions

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@ -3,3 +3,5 @@
#include "irrt/math.hpp" #include "irrt/math.hpp"
#include "irrt/ndarray.hpp" #include "irrt/ndarray.hpp"
#include "irrt/slice.hpp" #include "irrt/slice.hpp"
#include "irrt/ndarray/basic.hpp"
#include "irrt/ndarray/def.hpp"

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@ -2,6 +2,8 @@
#include "irrt/int_types.hpp" #include "irrt/int_types.hpp"
// TODO: To be deleted since NDArray with strides is done.
namespace { namespace {
template<typename SizeT> template<typename SizeT>
SizeT __nac3_ndarray_calc_size_impl(const SizeT* list_data, SizeT list_len, SizeT begin_idx, SizeT end_idx) { SizeT __nac3_ndarray_calc_size_impl(const SizeT* list_data, SizeT list_len, SizeT begin_idx, SizeT end_idx) {

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@ -0,0 +1,342 @@
#pragma once
#include "irrt/debug.hpp"
#include "irrt/exception.hpp"
#include "irrt/int_types.hpp"
#include "irrt/ndarray/def.hpp"
namespace {
namespace ndarray {
namespace basic {
/**
* @brief Assert that `shape` does not contain negative dimensions.
*
* @param ndims Number of dimensions in `shape`
* @param shape The shape to check on
*/
template<typename SizeT>
void assert_shape_no_negative(SizeT ndims, const SizeT* shape) {
for (SizeT axis = 0; axis < ndims; axis++) {
if (shape[axis] < 0) {
raise_exception(SizeT, EXN_VALUE_ERROR,
"negative dimensions are not allowed; axis {0} "
"has dimension {1}",
axis, shape[axis], NO_PARAM);
}
}
}
/**
* @brief Assert that two shapes are the same in the context of writing output to an ndarray.
*/
template<typename SizeT>
void assert_output_shape_same(SizeT ndarray_ndims,
const SizeT* ndarray_shape,
SizeT output_ndims,
const SizeT* output_shape) {
if (ndarray_ndims != output_ndims) {
// There is no corresponding NumPy error message like this.
raise_exception(SizeT, EXN_VALUE_ERROR, "Cannot write output of ndims {0} to an ndarray with ndims {1}",
output_ndims, ndarray_ndims, NO_PARAM);
}
for (SizeT axis = 0; axis < ndarray_ndims; axis++) {
if (ndarray_shape[axis] != output_shape[axis]) {
// There is no corresponding NumPy error message like this.
raise_exception(SizeT, EXN_VALUE_ERROR,
"Mismatched dimensions on axis {0}, output has "
"dimension {1}, but destination ndarray has dimension {2}.",
axis, output_shape[axis], ndarray_shape[axis]);
}
}
}
/**
* @brief Return the number of elements of an ndarray given its shape.
*
* @param ndims Number of dimensions in `shape`
* @param shape The shape of the ndarray
*/
template<typename SizeT>
SizeT calc_size_from_shape(SizeT ndims, const SizeT* shape) {
SizeT size = 1;
for (SizeT axis = 0; axis < ndims; axis++)
size *= shape[axis];
return size;
}
/**
* @brief Compute the array indices of the `nth` (0-based) element of an ndarray given only its shape.
*
* @param ndims Number of elements in `shape` and `indices`
* @param shape The shape of the ndarray
* @param indices The returned indices indexing the ndarray with shape `shape`.
* @param nth The index of the element of interest.
*/
template<typename SizeT>
void set_indices_by_nth(SizeT ndims, const SizeT* shape, SizeT* indices, SizeT nth) {
for (SizeT i = 0; i < ndims; i++) {
SizeT axis = ndims - i - 1;
SizeT dim = shape[axis];
indices[axis] = nth % dim;
nth /= dim;
}
}
/**
* @brief Return the number of elements of an `ndarray`
*
* This function corresponds to `<an_ndarray>.size`
*/
template<typename SizeT>
SizeT size(const NDArray<SizeT>* ndarray) {
return calc_size_from_shape(ndarray->ndims, ndarray->shape);
}
/**
* @brief Return of the number of its content of an `ndarray`.
*
* This function corresponds to `<an_ndarray>.nbytes`.
*/
template<typename SizeT>
SizeT nbytes(const NDArray<SizeT>* ndarray) {
return size(ndarray) * ndarray->itemsize;
}
/**
* @brief Get the `len()` of an ndarray, and asserts that `ndarray` is a sized object.
*
* This function corresponds to `<an_ndarray>.__len__`.
*
* @param dst_length The length.
*/
template<typename SizeT>
SizeT len(const NDArray<SizeT>* ndarray) {
if (ndarray->ndims != 0) {
return ndarray->shape[0];
}
// numpy prohibits `__len__` on unsized objects
raise_exception(SizeT, EXN_TYPE_ERROR, "len() of unsized object", NO_PARAM, NO_PARAM, NO_PARAM);
__builtin_unreachable();
}
/**
* @brief Return a boolean indicating if `ndarray` is (C-)contiguous.
*
* You may want to see ndarray's rules for C-contiguity:
* https://github.com/numpy/numpy/blob/df256d0d2f3bc6833699529824781c58f9c6e697/numpy/core/src/multiarray/flagsobject.c#L95C1-L99C45
*/
template<typename SizeT>
bool is_c_contiguous(const NDArray<SizeT>* ndarray) {
// References:
// - tinynumpy's implementation:
// https://github.com/wadetb/tinynumpy/blob/0d23d22e07062ffab2afa287374c7b366eebdda1/tinynumpy/tinynumpy.py#L102
// - ndarray's flags["C_CONTIGUOUS"]:
// https://numpy.org/doc/stable/reference/generated/numpy.ndarray.flags.html#numpy.ndarray.flags
// - ndarray's rules for C-contiguity:
// https://github.com/numpy/numpy/blob/df256d0d2f3bc6833699529824781c58f9c6e697/numpy/core/src/multiarray/flagsobject.c#L95C1-L99C45
// From
// https://github.com/numpy/numpy/blob/df256d0d2f3bc6833699529824781c58f9c6e697/numpy/core/src/multiarray/flagsobject.c#L95C1-L99C45:
//
// The traditional rule is that for an array to be flagged as C contiguous,
// the following must hold:
//
// strides[-1] == itemsize
// strides[i] == shape[i+1] * strides[i + 1]
// [...]
// According to these rules, a 0- or 1-dimensional array is either both
// C- and F-contiguous, or neither; and an array with 2+ dimensions
// can be C- or F- contiguous, or neither, but not both. Though there
// there are exceptions for arrays with zero or one item, in the first
// case the check is relaxed up to and including the first dimension
// with shape[i] == 0. In the second case `strides == itemsize` will
// can be true for all dimensions and both flags are set.
if (ndarray->ndims == 0) {
return true;
}
if (ndarray->strides[ndarray->ndims - 1] != ndarray->itemsize) {
return false;
}
for (SizeT i = 1; i < ndarray->ndims; i++) {
SizeT axis_i = ndarray->ndims - i - 1;
if (ndarray->strides[axis_i] != ndarray->shape[axis_i + 1] * ndarray->strides[axis_i + 1]) {
return false;
}
}
return true;
}
/**
* @brief Return the pointer to the element indexed by `indices` along the ndarray's axes.
*
* This function does no bound check.
*/
template<typename SizeT>
void* get_pelement_by_indices(const NDArray<SizeT>* ndarray, const SizeT* indices) {
void* element = ndarray->data;
for (SizeT dim_i = 0; dim_i < ndarray->ndims; dim_i++)
element = static_cast<uint8_t*>(element) + indices[dim_i] * ndarray->strides[dim_i];
return element;
}
/**
* @brief Return the pointer to the nth (0-based) element of `ndarray` in flattened view.
*
* This function does no bound check.
*/
template<typename SizeT>
void* get_nth_pelement(const NDArray<SizeT>* ndarray, SizeT nth) {
void* element = ndarray->data;
for (SizeT i = 0; i < ndarray->ndims; i++) {
SizeT axis = ndarray->ndims - i - 1;
SizeT dim = ndarray->shape[axis];
element = static_cast<uint8_t*>(element) + ndarray->strides[axis] * (nth % dim);
nth /= dim;
}
return element;
}
/**
* @brief Update the strides of an ndarray given an ndarray `shape` to be contiguous.
*
* You might want to read https://ajcr.net/stride-guide-part-1/.
*/
template<typename SizeT>
void set_strides_by_shape(NDArray<SizeT>* ndarray) {
SizeT stride_product = 1;
for (SizeT i = 0; i < ndarray->ndims; i++) {
SizeT axis = ndarray->ndims - i - 1;
ndarray->strides[axis] = stride_product * ndarray->itemsize;
stride_product *= ndarray->shape[axis];
}
}
/**
* @brief Set an element in `ndarray`.
*
* @param pelement Pointer to the element in `ndarray` to be set.
* @param pvalue Pointer to the value `pelement` will be set to.
*/
template<typename SizeT>
void set_pelement_value(NDArray<SizeT>* ndarray, void* pelement, const void* pvalue) {
__builtin_memcpy(pelement, pvalue, ndarray->itemsize);
}
/**
* @brief Copy data from one ndarray to another of the exact same size and itemsize.
*
* Both ndarrays will be viewed in their flatten views when copying the elements.
*/
template<typename SizeT>
void copy_data(const NDArray<SizeT>* src_ndarray, NDArray<SizeT>* dst_ndarray) {
// TODO: Make this faster with memcpy when we see a contiguous segment.
// TODO: Handle overlapping.
debug_assert_eq(SizeT, src_ndarray->itemsize, dst_ndarray->itemsize);
for (SizeT i = 0; i < size(src_ndarray); i++) {
auto src_element = ndarray::basic::get_nth_pelement(src_ndarray, i);
auto dst_element = ndarray::basic::get_nth_pelement(dst_ndarray, i);
ndarray::basic::set_pelement_value(dst_ndarray, dst_element, src_element);
}
}
} // namespace basic
} // namespace ndarray
} // namespace
extern "C" {
using namespace ndarray::basic;
void __nac3_ndarray_util_assert_shape_no_negative(int32_t ndims, int32_t* shape) {
assert_shape_no_negative(ndims, shape);
}
void __nac3_ndarray_util_assert_shape_no_negative64(int64_t ndims, int64_t* shape) {
assert_shape_no_negative(ndims, shape);
}
void __nac3_ndarray_util_assert_output_shape_same(int32_t ndarray_ndims,
const int32_t* ndarray_shape,
int32_t output_ndims,
const int32_t* output_shape) {
assert_output_shape_same(ndarray_ndims, ndarray_shape, output_ndims, output_shape);
}
void __nac3_ndarray_util_assert_output_shape_same64(int64_t ndarray_ndims,
const int64_t* ndarray_shape,
int64_t output_ndims,
const int64_t* output_shape) {
assert_output_shape_same(ndarray_ndims, ndarray_shape, output_ndims, output_shape);
}
uint32_t __nac3_ndarray_size(NDArray<int32_t>* ndarray) {
return size(ndarray);
}
uint64_t __nac3_ndarray_size64(NDArray<int64_t>* ndarray) {
return size(ndarray);
}
uint32_t __nac3_ndarray_nbytes(NDArray<int32_t>* ndarray) {
return nbytes(ndarray);
}
uint64_t __nac3_ndarray_nbytes64(NDArray<int64_t>* ndarray) {
return nbytes(ndarray);
}
int32_t __nac3_ndarray_len(NDArray<int32_t>* ndarray) {
return len(ndarray);
}
int64_t __nac3_ndarray_len64(NDArray<int64_t>* ndarray) {
return len(ndarray);
}
bool __nac3_ndarray_is_c_contiguous(NDArray<int32_t>* ndarray) {
return is_c_contiguous(ndarray);
}
bool __nac3_ndarray_is_c_contiguous64(NDArray<int64_t>* ndarray) {
return is_c_contiguous(ndarray);
}
void* __nac3_ndarray_get_nth_pelement(const NDArray<int32_t>* ndarray, int32_t nth) {
return get_nth_pelement(ndarray, nth);
}
void* __nac3_ndarray_get_nth_pelement64(const NDArray<int64_t>* ndarray, int64_t nth) {
return get_nth_pelement(ndarray, nth);
}
void* __nac3_ndarray_get_pelement_by_indices(const NDArray<int32_t>* ndarray, int32_t* indices) {
return get_pelement_by_indices(ndarray, indices);
}
void* __nac3_ndarray_get_pelement_by_indices64(const NDArray<int64_t>* ndarray, int64_t* indices) {
return get_pelement_by_indices(ndarray, indices);
}
void __nac3_ndarray_set_strides_by_shape(NDArray<int32_t>* ndarray) {
set_strides_by_shape(ndarray);
}
void __nac3_ndarray_set_strides_by_shape64(NDArray<int64_t>* ndarray) {
set_strides_by_shape(ndarray);
}
void __nac3_ndarray_copy_data(NDArray<int32_t>* src_ndarray, NDArray<int32_t>* dst_ndarray) {
copy_data(src_ndarray, dst_ndarray);
}
void __nac3_ndarray_copy_data64(NDArray<int64_t>* src_ndarray, NDArray<int64_t>* dst_ndarray) {
copy_data(src_ndarray, dst_ndarray);
}
}

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@ -0,0 +1,51 @@
#pragma once
#include "irrt/int_types.hpp"
namespace {
/**
* @brief The NDArray object
*
* Official numpy implementation:
* https://github.com/numpy/numpy/blob/735a477f0bc2b5b84d0e72d92f224bde78d4e069/doc/source/reference/c-api/types-and-structures.rst#pyarrayinterface
*
* Note that this implementation is based on `PyArrayInterface` rather of `PyArrayObject`. The
* difference between `PyArrayInterface` and `PyArrayObject` (relevant to our implementation) is
* that `PyArrayInterface` *has* `itemsize` and uses `void*` for its `data`, whereas `PyArrayObject`
* does not require `itemsize` (probably using `strides[-1]` instead) and uses `char*` for its
* `data`. There are also minor differences in the struct layout.
*/
template<typename SizeT>
struct NDArray {
/**
* @brief The number of bytes of a single element in `data`.
*/
SizeT itemsize;
/**
* @brief The number of dimensions of this shape.
*/
SizeT ndims;
/**
* @brief The NDArray shape, with length equal to `ndims`.
*
* Note that it may contain 0.
*/
SizeT* shape;
/**
* @brief Array strides, with length equal to `ndims`
*
* The stride values are in units of bytes, not number of elements.
*
* Note that `strides` can have negative values or contain 0.
*/
SizeT* strides;
/**
* @brief The underlying data this `ndarray` is pointing to.
*/
void* data;
};
} // namespace

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@ -59,6 +59,27 @@ pub fn load_irrt<'ctx>(ctx: &'ctx Context, symbol_resolver: &dyn SymbolResolver)
irrt_mod irrt_mod
} }
/// Returns the name of a function which contains variants for 32-bit and 64-bit `size_t`.
///
/// - When [`TypeContext::size_type`] is 32-bits, the function name is `fn_name}`.
/// - When [`TypeContext::size_type`] is 64-bits, the function name is `{fn_name}64`.
#[must_use]
pub fn get_usize_dependent_function_name<G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &CodeGenContext<'_, '_>,
name: &str,
) -> String {
let mut name = name.to_owned();
match generator.get_size_type(ctx.ctx).get_bit_width() {
32 => {}
64 => name.push_str("64"),
bit_width => {
panic!("Unsupported int type bit width {bit_width}, must be either 32-bits or 64-bits")
}
}
name
}
/// NOTE: the output value of the end index of this function should be compared ***inclusively***, /// NOTE: the output value of the end index of this function should be compared ***inclusively***,
/// because python allows `a[2::-1]`, whose semantic is `[a[2], a[1], a[0]]`, which is equivalent to /// because python allows `a[2::-1]`, whose semantic is `[a[2], a[1], a[0]]`, which is equivalent to
/// NO numeric slice in python. /// NO numeric slice in python.

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@ -0,0 +1,250 @@
use inkwell::{
values::{BasicValueEnum, IntValue, PointerValue},
AddressSpace,
};
use crate::codegen::{
expr::{create_and_call_function, infer_and_call_function},
irrt::get_usize_dependent_function_name,
types::ProxyType,
values::{NDArrayValue, ProxyValue},
CodeGenContext, CodeGenerator,
};
pub fn call_nac3_ndarray_util_assert_shape_no_negative<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndims: IntValue<'ctx>,
shape: PointerValue<'ctx>,
) {
let llvm_usize = generator.get_size_type(ctx.ctx);
let llvm_pusize = llvm_usize.ptr_type(AddressSpace::default());
let name = get_usize_dependent_function_name(
generator,
ctx,
"__nac3_ndarray_util_assert_shape_no_negative",
);
create_and_call_function(
ctx,
&name,
Some(llvm_usize.into()),
&[(llvm_usize.into(), ndims.into()), (llvm_pusize.into(), shape.into())],
None,
None,
);
}
pub fn call_nac3_ndarray_util_assert_output_shape_same<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndarray_ndims: IntValue<'ctx>,
ndarray_shape: PointerValue<'ctx>,
output_ndims: IntValue<'ctx>,
output_shape: IntValue<'ctx>,
) {
let llvm_usize = generator.get_size_type(ctx.ctx);
let llvm_pusize = llvm_usize.ptr_type(AddressSpace::default());
let name = get_usize_dependent_function_name(
generator,
ctx,
"__nac3_ndarray_util_assert_output_shape_same",
);
create_and_call_function(
ctx,
&name,
Some(llvm_usize.into()),
&[
(llvm_usize.into(), ndarray_ndims.into()),
(llvm_pusize.into(), ndarray_shape.into()),
(llvm_usize.into(), output_ndims.into()),
(llvm_pusize.into(), output_shape.into()),
],
None,
None,
);
}
pub fn call_nac3_ndarray_size<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndarray: NDArrayValue<'ctx>,
) -> IntValue<'ctx> {
let llvm_usize = generator.get_size_type(ctx.ctx);
let llvm_ndarray = ndarray.get_type().as_base_type();
let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_size");
create_and_call_function(
ctx,
&name,
Some(llvm_usize.into()),
&[(llvm_ndarray.into(), ndarray.as_base_value().into())],
Some("size"),
None,
)
.map(BasicValueEnum::into_int_value)
.unwrap()
}
pub fn call_nac3_ndarray_nbytes<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndarray: NDArrayValue<'ctx>,
) -> IntValue<'ctx> {
let llvm_usize = generator.get_size_type(ctx.ctx);
let llvm_ndarray = ndarray.get_type().as_base_type();
let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_nbytes");
create_and_call_function(
ctx,
&name,
Some(llvm_usize.into()),
&[(llvm_ndarray.into(), ndarray.as_base_value().into())],
Some("nbytes"),
None,
)
.map(BasicValueEnum::into_int_value)
.unwrap()
}
pub fn call_nac3_ndarray_len<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndarray: NDArrayValue<'ctx>,
) -> IntValue<'ctx> {
let llvm_usize = generator.get_size_type(ctx.ctx);
let llvm_ndarray = ndarray.get_type().as_base_type();
let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_len");
create_and_call_function(
ctx,
&name,
Some(llvm_usize.into()),
&[(llvm_ndarray.into(), ndarray.as_base_value().into())],
Some("len"),
None,
)
.map(BasicValueEnum::into_int_value)
.unwrap()
}
pub fn call_nac3_ndarray_is_c_contiguous<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndarray: NDArrayValue<'ctx>,
) -> IntValue<'ctx> {
let llvm_i1 = ctx.ctx.bool_type();
let llvm_ndarray = ndarray.get_type().as_base_type();
let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_is_c_contiguous");
create_and_call_function(
ctx,
&name,
Some(llvm_i1.into()),
&[(llvm_ndarray.into(), ndarray.as_base_value().into())],
Some("is_c_contiguous"),
None,
)
.map(BasicValueEnum::into_int_value)
.unwrap()
}
pub fn call_nac3_ndarray_get_nth_pelement<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndarray: NDArrayValue<'ctx>,
index: IntValue<'ctx>,
) -> PointerValue<'ctx> {
let llvm_i8 = ctx.ctx.i8_type();
let llvm_pi8 = llvm_i8.ptr_type(AddressSpace::default());
let llvm_usize = generator.get_size_type(ctx.ctx);
let llvm_ndarray = ndarray.get_type().as_base_type();
let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_get_nth_pelement");
create_and_call_function(
ctx,
&name,
Some(llvm_pi8.into()),
&[(llvm_ndarray.into(), ndarray.as_base_value().into()), (llvm_usize.into(), index.into())],
Some("pelement"),
None,
)
.map(BasicValueEnum::into_pointer_value)
.unwrap()
}
pub fn call_nac3_ndarray_get_pelement_by_indices<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndarray: NDArrayValue<'ctx>,
indices: PointerValue<'ctx>,
) -> PointerValue<'ctx> {
let llvm_i8 = ctx.ctx.i8_type();
let llvm_pi8 = llvm_i8.ptr_type(AddressSpace::default());
let llvm_usize = generator.get_size_type(ctx.ctx);
let llvm_pusize = llvm_usize.ptr_type(AddressSpace::default());
let llvm_ndarray = ndarray.get_type().as_base_type();
let name =
get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_get_pelement_by_indices");
create_and_call_function(
ctx,
&name,
Some(llvm_pi8.into()),
&[
(llvm_ndarray.into(), ndarray.as_base_value().into()),
(llvm_pusize.into(), indices.into()),
],
Some("pelement"),
None,
)
.map(BasicValueEnum::into_pointer_value)
.unwrap()
}
pub fn call_nac3_ndarray_set_strides_by_shape<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
ndarray: NDArrayValue<'ctx>,
) {
let llvm_ndarray = ndarray.get_type().as_base_type();
let name =
get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_set_strides_by_shape");
create_and_call_function(
ctx,
&name,
None,
&[(llvm_ndarray.into(), ndarray.as_base_value().into())],
None,
None,
);
}
pub fn call_nac3_ndarray_copy_data<'ctx, G: CodeGenerator + ?Sized>(
generator: &mut G,
ctx: &mut CodeGenContext<'ctx, '_>,
src_ndarray: NDArrayValue<'ctx>,
dst_ndarray: NDArrayValue<'ctx>,
) {
let name = get_usize_dependent_function_name(generator, ctx, "__nac3_ndarray_copy_data");
infer_and_call_function(
ctx,
&name,
None,
&[src_ndarray.as_base_value().into(), dst_ndarray.as_base_value().into()],
None,
None,
);
}

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@ -15,6 +15,9 @@ use crate::codegen::{
}, },
CodeGenContext, CodeGenerator, CodeGenContext, CodeGenerator,
}; };
pub use basic::*;
mod basic;
/// Generates a call to `__nac3_ndarray_calc_size`. Returns an [`IntValue`] representing the /// Generates a call to `__nac3_ndarray_calc_size`. Returns an [`IntValue`] representing the
/// calculated total size. /// calculated total size.