diff --git a/.buildkite/0_webui.yml b/.buildkite/0_webui.yml
index d5ba4e0ea7cf9..aed6a5e59d9c3 100644
--- a/.buildkite/0_webui.yml
+++ b/.buildkite/0_webui.yml
@@ -19,6 +19,6 @@ steps:
# Our signed pipelines must have a `signature` or `signature_file` parameter that
# verifies the treehash of the pipeline itself and the inputs listed in `inputs`
- signed_pipelines:
- - pipeline: .buildkite/signed_pipeline_test.yml
- signature: "U2FsdGVkX18aZgryp6AJTArgD2uOnVWyFFGVOP5qsY4WbGQ/LVAcYiMEp9cweV+2iht+vmEF949CuuGTeQPA1fKlhPwkG3nZ688752DUB6en9oM2nuL31NoDKWHhpygZ"
+ #signed_pipelines:
+ # - pipeline: .buildkite/signed_pipeline_test.yml
+ # signature: "U2FsdGVkX18aZgryp6AJTArgD2uOnVWyFFGVOP5qsY4WbGQ/LVAcYiMEp9cweV+2iht+vmEF949CuuGTeQPA1fKlhPwkG3nZ688752DUB6en9oM2nuL31NoDKWHhpygZ"
diff --git a/.buildkite/embedding.yml b/.buildkite/embedding.yml
new file mode 100644
index 0000000000000..faffeb1f7cc87
--- /dev/null
+++ b/.buildkite/embedding.yml
@@ -0,0 +1,37 @@
+# These steps should only run on `sandbox.jl` machines, not `docker`-isolated ones
+# since we need nestable sandboxing. The rootfs images being used here are built from
+# the `.buildkite/rootfs_images/llvm-passes.jl` file.
+agents:
+ queue: "julia"
+ # Only run on `sandbox.jl` machines (not `docker`-isolated ones) since we need nestable sandboxing
+ sandbox.jl: "true"
+ os: "linux"
+
+steps:
+ - label: "Run embedding tests"
+ key: embedding
+ plugins:
+ - JuliaCI/julia#v1:
+ version: 1.6
+ - staticfloat/sandbox#v1:
+ rootfs_url: https://github.com/JuliaCI/rootfs-images/releases/download/v1/llvm-passes.tar.gz
+ rootfs_treehash: "f3ed53f159e8f13edfba8b20ebdb8ece73c1b8a8"
+ uid: 1000
+ gid: 1000
+ workspaces:
+ # Include `/cache/repos` so that our `git` version introspection works.
+ - "/cache/repos:/cache/repos"
+ commands: |
+ prefix="/tmp/prefix"
+ echo "+++ Build julia, deploy to $${prefix}"
+ make -j$${JULIA_NUM_CORES} JULIA_PRECOMPILE=0 prefix=$${prefix} install
+
+ embedding_output="/tmp/embedding-test"
+ echo "+++ Run embedding tests, deploy to $${embedding_output}"
+ mkdir -p "$${embedding_output}"
+ make -j$${JULIA_NUM_CORES} -C test/embedding JULIA="$${prefix}/bin/julia" BIN="$${embedding_output}"
+
+ timeout_in_minutes: 60
+ notify:
+ - github_commit_status:
+ context: "embedding"
diff --git a/.buildkite/llvm_passes.yml b/.buildkite/llvm_passes.yml
index 862f748c18499..b4311f689d089 100644
--- a/.buildkite/llvm_passes.yml
+++ b/.buildkite/llvm_passes.yml
@@ -9,21 +9,29 @@ agents:
steps:
- label: "analyzegc"
+ key: analyzegc
plugins:
- JuliaCI/julia#v1:
version: 1.6
- staticfloat/sandbox#v1:
rootfs_url: https://github.com/JuliaCI/rootfs-images/releases/download/v1/llvm-passes.tar.gz
rootfs_treehash: "f3ed53f159e8f13edfba8b20ebdb8ece73c1b8a8"
+ workspaces:
+ # Include `/cache/repos` so that our `git` version introspection works.
+ - "/cache/repos:/cache/repos"
commands: |
echo "--- Install in-tree LLVM dependencies"
- make -j 6 -C deps install-llvm install-clang install-llvm-tools install-libuv install-utf8proc install-unwind
+ make -j$${JULIA_NUM_CORES} -C deps install-llvm install-clang install-llvm-tools install-libuv install-utf8proc install-unwind
echo "+++ run clangsa/analyzegc"
- make -j 6 -C test/clangsa
- make -j 6 -C src analyzegc
+ make -j$${JULIA_NUM_CORES} -C test/clangsa
+ make -j$${JULIA_NUM_CORES} -C src analyzegc
timeout_in_minutes: 60
+ notify:
+ - github_commit_status:
+ context: "analyzegc"
- label: "llvmpasses"
+ key: llvmpasses
plugins:
- JuliaCI/julia#v1:
version: 1.6
@@ -32,9 +40,16 @@ steps:
rootfs_treehash: "f3ed53f159e8f13edfba8b20ebdb8ece73c1b8a8"
uid: 1000
gid: 1000
+ workspaces:
+ - "/cache/repos:/cache/repos"
commands: |
- echo "+++ run llvmpasses"
- make -j 6 release
- make -j 6 -C src install-analysis-deps
- make -j 6 -C test/llvmpasses
+ echo "--- make release"
+ make -j$${JULIA_NUM_CORES} release JULIA_PRECOMPILE=0
+ echo "--- make src/install-analysis-deps"
+ make -j$${JULIA_NUM_CORES} -C src install-analysis-deps
+ echo "+++ make test/llvmpasses"
+ make -j$${JULIA_NUM_CORES} -C test/llvmpasses
timeout_in_minutes: 60
+ notify:
+ - github_commit_status:
+ context: "llvm passes"
diff --git a/.buildkite/pipeline.yml b/.buildkite/pipeline.yml
index d76f3fd77bd4f..0dee5f2aaa3f7 100644
--- a/.buildkite/pipeline.yml
+++ b/.buildkite/pipeline.yml
@@ -14,6 +14,8 @@
steps:
- label: ":buildkite: Launch unsigned pipelines"
commands: |
+ buildkite-agent pipeline upload .buildkite/whitespace.yml
buildkite-agent pipeline upload .buildkite/llvm_passes.yml
+ buildkite-agent pipeline upload .buildkite/embedding.yml
agents:
queue: julia
diff --git a/.buildkite/whitespace.yml b/.buildkite/whitespace.yml
new file mode 100644
index 0000000000000..37fa66f75a3d9
--- /dev/null
+++ b/.buildkite/whitespace.yml
@@ -0,0 +1,26 @@
+# These steps should only run on `sandbox.jl` machines, not `docker`-isolated ones
+# since we need nestable sandboxing. The rootfs images being used here are built from
+# the `.buildkite/rootfs_images/llvm-passes.jl` file.
+agents:
+ queue: "julia"
+ # Only run on `sandbox.jl` machines (not `docker`-isolated ones) since we need nestable sandboxing
+ sandbox.jl: "true"
+ os: "linux"
+
+steps:
+ - label: "Check whitespace"
+ key: whitespace
+ plugins:
+ - JuliaCI/julia#v1:
+ version: 1.6
+ - staticfloat/sandbox#v1:
+ rootfs_url: https://github.com/JuliaCI/rootfs-images/releases/download/v1/llvm-passes.tar.gz
+ rootfs_treehash: "f3ed53f159e8f13edfba8b20ebdb8ece73c1b8a8"
+ workspaces:
+ - "/cache/repos:/cache/repos"
+ commands: |
+ make -j$${JULIA_NUM_CORES} check-whitespace
+ timeout_in_minutes: 10
+ notify:
+ - github_commit_status:
+ context: "whitespace"
diff --git a/base/essentials.jl b/base/essentials.jl
index 96498a6a30a61..a01598ca4a6ca 100644
--- a/base/essentials.jl
+++ b/base/essentials.jl
@@ -447,7 +447,9 @@ reinterpret(::Type{T}, x) where {T} = bitcast(T, x)
sizeof(obj)
Size, in bytes, of the canonical binary representation of the given `DataType` `T`, if any.
-Size, in bytes, of object `obj` if it is not `DataType`.
+Or the size, in bytes, of object `obj` if it is not a `DataType`.
+
+See also [`summarysize`](@ref).
# Examples
```jldoctest
@@ -460,7 +462,7 @@ julia> sizeof(ComplexF64)
julia> sizeof(1.0)
8
-julia> sizeof([1.0:10.0;])
+julia> sizeof(collect(1.0:10.0))
80
```
diff --git a/base/multidimensional.jl b/base/multidimensional.jl
index 9169a1facd8e5..40338fda1564d 100644
--- a/base/multidimensional.jl
+++ b/base/multidimensional.jl
@@ -1103,48 +1103,48 @@ copyto!(::AbstractArray, ::CartesianIndices, ::AbstractArray, ::CartesianIndices
# Cartesian to Linear unaliased copy
function _unaliased_copyto!(::IndexLinear, dest::AbstractArray, ::IndexCartesian, src::AbstractArray)
@_inline_meta
- axs = axes(src)
- ax, iter = axs[1], CartesianIndices(tail(axs))
- len, j = length(ax), firstindex(dest)
+ ax = axes1(src)
+ iter = CartesianIndices(safe_tail(axes(src)))
+ j = firstindex(dest) - 1
@inbounds for I in iter
- n = 0
- while n < len
- dest[j + n] = src[first(ax) + n, I.I...]
- n += 1
+ for i in ax
+ dest[j += 1] = src[i, I]
end
- j += len
end
end
# Linear to Cartesian unaliased copy
function _unaliased_copyto!(::IndexCartesian, dest::AbstractArray, ::IndexLinear, src::AbstractArray)
@_inline_meta
- axs = axes(dest)
- ax, iter = axs[1], CartesianIndices(tail(axs))
- len, i = length(ax), firstindex(src)
- final = lastindex(src) + 1
+ ax = axes1(dest)
+ iter = CartesianIndices(safe_tail(axes(dest)))
+ len = length(ax)
+ i, final = firstindex(src) - 1, lastindex(src)
@inbounds for I in iter
- len′ = min(final - i, len)
- n = 0
- while n < len′
- dest[first(ax) + n, I.I...] = src[i + n]
- n += 1
+ if final - i > len
+ for j in ax
+ dest[j, I] = src[i += 1]
+ end
+ else
+ j = first(ax) - 1
+ while i < final
+ dest[j += 1, I] = src[i += 1]
+ end
+ break
end
- (i += len′) == final && break
end
end
-# Cartesian to Cartesian unaliased copy
function _unaliased_copyto!(::IndexCartesian, dest::AbstractArray, ::IndexCartesian, src::AbstractArray)
@_inline_meta
axdest, axsrc = axes(dest), axes(src)
- if axdest == axsrc
+ if axdest == axsrc
# shared iterator (manually expended)
- ax, iter = axsrc[1], CartesianIndices(tail(axsrc))
+ ax = axes1(dest)
+ iter = CartesianIndices(safe_tail(axdest))
@inbounds for I in iter
for i in ax
- I′ = CartesianIndex(i, I.I...)
- dest[I′] = src[I′]
+ dest[i, I] = src[i, I]
end
end
else
diff --git a/base/summarysize.jl b/base/summarysize.jl
index 916214a69f88f..8c0a38d511648 100644
--- a/base/summarysize.jl
+++ b/base/summarysize.jl
@@ -17,6 +17,20 @@ Compute the amount of memory, in bytes, used by all unique objects reachable fro
- `exclude`: specifies the types of objects to exclude from the traversal.
- `chargeall`: specifies the types of objects to always charge the size of all of their
fields, even if those fields would normally be excluded.
+
+See also [`sizeof`](@ref).
+
+# Examples
+```jldoctest
+julia> Base.summarysize(1.0)
+8
+
+julia> Base.summarysize(Ref(rand(100)))
+848
+
+julia> sizeof(Ref(rand(100)))
+8
+```
"""
function summarysize(obj;
exclude = Union{DataType, Core.TypeName, Core.MethodInstance},
diff --git a/contrib/check-whitespace.sh b/contrib/check-whitespace.sh
index c380d7bdd2969..ff5bd24ab2cbe 100755
--- a/contrib/check-whitespace.sh
+++ b/contrib/check-whitespace.sh
@@ -35,3 +35,5 @@ if git --no-pager grep --color -n --full-name -e ' $' -- $file_patterns; then
echo "and then a forced push of the correct branch"
exit 1
fi
+
+echo "Whitespace check found no issues"
diff --git a/deps/openblas.mk b/deps/openblas.mk
index d86663efcbde7..a1ce15100ac4c 100644
--- a/deps/openblas.mk
+++ b/deps/openblas.mk
@@ -108,12 +108,12 @@ $(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-exshift.patch-applied: $(BUILDDIR)/$(OP
patch -p1 -f < $(SRCDIR)/patches/openblas-exshift.patch
echo 1 > $@
-$(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-filter-out-mavx-flag-on-zgemm-kernels.patch-applied: $(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-openblas-exshift.patch-applied
+$(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-filter-out-mavx-flag-on-zgemm-kernels.patch-applied: $(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-exshift.patch-applied
cd $(BUILDDIR)/$(OPENBLAS_SRC_DIR) && \
patch -p1 -f < $(SRCDIR)/patches/openblas-filter-out-mavx-flag-on-zgemm-kernels.patch
echo 1 > $@
-$(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-Only-filter-out-mavx-on-Sandybridge.patch-applied: $(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-filter-out-mavx-flag-on-zgemm-kernels.patch
+$(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-Only-filter-out-mavx-on-Sandybridge.patch-applied: $(BUILDDIR)/$(OPENBLAS_SRC_DIR)/openblas-filter-out-mavx-flag-on-zgemm-kernels.patch-applied
cd $(BUILDDIR)/$(OPENBLAS_SRC_DIR) && \
patch -p1 -f < $(SRCDIR)/patches/openblas-Only-filter-out-mavx-on-Sandybridge.patch
echo 1 > $@
diff --git a/src/codegen.cpp b/src/codegen.cpp
index 3d8ad33516080..d59b312716b2d 100644
--- a/src/codegen.cpp
+++ b/src/codegen.cpp
@@ -1157,7 +1157,7 @@ static void allocate_gc_frame(jl_codectx_t &ctx, BasicBlock *b0);
static Value *get_current_task(jl_codectx_t &ctx);
static Value *get_current_ptls(jl_codectx_t &ctx);
static Value *get_current_signal_page(jl_codectx_t &ctx);
-static void CreateTrap(IRBuilder<> &irbuilder);
+static void CreateTrap(IRBuilder<> &irbuilder, bool create_new_block = true);
static CallInst *emit_jlcall(jl_codectx_t &ctx, Function *theFptr, Value *theF,
jl_cgval_t *args, size_t nargs, CallingConv::ID cc);
static CallInst *emit_jlcall(jl_codectx_t &ctx, JuliaFunction *theFptr, Value *theF,
@@ -1456,7 +1456,7 @@ static Constant *undef_value_for_type(Type *T) {
return undef;
}
-static void CreateTrap(IRBuilder<> &irbuilder)
+static void CreateTrap(IRBuilder<> &irbuilder, bool create_new_block)
{
Function *f = irbuilder.GetInsertBlock()->getParent();
Function *trap_func = Intrinsic::getDeclaration(
@@ -1464,8 +1464,13 @@ static void CreateTrap(IRBuilder<> &irbuilder)
Intrinsic::trap);
irbuilder.CreateCall(trap_func);
irbuilder.CreateUnreachable();
- BasicBlock *newBB = BasicBlock::Create(irbuilder.getContext(), "after_noret", f);
- irbuilder.SetInsertPoint(newBB);
+ if (create_new_block) {
+ BasicBlock *newBB = BasicBlock::Create(irbuilder.getContext(), "after_noret", f);
+ irbuilder.SetInsertPoint(newBB);
+ }
+ else {
+ irbuilder.ClearInsertionPoint();
+ }
}
#if 0 // this code is likely useful, but currently unused
@@ -6901,8 +6906,8 @@ static std::pair<std::unique_ptr<Module>, jl_llvm_functions_t>
if (seq_next >= 0 && (unsigned)seq_next < stmtslen) {
workstack.push_back(seq_next);
}
- else if (!ctx.builder.GetInsertBlock()->getTerminator()) {
- ctx.builder.CreateUnreachable();
+ else if (ctx.builder.GetInsertBlock() && !ctx.builder.GetInsertBlock()->getTerminator()) {
+ CreateTrap(ctx.builder, false);
}
while (!workstack.empty()) {
int item = workstack.back();
@@ -6912,7 +6917,7 @@ static std::pair<std::unique_ptr<Module>, jl_llvm_functions_t>
cursor = item;
return;
}
- if (seq_next != -1 && !ctx.builder.GetInsertBlock()->getTerminator()) {
+ if (seq_next != -1 && ctx.builder.GetInsertBlock() && !ctx.builder.GetInsertBlock()->getTerminator()) {
come_from_bb[cursor + 1] = ctx.builder.GetInsertBlock();
ctx.builder.CreateBr(nextbb->second);
}
@@ -7050,7 +7055,7 @@ static std::pair<std::unique_ptr<Module>, jl_llvm_functions_t>
if (jl_is_returnnode(stmt)) {
jl_value_t *retexpr = jl_returnnode_value(stmt);
if (retexpr == NULL) {
- ctx.builder.CreateUnreachable();
+ CreateTrap(ctx.builder, false);
find_next_stmt(-1);
continue;
}
@@ -7059,7 +7064,7 @@ static std::pair<std::unique_ptr<Module>, jl_llvm_functions_t>
jl_cgval_t retvalinfo = emit_expr(ctx, retexpr);
retvalinfo = convert_julia_type(ctx, retvalinfo, jlrettype);
if (retvalinfo.typ == jl_bottom_type) {
- ctx.builder.CreateUnreachable();
+ CreateTrap(ctx.builder, false);
find_next_stmt(-1);
continue;
}
diff --git a/src/intrinsics.cpp b/src/intrinsics.cpp
index 7d0e94fd30783..e37ee264398e9 100644
--- a/src/intrinsics.cpp
+++ b/src/intrinsics.cpp
@@ -284,7 +284,6 @@ static Value *emit_unboxed_coercion(jl_codectx_t &ctx, Type *to, Value *unboxed)
Type *ty = unboxed->getType();
if (ty == to)
return unboxed;
- assert(to->isIntOrPtrTy() || to->isFloatingPointTy());
bool frompointer = ty->isPointerTy();
bool topointer = to->isPointerTy();
const DataLayout &DL = jl_data_layout;
diff --git a/src/jl_exported_data.inc b/src/jl_exported_data.inc
index bad61d4ade35a..3cebe459bf643 100644
--- a/src/jl_exported_data.inc
+++ b/src/jl_exported_data.inc
@@ -5,11 +5,11 @@
XX(jl_abstractstring_type) \
XX(jl_an_empty_string) \
XX(jl_an_empty_vec_any) \
- XX(jl_any_type) \
XX(jl_anytuple_type) \
XX(jl_anytuple_type_type) \
- XX(jl_argument_type) \
+ XX(jl_any_type) \
XX(jl_argumenterror_type) \
+ XX(jl_argument_type) \
XX(jl_array_any_type) \
XX(jl_array_int32_type) \
XX(jl_array_symbol_type) \
@@ -25,8 +25,8 @@
XX(jl_char_type) \
XX(jl_code_info_type) \
XX(jl_code_instance_type) \
- XX(jl_core_module) \
XX(jl_const_type) \
+ XX(jl_core_module) \
XX(jl_datatype_type) \
XX(jl_densearray_type) \
XX(jl_diverror_exception) \
@@ -49,6 +49,7 @@
XX(jl_int32_type) \
XX(jl_int64_type) \
XX(jl_int8_type) \
+ XX(jl_interconditional_type) \
XX(jl_interrupt_exception) \
XX(jl_intrinsic_type) \
XX(jl_lineinfonode_type) \
@@ -58,10 +59,10 @@
XX(jl_loaderror_type) \
XX(jl_main_module) \
XX(jl_memory_exception) \
+ XX(jl_methoderror_type) \
XX(jl_method_instance_type) \
XX(jl_method_match_type) \
XX(jl_method_type) \
- XX(jl_methoderror_type) \
XX(jl_methtable_type) \
XX(jl_module_type) \
XX(jl_namedtuple_type) \
@@ -71,9 +72,10 @@
XX(jl_nothing) \
XX(jl_nothing_type) \
XX(jl_number_type) \
- XX(jl_partial_struct_type) \
+ XX(jl_opaque_closure_type) \
+ XX(jl_opaque_closure_typename) \
XX(jl_partial_opaque_type) \
- XX(jl_interconditional_type) \
+ XX(jl_partial_struct_type) \
XX(jl_phicnode_type) \
XX(jl_phinode_type) \
XX(jl_pinode_type) \
@@ -95,20 +97,20 @@
XX(jl_true) \
XX(jl_tuple_typename) \
XX(jl_tvar_type) \
- XX(jl_type_type) \
- XX(jl_type_type_mt) \
- XX(jl_type_typename) \
XX(jl_typedslot_type) \
XX(jl_typeerror_type) \
XX(jl_typemap_entry_type) \
XX(jl_typemap_level_type) \
XX(jl_typename_type) \
XX(jl_typeofbottom_type) \
+ XX(jl_type_type) \
+ XX(jl_type_type_mt) \
+ XX(jl_type_typename) \
XX(jl_uint16_type) \
XX(jl_uint32_type) \
XX(jl_uint64_type) \
- XX(jl_uint8_type) \
XX(jl_uint8pointer_type) \
+ XX(jl_uint8_type) \
XX(jl_undefref_exception) \
XX(jl_undefvarerror_type) \
XX(jl_unionall_type) \
@@ -116,11 +118,9 @@
XX(jl_upsilonnode_type) \
XX(jl_vararg_type) \
XX(jl_vecelement_typename) \
- XX(jl_void_type) \
XX(jl_voidpointer_type) \
+ XX(jl_void_type) \
XX(jl_weakref_type) \
- XX(jl_opaque_closure_type) \
- XX(jl_opaque_closure_typename)
// Data symbols that are defined inside the public libjulia
#define JL_EXPORTED_DATA_SYMBOLS(XX) \
diff --git a/src/jl_exported_funcs.inc b/src/jl_exported_funcs.inc
index 81e68f3b78ee7..0e82304d82e5c 100644
--- a/src/jl_exported_funcs.inc
+++ b/src/jl_exported_funcs.inc
@@ -247,6 +247,7 @@
XX(jl_get_nth_field_checked) \
XX(jl_get_nth_field_noalloc) \
XX(jl_getpagesize) \
+ XX(jl_get_pgcstack) \
XX(jl_getpid) \
XX(jl_get_ptls_states) \
XX(jl_get_root_symbol) \
@@ -273,10 +274,10 @@
XX(jl_id_start_char) \
XX(jl_idtable_rehash) \
XX(jl_infer_thunk) \
- XX(jl_init_restored_modules) \
XX(jl_init) \
- XX(jl_init_with_image) \
XX(jl_init__threading) \
+ XX(jl_init_restored_modules) \
+ XX(jl_init_with_image) \
XX(jl_init_with_image__threading) \
XX(jl_install_sigint_handler) \
XX(jl_instantiate_type_in_env) \
@@ -391,6 +392,7 @@
XX(jl_pop_handler) \
XX(jl_preload_sysimg_so) \
XX(jl_prepend_cwd) \
+ XX(jl_print_backtrace) \
XX(jl_printf) \
XX(jl_process_events) \
XX(jl_profile_clear_data) \
@@ -541,5 +543,3 @@
XX(jl_vprintf) \
XX(jl_wakeup_thread) \
XX(jl_yield) \
- XX(jl_print_backtrace) \
- XX(jl_get_pgcstack)
diff --git a/stdlib/LinearAlgebra/src/cholesky.jl b/stdlib/LinearAlgebra/src/cholesky.jl
index 2ad2135da5d9c..bf738d5d203ec 100644
--- a/stdlib/LinearAlgebra/src/cholesky.jl
+++ b/stdlib/LinearAlgebra/src/cholesky.jl
@@ -110,8 +110,10 @@ positive semi-definite matrix `A`. This is the return type of [`cholesky(_, Val(
the corresponding matrix factorization function.
The triangular Cholesky factor can be obtained from the factorization `F::CholeskyPivoted`
-via `F.L` and `F.U`, and the permutation via `F.p`, where `A[F.p, F.p] ≈ F.U' * F.U ≈ F.L * F.L'`,
-or alternatively `A ≈ F.U[:, F.p]' * F.U[:, F.p] ≈ F.L[F.p, :] * F.L[F.p, :]'`.
+via `F.L` and `F.U`, and the permutation via `F.p`, where `A[F.p, F.p] ≈ Ur' * Ur ≈ Lr * Lr'`
+with `Ur = F.U[1:F.rank, :]` and `Lr = F.L[:, 1:F.rank]`, or alternatively
+`A ≈ Up' * Up ≈ Lp * Lp'` with `Up = F.U[1:F.rank, invperm(F.p)]` and
+`Lp = F.L[invperm(F.p), 1:F.rank]`.
The following functions are available for `CholeskyPivoted` objects:
[`size`](@ref), [`\\`](@ref), [`inv`](@ref), [`det`](@ref), and [`rank`](@ref).
@@ -120,25 +122,28 @@ Iterating the decomposition produces the components `L` and `U`.
# Examples
```jldoctest
-julia> A = [4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
-3×3 Matrix{Float64}:
- 4.0 12.0 -16.0
- 12.0 37.0 -43.0
- -16.0 -43.0 98.0
+julia> X = [1.0, 2.0, 3.0, 4.0];
-julia> C = cholesky(A, Val(true))
+julia> A = X * X';
+
+julia> C = cholesky(A, Val(true), check = false)
CholeskyPivoted{Float64, Matrix{Float64}}
-U factor with rank 3:
-3×3 UpperTriangular{Float64, Matrix{Float64}}:
- 9.89949 -4.34366 -1.61624
- ⋅ 4.25825 1.1694
- ⋅ ⋅ 0.142334
+U factor with rank 1:
+4×4 UpperTriangular{Float64, Matrix{Float64}}:
+ 4.0 2.0 3.0 1.0
+ ⋅ 0.0 6.0 2.0
+ ⋅ ⋅ 9.0 3.0
+ ⋅ ⋅ ⋅ 1.0
permutation:
-3-element Vector{Int64}:
- 3
+4-element Vector{Int64}:
+ 4
2
+ 3
1
+julia> C.U[1:C.rank, :]' * C.U[1:C.rank, :] ≈ A[C.p, C.p]
+true
+
julia> l, u = C; # destructuring via iteration
julia> l == C.L && u == C.U
@@ -403,8 +408,9 @@ and return a [`CholeskyPivoted`](@ref) factorization. The matrix `A` can either
or [`Hermitian`](@ref) [`StridedMatrix`](@ref) or a *perfectly* symmetric or Hermitian `StridedMatrix`.
The triangular Cholesky factor can be obtained from the factorization `F` via `F.L` and `F.U`,
-and the permutation via `F.p`, where `A[F.p, F.p] ≈ F.U' * F.U ≈ F.L * F.L'`, or alternatively
-`A ≈ F.U[:, F.p]' * F.U[:, F.p] ≈ F.L[F.p, :] * F.L[F.p, :]'`.
+and the permutation via `F.p`, where `A[F.p, F.p] ≈ Ur' * Ur ≈ Lr * Lr'` with `Ur = F.U[1:F.rank, :]`
+and `Lr = F.L[:, 1:F.rank]`, or alternatively `A ≈ Up' * Up ≈ Lp * Lp'` with
+`Up = F.U[1:F.rank, invperm(F.p)]` and `Lp = F.L[invperm(F.p), 1:F.rank]`.
The following functions are available for `CholeskyPivoted` objects:
[`size`](@ref), [`\\`](@ref), [`inv`](@ref), [`det`](@ref), and [`rank`](@ref).
@@ -421,26 +427,26 @@ validity (via [`issuccess`](@ref)) lies with the user.
# Examples
```jldoctest
-julia> A = [4. 12. -16.; 12. 37. -43.; -16. -43. 98.]
-3×3 Matrix{Float64}:
- 4.0 12.0 -16.0
- 12.0 37.0 -43.0
- -16.0 -43.0 98.0
+julia> X = [1.0, 2.0, 3.0, 4.0];
+
+julia> A = X * X';
-julia> C = cholesky(A, Val(true))
+julia> C = cholesky(A, Val(true), check = false)
CholeskyPivoted{Float64, Matrix{Float64}}
-U factor with rank 3:
-3×3 UpperTriangular{Float64, Matrix{Float64}}:
- 9.89949 -4.34366 -1.61624
- ⋅ 4.25825 1.1694
- ⋅ ⋅ 0.142334
+U factor with rank 1:
+4×4 UpperTriangular{Float64, Matrix{Float64}}:
+ 4.0 2.0 3.0 1.0
+ ⋅ 0.0 6.0 2.0
+ ⋅ ⋅ 9.0 3.0
+ ⋅ ⋅ ⋅ 1.0
permutation:
-3-element Vector{Int64}:
- 3
+4-element Vector{Int64}:
+ 4
2
+ 3
1
-julia> C.U[:, C.p]' * C.U[:, C.p] ≈ A
+julia> C.U[1:C.rank, :]' * C.U[1:C.rank, :] ≈ A[C.p, C.p]
true
julia> l, u = C; # destructuring via iteration
diff --git a/stdlib/SparseArrays/src/sparsematrix.jl b/stdlib/SparseArrays/src/sparsematrix.jl
index bcc518f527f63..af5eb4e4ab726 100644
--- a/stdlib/SparseArrays/src/sparsematrix.jl
+++ b/stdlib/SparseArrays/src/sparsematrix.jl
@@ -81,6 +81,7 @@ size(S::SparseMatrixCSC) = (getfield(S, :m), getfield(S, :n))
_goodbuffers(S::SparseMatrixCSC) = _goodbuffers(size(S)..., getcolptr(S), getrowval(S), nonzeros(S))
_checkbuffers(S::SparseMatrixCSC) = (@assert _goodbuffers(S); S)
+_checkbuffers(S::Union{Adjoint, Transpose}) = (_checkbuffers(parent(S)); S)
function _goodbuffers(m, n, colptr, rowval, nzval)
(length(colptr) == n + 1 && colptr[end] - 1 == length(rowval) == length(nzval))
@@ -125,6 +126,8 @@ julia> nnz(A)
"""
nnz(S::AbstractSparseMatrixCSC) = Int(getcolptr(S)[size(S, 2) + 1]) - 1
nnz(S::ReshapedArray{<:Any,1,<:AbstractSparseMatrixCSC}) = nnz(parent(S))
+nnz(S::Adjoint{<:Any,<:AbstractSparseMatrixCSC}) = nnz(parent(S))
+nnz(S::Transpose{<:Any,<:AbstractSparseMatrixCSC}) = nnz(parent(S))
nnz(S::UpperTriangular{<:Any,<:AbstractSparseMatrixCSC}) = nnz1(S)
nnz(S::LowerTriangular{<:Any,<:AbstractSparseMatrixCSC}) = nnz1(S)
nnz(S::SparseMatrixCSCView) = nnz1(S)
@@ -215,6 +218,7 @@ nzrange(S::SparseMatrixCSCView, col::Integer) = nzrange(S.parent, S.indices[2][c
nzrange(S::UpperTriangular{<:Any,<:SparseMatrixCSCUnion}, i::Integer) = nzrangeup(S.data, i)
nzrange(S::LowerTriangular{<:Any,<:SparseMatrixCSCUnion}, i::Integer) = nzrangelo(S.data, i)
+const AbstractSparseMatrixCSCInclAdjointAndTranspose = Union{AbstractSparseMatrixCSC,Adjoint{<:Any,<:AbstractSparseMatrixCSC},Transpose{<:Any,<:AbstractSparseMatrixCSC}}
function Base.isstored(A::AbstractSparseMatrixCSC, i::Integer, j::Integer)
@boundscheck checkbounds(A, i, j)
rows = rowvals(A)
@@ -224,11 +228,21 @@ function Base.isstored(A::AbstractSparseMatrixCSC, i::Integer, j::Integer)
return false
end
-Base.replace_in_print_matrix(A::AbstractSparseMatrix, i::Integer, j::Integer, s::AbstractString) =
+function Base.isstored(A::Union{Adjoint{<:Any,<:AbstractSparseMatrixCSC},Transpose{<:Any,<:AbstractSparseMatrixCSC}}, i::Integer, j::Integer)
+ @boundscheck checkbounds(A, i, j)
+ cols = rowvals(parent(A))
+ for istored in nzrange(parent(A), i)
+ j == cols[istored] && return true
+ end
+ return false
+end
+
+Base.replace_in_print_matrix(A::AbstractSparseMatrixCSCInclAdjointAndTranspose, i::Integer, j::Integer, s::AbstractString) =
Base.isstored(A, i, j) ? s : Base.replace_with_centered_mark(s)
-function Base.array_summary(io::IO, S::AbstractSparseMatrixCSC, dims::Tuple{Vararg{Base.OneTo}})
+function Base.array_summary(io::IO, S::AbstractSparseMatrixCSCInclAdjointAndTranspose, dims::Tuple{Vararg{Base.OneTo}})
_checkbuffers(S)
+
xnnz = nnz(S)
m, n = size(S)
print(io, m, "×", n, " ", typeof(S), " with ", xnnz, " stored ",
@@ -236,8 +250,8 @@ function Base.array_summary(io::IO, S::AbstractSparseMatrixCSC, dims::Tuple{Vara
nothing
end
-# called by `show(io, MIME("text/plain"), ::AbstractSparseMatrixCSC)`
-function Base.print_array(io::IO, S::AbstractSparseMatrixCSC)
+# called by `show(io, MIME("text/plain"), ::AbstractSparseMatrixCSCInclAdjointAndTranspose)`
+function Base.print_array(io::IO, S::AbstractSparseMatrixCSCInclAdjointAndTranspose)
if max(size(S)...) < 16
Base.print_matrix(io, S)
else
@@ -246,7 +260,7 @@ function Base.print_array(io::IO, S::AbstractSparseMatrixCSC)
end
# always show matrices as `sparse(I, J, K)`
-function Base.show(io::IO, S::AbstractSparseMatrixCSC)
+function Base.show(io::IO, S::AbstractSparseMatrixCSCInclAdjointAndTranspose)
_checkbuffers(S)
# can't use `findnz`, because that expects all values not to be #undef
I = rowvals(S)
@@ -257,7 +271,7 @@ function Base.show(io::IO, S::AbstractSparseMatrixCSC)
end
const brailleBlocks = UInt16['⠁', '⠂', '⠄', '⡀', '⠈', '⠐', '⠠', '⢀']
-function _show_with_braille_patterns(io::IO, S::AbstractSparseMatrixCSC)
+function _show_with_braille_patterns(io::IO, S::AbstractSparseMatrixCSCInclAdjointAndTranspose)
m, n = size(S)
(m == 0 || n == 0) && return show(io, MIME("text/plain"), S)
@@ -291,28 +305,43 @@ function _show_with_braille_patterns(io::IO, S::AbstractSparseMatrixCSC)
brailleGrid = fill(UInt16(10240), (scaleWidth - 1) ÷ 2 + 2, (scaleHeight - 1) ÷ 4 + 1)
brailleGrid[end, :] .= '\n'
- rvals = rowvals(S)
+ rvals = rowvals(parent(S))
rowscale = max(1, scaleHeight - 1) / max(1, m - 1)
colscale = max(1, scaleWidth - 1) / max(1, n - 1)
- @inbounds for j = 1:n
- # Scale the column index `j` to the best matching column index
- # of a matrix of size `scaleHeight × scaleWidth`
- sj = round(Int, (j - 1) * colscale + 1)
- for x in nzrange(S, j)
- # Scale the row index `i` to the best matching row index
+ if isa(S, AbstractSparseMatrixCSC)
+ @inbounds for j = 1:n
+ # Scale the column index `j` to the best matching column index
# of a matrix of size `scaleHeight × scaleWidth`
- si = round(Int, (rvals[x] - 1) * rowscale + 1)
-
- # Given the index pair `(si, sj)` of the scaled matrix,
- # calculate the corresponding triple `(k, l, p)` such that the
- # element at `(si, sj)` can be found at position `(k, l)` in the
- # braille grid `brailleGrid` and corresponds to the 1-dot braille
- # character `brailleBlocks[p]`
- k = (sj - 1) ÷ 2 + 1
- l = (si - 1) ÷ 4 + 1
- p = ((sj - 1) % 2) * 4 + ((si - 1) % 4 + 1)
-
- brailleGrid[k, l] |= brailleBlocks[p]
+ sj = round(Int, (j - 1) * colscale + 1)
+ for x in nzrange(S, j)
+ # Scale the row index `i` to the best matching row index
+ # of a matrix of size `scaleHeight × scaleWidth`
+ si = round(Int, (rvals[x] - 1) * rowscale + 1)
+
+ # Given the index pair `(si, sj)` of the scaled matrix,
+ # calculate the corresponding triple `(k, l, p)` such that the
+ # element at `(si, sj)` can be found at position `(k, l)` in the
+ # braille grid `brailleGrid` and corresponds to the 1-dot braille
+ # character `brailleBlocks[p]`
+ k = (sj - 1) ÷ 2 + 1
+ l = (si - 1) ÷ 4 + 1
+ p = ((sj - 1) % 2) * 4 + ((si - 1) % 4 + 1)
+
+ brailleGrid[k, l] |= brailleBlocks[p]
+ end
+ end
+ else
+ # If `S` is a adjoint or transpose of a sparse matrix we invert the
+ # roles of the indices `i` and `j`
+ @inbounds for i = 1:m
+ si = round(Int, (i - 1) * rowscale + 1)
+ for x in nzrange(parent(S), i)
+ sj = round(Int, (rvals[x] - 1) * colscale + 1)
+ k = (sj - 1) ÷ 2 + 1
+ l = (si - 1) ÷ 4 + 1
+ p = ((sj - 1) % 2) * 4 + ((si - 1) % 4 + 1)
+ brailleGrid[k, l] |= brailleBlocks[p]
+ end
end
end
foreach(c -> print(io, Char(c)), @view brailleGrid[1:end-1])
diff --git a/stdlib/SparseArrays/test/sparse.jl b/stdlib/SparseArrays/test/sparse.jl
index 2e07f42182a5e..221997a8f3384 100644
--- a/stdlib/SparseArrays/test/sparse.jl
+++ b/stdlib/SparseArrays/test/sparse.jl
@@ -2365,22 +2365,70 @@ end
for c in unstored_indices
@test Base.isstored(A, c[1], c[2]) == false
end
+
+ # `isstored` for adjoint and tranposed matrices:
+ for trans in (adjoint, transpose)
+ B = trans(A)
+ stored_indices = [CartesianIndex(j, i) for (j, i) in zip(J, I)]
+ unstored_indices = [c for c in CartesianIndices((n, m)) if !(c in stored_indices)]
+ for c in stored_indices
+ @test Base.isstored(B, c[1], c[2]) == true
+ end
+ for c in unstored_indices
+ @test Base.isstored(B, c[1], c[2]) == false
+ end
+ end
end
@testset "show" begin
io = IOBuffer()
- show(io, MIME"text/plain"(), spzeros(Float64, Int64, 0, 0))
- @test String(take!(io)) == "0×0 SparseArrays.SparseMatrixCSC{Float64, Int64} with 0 stored entries"
- show(io, MIME"text/plain"(), sparse(Int64[1], Int64[1], [1.0]))
- @test String(take!(io)) == "1×1 SparseArrays.SparseMatrixCSC{Float64, Int64} with 1 stored entry:\n 1.0"
- show(io, MIME"text/plain"(), spzeros(Float32, Int64, 2, 2))
- @test String(take!(io)) == "2×2 SparseArrays.SparseMatrixCSC{Float32, Int64} with 0 stored entries:\n ⋅ ⋅ \n ⋅ ⋅ "
+
+ A = spzeros(Float64, Int64, 0, 0)
+ for (transform, showstring) in zip(
+ (identity, adjoint, transpose), (
+ "0×0 $SparseMatrixCSC{Float64, Int64} with 0 stored entries",
+ "0×0 $Adjoint{Float64, $SparseMatrixCSC{Float64, Int64}} with 0 stored entries",
+ "0×0 $Transpose{Float64, $SparseMatrixCSC{Float64, Int64}} with 0 stored entries"
+ ))
+ show(io, MIME"text/plain"(), transform(A))
+ @test String(take!(io)) == showstring
+ end
+
+ A = sparse(Int64[1], Int64[1], [1.0])
+ for (transform, showstring) in zip(
+ (identity, adjoint, transpose), (
+ "1×1 $SparseMatrixCSC{Float64, Int64} with 1 stored entry:\n 1.0",
+ "1×1 $Adjoint{Float64, $SparseMatrixCSC{Float64, Int64}} with 1 stored entry:\n 1.0",
+ "1×1 $Transpose{Float64, $SparseMatrixCSC{Float64, Int64}} with 1 stored entry:\n 1.0",
+ ))
+ show(io, MIME"text/plain"(), transform(A))
+ @test String(take!(io)) == showstring
+ end
+
+ A = spzeros(Float32, Int64, 2, 2)
+ for (transform, showstring) in zip(
+ (identity, adjoint, transpose), (
+ "2×2 $SparseMatrixCSC{Float32, Int64} with 0 stored entries:\n ⋅ ⋅ \n ⋅ ⋅ ",
+ "2×2 $Adjoint{Float32, $SparseMatrixCSC{Float32, Int64}} with 0 stored entries:\n ⋅ ⋅ \n ⋅ ⋅ ",
+ "2×2 $Transpose{Float32, $SparseMatrixCSC{Float32, Int64}} with 0 stored entries:\n ⋅ ⋅ \n ⋅ ⋅ ",
+ ))
+ show(io, MIME"text/plain"(), transform(A))
+ @test String(take!(io)) == showstring
+ end
A = sparse(Int64[1, 1], Int64[1, 2], [1.0, 2.0])
- show(io, MIME"text/plain"(), A)
- @test String(take!(io)) == "1×2 SparseArrays.SparseMatrixCSC{Float64, Int64} with 2 stored entries:\n 1.0 2.0"
- _show_with_braille_patterns(convert(IOContext, io), A)
- @test String(take!(io)) == "⠉"
+ for (transform, showstring, braille) in zip(
+ (identity, adjoint, transpose), (
+ "1×2 $SparseMatrixCSC{Float64, Int64} with 2 stored entries:\n 1.0 2.0",
+ "2×1 $Adjoint{Float64, $SparseMatrixCSC{Float64, Int64}} with 2 stored entries:\n 1.0\n 2.0",
+ "2×1 $Transpose{Float64, $SparseMatrixCSC{Float64, Int64}} with 2 stored entries:\n 1.0\n 2.0",
+ ),
+ ("⠉", "⠃", "⠃"))
+ show(io, MIME"text/plain"(), transform(A))
+ @test String(take!(io)) == showstring
+ _show_with_braille_patterns(convert(IOContext, io), transform(A))
+ @test String(take!(io)) == braille
+ end
# every 1-dot braille pattern
for (i, b) in enumerate(split("⠁⠂⠄⡀⠈⠐⠠⢀", ""))
@@ -2392,28 +2440,50 @@ end
# empty braille pattern Char(10240)
A = spzeros(Int64, Int64, 4, 2)
- _show_with_braille_patterns(convert(IOContext, io), A)
- @test String(take!(io)) == "" * Char(10240)
+ for (transform, braille) in zip(
+ (identity, adjoint, transpose),
+ ("" * Char(10240), "" * Char(10240)^2, "" * Char(10240)^2))
+ _show_with_braille_patterns(convert(IOContext, io), transform(A))
+ @test String(take!(io)) == braille
+ end
A = sparse(Int64[1, 2, 4, 2, 3], Int64[1, 1, 1, 2, 2], Int64[1, 1, 1, 1, 1], 4, 2)
- show(io, MIME"text/plain"(), A)
- @test String(take!(io)) == "4×2 SparseArrays.SparseMatrixCSC{Int64, Int64} with 5 stored entries:\n 1 ⋅\n 1 1\n ⋅ 1\n 1 ⋅"
- _show_with_braille_patterns(convert(IOContext, io), A)
- @test String(take!(io)) == "⡳"
+ for (transform, showstring, braille) in zip(
+ (identity, adjoint, transpose), (
+ "4×2 $SparseMatrixCSC{Int64, Int64} with 5 stored entries:\n 1 ⋅\n 1 1\n ⋅ 1\n 1 ⋅",
+ "2×4 $Adjoint{Int64, $SparseMatrixCSC{Int64, Int64}} with 5 stored entries:\n 1 1 ⋅ 1\n ⋅ 1 1 ⋅",
+ "2×4 $Transpose{Int64, $SparseMatrixCSC{Int64, Int64}} with 5 stored entries:\n 1 1 ⋅ 1\n ⋅ 1 1 ⋅",
+ ),
+ ("⡳", "⠙⠊", "⠙⠊"))
+ show(io, MIME"text/plain"(), transform(A))
+ @test String(take!(io)) == showstring
+ _show_with_braille_patterns(convert(IOContext, io), transform(A))
+ @test String(take!(io)) == braille
+ end
A = sparse(Int64[1, 3, 2, 4], Int64[1, 1, 2, 2], Int64[1, 1, 1, 1], 7, 3)
- show(io, MIME"text/plain"(), A)
- @test String(take!(io)) == "7×3 SparseArrays.SparseMatrixCSC{Int64, Int64} with 4 stored entries:\n 1 ⋅ ⋅\n ⋅ 1 ⋅\n 1 ⋅ ⋅\n ⋅ 1 ⋅\n ⋅ ⋅ ⋅\n ⋅ ⋅ ⋅\n ⋅ ⋅ ⋅"
- _show_with_braille_patterns(convert(IOContext, io), A)
- @test String(take!(io)) == "⢕" * Char(10240) * "\n" * Char(10240)^2
+ for (transform, showstring, braille) in zip(
+ (identity, adjoint, transpose), (
+ "7×3 $SparseMatrixCSC{Int64, Int64} with 4 stored entries:\n 1 ⋅ ⋅\n ⋅ 1 ⋅\n 1 ⋅ ⋅\n ⋅ 1 ⋅\n ⋅ ⋅ ⋅\n ⋅ ⋅ ⋅\n ⋅ ⋅ ⋅",
+ "3×7 $Adjoint{Int64, $SparseMatrixCSC{Int64, Int64}} with 4 stored entries:\n 1 ⋅ 1 ⋅ ⋅ ⋅ ⋅\n ⋅ 1 ⋅ 1 ⋅ ⋅ ⋅\n ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅",
+ "3×7 $Transpose{Int64, $SparseMatrixCSC{Int64, Int64}} with 4 stored entries:\n 1 ⋅ 1 ⋅ ⋅ ⋅ ⋅\n ⋅ 1 ⋅ 1 ⋅ ⋅ ⋅\n ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅",
+ ),
+ ("⢕" * Char(10240) * "\n" * Char(10240)^2, "⠑⠑" * Char(10240)^2, "⠑⠑" * Char(10240)^2))
+ show(io, MIME"text/plain"(), transform(A))
+ @test String(take!(io)) == showstring
+ _show_with_braille_patterns(convert(IOContext, io), transform(A))
+ @test String(take!(io)) == braille
+ end
A = sparse(Int64[1:10;], Int64[1:10;], fill(Float64(1), 10))
- _show_with_braille_patterns(convert(IOContext, io), A)
brailleString = "⠑⢄" * Char(10240)^3 * "\n" * Char(10240)^2 * "⠑⢄" * Char(10240) * "\n" * Char(10240)^4 * "⠑"
- @test String(take!(io)) == brailleString
+ for transform in (identity, adjoint, transpose)
+ _show_with_braille_patterns(convert(IOContext, io), transform(A))
+ @test String(take!(io)) == brailleString
+ end
# Issue #30589
- @test repr("text/plain", sparse([true true])) == "1×2 SparseArrays.SparseMatrixCSC{Bool, $Int} with 2 stored entries:\n 1 1"
+ @test repr("text/plain", sparse([true true])) == "1×2 $SparseMatrixCSC{Bool, $Int} with 2 stored entries:\n 1 1"
function _filled_sparse(m::Integer, n::Integer)
C = CartesianIndices((m, n))[:]
diff --git a/test/compiler/codegen.jl b/test/compiler/codegen.jl
index df29a339d5a85..f232b246a9fc9 100644
--- a/test/compiler/codegen.jl
+++ b/test/compiler/codegen.jl
@@ -593,3 +593,7 @@ f41438(y) = y[].x
@test B41438.body.layout === C_NULL
@test f41438(Ref{A41438}(A41438(C_NULL))) === C_NULL
@test f41438(Ref{B41438}(B41438(C_NULL))) === C_NULL
+
+# issue #41157
+f41157(a, b) = a[1] = b[1]
+@test_throws BoundsError f41157(Tuple{Int}[], Tuple{Union{}}[])