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bpo-43693: Add the MAKE_CELL opcode and interleave fast locals offsets. #26396

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merged 14 commits into from
Jun 7, 2021
Merged

bpo-43693: Add the MAKE_CELL opcode and interleave fast locals offsets. #26396

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110a891
Add the MAKE_CELL opcode.
ericsnowcurrently May 5, 2021
4d1056b
Insert MAKE_CELL for each cellvar.
ericsnowcurrently May 7, 2021
e18489b
Implement MAKE_CELL.
ericsnowcurrently May 7, 2021
21acbc2
Add a NEWS entry.
ericsnowcurrently May 27, 2021
167cdc1
Update the dis docs.
ericsnowcurrently May 27, 2021
409b92a
offset_derefs() -> fix_cell_offsets().
ericsnowcurrently May 10, 2021
da503d0
Mark MAKE_CELL as "hasfree".
ericsnowcurrently May 27, 2021
1a8400e
Drop _Py_MAX_OPARG (and add a note about max oparg size).
ericsnowcurrently Jun 4, 2021
09f718f
Update the NEWS entry.
ericsnowcurrently Jun 4, 2021
cd2508f
Add some explicit casts to int.
ericsnowcurrently Jun 4, 2021
362088d
Do not create cells in PyFrame_LocalsToFast().
ericsnowcurrently Jun 4, 2021
9cdc8ba
Fix PyFrame_FastToLocals() and PyFrame_LocalsToFast() when the frame …
ericsnowcurrently Jun 7, 2021
5a4d984
Use the right offset in super_init_without_args().
ericsnowcurrently Jun 7, 2021
05accc0
Py_ssize_t -> int.
ericsnowcurrently Jun 7, 2021
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8 changes: 8 additions & 0 deletions Doc/library/dis.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -1056,6 +1056,14 @@ All of the following opcodes use their arguments.
Deletes local ``co_varnames[var_num]``.


.. opcode:: MAKE_CELL (i)

Creates a new cell in slot ``i``. If that slot is empty then
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that value is stored into the new cell.

.. versionadded:: 3.11


.. opcode:: LOAD_CLOSURE (i)

Pushes a reference to the cell contained in slot ``i`` of the "fast locals"
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11 changes: 9 additions & 2 deletions Include/cpython/code.h
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Expand Up @@ -2,9 +2,16 @@
# error "this header file must not be included directly"
#endif

/* Each instruction in a code object is a fixed-width value,
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* currently 2 bytes: 1-byte opcode + 1-byte oparg. The EXTENDED_ARG
* opcode allows for larger values but the current limit is 3 uses
* of EXTENDED_ARG (see Python/wordcode_helpers.h), for a maximum
* 32-bit value. This aligns with the note in Python/compile.c
* (compiler_addop_i_line) indicating that the max oparg value is
* 2**32 - 1, rather than INT_MAX.
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*/

typedef uint16_t _Py_CODEUNIT;
// Each oparg must fit in the second half of _Py_CODEUNIT, hence 8 bits.
#define _Py_MAX_OPARG 255

#ifdef WORDS_BIGENDIAN
# define _Py_OPCODE(word) ((word) >> 8)
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2 changes: 2 additions & 0 deletions Include/internal/pycore_frame.h
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Expand Up @@ -32,6 +32,8 @@ _PyFrame_GetBuiltins(PyFrameObject *f)

int _PyFrame_TakeLocals(PyFrameObject *f);

PyAPI_FUNC(int) _PyFrame_OpAlreadyRan(PyFrameObject *f, int opcode, int oparg);

#ifdef __cplusplus
}
#endif
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9 changes: 5 additions & 4 deletions Include/opcode.h
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3 changes: 2 additions & 1 deletion Lib/importlib/_bootstrap_external.py
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Expand Up @@ -357,6 +357,7 @@ def _write_atomic(path, data, mode=0o666):
# Python 3.11a1 3452 (drop nlocals from marshaled code objects)
# Python 3.11a1 3453 (add co_fastlocalnames and co_fastlocalkinds)
# Python 3.11a1 3454 (compute cell offsets relative to locals bpo-43693)
# Python 3.11a1 3455 (add MAKE_CELL bpo-43693)

#
# MAGIC must change whenever the bytecode emitted by the compiler may no
Expand All @@ -366,7 +367,7 @@ def _write_atomic(path, data, mode=0o666):
# Whenever MAGIC_NUMBER is changed, the ranges in the magic_values array
# in PC/launcher.c must also be updated.

MAGIC_NUMBER = (3454).to_bytes(2, 'little') + b'\r\n'
MAGIC_NUMBER = (3455).to_bytes(2, 'little') + b'\r\n'
_RAW_MAGIC_NUMBER = int.from_bytes(MAGIC_NUMBER, 'little') # For import.c

_PYCACHE = '__pycache__'
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10 changes: 6 additions & 4 deletions Lib/opcode.py
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Expand Up @@ -181,14 +181,16 @@ def jabs_op(name, op):
def_op('MAKE_FUNCTION', 132) # Flags
def_op('BUILD_SLICE', 133) # Number of items

def_op('LOAD_CLOSURE', 135)
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Why the opcode shuffle?

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My initial impression was that MAKE_CELL should be at the front of the cell-related list and I figured it would be better to preserve the gap at 134. I figured it wouldn't matter but if it's a problem I can put MAKE_CELL at 139.

def_op('MAKE_CELL', 135)
hasfree.append(135)
def_op('LOAD_DEREF', 136)
def_op('LOAD_CLOSURE', 136)
hasfree.append(136)
def_op('STORE_DEREF', 137)
def_op('LOAD_DEREF', 137)
hasfree.append(137)
def_op('DELETE_DEREF', 138)
def_op('STORE_DEREF', 138)
hasfree.append(138)
def_op('DELETE_DEREF', 139)
hasfree.append(139)

def_op('CALL_FUNCTION_KW', 141) # #args + #kwargs
def_op('CALL_FUNCTION_EX', 142) # Flags
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131 changes: 70 additions & 61 deletions Lib/test/test_dis.py
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Expand Up @@ -427,15 +427,17 @@ def foo(x):
return foo

dis_nested_0 = """\
%3d 0 LOAD_CLOSURE 2 (y)
2 BUILD_TUPLE 1
4 LOAD_CONST 1 (<code object foo at 0x..., file "%s", line %d>)
6 LOAD_CONST 2 ('_h.<locals>.foo')
8 MAKE_FUNCTION 8 (closure)
10 STORE_FAST 1 (foo)

%3d 12 LOAD_FAST 1 (foo)
14 RETURN_VALUE
0 MAKE_CELL 2 (y)

%3d 2 LOAD_CLOSURE 2 (y)
4 BUILD_TUPLE 1
6 LOAD_CONST 1 (<code object foo at 0x..., file "%s", line %d>)
8 LOAD_CONST 2 ('_h.<locals>.foo')
10 MAKE_FUNCTION 8 (closure)
12 STORE_FAST 1 (foo)

%3d 14 LOAD_FAST 1 (foo)
16 RETURN_VALUE
""" % (_h.__code__.co_firstlineno + 1,
__file__,
_h.__code__.co_firstlineno + 1,
Expand All @@ -444,15 +446,17 @@ def foo(x):

dis_nested_1 = """%s
Disassembly of <code object foo at 0x..., file "%s", line %d>:
%3d 0 LOAD_CLOSURE 1 (x)
2 BUILD_TUPLE 1
4 LOAD_CONST 1 (<code object <listcomp> at 0x..., file "%s", line %d>)
6 LOAD_CONST 2 ('_h.<locals>.foo.<locals>.<listcomp>')
8 MAKE_FUNCTION 8 (closure)
10 LOAD_DEREF 2 (y)
12 GET_ITER
14 CALL_FUNCTION 1
16 RETURN_VALUE
0 MAKE_CELL 1 (x)

%3d 2 LOAD_CLOSURE 1 (x)
4 BUILD_TUPLE 1
6 LOAD_CONST 1 (<code object <listcomp> at 0x..., file "%s", line %d>)
8 LOAD_CONST 2 ('_h.<locals>.foo.<locals>.<listcomp>')
10 MAKE_FUNCTION 8 (closure)
12 LOAD_DEREF 2 (y)
14 GET_ITER
16 CALL_FUNCTION 1
18 RETURN_VALUE
""" % (dis_nested_0,
__file__,
_h.__code__.co_firstlineno + 1,
Expand Down Expand Up @@ -958,59 +962,64 @@ def jumpy():
#print('expected_opinfo_jumpy = [\n ',
#',\n '.join(map(str, _instructions)), ',\n]', sep='')

#dis.dis(outer)

Instruction = dis.Instruction
expected_opinfo_outer = [
Instruction(opname='LOAD_CONST', opcode=100, arg=8, argval=(3, 4), argrepr='(3, 4)', offset=0, starts_line=2, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=135, arg=3, argval='a', argrepr='a', offset=2, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=135, arg=4, argval='b', argrepr='b', offset=4, starts_line=None, is_jump_target=False),
Instruction(opname='BUILD_TUPLE', opcode=102, arg=2, argval=2, argrepr='', offset=6, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=3, argval=code_object_f, argrepr=repr(code_object_f), offset=8, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=4, argval='outer.<locals>.f', argrepr="'outer.<locals>.f'", offset=10, starts_line=None, is_jump_target=False),
Instruction(opname='MAKE_FUNCTION', opcode=132, arg=9, argval=9, argrepr='defaults, closure', offset=12, starts_line=None, is_jump_target=False),
Instruction(opname='STORE_FAST', opcode=125, arg=2, argval='f', argrepr='f', offset=14, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_GLOBAL', opcode=116, arg=0, argval='print', argrepr='print', offset=16, starts_line=7, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=3, argval='a', argrepr='a', offset=18, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=4, argval='b', argrepr='b', offset=20, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=5, argval='', argrepr="''", offset=22, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=6, argval=1, argrepr='1', offset=24, starts_line=None, is_jump_target=False),
Instruction(opname='BUILD_LIST', opcode=103, arg=0, argval=0, argrepr='', offset=26, starts_line=None, is_jump_target=False),
Instruction(opname='BUILD_MAP', opcode=105, arg=0, argval=0, argrepr='', offset=28, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=7, argval='Hello world!', argrepr="'Hello world!'", offset=30, starts_line=None, is_jump_target=False),
Instruction(opname='CALL_FUNCTION', opcode=131, arg=7, argval=7, argrepr='', offset=32, starts_line=None, is_jump_target=False),
Instruction(opname='POP_TOP', opcode=1, arg=None, argval=None, argrepr='', offset=34, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_FAST', opcode=124, arg=2, argval='f', argrepr='f', offset=36, starts_line=8, is_jump_target=False),
Instruction(opname='RETURN_VALUE', opcode=83, arg=None, argval=None, argrepr='', offset=38, starts_line=None, is_jump_target=False),
Instruction(opname='MAKE_CELL', opcode=135, arg=3, argval='a', argrepr='a', offset=0, starts_line=None, is_jump_target=False),
Instruction(opname='MAKE_CELL', opcode=135, arg=4, argval='b', argrepr='b', offset=2, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=8, argval=(3, 4), argrepr='(3, 4)', offset=4, starts_line=2, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=136, arg=3, argval='a', argrepr='a', offset=6, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=136, arg=4, argval='b', argrepr='b', offset=8, starts_line=None, is_jump_target=False),
Instruction(opname='BUILD_TUPLE', opcode=102, arg=2, argval=2, argrepr='', offset=10, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=3, argval=code_object_f, argrepr=repr(code_object_f), offset=12, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=4, argval='outer.<locals>.f', argrepr="'outer.<locals>.f'", offset=14, starts_line=None, is_jump_target=False),
Instruction(opname='MAKE_FUNCTION', opcode=132, arg=9, argval=9, argrepr='defaults, closure', offset=16, starts_line=None, is_jump_target=False),
Instruction(opname='STORE_FAST', opcode=125, arg=2, argval='f', argrepr='f', offset=18, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_GLOBAL', opcode=116, arg=0, argval='print', argrepr='print', offset=20, starts_line=7, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=3, argval='a', argrepr='a', offset=22, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=4, argval='b', argrepr='b', offset=24, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=5, argval='', argrepr="''", offset=26, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=6, argval=1, argrepr='1', offset=28, starts_line=None, is_jump_target=False),
Instruction(opname='BUILD_LIST', opcode=103, arg=0, argval=0, argrepr='', offset=30, starts_line=None, is_jump_target=False),
Instruction(opname='BUILD_MAP', opcode=105, arg=0, argval=0, argrepr='', offset=32, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=7, argval='Hello world!', argrepr="'Hello world!'", offset=34, starts_line=None, is_jump_target=False),
Instruction(opname='CALL_FUNCTION', opcode=131, arg=7, argval=7, argrepr='', offset=36, starts_line=None, is_jump_target=False),
Instruction(opname='POP_TOP', opcode=1, arg=None, argval=None, argrepr='', offset=38, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_FAST', opcode=124, arg=2, argval='f', argrepr='f', offset=40, starts_line=8, is_jump_target=False),
Instruction(opname='RETURN_VALUE', opcode=83, arg=None, argval=None, argrepr='', offset=42, starts_line=None, is_jump_target=False),
]

expected_opinfo_f = [
Instruction(opname='LOAD_CONST', opcode=100, arg=5, argval=(5, 6), argrepr='(5, 6)', offset=0, starts_line=3, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=135, arg=5, argval='a', argrepr='a', offset=2, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=135, arg=6, argval='b', argrepr='b', offset=4, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=135, arg=3, argval='c', argrepr='c', offset=6, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=135, arg=4, argval='d', argrepr='d', offset=8, starts_line=None, is_jump_target=False),
Instruction(opname='BUILD_TUPLE', opcode=102, arg=4, argval=4, argrepr='', offset=10, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=3, argval=code_object_inner, argrepr=repr(code_object_inner), offset=12, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=4, argval='outer.<locals>.f.<locals>.inner', argrepr="'outer.<locals>.f.<locals>.inner'", offset=14, starts_line=None, is_jump_target=False),
Instruction(opname='MAKE_FUNCTION', opcode=132, arg=9, argval=9, argrepr='defaults, closure', offset=16, starts_line=None, is_jump_target=False),
Instruction(opname='STORE_FAST', opcode=125, arg=2, argval='inner', argrepr='inner', offset=18, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_GLOBAL', opcode=116, arg=0, argval='print', argrepr='print', offset=20, starts_line=5, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=5, argval='a', argrepr='a', offset=22, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=6, argval='b', argrepr='b', offset=24, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=3, argval='c', argrepr='c', offset=26, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=4, argval='d', argrepr='d', offset=28, starts_line=None, is_jump_target=False),
Instruction(opname='CALL_FUNCTION', opcode=131, arg=4, argval=4, argrepr='', offset=30, starts_line=None, is_jump_target=False),
Instruction(opname='POP_TOP', opcode=1, arg=None, argval=None, argrepr='', offset=32, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_FAST', opcode=124, arg=2, argval='inner', argrepr='inner', offset=34, starts_line=6, is_jump_target=False),
Instruction(opname='RETURN_VALUE', opcode=83, arg=None, argval=None, argrepr='', offset=36, starts_line=None, is_jump_target=False),
Instruction(opname='MAKE_CELL', opcode=135, arg=3, argval='c', argrepr='c', offset=0, starts_line=None, is_jump_target=False),
Instruction(opname='MAKE_CELL', opcode=135, arg=4, argval='d', argrepr='d', offset=2, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=5, argval=(5, 6), argrepr='(5, 6)', offset=4, starts_line=3, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=136, arg=5, argval='a', argrepr='a', offset=6, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=136, arg=6, argval='b', argrepr='b', offset=8, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=136, arg=3, argval='c', argrepr='c', offset=10, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CLOSURE', opcode=136, arg=4, argval='d', argrepr='d', offset=12, starts_line=None, is_jump_target=False),
Instruction(opname='BUILD_TUPLE', opcode=102, arg=4, argval=4, argrepr='', offset=14, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=3, argval=code_object_inner, argrepr=repr(code_object_inner), offset=16, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_CONST', opcode=100, arg=4, argval='outer.<locals>.f.<locals>.inner', argrepr="'outer.<locals>.f.<locals>.inner'", offset=18, starts_line=None, is_jump_target=False),
Instruction(opname='MAKE_FUNCTION', opcode=132, arg=9, argval=9, argrepr='defaults, closure', offset=20, starts_line=None, is_jump_target=False),
Instruction(opname='STORE_FAST', opcode=125, arg=2, argval='inner', argrepr='inner', offset=22, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_GLOBAL', opcode=116, arg=0, argval='print', argrepr='print', offset=24, starts_line=5, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=5, argval='a', argrepr='a', offset=26, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=6, argval='b', argrepr='b', offset=28, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=3, argval='c', argrepr='c', offset=30, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=4, argval='d', argrepr='d', offset=32, starts_line=None, is_jump_target=False),
Instruction(opname='CALL_FUNCTION', opcode=131, arg=4, argval=4, argrepr='', offset=34, starts_line=None, is_jump_target=False),
Instruction(opname='POP_TOP', opcode=1, arg=None, argval=None, argrepr='', offset=36, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_FAST', opcode=124, arg=2, argval='inner', argrepr='inner', offset=38, starts_line=6, is_jump_target=False),
Instruction(opname='RETURN_VALUE', opcode=83, arg=None, argval=None, argrepr='', offset=40, starts_line=None, is_jump_target=False),
]

expected_opinfo_inner = [
Instruction(opname='LOAD_GLOBAL', opcode=116, arg=0, argval='print', argrepr='print', offset=0, starts_line=4, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=2, argval='a', argrepr='a', offset=2, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=3, argval='b', argrepr='b', offset=4, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=4, argval='c', argrepr='c', offset=6, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=136, arg=5, argval='d', argrepr='d', offset=8, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=2, argval='a', argrepr='a', offset=2, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=3, argval='b', argrepr='b', offset=4, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=4, argval='c', argrepr='c', offset=6, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_DEREF', opcode=137, arg=5, argval='d', argrepr='d', offset=8, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_FAST', opcode=124, arg=0, argval='e', argrepr='e', offset=10, starts_line=None, is_jump_target=False),
Instruction(opname='LOAD_FAST', opcode=124, arg=1, argval='f', argrepr='f', offset=12, starts_line=None, is_jump_target=False),
Instruction(opname='CALL_FUNCTION', opcode=131, arg=6, argval=6, argrepr='', offset=14, starts_line=None, is_jump_target=False),
Expand Down
51 changes: 51 additions & 0 deletions Lib/test/test_scope.py
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Original file line number Diff line number Diff line change
Expand Up @@ -176,6 +176,57 @@ def bar():
self.assertEqual(foo(a=42), 50)
self.assertEqual(foo(), 25)

def testCellIsArgAndEscapes(self):
# We need to be sure that a cell passed in as an arg still
# gets wrapped in a new cell if the arg escapes into an
# inner function (closure).

def external():
value = 42
def inner():
return value
cell, = inner.__closure__
return cell
cell_ext = external()

def spam(arg):
def eggs():
return arg
return eggs

eggs = spam(cell_ext)
cell_closure, = eggs.__closure__
cell_eggs = eggs()

self.assertIs(cell_eggs, cell_ext)
self.assertIsNot(cell_eggs, cell_closure)

def testCellIsLocalAndEscapes(self):
# We need to be sure that a cell bound to a local still
# gets wrapped in a new cell if the local escapes into an
# inner function (closure).

def external():
value = 42
def inner():
return value
cell, = inner.__closure__
return cell
cell_ext = external()

def spam(arg):
cell = arg
def eggs():
return cell
return eggs

eggs = spam(cell_ext)
cell_closure, = eggs.__closure__
cell_eggs = eggs()

self.assertIs(cell_eggs, cell_ext)
self.assertIsNot(cell_eggs, cell_closure)

def testRecursion(self):

def f(x):
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