Integer Objects

All integers are implemented as "long" integer objects of arbitrary size.

On error, most PyLong_As* APIs return (return type)-1 which cannot be distinguished from a number. Use PyErr_Occurred to disambiguate.

This subtype of PyObject represents a Python integer object.

This instance of PyTypeObject represents the Python integer type. This is the same object as int in the Python layer.

Return true if its argument is a PyLongObject or a subtype of PyLongObject. This function always succeeds.

Return true if its argument is a PyLongObject, but not a subtype of PyLongObject. This function always succeeds.

Return a new PyLongObject object from v, or NULL on failure.

CPython keeps an array of integer objects for all integers between -5 and 1024. When you create an int in that range you actually just get back a reference to the existing object.

Return a new PyLongObject object from a C unsigned long, or NULL on failure.

Return a new PyLongObject object from a C Py_ssize_t, or NULL on failure.

Return a new PyLongObject object from a C size_t, or NULL on failure.

Return a new PyLongObject object from a C long long, or NULL on failure.

Return a new PyLongObject object from a C unsigned long long, or NULL on failure.

Return a new PyLongObject object from the integer part of v, or NULL on failure.

Return a new PyLongObject based on the string value in str, which is interpreted according to the radix in base, or NULL on failure. If pend is non-NULL, *pend will point to the end of str on success or to the first character that could not be processed on error. If base is 0, str is interpreted using the integers definition; in this case, leading zeros in a non-zero decimal number raises a ValueError. If base is not 0, it must be between 2 and 36, inclusive. Leading and trailing whitespace and single underscores after a base specifier and between digits are ignored. If there are no digits or str is not NULL-terminated following the digits and trailing whitespace, ValueError will be raised.

PyLong_AsNativeBytes() and PyLong_FromNativeBytes() functions can be used to convert a PyLongObject to/from an array of bytes in base 256.

Convert a sequence of Unicode digits in the string u to a Python integer value.

3.3

Create a Python integer from the pointer p. The pointer value can be retrieved from the resulting value using PyLong_AsVoidPtr.

Create a Python integer from the value contained in the first n_bytes of buffer, interpreted as a two's-complement signed number.

flags are as for PyLong_AsNativeBytes. Passing -1 will select the native endian that CPython was compiled with and assume that the most-significant bit is a sign bit. Passing Py_ASNATIVEBYTES_UNSIGNED_BUFFER will produce the same result as calling PyLong_FromUnsignedNativeBytes. Other flags are ignored.

3.13

Create a Python integer from the value contained in the first n_bytes of buffer, interpreted as an unsigned number.

flags are as for PyLong_AsNativeBytes. Passing -1 will select the native endian that CPython was compiled with and assume that the most-significant bit is not a sign bit. Flags other than endian are ignored.

3.13

Macro for creating a Python integer from a process identifier.

This can be defined as an alias to PyLong_FromLong or PyLong_FromLongLong, depending on the size of the system's PID type.

3.2

single: LONG_MAX (C macro) single: OverflowError (built-in exception)

Return a C long representation of obj. If obj is not an instance of PyLongObject, first call its ~object.__index__ method (if present) to convert it to a PyLongObject.

Raise OverflowError if the value of obj is out of range for a long.

Returns -1 on error. Use PyErr_Occurred to disambiguate.

3.8 Use ~object.__index__ if available.

3.10 This function will no longer use ~object.__int__.

Exactly equivalent to the preferred PyLong_AsLong. In particular, it can fail with OverflowError or another exception.

3.14

Similar to PyLong_AsLong, but store the result in a C int instead of a C long.

3.13

Return a C long representation of obj. If obj is not an instance of PyLongObject, first call its ~object.__index__ method (if present) to convert it to a PyLongObject.

If the value of obj is greater than LONG_MAX or less than LONG_MIN, set *overflow to 1 or -1, respectively, and return -1; otherwise, set *overflow to 0. If any other exception occurs set *overflow to 0 and return -1 as usual.

Returns -1 on error. Use PyErr_Occurred to disambiguate.

3.8 Use ~object.__index__ if available.

3.10 This function will no longer use ~object.__int__.

single: OverflowError (built-in exception)

Return a C long long representation of obj. If obj is not an instance of PyLongObject, first call its ~object.__index__ method (if present) to convert it to a PyLongObject.

Raise OverflowError if the value of obj is out of range for a long long.

Returns -1 on error. Use PyErr_Occurred to disambiguate.

3.8 Use ~object.__index__ if available.

3.10 This function will no longer use ~object.__int__.

Return a C long long representation of obj. If obj is not an instance of PyLongObject, first call its ~object.__index__ method (if present) to convert it to a PyLongObject.

If the value of obj is greater than LLONG_MAX or less than LLONG_MIN, set *overflow to 1 or -1, respectively, and return -1; otherwise, set *overflow to 0. If any other exception occurs set *overflow to 0 and return -1 as usual.

Returns -1 on error. Use PyErr_Occurred to disambiguate.

3.2

3.8 Use ~object.__index__ if available.

3.10 This function will no longer use ~object.__int__.

single: PY_SSIZE_T_MAX (C macro) single: OverflowError (built-in exception)

Return a C Py_ssize_t representation of pylong. pylong must be an instance of PyLongObject.

Raise OverflowError if the value of pylong is out of range for a Py_ssize_t.

Returns -1 on error. Use PyErr_Occurred to disambiguate.

single: ULONG_MAX (C macro) single: OverflowError (built-in exception)

Return a C unsigned long representation of pylong. pylong must be an instance of PyLongObject.

Raise OverflowError if the value of pylong is out of range for a unsigned long.

Returns (unsigned long)-1 on error. Use PyErr_Occurred to disambiguate.

single: SIZE_MAX (C macro) single: OverflowError (built-in exception)

Return a C size_t representation of pylong. pylong must be an instance of PyLongObject.

Raise OverflowError if the value of pylong is out of range for a size_t.

Returns (size_t)-1 on error. Use PyErr_Occurred to disambiguate.

single: OverflowError (built-in exception)

Return a C unsigned long long representation of pylong. pylong must be an instance of PyLongObject.

Raise OverflowError if the value of pylong is out of range for an unsigned long long.

Returns (unsigned long long)-1 on error. Use PyErr_Occurred to disambiguate.

3.1 A negative pylong now raises OverflowError, not TypeError.

Return a C unsigned long representation of obj. If obj is not an instance of PyLongObject, first call its ~object.__index__ method (if present) to convert it to a PyLongObject.

If the value of obj is out of range for an unsigned long, return the reduction of that value modulo ULONG_MAX + 1.

Returns (unsigned long)-1 on error. Use PyErr_Occurred to disambiguate.

3.8 Use ~object.__index__ if available.

3.10 This function will no longer use ~object.__int__.

Return a C unsigned long long representation of obj. If obj is not an instance of PyLongObject, first call its ~object.__index__ method (if present) to convert it to a PyLongObject.

If the value of obj is out of range for an unsigned long long, return the reduction of that value modulo ULLONG_MAX + 1.

Returns (unsigned long long)-1 on error. Use PyErr_Occurred to disambiguate.

3.8 Use ~object.__index__ if available.

3.10 This function will no longer use ~object.__int__.

Return a C double representation of pylong. pylong must be an instance of PyLongObject.

Raise OverflowError if the value of pylong is out of range for a double.

Returns -1.0 on error. Use PyErr_Occurred to disambiguate.

Convert a Python integer pylong to a C void pointer. If pylong cannot be converted, an OverflowError will be raised. This is only assured to produce a usable void pointer for values created with PyLong_FromVoidPtr.

Returns NULL on error. Use PyErr_Occurred to disambiguate.

Copy the Python integer value pylong to a native buffer of size n_bytes. The flags can be set to -1 to behave similarly to a C cast, or to values documented below to control the behavior.

Returns -1 with an exception raised on error. This may happen if pylong cannot be interpreted as an integer, or if pylong was negative and the Py_ASNATIVEBYTES_REJECT_NEGATIVE flag was set.

Otherwise, returns the number of bytes required to store the value. If this is equal to or less than n_bytes, the entire value was copied. All n_bytes of the buffer are written: remaining bytes filled by copies of the sign bit.

If the returned value is greater than n_bytes, the value was truncated: as many of the lowest bits of the value as could fit are written, and the higher bits are ignored. This matches the typical behavior of a C-style downcast.

[!NOTE] Overflow is not considered an error. If the returned value is larger than n_bytes, most significant bits were discarded.

0 will never be returned.

Values are always copied as two's-complement.

Usage example:

int32_t value;
Py_ssize_t bytes = PyLong_AsNativeBytes(pylong, &value, sizeof(value), -1);
if (bytes < 0) {
    // Failed. A Python exception was set with the reason.
    return NULL;
}
else if (bytes <= (Py_ssize_t)sizeof(value)) {
    // Success!
}
else {
    // Overflow occurred, but 'value' contains the truncated
    // lowest bits of pylong.
}

Passing zero to n_bytes will return the size of a buffer that would be large enough to hold the value. This may be larger than technically necessary, but not unreasonably so. If n_bytes=0, buffer may be NULL.

[!NOTE] Passing n_bytes=0 to this function is not an accurate way to determine the bit length of the value.

To get at the entire Python value of an unknown size, the function can be called twice: first to determine the buffer size, then to fill it:

// Ask how much space we need.
Py_ssize_t expected = PyLong_AsNativeBytes(pylong, NULL, 0, -1);
if (expected < 0) {
    // Failed. A Python exception was set with the reason.
    return NULL;
}
assert(expected != 0);  // Impossible per the API definition.
uint8_t *bignum = malloc(expected);
if (!bignum) {
    PyErr_SetString(PyExc_MemoryError, "bignum malloc failed.");
    return NULL;
}
// Safely get the entire value.
Py_ssize_t bytes = PyLong_AsNativeBytes(pylong, bignum, expected, -1);
if (bytes < 0) {  // Exception has been set.
    free(bignum);
    return NULL;
}
else if (bytes > expected) {  // This should not be possible.
    PyErr_SetString(PyExc_RuntimeError,
        "Unexpected bignum truncation after a size check.");
    free(bignum);
    return NULL;
}
// The expected success given the above pre-check.
// ... use bignum ...
free(bignum);

flags is either -1 (Py_ASNATIVEBYTES_DEFAULTS) to select defaults that behave most like a C cast, or a combination of the other flags in the table below. Note that -1 cannot be combined with other flags.

Currently, -1 corresponds to Py_ASNATIVEBYTES_NATIVE_ENDIAN | Py_ASNATIVEBYTES_UNSIGNED_BUFFER.

These values are available when compiling for the Stable ABI <stable> since version 3.14.

Flag	Value
	-1
	0
	1
	3
	4
	8
	16

Specifying Py_ASNATIVEBYTES_NATIVE_ENDIAN will override any other endian flags. Passing 2 is reserved.

By default, sufficient buffer will be requested to include a sign bit. For example, when converting 128 with n_bytes=1, the function will return 2 (or more) in order to store a zero sign bit.

If Py_ASNATIVEBYTES_UNSIGNED_BUFFER is specified, a zero sign bit will be omitted from size calculations. This allows, for example, 128 to fit in a single-byte buffer. If the destination buffer is later treated as signed, a positive input value may become negative. Note that the flag does not affect handling of negative values: for those, space for a sign bit is always requested.

Specifying Py_ASNATIVEBYTES_REJECT_NEGATIVE causes an exception to be set if pylong is negative. Without this flag, negative values will be copied provided there is enough space for at least one sign bit, regardless of whether Py_ASNATIVEBYTES_UNSIGNED_BUFFER was specified.

If Py_ASNATIVEBYTES_ALLOW_INDEX is specified and a non-integer value is passed, its ~object.__index__ method will be called first. This may result in Python code executing and other threads being allowed to run, which could cause changes to other objects or values in use. When flags is -1, this option is not set, and non-integer values will raise TypeError.

[!NOTE] With the default flags (-1, or UNSIGNED_BUFFER without REJECT_NEGATIVE), multiple Python integers can map to a single value without overflow. For example, both 255 and -1 fit a single-byte buffer and set all its bits. This matches typical C cast behavior.

3.13

Macro for converting a Python integer into a process identifier.

This can be defined as an alias to PyLong_AsLong, PyLong_FromLongLong, or PyLong_AsInt, depending on the size of the system's PID type.

3.2

Get the sign of the integer object obj.

On success, set *sign to the integer sign (0, -1 or +1 for zero, negative or positive integer, respectively) and return 0.

On failure, return -1 with an exception set. This function always succeeds if obj is a PyLongObject or its subtype.

3.14

Check if the integer object obj is positive (obj > 0).

If obj is an instance of PyLongObject or its subtype, return 1 when it's positive and 0 otherwise. Else set an exception and return -1.

3.14

Check if the integer object obj is negative (obj < 0).

If obj is an instance of PyLongObject or its subtype, return 1 when it's negative and 0 otherwise. Else set an exception and return -1.

3.14

Check if the integer object obj is zero.

If obj is an instance of PyLongObject or its subtype, return 1 when it's zero and 0 otherwise. Else set an exception and return -1.

3.14

On success, return a read only named tuple, that holds information about Python's internal representation of integers. See sys.int_info for description of individual fields.

On failure, return NULL with an exception set.

3.1

Return 1 if op is compact, 0 otherwise.

This function makes it possible for performance-critical code to implement a “fast path” for small integers. For compact values use PyUnstable_Long_CompactValue; for others fall back to a PyLong_As* <PyLong_AsSize_t> function or PyLong_AsNativeBytes.

The speedup is expected to be negligible for most users.

Exactly what values are considered compact is an implementation detail and is subject to change.

3.12

If op is compact, as determined by PyUnstable_Long_IsCompact, return its value.

Otherwise, the return value is undefined.

3.12

Build configuration

The number of bits in each digit of CPython's native representation of integers. The value can currently be either 30 (the default) or 15, selected with --enable-big-digits when building Python.

To access the native representation of integers, use PyLong_GetNativeLayout and its ~PyLongLayout.bits_per_digit member instead.

Export API

Layout of an array of "digits" ("limbs" in the GMP terminology), used to represent absolute value for arbitrary precision integers.

Use PyLong_GetNativeLayout to get the native layout of Python int objects, used internally for integers with "big enough" absolute value.

See also sys.int_info which exposes similar information in Python.

Bits per digit. For example, a 15 bit digit means that bits 0-14 contain meaningful information.

Digit size in bytes. For example, a 15 bit digit will require at least 2 bytes.

Digits order:

• 1 for most significant digit first
• -1 for least significant digit first

Digit endianness:

• 1 for most significant byte first (big endian)
• -1 for least significant byte first (little endian)

Get the native layout of Python int objects.

See the PyLongLayout structure.

The function must not be called before Python initialization nor after Python finalization. The returned layout is valid until Python is finalized. The layout is the same for all Python sub-interpreters in a process, and so it can be cached.

Export of a Python int object.

There are two cases:

• If digits is NULL, only use the value member.
• If digits is not NULL, use negative, ndigits and digits members.

The native integer value of the exported int object. Only valid if digits is NULL.

1 if the number is negative, 0 otherwise. Only valid if digits is not NULL.

Number of digits in digits array. Only valid if digits is not NULL.

Read-only array of unsigned digits. Can be NULL.

Export a Python int object.

export_long must point to a PyLongExport structure allocated by the caller. It must not be NULL.

On success, fill in *export_long and return 0. On error, set an exception and return -1.

PyLong_FreeExport must be called when the export is no longer needed.

This function always succeeds if obj is a Python int object or a subclass.

Release the export export_long created by PyLong_Export.

Calling PyLong_FreeExport is optional if export_long->digits is NULL.

PyLongWriter API

The PyLongWriter API can be used to import an integer.

A Python int writer instance.

The instance must be destroyed by PyLongWriter_Finish or PyLongWriter_Discard.

Create a PyLongWriter.

On success, allocate *digits and return a writer. On error, set an exception and return NULL.

negative is 1 if the number is negative, or 0 otherwise.

ndigits is the number of digits in the digits array. It must be greater than 0.

digits must not be NULL.

After a successful call to this function, the caller should fill in the array of digits digits and then call PyLongWriter_Finish to get a Python int. The layout of digits is described by PyLong_GetNativeLayout.

Digits must be in the range [0; (1 << bits_per_digit) - 1] (where the ~PyLongLayout.bits_per_digit is the number of bits per digit). Any unused most significant digits must be set to 0.

Alternately, call PyLongWriter_Discard to destroy the writer instance without creating an ~int object.

Finish a PyLongWriter created by PyLongWriter_Create.

On success, return a Python int object. On error, set an exception and return NULL.

The function takes care of normalizing the digits and converts the object to a compact integer if needed.

The writer instance and the digits array are invalid after the call.

Discard a PyLongWriter created by PyLongWriter_Create.

If writer is NULL, no operation is performed.

The writer instance and the digits array are invalid after the call.

Deprecated API

These macros are soft deprecated. They describe parameters of the internal representation of PyLongObject instances.

Use PyLong_GetNativeLayout instead, along with PyLong_Export to read integer data or PyLongWriter to write it. These currently use the same layout, but are designed to continue working correctly even if CPython's internal integer representation changes.

This is equivalent to ~PyLongLayout.bits_per_digit in the output of PyLong_GetNativeLayout.

This is currently equivalent to 1 << PyLong_SHIFT.

This is currently equivalent to (1 << PyLong_SHIFT) - 1