# 整數物件

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.

type PyLongObject
  為 受限 API 的一部分 （做為一個不透明結構 (opaque struct)）.

  This subtype of `PyObject` represents a Python integer object.

PyTypeObject PyLong_Type
  為 穩定 ABI 的一部分.

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

int PyLong_Check(PyObject *p)

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

int PyLong_CheckExact(PyObject *p)

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

PyObject *PyLong_FromLong(long v)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

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

  CPython 實作細節： CPython keeps an array of integer objects for all integers between `-5` and `256`. When you create an int in that range you actually just get back a reference to the existing object.

PyObject *PyLong_FromUnsignedLong(unsigned long v)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

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

PyObject *PyLong_FromSsize_t(Py_ssize_t v)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

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

PyObject *PyLong_FromSize_t(size_t v)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

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

PyObject *PyLong_FromLongLong(long long v)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

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

PyObject *PyLong_FromUnsignedLongLong(unsigned long long v)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

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

PyObject *PyLong_FromDouble(double v)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

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

PyObject *PyLong_FromString(const char *str, char **pend, int base)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

  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 Integer literals 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.

  也參考

  Python methods `int.to_bytes()` and `int.from_bytes()` to convert a `PyLongObject` to/from an array of bytes in base `256`. You can call those from C using `PyObject_CallMethod()`.

PyObject *PyLong_FromUnicodeObject(PyObject *u, int base)
  回傳值：新的參照。

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

  在 3.3 版被加入.

PyObject *PyLong_FromVoidPtr(void *p)
  回傳值：新的參照。 為 穩定 ABI 的一部分.

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

PyObject *PyLong_FromNativeBytes(const void *buffer, size_t n_bytes, int flags)

  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.

  在 3.13 版被加入.

PyObject *PyLong_FromUnsignedNativeBytes(const void *buffer, size_t n_bytes, int flags)

  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.

  在 3.13 版被加入.

PyLong_FromPid(pid)

  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.

  在 3.2 版被加入.

long PyLong_AsLong(PyObject *obj)
  為 穩定 ABI 的一部分.

  Return a C long representation of obj. If obj is not an instance of `PyLongObject`, first call its `__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.

  在 3.8 版的變更: Use `__index__()` if available.

  在 3.10 版的變更: This function will no longer use `__int__()`.

  long PyLong_AS_LONG(PyObject *obj)

    A soft deprecated alias. Exactly equivalent to the preferred `PyLong_AsLong`. In particular, it can fail with `OverflowError` or another exception.

    在 3.14 版之後被棄用: The function is soft deprecated.

int PyLong_AsInt(PyObject *obj)
  為 穩定 ABI 的一部分 自 3.13 版本開始.

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

  在 3.13 版被加入.

long PyLong_AsLongAndOverflow(PyObject *obj, int *overflow)
  為 穩定 ABI 的一部分.

  Return a C long representation of obj. If obj is not an instance of `PyLongObject`, first call its `__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.

  在 3.8 版的變更: Use `__index__()` if available.

  在 3.10 版的變更: This function will no longer use `__int__()`.

long long PyLong_AsLongLong(PyObject *obj)
  為 穩定 ABI 的一部分.

  Return a C long long representation of obj. If obj is not an instance of `PyLongObject`, first call its `__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.

  在 3.8 版的變更: Use `__index__()` if available.

  在 3.10 版的變更: This function will no longer use `__int__()`.

long long PyLong_AsLongLongAndOverflow(PyObject *obj, int *overflow)
  為 穩定 ABI 的一部分.

  Return a C long long representation of obj. If obj is not an instance of `PyLongObject`, first call its `__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.

  在 3.2 版被加入.

  在 3.8 版的變更: Use `__index__()` if available.

  在 3.10 版的變更: This function will no longer use `__int__()`.

Py_ssize_t PyLong_AsSsize_t(PyObject *pylong)
  為 穩定 ABI 的一部分.

  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.

unsigned long PyLong_AsUnsignedLong(PyObject *pylong)
  為 穩定 ABI 的一部分.

  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.

size_t PyLong_AsSize_t(PyObject *pylong)
  為 穩定 ABI 的一部分.

  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.

unsigned long long PyLong_AsUnsignedLongLong(PyObject *pylong)
  為 穩定 ABI 的一部分.

  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.

  在 3.1 版的變更: A negative pylong now raises `OverflowError`, not `TypeError`.

unsigned long PyLong_AsUnsignedLongMask(PyObject *obj)
  為 穩定 ABI 的一部分.

  Return a C unsigned long representation of obj. If obj is not an instance of `PyLongObject`, first call its `__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.

  在 3.8 版的變更: Use `__index__()` if available.

  在 3.10 版的變更: This function will no longer use `__int__()`.

unsigned long long PyLong_AsUnsignedLongLongMask(PyObject *obj)
  為 穩定 ABI 的一部分.

  Return a C unsigned long long representation of obj. If obj is not an instance of `PyLongObject`, first call its `__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.

  在 3.8 版的變更: Use `__index__()` if available.

  在 3.10 版的變更: This function will no longer use `__int__()`.

double PyLong_AsDouble(PyObject *pylong)
  為 穩定 ABI 的一部分.

  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.

void *PyLong_AsVoidPtr(PyObject *pylong)
  為 穩定 ABI 的一部分.

  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.

PyLong_AsPid(pid)

  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.

  在 3.2 版被加入.

Py_ssize_t PyLong_AsNativeBytes(PyObject *pylong, void *buffer, Py_ssize_t n_bytes, int flags)

  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.

  備註

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

  `0` 將永不被回傳。

  Values are always copied as two's-complement.

  使用範例：

      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`.

  備註

  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`.

  旗標 | 數值
  --- | ---
  Py_ASNATIVEBYTES_DEFAULTS | `-1`
  Py_ASNATIVEBYTES_BIG_ENDIAN | `0`
  Py_ASNATIVEBYTES_LITTLE_ENDIAN | `1`
  Py_ASNATIVEBYTES_NATIVE_ENDIAN | `3`
  Py_ASNATIVEBYTES_UNSIGNED_BUFFER | `4`
  Py_ASNATIVEBYTES_REJECT_NEGATIVE | `8`
  Py_ASNATIVEBYTES_ALLOW_INDEX | `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 `__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`.

  備註

  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.

  在 3.13 版被加入.

PyObject *PyLong_GetInfo(void)
  為 穩定 ABI 的一部分.

  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.

  在失敗時，會回傳 `NULL` 並設定例外。

  在 3.1 版被加入.

int PyUnstable_Long_IsCompact(const PyLongObject *op)
  這是 不穩定 API，它可能在小版本發布中沒有任何警告地被變更。

  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*` 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.

  在 3.12 版被加入.

Py_ssize_t PyUnstable_Long_CompactValue(const PyLongObject *op)
  這是 不穩定 API，它可能在小版本發布中沒有任何警告地被變更。

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

  Otherwise, the return value is undefined.

  在 3.12 版被加入.