mirror of
https://github.com/python/cpython
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![Serhiy Storchaka](/assets/img/avatar_default.png)
ValueError always is raised rather than OverflowError for negative counts. Shifting zero with non-negative count always returns zero.
5553 lines
167 KiB
C
5553 lines
167 KiB
C
/* Long (arbitrary precision) integer object implementation */
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/* XXX The functional organization of this file is terrible */
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#include "Python.h"
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#include "longintrepr.h"
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#include <float.h>
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#include <ctype.h>
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#include <stddef.h>
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#include "clinic/longobject.c.h"
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/*[clinic input]
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class int "PyObject *" "&PyLong_Type"
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[clinic start generated code]*/
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/*[clinic end generated code: output=da39a3ee5e6b4b0d input=ec0275e3422a36e3]*/
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#ifndef NSMALLPOSINTS
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#define NSMALLPOSINTS 257
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#endif
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#ifndef NSMALLNEGINTS
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#define NSMALLNEGINTS 5
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#endif
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_Py_IDENTIFIER(little);
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_Py_IDENTIFIER(big);
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/* convert a PyLong of size 1, 0 or -1 to an sdigit */
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#define MEDIUM_VALUE(x) (assert(-1 <= Py_SIZE(x) && Py_SIZE(x) <= 1), \
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Py_SIZE(x) < 0 ? -(sdigit)(x)->ob_digit[0] : \
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(Py_SIZE(x) == 0 ? (sdigit)0 : \
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(sdigit)(x)->ob_digit[0]))
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PyObject *_PyLong_Zero = NULL;
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PyObject *_PyLong_One = NULL;
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#if NSMALLNEGINTS + NSMALLPOSINTS > 0
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/* Small integers are preallocated in this array so that they
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can be shared.
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The integers that are preallocated are those in the range
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-NSMALLNEGINTS (inclusive) to NSMALLPOSINTS (not inclusive).
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*/
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static PyLongObject small_ints[NSMALLNEGINTS + NSMALLPOSINTS];
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#ifdef COUNT_ALLOCS
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Py_ssize_t quick_int_allocs, quick_neg_int_allocs;
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#endif
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static PyObject *
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get_small_int(sdigit ival)
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{
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PyObject *v;
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assert(-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS);
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v = (PyObject *)&small_ints[ival + NSMALLNEGINTS];
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Py_INCREF(v);
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#ifdef COUNT_ALLOCS
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if (ival >= 0)
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quick_int_allocs++;
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else
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quick_neg_int_allocs++;
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#endif
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return v;
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}
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#define CHECK_SMALL_INT(ival) \
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do if (-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS) { \
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return get_small_int((sdigit)ival); \
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} while(0)
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static PyLongObject *
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maybe_small_long(PyLongObject *v)
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{
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if (v && Py_ABS(Py_SIZE(v)) <= 1) {
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sdigit ival = MEDIUM_VALUE(v);
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if (-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS) {
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Py_DECREF(v);
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return (PyLongObject *)get_small_int(ival);
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}
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}
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return v;
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}
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#else
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#define CHECK_SMALL_INT(ival)
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#define maybe_small_long(val) (val)
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#endif
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/* If a freshly-allocated int is already shared, it must
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be a small integer, so negating it must go to PyLong_FromLong */
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Py_LOCAL_INLINE(void)
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_PyLong_Negate(PyLongObject **x_p)
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{
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PyLongObject *x;
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x = (PyLongObject *)*x_p;
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if (Py_REFCNT(x) == 1) {
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Py_SIZE(x) = -Py_SIZE(x);
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return;
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}
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*x_p = (PyLongObject *)PyLong_FromLong(-MEDIUM_VALUE(x));
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Py_DECREF(x);
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}
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/* For int multiplication, use the O(N**2) school algorithm unless
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* both operands contain more than KARATSUBA_CUTOFF digits (this
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* being an internal Python int digit, in base BASE).
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*/
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#define KARATSUBA_CUTOFF 70
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#define KARATSUBA_SQUARE_CUTOFF (2 * KARATSUBA_CUTOFF)
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/* For exponentiation, use the binary left-to-right algorithm
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* unless the exponent contains more than FIVEARY_CUTOFF digits.
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* In that case, do 5 bits at a time. The potential drawback is that
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* a table of 2**5 intermediate results is computed.
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*/
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#define FIVEARY_CUTOFF 8
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#define SIGCHECK(PyTryBlock) \
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do { \
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if (PyErr_CheckSignals()) PyTryBlock \
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} while(0)
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/* Normalize (remove leading zeros from) an int object.
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Doesn't attempt to free the storage--in most cases, due to the nature
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of the algorithms used, this could save at most be one word anyway. */
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static PyLongObject *
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long_normalize(PyLongObject *v)
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{
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Py_ssize_t j = Py_ABS(Py_SIZE(v));
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Py_ssize_t i = j;
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while (i > 0 && v->ob_digit[i-1] == 0)
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--i;
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if (i != j)
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Py_SIZE(v) = (Py_SIZE(v) < 0) ? -(i) : i;
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return v;
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}
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/* _PyLong_FromNbInt: Convert the given object to a PyLongObject
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using the nb_int slot, if available. Raise TypeError if either the
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nb_int slot is not available or the result of the call to nb_int
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returns something not of type int.
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*/
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PyLongObject *
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_PyLong_FromNbInt(PyObject *integral)
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{
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PyNumberMethods *nb;
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PyObject *result;
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/* Fast path for the case that we already have an int. */
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if (PyLong_CheckExact(integral)) {
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Py_INCREF(integral);
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return (PyLongObject *)integral;
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}
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nb = Py_TYPE(integral)->tp_as_number;
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if (nb == NULL || nb->nb_int == NULL) {
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PyErr_Format(PyExc_TypeError,
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"an integer is required (got type %.200s)",
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Py_TYPE(integral)->tp_name);
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return NULL;
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}
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/* Convert using the nb_int slot, which should return something
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of exact type int. */
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result = nb->nb_int(integral);
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if (!result || PyLong_CheckExact(result))
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return (PyLongObject *)result;
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if (!PyLong_Check(result)) {
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PyErr_Format(PyExc_TypeError,
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"__int__ returned non-int (type %.200s)",
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result->ob_type->tp_name);
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Py_DECREF(result);
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return NULL;
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}
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/* Issue #17576: warn if 'result' not of exact type int. */
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if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
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"__int__ returned non-int (type %.200s). "
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"The ability to return an instance of a strict subclass of int "
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"is deprecated, and may be removed in a future version of Python.",
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result->ob_type->tp_name)) {
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Py_DECREF(result);
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return NULL;
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}
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return (PyLongObject *)result;
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}
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/* Allocate a new int object with size digits.
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Return NULL and set exception if we run out of memory. */
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#define MAX_LONG_DIGITS \
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((PY_SSIZE_T_MAX - offsetof(PyLongObject, ob_digit))/sizeof(digit))
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PyLongObject *
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_PyLong_New(Py_ssize_t size)
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{
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PyLongObject *result;
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/* Number of bytes needed is: offsetof(PyLongObject, ob_digit) +
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sizeof(digit)*size. Previous incarnations of this code used
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sizeof(PyVarObject) instead of the offsetof, but this risks being
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incorrect in the presence of padding between the PyVarObject header
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and the digits. */
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if (size > (Py_ssize_t)MAX_LONG_DIGITS) {
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PyErr_SetString(PyExc_OverflowError,
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"too many digits in integer");
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return NULL;
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}
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result = PyObject_MALLOC(offsetof(PyLongObject, ob_digit) +
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size*sizeof(digit));
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if (!result) {
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PyErr_NoMemory();
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return NULL;
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}
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return (PyLongObject*)PyObject_INIT_VAR(result, &PyLong_Type, size);
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}
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PyObject *
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_PyLong_Copy(PyLongObject *src)
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{
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PyLongObject *result;
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Py_ssize_t i;
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assert(src != NULL);
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i = Py_SIZE(src);
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if (i < 0)
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i = -(i);
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if (i < 2) {
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sdigit ival = MEDIUM_VALUE(src);
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CHECK_SMALL_INT(ival);
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}
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result = _PyLong_New(i);
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if (result != NULL) {
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Py_SIZE(result) = Py_SIZE(src);
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while (--i >= 0)
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result->ob_digit[i] = src->ob_digit[i];
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}
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return (PyObject *)result;
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}
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/* Create a new int object from a C long int */
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PyObject *
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PyLong_FromLong(long ival)
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{
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PyLongObject *v;
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unsigned long abs_ival;
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unsigned long t; /* unsigned so >> doesn't propagate sign bit */
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int ndigits = 0;
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int sign;
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CHECK_SMALL_INT(ival);
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if (ival < 0) {
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/* negate: can't write this as abs_ival = -ival since that
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invokes undefined behaviour when ival is LONG_MIN */
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abs_ival = 0U-(unsigned long)ival;
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sign = -1;
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}
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else {
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abs_ival = (unsigned long)ival;
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sign = ival == 0 ? 0 : 1;
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}
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/* Fast path for single-digit ints */
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if (!(abs_ival >> PyLong_SHIFT)) {
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v = _PyLong_New(1);
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if (v) {
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Py_SIZE(v) = sign;
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v->ob_digit[0] = Py_SAFE_DOWNCAST(
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abs_ival, unsigned long, digit);
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}
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return (PyObject*)v;
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}
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#if PyLong_SHIFT==15
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/* 2 digits */
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if (!(abs_ival >> 2*PyLong_SHIFT)) {
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v = _PyLong_New(2);
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if (v) {
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Py_SIZE(v) = 2*sign;
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v->ob_digit[0] = Py_SAFE_DOWNCAST(
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abs_ival & PyLong_MASK, unsigned long, digit);
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v->ob_digit[1] = Py_SAFE_DOWNCAST(
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abs_ival >> PyLong_SHIFT, unsigned long, digit);
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}
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return (PyObject*)v;
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}
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#endif
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/* Larger numbers: loop to determine number of digits */
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t = abs_ival;
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while (t) {
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++ndigits;
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t >>= PyLong_SHIFT;
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}
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v = _PyLong_New(ndigits);
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if (v != NULL) {
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digit *p = v->ob_digit;
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Py_SIZE(v) = ndigits*sign;
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t = abs_ival;
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while (t) {
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*p++ = Py_SAFE_DOWNCAST(
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t & PyLong_MASK, unsigned long, digit);
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t >>= PyLong_SHIFT;
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}
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}
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return (PyObject *)v;
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}
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/* Create a new int object from a C unsigned long int */
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PyObject *
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PyLong_FromUnsignedLong(unsigned long ival)
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{
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PyLongObject *v;
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unsigned long t;
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int ndigits = 0;
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if (ival < PyLong_BASE)
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return PyLong_FromLong(ival);
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/* Count the number of Python digits. */
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t = ival;
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while (t) {
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++ndigits;
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t >>= PyLong_SHIFT;
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}
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v = _PyLong_New(ndigits);
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if (v != NULL) {
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digit *p = v->ob_digit;
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while (ival) {
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*p++ = (digit)(ival & PyLong_MASK);
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ival >>= PyLong_SHIFT;
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}
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}
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return (PyObject *)v;
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}
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/* Create a new int object from a C double */
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PyObject *
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PyLong_FromDouble(double dval)
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{
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PyLongObject *v;
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double frac;
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int i, ndig, expo, neg;
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neg = 0;
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if (Py_IS_INFINITY(dval)) {
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PyErr_SetString(PyExc_OverflowError,
|
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"cannot convert float infinity to integer");
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return NULL;
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}
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if (Py_IS_NAN(dval)) {
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PyErr_SetString(PyExc_ValueError,
|
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"cannot convert float NaN to integer");
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return NULL;
|
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}
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if (dval < 0.0) {
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neg = 1;
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dval = -dval;
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}
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frac = frexp(dval, &expo); /* dval = frac*2**expo; 0.0 <= frac < 1.0 */
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if (expo <= 0)
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return PyLong_FromLong(0L);
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ndig = (expo-1) / PyLong_SHIFT + 1; /* Number of 'digits' in result */
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v = _PyLong_New(ndig);
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if (v == NULL)
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return NULL;
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frac = ldexp(frac, (expo-1) % PyLong_SHIFT + 1);
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for (i = ndig; --i >= 0; ) {
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digit bits = (digit)frac;
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v->ob_digit[i] = bits;
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frac = frac - (double)bits;
|
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frac = ldexp(frac, PyLong_SHIFT);
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}
|
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if (neg)
|
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Py_SIZE(v) = -(Py_SIZE(v));
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return (PyObject *)v;
|
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}
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|
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/* Checking for overflow in PyLong_AsLong is a PITA since C doesn't define
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* anything about what happens when a signed integer operation overflows,
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* and some compilers think they're doing you a favor by being "clever"
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* then. The bit pattern for the largest positive signed long is
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* (unsigned long)LONG_MAX, and for the smallest negative signed long
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* it is abs(LONG_MIN), which we could write -(unsigned long)LONG_MIN.
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* However, some other compilers warn about applying unary minus to an
|
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* unsigned operand. Hence the weird "0-".
|
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*/
|
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#define PY_ABS_LONG_MIN (0-(unsigned long)LONG_MIN)
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#define PY_ABS_SSIZE_T_MIN (0-(size_t)PY_SSIZE_T_MIN)
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|
|
/* Get a C long int from an int object or any object that has an __int__
|
|
method.
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|
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On overflow, return -1 and set *overflow to 1 or -1 depending on the sign of
|
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the result. Otherwise *overflow is 0.
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|
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For other errors (e.g., TypeError), return -1 and set an error condition.
|
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In this case *overflow will be 0.
|
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*/
|
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|
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long
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PyLong_AsLongAndOverflow(PyObject *vv, int *overflow)
|
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{
|
|
/* This version by Tim Peters */
|
|
PyLongObject *v;
|
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unsigned long x, prev;
|
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long res;
|
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Py_ssize_t i;
|
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int sign;
|
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int do_decref = 0; /* if nb_int was called */
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|
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*overflow = 0;
|
|
if (vv == NULL) {
|
|
PyErr_BadInternalCall();
|
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return -1;
|
|
}
|
|
|
|
if (PyLong_Check(vv)) {
|
|
v = (PyLongObject *)vv;
|
|
}
|
|
else {
|
|
v = _PyLong_FromNbInt(vv);
|
|
if (v == NULL)
|
|
return -1;
|
|
do_decref = 1;
|
|
}
|
|
|
|
res = -1;
|
|
i = Py_SIZE(v);
|
|
|
|
switch (i) {
|
|
case -1:
|
|
res = -(sdigit)v->ob_digit[0];
|
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break;
|
|
case 0:
|
|
res = 0;
|
|
break;
|
|
case 1:
|
|
res = v->ob_digit[0];
|
|
break;
|
|
default:
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -(i);
|
|
}
|
|
while (--i >= 0) {
|
|
prev = x;
|
|
x = (x << PyLong_SHIFT) | v->ob_digit[i];
|
|
if ((x >> PyLong_SHIFT) != prev) {
|
|
*overflow = sign;
|
|
goto exit;
|
|
}
|
|
}
|
|
/* Haven't lost any bits, but casting to long requires extra
|
|
* care (see comment above).
|
|
*/
|
|
if (x <= (unsigned long)LONG_MAX) {
|
|
res = (long)x * sign;
|
|
}
|
|
else if (sign < 0 && x == PY_ABS_LONG_MIN) {
|
|
res = LONG_MIN;
|
|
}
|
|
else {
|
|
*overflow = sign;
|
|
/* res is already set to -1 */
|
|
}
|
|
}
|
|
exit:
|
|
if (do_decref) {
|
|
Py_DECREF(v);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
/* Get a C long int from an int object or any object that has an __int__
|
|
method. Return -1 and set an error if overflow occurs. */
|
|
|
|
long
|
|
PyLong_AsLong(PyObject *obj)
|
|
{
|
|
int overflow;
|
|
long result = PyLong_AsLongAndOverflow(obj, &overflow);
|
|
if (overflow) {
|
|
/* XXX: could be cute and give a different
|
|
message for overflow == -1 */
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"Python int too large to convert to C long");
|
|
}
|
|
return result;
|
|
}
|
|
|
|
/* Get a C int from an int object or any object that has an __int__
|
|
method. Return -1 and set an error if overflow occurs. */
|
|
|
|
int
|
|
_PyLong_AsInt(PyObject *obj)
|
|
{
|
|
int overflow;
|
|
long result = PyLong_AsLongAndOverflow(obj, &overflow);
|
|
if (overflow || result > INT_MAX || result < INT_MIN) {
|
|
/* XXX: could be cute and give a different
|
|
message for overflow == -1 */
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"Python int too large to convert to C int");
|
|
return -1;
|
|
}
|
|
return (int)result;
|
|
}
|
|
|
|
/* Get a Py_ssize_t from an int object.
|
|
Returns -1 and sets an error condition if overflow occurs. */
|
|
|
|
Py_ssize_t
|
|
PyLong_AsSsize_t(PyObject *vv) {
|
|
PyLongObject *v;
|
|
size_t x, prev;
|
|
Py_ssize_t i;
|
|
int sign;
|
|
|
|
if (vv == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
if (!PyLong_Check(vv)) {
|
|
PyErr_SetString(PyExc_TypeError, "an integer is required");
|
|
return -1;
|
|
}
|
|
|
|
v = (PyLongObject *)vv;
|
|
i = Py_SIZE(v);
|
|
switch (i) {
|
|
case -1: return -(sdigit)v->ob_digit[0];
|
|
case 0: return 0;
|
|
case 1: return v->ob_digit[0];
|
|
}
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -(i);
|
|
}
|
|
while (--i >= 0) {
|
|
prev = x;
|
|
x = (x << PyLong_SHIFT) | v->ob_digit[i];
|
|
if ((x >> PyLong_SHIFT) != prev)
|
|
goto overflow;
|
|
}
|
|
/* Haven't lost any bits, but casting to a signed type requires
|
|
* extra care (see comment above).
|
|
*/
|
|
if (x <= (size_t)PY_SSIZE_T_MAX) {
|
|
return (Py_ssize_t)x * sign;
|
|
}
|
|
else if (sign < 0 && x == PY_ABS_SSIZE_T_MIN) {
|
|
return PY_SSIZE_T_MIN;
|
|
}
|
|
/* else overflow */
|
|
|
|
overflow:
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"Python int too large to convert to C ssize_t");
|
|
return -1;
|
|
}
|
|
|
|
/* Get a C unsigned long int from an int object.
|
|
Returns -1 and sets an error condition if overflow occurs. */
|
|
|
|
unsigned long
|
|
PyLong_AsUnsignedLong(PyObject *vv)
|
|
{
|
|
PyLongObject *v;
|
|
unsigned long x, prev;
|
|
Py_ssize_t i;
|
|
|
|
if (vv == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long)-1;
|
|
}
|
|
if (!PyLong_Check(vv)) {
|
|
PyErr_SetString(PyExc_TypeError, "an integer is required");
|
|
return (unsigned long)-1;
|
|
}
|
|
|
|
v = (PyLongObject *)vv;
|
|
i = Py_SIZE(v);
|
|
x = 0;
|
|
if (i < 0) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"can't convert negative value to unsigned int");
|
|
return (unsigned long) -1;
|
|
}
|
|
switch (i) {
|
|
case 0: return 0;
|
|
case 1: return v->ob_digit[0];
|
|
}
|
|
while (--i >= 0) {
|
|
prev = x;
|
|
x = (x << PyLong_SHIFT) | v->ob_digit[i];
|
|
if ((x >> PyLong_SHIFT) != prev) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"Python int too large to convert "
|
|
"to C unsigned long");
|
|
return (unsigned long) -1;
|
|
}
|
|
}
|
|
return x;
|
|
}
|
|
|
|
/* Get a C size_t from an int object. Returns (size_t)-1 and sets
|
|
an error condition if overflow occurs. */
|
|
|
|
size_t
|
|
PyLong_AsSize_t(PyObject *vv)
|
|
{
|
|
PyLongObject *v;
|
|
size_t x, prev;
|
|
Py_ssize_t i;
|
|
|
|
if (vv == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return (size_t) -1;
|
|
}
|
|
if (!PyLong_Check(vv)) {
|
|
PyErr_SetString(PyExc_TypeError, "an integer is required");
|
|
return (size_t)-1;
|
|
}
|
|
|
|
v = (PyLongObject *)vv;
|
|
i = Py_SIZE(v);
|
|
x = 0;
|
|
if (i < 0) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"can't convert negative value to size_t");
|
|
return (size_t) -1;
|
|
}
|
|
switch (i) {
|
|
case 0: return 0;
|
|
case 1: return v->ob_digit[0];
|
|
}
|
|
while (--i >= 0) {
|
|
prev = x;
|
|
x = (x << PyLong_SHIFT) | v->ob_digit[i];
|
|
if ((x >> PyLong_SHIFT) != prev) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"Python int too large to convert to C size_t");
|
|
return (size_t) -1;
|
|
}
|
|
}
|
|
return x;
|
|
}
|
|
|
|
/* Get a C unsigned long int from an int object, ignoring the high bits.
|
|
Returns -1 and sets an error condition if an error occurs. */
|
|
|
|
static unsigned long
|
|
_PyLong_AsUnsignedLongMask(PyObject *vv)
|
|
{
|
|
PyLongObject *v;
|
|
unsigned long x;
|
|
Py_ssize_t i;
|
|
int sign;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long) -1;
|
|
}
|
|
v = (PyLongObject *)vv;
|
|
i = Py_SIZE(v);
|
|
switch (i) {
|
|
case 0: return 0;
|
|
case 1: return v->ob_digit[0];
|
|
}
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -i;
|
|
}
|
|
while (--i >= 0) {
|
|
x = (x << PyLong_SHIFT) | v->ob_digit[i];
|
|
}
|
|
return x * sign;
|
|
}
|
|
|
|
unsigned long
|
|
PyLong_AsUnsignedLongMask(PyObject *op)
|
|
{
|
|
PyLongObject *lo;
|
|
unsigned long val;
|
|
|
|
if (op == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long)-1;
|
|
}
|
|
|
|
if (PyLong_Check(op)) {
|
|
return _PyLong_AsUnsignedLongMask(op);
|
|
}
|
|
|
|
lo = _PyLong_FromNbInt(op);
|
|
if (lo == NULL)
|
|
return (unsigned long)-1;
|
|
|
|
val = _PyLong_AsUnsignedLongMask((PyObject *)lo);
|
|
Py_DECREF(lo);
|
|
return val;
|
|
}
|
|
|
|
int
|
|
_PyLong_Sign(PyObject *vv)
|
|
{
|
|
PyLongObject *v = (PyLongObject *)vv;
|
|
|
|
assert(v != NULL);
|
|
assert(PyLong_Check(v));
|
|
|
|
return Py_SIZE(v) == 0 ? 0 : (Py_SIZE(v) < 0 ? -1 : 1);
|
|
}
|
|
|
|
/* bits_in_digit(d) returns the unique integer k such that 2**(k-1) <= d <
|
|
2**k if d is nonzero, else 0. */
|
|
|
|
static const unsigned char BitLengthTable[32] = {
|
|
0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
|
|
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
|
|
};
|
|
|
|
static int
|
|
bits_in_digit(digit d)
|
|
{
|
|
int d_bits = 0;
|
|
while (d >= 32) {
|
|
d_bits += 6;
|
|
d >>= 6;
|
|
}
|
|
d_bits += (int)BitLengthTable[d];
|
|
return d_bits;
|
|
}
|
|
|
|
size_t
|
|
_PyLong_NumBits(PyObject *vv)
|
|
{
|
|
PyLongObject *v = (PyLongObject *)vv;
|
|
size_t result = 0;
|
|
Py_ssize_t ndigits;
|
|
int msd_bits;
|
|
|
|
assert(v != NULL);
|
|
assert(PyLong_Check(v));
|
|
ndigits = Py_ABS(Py_SIZE(v));
|
|
assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
|
|
if (ndigits > 0) {
|
|
digit msd = v->ob_digit[ndigits - 1];
|
|
if ((size_t)(ndigits - 1) > SIZE_MAX / (size_t)PyLong_SHIFT)
|
|
goto Overflow;
|
|
result = (size_t)(ndigits - 1) * (size_t)PyLong_SHIFT;
|
|
msd_bits = bits_in_digit(msd);
|
|
if (SIZE_MAX - msd_bits < result)
|
|
goto Overflow;
|
|
result += msd_bits;
|
|
}
|
|
return result;
|
|
|
|
Overflow:
|
|
PyErr_SetString(PyExc_OverflowError, "int has too many bits "
|
|
"to express in a platform size_t");
|
|
return (size_t)-1;
|
|
}
|
|
|
|
PyObject *
|
|
_PyLong_FromByteArray(const unsigned char* bytes, size_t n,
|
|
int little_endian, int is_signed)
|
|
{
|
|
const unsigned char* pstartbyte; /* LSB of bytes */
|
|
int incr; /* direction to move pstartbyte */
|
|
const unsigned char* pendbyte; /* MSB of bytes */
|
|
size_t numsignificantbytes; /* number of bytes that matter */
|
|
Py_ssize_t ndigits; /* number of Python int digits */
|
|
PyLongObject* v; /* result */
|
|
Py_ssize_t idigit = 0; /* next free index in v->ob_digit */
|
|
|
|
if (n == 0)
|
|
return PyLong_FromLong(0L);
|
|
|
|
if (little_endian) {
|
|
pstartbyte = bytes;
|
|
pendbyte = bytes + n - 1;
|
|
incr = 1;
|
|
}
|
|
else {
|
|
pstartbyte = bytes + n - 1;
|
|
pendbyte = bytes;
|
|
incr = -1;
|
|
}
|
|
|
|
if (is_signed)
|
|
is_signed = *pendbyte >= 0x80;
|
|
|
|
/* Compute numsignificantbytes. This consists of finding the most
|
|
significant byte. Leading 0 bytes are insignificant if the number
|
|
is positive, and leading 0xff bytes if negative. */
|
|
{
|
|
size_t i;
|
|
const unsigned char* p = pendbyte;
|
|
const int pincr = -incr; /* search MSB to LSB */
|
|
const unsigned char insignificant = is_signed ? 0xff : 0x00;
|
|
|
|
for (i = 0; i < n; ++i, p += pincr) {
|
|
if (*p != insignificant)
|
|
break;
|
|
}
|
|
numsignificantbytes = n - i;
|
|
/* 2's-comp is a bit tricky here, e.g. 0xff00 == -0x0100, so
|
|
actually has 2 significant bytes. OTOH, 0xff0001 ==
|
|
-0x00ffff, so we wouldn't *need* to bump it there; but we
|
|
do for 0xffff = -0x0001. To be safe without bothering to
|
|
check every case, bump it regardless. */
|
|
if (is_signed && numsignificantbytes < n)
|
|
++numsignificantbytes;
|
|
}
|
|
|
|
/* How many Python int digits do we need? We have
|
|
8*numsignificantbytes bits, and each Python int digit has
|
|
PyLong_SHIFT bits, so it's the ceiling of the quotient. */
|
|
/* catch overflow before it happens */
|
|
if (numsignificantbytes > (PY_SSIZE_T_MAX - PyLong_SHIFT) / 8) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"byte array too long to convert to int");
|
|
return NULL;
|
|
}
|
|
ndigits = (numsignificantbytes * 8 + PyLong_SHIFT - 1) / PyLong_SHIFT;
|
|
v = _PyLong_New(ndigits);
|
|
if (v == NULL)
|
|
return NULL;
|
|
|
|
/* Copy the bits over. The tricky parts are computing 2's-comp on
|
|
the fly for signed numbers, and dealing with the mismatch between
|
|
8-bit bytes and (probably) 15-bit Python digits.*/
|
|
{
|
|
size_t i;
|
|
twodigits carry = 1; /* for 2's-comp calculation */
|
|
twodigits accum = 0; /* sliding register */
|
|
unsigned int accumbits = 0; /* number of bits in accum */
|
|
const unsigned char* p = pstartbyte;
|
|
|
|
for (i = 0; i < numsignificantbytes; ++i, p += incr) {
|
|
twodigits thisbyte = *p;
|
|
/* Compute correction for 2's comp, if needed. */
|
|
if (is_signed) {
|
|
thisbyte = (0xff ^ thisbyte) + carry;
|
|
carry = thisbyte >> 8;
|
|
thisbyte &= 0xff;
|
|
}
|
|
/* Because we're going LSB to MSB, thisbyte is
|
|
more significant than what's already in accum,
|
|
so needs to be prepended to accum. */
|
|
accum |= thisbyte << accumbits;
|
|
accumbits += 8;
|
|
if (accumbits >= PyLong_SHIFT) {
|
|
/* There's enough to fill a Python digit. */
|
|
assert(idigit < ndigits);
|
|
v->ob_digit[idigit] = (digit)(accum & PyLong_MASK);
|
|
++idigit;
|
|
accum >>= PyLong_SHIFT;
|
|
accumbits -= PyLong_SHIFT;
|
|
assert(accumbits < PyLong_SHIFT);
|
|
}
|
|
}
|
|
assert(accumbits < PyLong_SHIFT);
|
|
if (accumbits) {
|
|
assert(idigit < ndigits);
|
|
v->ob_digit[idigit] = (digit)accum;
|
|
++idigit;
|
|
}
|
|
}
|
|
|
|
Py_SIZE(v) = is_signed ? -idigit : idigit;
|
|
return (PyObject *)long_normalize(v);
|
|
}
|
|
|
|
int
|
|
_PyLong_AsByteArray(PyLongObject* v,
|
|
unsigned char* bytes, size_t n,
|
|
int little_endian, int is_signed)
|
|
{
|
|
Py_ssize_t i; /* index into v->ob_digit */
|
|
Py_ssize_t ndigits; /* |v->ob_size| */
|
|
twodigits accum; /* sliding register */
|
|
unsigned int accumbits; /* # bits in accum */
|
|
int do_twos_comp; /* store 2's-comp? is_signed and v < 0 */
|
|
digit carry; /* for computing 2's-comp */
|
|
size_t j; /* # bytes filled */
|
|
unsigned char* p; /* pointer to next byte in bytes */
|
|
int pincr; /* direction to move p */
|
|
|
|
assert(v != NULL && PyLong_Check(v));
|
|
|
|
if (Py_SIZE(v) < 0) {
|
|
ndigits = -(Py_SIZE(v));
|
|
if (!is_signed) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"can't convert negative int to unsigned");
|
|
return -1;
|
|
}
|
|
do_twos_comp = 1;
|
|
}
|
|
else {
|
|
ndigits = Py_SIZE(v);
|
|
do_twos_comp = 0;
|
|
}
|
|
|
|
if (little_endian) {
|
|
p = bytes;
|
|
pincr = 1;
|
|
}
|
|
else {
|
|
p = bytes + n - 1;
|
|
pincr = -1;
|
|
}
|
|
|
|
/* Copy over all the Python digits.
|
|
It's crucial that every Python digit except for the MSD contribute
|
|
exactly PyLong_SHIFT bits to the total, so first assert that the int is
|
|
normalized. */
|
|
assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
|
|
j = 0;
|
|
accum = 0;
|
|
accumbits = 0;
|
|
carry = do_twos_comp ? 1 : 0;
|
|
for (i = 0; i < ndigits; ++i) {
|
|
digit thisdigit = v->ob_digit[i];
|
|
if (do_twos_comp) {
|
|
thisdigit = (thisdigit ^ PyLong_MASK) + carry;
|
|
carry = thisdigit >> PyLong_SHIFT;
|
|
thisdigit &= PyLong_MASK;
|
|
}
|
|
/* Because we're going LSB to MSB, thisdigit is more
|
|
significant than what's already in accum, so needs to be
|
|
prepended to accum. */
|
|
accum |= (twodigits)thisdigit << accumbits;
|
|
|
|
/* The most-significant digit may be (probably is) at least
|
|
partly empty. */
|
|
if (i == ndigits - 1) {
|
|
/* Count # of sign bits -- they needn't be stored,
|
|
* although for signed conversion we need later to
|
|
* make sure at least one sign bit gets stored. */
|
|
digit s = do_twos_comp ? thisdigit ^ PyLong_MASK : thisdigit;
|
|
while (s != 0) {
|
|
s >>= 1;
|
|
accumbits++;
|
|
}
|
|
}
|
|
else
|
|
accumbits += PyLong_SHIFT;
|
|
|
|
/* Store as many bytes as possible. */
|
|
while (accumbits >= 8) {
|
|
if (j >= n)
|
|
goto Overflow;
|
|
++j;
|
|
*p = (unsigned char)(accum & 0xff);
|
|
p += pincr;
|
|
accumbits -= 8;
|
|
accum >>= 8;
|
|
}
|
|
}
|
|
|
|
/* Store the straggler (if any). */
|
|
assert(accumbits < 8);
|
|
assert(carry == 0); /* else do_twos_comp and *every* digit was 0 */
|
|
if (accumbits > 0) {
|
|
if (j >= n)
|
|
goto Overflow;
|
|
++j;
|
|
if (do_twos_comp) {
|
|
/* Fill leading bits of the byte with sign bits
|
|
(appropriately pretending that the int had an
|
|
infinite supply of sign bits). */
|
|
accum |= (~(twodigits)0) << accumbits;
|
|
}
|
|
*p = (unsigned char)(accum & 0xff);
|
|
p += pincr;
|
|
}
|
|
else if (j == n && n > 0 && is_signed) {
|
|
/* The main loop filled the byte array exactly, so the code
|
|
just above didn't get to ensure there's a sign bit, and the
|
|
loop below wouldn't add one either. Make sure a sign bit
|
|
exists. */
|
|
unsigned char msb = *(p - pincr);
|
|
int sign_bit_set = msb >= 0x80;
|
|
assert(accumbits == 0);
|
|
if (sign_bit_set == do_twos_comp)
|
|
return 0;
|
|
else
|
|
goto Overflow;
|
|
}
|
|
|
|
/* Fill remaining bytes with copies of the sign bit. */
|
|
{
|
|
unsigned char signbyte = do_twos_comp ? 0xffU : 0U;
|
|
for ( ; j < n; ++j, p += pincr)
|
|
*p = signbyte;
|
|
}
|
|
|
|
return 0;
|
|
|
|
Overflow:
|
|
PyErr_SetString(PyExc_OverflowError, "int too big to convert");
|
|
return -1;
|
|
|
|
}
|
|
|
|
/* Create a new int object from a C pointer */
|
|
|
|
PyObject *
|
|
PyLong_FromVoidPtr(void *p)
|
|
{
|
|
#if SIZEOF_VOID_P <= SIZEOF_LONG
|
|
return PyLong_FromUnsignedLong((unsigned long)(uintptr_t)p);
|
|
#else
|
|
|
|
#if SIZEOF_LONG_LONG < SIZEOF_VOID_P
|
|
# error "PyLong_FromVoidPtr: sizeof(long long) < sizeof(void*)"
|
|
#endif
|
|
return PyLong_FromUnsignedLongLong((unsigned long long)(uintptr_t)p);
|
|
#endif /* SIZEOF_VOID_P <= SIZEOF_LONG */
|
|
|
|
}
|
|
|
|
/* Get a C pointer from an int object. */
|
|
|
|
void *
|
|
PyLong_AsVoidPtr(PyObject *vv)
|
|
{
|
|
#if SIZEOF_VOID_P <= SIZEOF_LONG
|
|
long x;
|
|
|
|
if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
|
|
x = PyLong_AsLong(vv);
|
|
else
|
|
x = PyLong_AsUnsignedLong(vv);
|
|
#else
|
|
|
|
#if SIZEOF_LONG_LONG < SIZEOF_VOID_P
|
|
# error "PyLong_AsVoidPtr: sizeof(long long) < sizeof(void*)"
|
|
#endif
|
|
long long x;
|
|
|
|
if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
|
|
x = PyLong_AsLongLong(vv);
|
|
else
|
|
x = PyLong_AsUnsignedLongLong(vv);
|
|
|
|
#endif /* SIZEOF_VOID_P <= SIZEOF_LONG */
|
|
|
|
if (x == -1 && PyErr_Occurred())
|
|
return NULL;
|
|
return (void *)x;
|
|
}
|
|
|
|
/* Initial long long support by Chris Herborth (chrish@qnx.com), later
|
|
* rewritten to use the newer PyLong_{As,From}ByteArray API.
|
|
*/
|
|
|
|
#define PY_ABS_LLONG_MIN (0-(unsigned long long)PY_LLONG_MIN)
|
|
|
|
/* Create a new int object from a C long long int. */
|
|
|
|
PyObject *
|
|
PyLong_FromLongLong(long long ival)
|
|
{
|
|
PyLongObject *v;
|
|
unsigned long long abs_ival;
|
|
unsigned long long t; /* unsigned so >> doesn't propagate sign bit */
|
|
int ndigits = 0;
|
|
int negative = 0;
|
|
|
|
CHECK_SMALL_INT(ival);
|
|
if (ival < 0) {
|
|
/* avoid signed overflow on negation; see comments
|
|
in PyLong_FromLong above. */
|
|
abs_ival = (unsigned long long)(-1-ival) + 1;
|
|
negative = 1;
|
|
}
|
|
else {
|
|
abs_ival = (unsigned long long)ival;
|
|
}
|
|
|
|
/* Count the number of Python digits.
|
|
We used to pick 5 ("big enough for anything"), but that's a
|
|
waste of time and space given that 5*15 = 75 bits are rarely
|
|
needed. */
|
|
t = abs_ival;
|
|
while (t) {
|
|
++ndigits;
|
|
t >>= PyLong_SHIFT;
|
|
}
|
|
v = _PyLong_New(ndigits);
|
|
if (v != NULL) {
|
|
digit *p = v->ob_digit;
|
|
Py_SIZE(v) = negative ? -ndigits : ndigits;
|
|
t = abs_ival;
|
|
while (t) {
|
|
*p++ = (digit)(t & PyLong_MASK);
|
|
t >>= PyLong_SHIFT;
|
|
}
|
|
}
|
|
return (PyObject *)v;
|
|
}
|
|
|
|
/* Create a new int object from a C unsigned long long int. */
|
|
|
|
PyObject *
|
|
PyLong_FromUnsignedLongLong(unsigned long long ival)
|
|
{
|
|
PyLongObject *v;
|
|
unsigned long long t;
|
|
int ndigits = 0;
|
|
|
|
if (ival < PyLong_BASE)
|
|
return PyLong_FromLong((long)ival);
|
|
/* Count the number of Python digits. */
|
|
t = ival;
|
|
while (t) {
|
|
++ndigits;
|
|
t >>= PyLong_SHIFT;
|
|
}
|
|
v = _PyLong_New(ndigits);
|
|
if (v != NULL) {
|
|
digit *p = v->ob_digit;
|
|
while (ival) {
|
|
*p++ = (digit)(ival & PyLong_MASK);
|
|
ival >>= PyLong_SHIFT;
|
|
}
|
|
}
|
|
return (PyObject *)v;
|
|
}
|
|
|
|
/* Create a new int object from a C Py_ssize_t. */
|
|
|
|
PyObject *
|
|
PyLong_FromSsize_t(Py_ssize_t ival)
|
|
{
|
|
PyLongObject *v;
|
|
size_t abs_ival;
|
|
size_t t; /* unsigned so >> doesn't propagate sign bit */
|
|
int ndigits = 0;
|
|
int negative = 0;
|
|
|
|
CHECK_SMALL_INT(ival);
|
|
if (ival < 0) {
|
|
/* avoid signed overflow when ival = SIZE_T_MIN */
|
|
abs_ival = (size_t)(-1-ival)+1;
|
|
negative = 1;
|
|
}
|
|
else {
|
|
abs_ival = (size_t)ival;
|
|
}
|
|
|
|
/* Count the number of Python digits. */
|
|
t = abs_ival;
|
|
while (t) {
|
|
++ndigits;
|
|
t >>= PyLong_SHIFT;
|
|
}
|
|
v = _PyLong_New(ndigits);
|
|
if (v != NULL) {
|
|
digit *p = v->ob_digit;
|
|
Py_SIZE(v) = negative ? -ndigits : ndigits;
|
|
t = abs_ival;
|
|
while (t) {
|
|
*p++ = (digit)(t & PyLong_MASK);
|
|
t >>= PyLong_SHIFT;
|
|
}
|
|
}
|
|
return (PyObject *)v;
|
|
}
|
|
|
|
/* Create a new int object from a C size_t. */
|
|
|
|
PyObject *
|
|
PyLong_FromSize_t(size_t ival)
|
|
{
|
|
PyLongObject *v;
|
|
size_t t;
|
|
int ndigits = 0;
|
|
|
|
if (ival < PyLong_BASE)
|
|
return PyLong_FromLong((long)ival);
|
|
/* Count the number of Python digits. */
|
|
t = ival;
|
|
while (t) {
|
|
++ndigits;
|
|
t >>= PyLong_SHIFT;
|
|
}
|
|
v = _PyLong_New(ndigits);
|
|
if (v != NULL) {
|
|
digit *p = v->ob_digit;
|
|
Py_SIZE(v) = ndigits;
|
|
while (ival) {
|
|
*p++ = (digit)(ival & PyLong_MASK);
|
|
ival >>= PyLong_SHIFT;
|
|
}
|
|
}
|
|
return (PyObject *)v;
|
|
}
|
|
|
|
/* Get a C long long int from an int object or any object that has an
|
|
__int__ method. Return -1 and set an error if overflow occurs. */
|
|
|
|
long long
|
|
PyLong_AsLongLong(PyObject *vv)
|
|
{
|
|
PyLongObject *v;
|
|
long long bytes;
|
|
int res;
|
|
int do_decref = 0; /* if nb_int was called */
|
|
|
|
if (vv == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
|
|
if (PyLong_Check(vv)) {
|
|
v = (PyLongObject *)vv;
|
|
}
|
|
else {
|
|
v = _PyLong_FromNbInt(vv);
|
|
if (v == NULL)
|
|
return -1;
|
|
do_decref = 1;
|
|
}
|
|
|
|
res = 0;
|
|
switch(Py_SIZE(v)) {
|
|
case -1:
|
|
bytes = -(sdigit)v->ob_digit[0];
|
|
break;
|
|
case 0:
|
|
bytes = 0;
|
|
break;
|
|
case 1:
|
|
bytes = v->ob_digit[0];
|
|
break;
|
|
default:
|
|
res = _PyLong_AsByteArray((PyLongObject *)v, (unsigned char *)&bytes,
|
|
SIZEOF_LONG_LONG, PY_LITTLE_ENDIAN, 1);
|
|
}
|
|
if (do_decref) {
|
|
Py_DECREF(v);
|
|
}
|
|
|
|
/* Plan 9 can't handle long long in ? : expressions */
|
|
if (res < 0)
|
|
return (long long)-1;
|
|
else
|
|
return bytes;
|
|
}
|
|
|
|
/* Get a C unsigned long long int from an int object.
|
|
Return -1 and set an error if overflow occurs. */
|
|
|
|
unsigned long long
|
|
PyLong_AsUnsignedLongLong(PyObject *vv)
|
|
{
|
|
PyLongObject *v;
|
|
unsigned long long bytes;
|
|
int res;
|
|
|
|
if (vv == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long long)-1;
|
|
}
|
|
if (!PyLong_Check(vv)) {
|
|
PyErr_SetString(PyExc_TypeError, "an integer is required");
|
|
return (unsigned long long)-1;
|
|
}
|
|
|
|
v = (PyLongObject*)vv;
|
|
switch(Py_SIZE(v)) {
|
|
case 0: return 0;
|
|
case 1: return v->ob_digit[0];
|
|
}
|
|
|
|
res = _PyLong_AsByteArray((PyLongObject *)vv, (unsigned char *)&bytes,
|
|
SIZEOF_LONG_LONG, PY_LITTLE_ENDIAN, 0);
|
|
|
|
/* Plan 9 can't handle long long in ? : expressions */
|
|
if (res < 0)
|
|
return (unsigned long long)res;
|
|
else
|
|
return bytes;
|
|
}
|
|
|
|
/* Get a C unsigned long int from an int object, ignoring the high bits.
|
|
Returns -1 and sets an error condition if an error occurs. */
|
|
|
|
static unsigned long long
|
|
_PyLong_AsUnsignedLongLongMask(PyObject *vv)
|
|
{
|
|
PyLongObject *v;
|
|
unsigned long long x;
|
|
Py_ssize_t i;
|
|
int sign;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long) -1;
|
|
}
|
|
v = (PyLongObject *)vv;
|
|
switch(Py_SIZE(v)) {
|
|
case 0: return 0;
|
|
case 1: return v->ob_digit[0];
|
|
}
|
|
i = Py_SIZE(v);
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -i;
|
|
}
|
|
while (--i >= 0) {
|
|
x = (x << PyLong_SHIFT) | v->ob_digit[i];
|
|
}
|
|
return x * sign;
|
|
}
|
|
|
|
unsigned long long
|
|
PyLong_AsUnsignedLongLongMask(PyObject *op)
|
|
{
|
|
PyLongObject *lo;
|
|
unsigned long long val;
|
|
|
|
if (op == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long)-1;
|
|
}
|
|
|
|
if (PyLong_Check(op)) {
|
|
return _PyLong_AsUnsignedLongLongMask(op);
|
|
}
|
|
|
|
lo = _PyLong_FromNbInt(op);
|
|
if (lo == NULL)
|
|
return (unsigned long long)-1;
|
|
|
|
val = _PyLong_AsUnsignedLongLongMask((PyObject *)lo);
|
|
Py_DECREF(lo);
|
|
return val;
|
|
}
|
|
|
|
/* Get a C long long int from an int object or any object that has an
|
|
__int__ method.
|
|
|
|
On overflow, return -1 and set *overflow to 1 or -1 depending on the sign of
|
|
the result. Otherwise *overflow is 0.
|
|
|
|
For other errors (e.g., TypeError), return -1 and set an error condition.
|
|
In this case *overflow will be 0.
|
|
*/
|
|
|
|
long long
|
|
PyLong_AsLongLongAndOverflow(PyObject *vv, int *overflow)
|
|
{
|
|
/* This version by Tim Peters */
|
|
PyLongObject *v;
|
|
unsigned long long x, prev;
|
|
long long res;
|
|
Py_ssize_t i;
|
|
int sign;
|
|
int do_decref = 0; /* if nb_int was called */
|
|
|
|
*overflow = 0;
|
|
if (vv == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
|
|
if (PyLong_Check(vv)) {
|
|
v = (PyLongObject *)vv;
|
|
}
|
|
else {
|
|
v = _PyLong_FromNbInt(vv);
|
|
if (v == NULL)
|
|
return -1;
|
|
do_decref = 1;
|
|
}
|
|
|
|
res = -1;
|
|
i = Py_SIZE(v);
|
|
|
|
switch (i) {
|
|
case -1:
|
|
res = -(sdigit)v->ob_digit[0];
|
|
break;
|
|
case 0:
|
|
res = 0;
|
|
break;
|
|
case 1:
|
|
res = v->ob_digit[0];
|
|
break;
|
|
default:
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -(i);
|
|
}
|
|
while (--i >= 0) {
|
|
prev = x;
|
|
x = (x << PyLong_SHIFT) + v->ob_digit[i];
|
|
if ((x >> PyLong_SHIFT) != prev) {
|
|
*overflow = sign;
|
|
goto exit;
|
|
}
|
|
}
|
|
/* Haven't lost any bits, but casting to long requires extra
|
|
* care (see comment above).
|
|
*/
|
|
if (x <= (unsigned long long)PY_LLONG_MAX) {
|
|
res = (long long)x * sign;
|
|
}
|
|
else if (sign < 0 && x == PY_ABS_LLONG_MIN) {
|
|
res = PY_LLONG_MIN;
|
|
}
|
|
else {
|
|
*overflow = sign;
|
|
/* res is already set to -1 */
|
|
}
|
|
}
|
|
exit:
|
|
if (do_decref) {
|
|
Py_DECREF(v);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
#define CHECK_BINOP(v,w) \
|
|
do { \
|
|
if (!PyLong_Check(v) || !PyLong_Check(w)) \
|
|
Py_RETURN_NOTIMPLEMENTED; \
|
|
} while(0)
|
|
|
|
/* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required. x[0:n]
|
|
* is modified in place, by adding y to it. Carries are propagated as far as
|
|
* x[m-1], and the remaining carry (0 or 1) is returned.
|
|
*/
|
|
static digit
|
|
v_iadd(digit *x, Py_ssize_t m, digit *y, Py_ssize_t n)
|
|
{
|
|
Py_ssize_t i;
|
|
digit carry = 0;
|
|
|
|
assert(m >= n);
|
|
for (i = 0; i < n; ++i) {
|
|
carry += x[i] + y[i];
|
|
x[i] = carry & PyLong_MASK;
|
|
carry >>= PyLong_SHIFT;
|
|
assert((carry & 1) == carry);
|
|
}
|
|
for (; carry && i < m; ++i) {
|
|
carry += x[i];
|
|
x[i] = carry & PyLong_MASK;
|
|
carry >>= PyLong_SHIFT;
|
|
assert((carry & 1) == carry);
|
|
}
|
|
return carry;
|
|
}
|
|
|
|
/* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required. x[0:n]
|
|
* is modified in place, by subtracting y from it. Borrows are propagated as
|
|
* far as x[m-1], and the remaining borrow (0 or 1) is returned.
|
|
*/
|
|
static digit
|
|
v_isub(digit *x, Py_ssize_t m, digit *y, Py_ssize_t n)
|
|
{
|
|
Py_ssize_t i;
|
|
digit borrow = 0;
|
|
|
|
assert(m >= n);
|
|
for (i = 0; i < n; ++i) {
|
|
borrow = x[i] - y[i] - borrow;
|
|
x[i] = borrow & PyLong_MASK;
|
|
borrow >>= PyLong_SHIFT;
|
|
borrow &= 1; /* keep only 1 sign bit */
|
|
}
|
|
for (; borrow && i < m; ++i) {
|
|
borrow = x[i] - borrow;
|
|
x[i] = borrow & PyLong_MASK;
|
|
borrow >>= PyLong_SHIFT;
|
|
borrow &= 1;
|
|
}
|
|
return borrow;
|
|
}
|
|
|
|
/* Shift digit vector a[0:m] d bits left, with 0 <= d < PyLong_SHIFT. Put
|
|
* result in z[0:m], and return the d bits shifted out of the top.
|
|
*/
|
|
static digit
|
|
v_lshift(digit *z, digit *a, Py_ssize_t m, int d)
|
|
{
|
|
Py_ssize_t i;
|
|
digit carry = 0;
|
|
|
|
assert(0 <= d && d < PyLong_SHIFT);
|
|
for (i=0; i < m; i++) {
|
|
twodigits acc = (twodigits)a[i] << d | carry;
|
|
z[i] = (digit)acc & PyLong_MASK;
|
|
carry = (digit)(acc >> PyLong_SHIFT);
|
|
}
|
|
return carry;
|
|
}
|
|
|
|
/* Shift digit vector a[0:m] d bits right, with 0 <= d < PyLong_SHIFT. Put
|
|
* result in z[0:m], and return the d bits shifted out of the bottom.
|
|
*/
|
|
static digit
|
|
v_rshift(digit *z, digit *a, Py_ssize_t m, int d)
|
|
{
|
|
Py_ssize_t i;
|
|
digit carry = 0;
|
|
digit mask = ((digit)1 << d) - 1U;
|
|
|
|
assert(0 <= d && d < PyLong_SHIFT);
|
|
for (i=m; i-- > 0;) {
|
|
twodigits acc = (twodigits)carry << PyLong_SHIFT | a[i];
|
|
carry = (digit)acc & mask;
|
|
z[i] = (digit)(acc >> d);
|
|
}
|
|
return carry;
|
|
}
|
|
|
|
/* Divide long pin, w/ size digits, by non-zero digit n, storing quotient
|
|
in pout, and returning the remainder. pin and pout point at the LSD.
|
|
It's OK for pin == pout on entry, which saves oodles of mallocs/frees in
|
|
_PyLong_Format, but that should be done with great care since ints are
|
|
immutable. */
|
|
|
|
static digit
|
|
inplace_divrem1(digit *pout, digit *pin, Py_ssize_t size, digit n)
|
|
{
|
|
twodigits rem = 0;
|
|
|
|
assert(n > 0 && n <= PyLong_MASK);
|
|
pin += size;
|
|
pout += size;
|
|
while (--size >= 0) {
|
|
digit hi;
|
|
rem = (rem << PyLong_SHIFT) | *--pin;
|
|
*--pout = hi = (digit)(rem / n);
|
|
rem -= (twodigits)hi * n;
|
|
}
|
|
return (digit)rem;
|
|
}
|
|
|
|
/* Divide an integer by a digit, returning both the quotient
|
|
(as function result) and the remainder (through *prem).
|
|
The sign of a is ignored; n should not be zero. */
|
|
|
|
static PyLongObject *
|
|
divrem1(PyLongObject *a, digit n, digit *prem)
|
|
{
|
|
const Py_ssize_t size = Py_ABS(Py_SIZE(a));
|
|
PyLongObject *z;
|
|
|
|
assert(n > 0 && n <= PyLong_MASK);
|
|
z = _PyLong_New(size);
|
|
if (z == NULL)
|
|
return NULL;
|
|
*prem = inplace_divrem1(z->ob_digit, a->ob_digit, size, n);
|
|
return long_normalize(z);
|
|
}
|
|
|
|
/* Convert an integer to a base 10 string. Returns a new non-shared
|
|
string. (Return value is non-shared so that callers can modify the
|
|
returned value if necessary.) */
|
|
|
|
static int
|
|
long_to_decimal_string_internal(PyObject *aa,
|
|
PyObject **p_output,
|
|
_PyUnicodeWriter *writer,
|
|
_PyBytesWriter *bytes_writer,
|
|
char **bytes_str)
|
|
{
|
|
PyLongObject *scratch, *a;
|
|
PyObject *str = NULL;
|
|
Py_ssize_t size, strlen, size_a, i, j;
|
|
digit *pout, *pin, rem, tenpow;
|
|
int negative;
|
|
int d;
|
|
enum PyUnicode_Kind kind;
|
|
|
|
a = (PyLongObject *)aa;
|
|
if (a == NULL || !PyLong_Check(a)) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
size_a = Py_ABS(Py_SIZE(a));
|
|
negative = Py_SIZE(a) < 0;
|
|
|
|
/* quick and dirty upper bound for the number of digits
|
|
required to express a in base _PyLong_DECIMAL_BASE:
|
|
|
|
#digits = 1 + floor(log2(a) / log2(_PyLong_DECIMAL_BASE))
|
|
|
|
But log2(a) < size_a * PyLong_SHIFT, and
|
|
log2(_PyLong_DECIMAL_BASE) = log2(10) * _PyLong_DECIMAL_SHIFT
|
|
> 3.3 * _PyLong_DECIMAL_SHIFT
|
|
|
|
size_a * PyLong_SHIFT / (3.3 * _PyLong_DECIMAL_SHIFT) =
|
|
size_a + size_a / d < size_a + size_a / floor(d),
|
|
where d = (3.3 * _PyLong_DECIMAL_SHIFT) /
|
|
(PyLong_SHIFT - 3.3 * _PyLong_DECIMAL_SHIFT)
|
|
*/
|
|
d = (33 * _PyLong_DECIMAL_SHIFT) /
|
|
(10 * PyLong_SHIFT - 33 * _PyLong_DECIMAL_SHIFT);
|
|
assert(size_a < PY_SSIZE_T_MAX/2);
|
|
size = 1 + size_a + size_a / d;
|
|
scratch = _PyLong_New(size);
|
|
if (scratch == NULL)
|
|
return -1;
|
|
|
|
/* convert array of base _PyLong_BASE digits in pin to an array of
|
|
base _PyLong_DECIMAL_BASE digits in pout, following Knuth (TAOCP,
|
|
Volume 2 (3rd edn), section 4.4, Method 1b). */
|
|
pin = a->ob_digit;
|
|
pout = scratch->ob_digit;
|
|
size = 0;
|
|
for (i = size_a; --i >= 0; ) {
|
|
digit hi = pin[i];
|
|
for (j = 0; j < size; j++) {
|
|
twodigits z = (twodigits)pout[j] << PyLong_SHIFT | hi;
|
|
hi = (digit)(z / _PyLong_DECIMAL_BASE);
|
|
pout[j] = (digit)(z - (twodigits)hi *
|
|
_PyLong_DECIMAL_BASE);
|
|
}
|
|
while (hi) {
|
|
pout[size++] = hi % _PyLong_DECIMAL_BASE;
|
|
hi /= _PyLong_DECIMAL_BASE;
|
|
}
|
|
/* check for keyboard interrupt */
|
|
SIGCHECK({
|
|
Py_DECREF(scratch);
|
|
return -1;
|
|
});
|
|
}
|
|
/* pout should have at least one digit, so that the case when a = 0
|
|
works correctly */
|
|
if (size == 0)
|
|
pout[size++] = 0;
|
|
|
|
/* calculate exact length of output string, and allocate */
|
|
strlen = negative + 1 + (size - 1) * _PyLong_DECIMAL_SHIFT;
|
|
tenpow = 10;
|
|
rem = pout[size-1];
|
|
while (rem >= tenpow) {
|
|
tenpow *= 10;
|
|
strlen++;
|
|
}
|
|
if (writer) {
|
|
if (_PyUnicodeWriter_Prepare(writer, strlen, '9') == -1) {
|
|
Py_DECREF(scratch);
|
|
return -1;
|
|
}
|
|
kind = writer->kind;
|
|
}
|
|
else if (bytes_writer) {
|
|
*bytes_str = _PyBytesWriter_Prepare(bytes_writer, *bytes_str, strlen);
|
|
if (*bytes_str == NULL) {
|
|
Py_DECREF(scratch);
|
|
return -1;
|
|
}
|
|
}
|
|
else {
|
|
str = PyUnicode_New(strlen, '9');
|
|
if (str == NULL) {
|
|
Py_DECREF(scratch);
|
|
return -1;
|
|
}
|
|
kind = PyUnicode_KIND(str);
|
|
}
|
|
|
|
#define WRITE_DIGITS(p) \
|
|
do { \
|
|
/* pout[0] through pout[size-2] contribute exactly \
|
|
_PyLong_DECIMAL_SHIFT digits each */ \
|
|
for (i=0; i < size - 1; i++) { \
|
|
rem = pout[i]; \
|
|
for (j = 0; j < _PyLong_DECIMAL_SHIFT; j++) { \
|
|
*--p = '0' + rem % 10; \
|
|
rem /= 10; \
|
|
} \
|
|
} \
|
|
/* pout[size-1]: always produce at least one decimal digit */ \
|
|
rem = pout[i]; \
|
|
do { \
|
|
*--p = '0' + rem % 10; \
|
|
rem /= 10; \
|
|
} while (rem != 0); \
|
|
\
|
|
/* and sign */ \
|
|
if (negative) \
|
|
*--p = '-'; \
|
|
} while (0)
|
|
|
|
#define WRITE_UNICODE_DIGITS(TYPE) \
|
|
do { \
|
|
if (writer) \
|
|
p = (TYPE*)PyUnicode_DATA(writer->buffer) + writer->pos + strlen; \
|
|
else \
|
|
p = (TYPE*)PyUnicode_DATA(str) + strlen; \
|
|
\
|
|
WRITE_DIGITS(p); \
|
|
\
|
|
/* check we've counted correctly */ \
|
|
if (writer) \
|
|
assert(p == ((TYPE*)PyUnicode_DATA(writer->buffer) + writer->pos)); \
|
|
else \
|
|
assert(p == (TYPE*)PyUnicode_DATA(str)); \
|
|
} while (0)
|
|
|
|
/* fill the string right-to-left */
|
|
if (bytes_writer) {
|
|
char *p = *bytes_str + strlen;
|
|
WRITE_DIGITS(p);
|
|
assert(p == *bytes_str);
|
|
}
|
|
else if (kind == PyUnicode_1BYTE_KIND) {
|
|
Py_UCS1 *p;
|
|
WRITE_UNICODE_DIGITS(Py_UCS1);
|
|
}
|
|
else if (kind == PyUnicode_2BYTE_KIND) {
|
|
Py_UCS2 *p;
|
|
WRITE_UNICODE_DIGITS(Py_UCS2);
|
|
}
|
|
else {
|
|
Py_UCS4 *p;
|
|
assert (kind == PyUnicode_4BYTE_KIND);
|
|
WRITE_UNICODE_DIGITS(Py_UCS4);
|
|
}
|
|
#undef WRITE_DIGITS
|
|
#undef WRITE_UNICODE_DIGITS
|
|
|
|
Py_DECREF(scratch);
|
|
if (writer) {
|
|
writer->pos += strlen;
|
|
}
|
|
else if (bytes_writer) {
|
|
(*bytes_str) += strlen;
|
|
}
|
|
else {
|
|
assert(_PyUnicode_CheckConsistency(str, 1));
|
|
*p_output = (PyObject *)str;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
static PyObject *
|
|
long_to_decimal_string(PyObject *aa)
|
|
{
|
|
PyObject *v;
|
|
if (long_to_decimal_string_internal(aa, &v, NULL, NULL, NULL) == -1)
|
|
return NULL;
|
|
return v;
|
|
}
|
|
|
|
/* Convert an int object to a string, using a given conversion base,
|
|
which should be one of 2, 8 or 16. Return a string object.
|
|
If base is 2, 8 or 16, add the proper prefix '0b', '0o' or '0x'
|
|
if alternate is nonzero. */
|
|
|
|
static int
|
|
long_format_binary(PyObject *aa, int base, int alternate,
|
|
PyObject **p_output, _PyUnicodeWriter *writer,
|
|
_PyBytesWriter *bytes_writer, char **bytes_str)
|
|
{
|
|
PyLongObject *a = (PyLongObject *)aa;
|
|
PyObject *v = NULL;
|
|
Py_ssize_t sz;
|
|
Py_ssize_t size_a;
|
|
enum PyUnicode_Kind kind;
|
|
int negative;
|
|
int bits;
|
|
|
|
assert(base == 2 || base == 8 || base == 16);
|
|
if (a == NULL || !PyLong_Check(a)) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
size_a = Py_ABS(Py_SIZE(a));
|
|
negative = Py_SIZE(a) < 0;
|
|
|
|
/* Compute a rough upper bound for the length of the string */
|
|
switch (base) {
|
|
case 16:
|
|
bits = 4;
|
|
break;
|
|
case 8:
|
|
bits = 3;
|
|
break;
|
|
case 2:
|
|
bits = 1;
|
|
break;
|
|
default:
|
|
assert(0); /* shouldn't ever get here */
|
|
bits = 0; /* to silence gcc warning */
|
|
}
|
|
|
|
/* Compute exact length 'sz' of output string. */
|
|
if (size_a == 0) {
|
|
sz = 1;
|
|
}
|
|
else {
|
|
Py_ssize_t size_a_in_bits;
|
|
/* Ensure overflow doesn't occur during computation of sz. */
|
|
if (size_a > (PY_SSIZE_T_MAX - 3) / PyLong_SHIFT) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"int too large to format");
|
|
return -1;
|
|
}
|
|
size_a_in_bits = (size_a - 1) * PyLong_SHIFT +
|
|
bits_in_digit(a->ob_digit[size_a - 1]);
|
|
/* Allow 1 character for a '-' sign. */
|
|
sz = negative + (size_a_in_bits + (bits - 1)) / bits;
|
|
}
|
|
if (alternate) {
|
|
/* 2 characters for prefix */
|
|
sz += 2;
|
|
}
|
|
|
|
if (writer) {
|
|
if (_PyUnicodeWriter_Prepare(writer, sz, 'x') == -1)
|
|
return -1;
|
|
kind = writer->kind;
|
|
}
|
|
else if (bytes_writer) {
|
|
*bytes_str = _PyBytesWriter_Prepare(bytes_writer, *bytes_str, sz);
|
|
if (*bytes_str == NULL)
|
|
return -1;
|
|
}
|
|
else {
|
|
v = PyUnicode_New(sz, 'x');
|
|
if (v == NULL)
|
|
return -1;
|
|
kind = PyUnicode_KIND(v);
|
|
}
|
|
|
|
#define WRITE_DIGITS(p) \
|
|
do { \
|
|
if (size_a == 0) { \
|
|
*--p = '0'; \
|
|
} \
|
|
else { \
|
|
/* JRH: special case for power-of-2 bases */ \
|
|
twodigits accum = 0; \
|
|
int accumbits = 0; /* # of bits in accum */ \
|
|
Py_ssize_t i; \
|
|
for (i = 0; i < size_a; ++i) { \
|
|
accum |= (twodigits)a->ob_digit[i] << accumbits; \
|
|
accumbits += PyLong_SHIFT; \
|
|
assert(accumbits >= bits); \
|
|
do { \
|
|
char cdigit; \
|
|
cdigit = (char)(accum & (base - 1)); \
|
|
cdigit += (cdigit < 10) ? '0' : 'a'-10; \
|
|
*--p = cdigit; \
|
|
accumbits -= bits; \
|
|
accum >>= bits; \
|
|
} while (i < size_a-1 ? accumbits >= bits : accum > 0); \
|
|
} \
|
|
} \
|
|
\
|
|
if (alternate) { \
|
|
if (base == 16) \
|
|
*--p = 'x'; \
|
|
else if (base == 8) \
|
|
*--p = 'o'; \
|
|
else /* (base == 2) */ \
|
|
*--p = 'b'; \
|
|
*--p = '0'; \
|
|
} \
|
|
if (negative) \
|
|
*--p = '-'; \
|
|
} while (0)
|
|
|
|
#define WRITE_UNICODE_DIGITS(TYPE) \
|
|
do { \
|
|
if (writer) \
|
|
p = (TYPE*)PyUnicode_DATA(writer->buffer) + writer->pos + sz; \
|
|
else \
|
|
p = (TYPE*)PyUnicode_DATA(v) + sz; \
|
|
\
|
|
WRITE_DIGITS(p); \
|
|
\
|
|
if (writer) \
|
|
assert(p == ((TYPE*)PyUnicode_DATA(writer->buffer) + writer->pos)); \
|
|
else \
|
|
assert(p == (TYPE*)PyUnicode_DATA(v)); \
|
|
} while (0)
|
|
|
|
if (bytes_writer) {
|
|
char *p = *bytes_str + sz;
|
|
WRITE_DIGITS(p);
|
|
assert(p == *bytes_str);
|
|
}
|
|
else if (kind == PyUnicode_1BYTE_KIND) {
|
|
Py_UCS1 *p;
|
|
WRITE_UNICODE_DIGITS(Py_UCS1);
|
|
}
|
|
else if (kind == PyUnicode_2BYTE_KIND) {
|
|
Py_UCS2 *p;
|
|
WRITE_UNICODE_DIGITS(Py_UCS2);
|
|
}
|
|
else {
|
|
Py_UCS4 *p;
|
|
assert (kind == PyUnicode_4BYTE_KIND);
|
|
WRITE_UNICODE_DIGITS(Py_UCS4);
|
|
}
|
|
#undef WRITE_DIGITS
|
|
#undef WRITE_UNICODE_DIGITS
|
|
|
|
if (writer) {
|
|
writer->pos += sz;
|
|
}
|
|
else if (bytes_writer) {
|
|
(*bytes_str) += sz;
|
|
}
|
|
else {
|
|
assert(_PyUnicode_CheckConsistency(v, 1));
|
|
*p_output = v;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
PyObject *
|
|
_PyLong_Format(PyObject *obj, int base)
|
|
{
|
|
PyObject *str;
|
|
int err;
|
|
if (base == 10)
|
|
err = long_to_decimal_string_internal(obj, &str, NULL, NULL, NULL);
|
|
else
|
|
err = long_format_binary(obj, base, 1, &str, NULL, NULL, NULL);
|
|
if (err == -1)
|
|
return NULL;
|
|
return str;
|
|
}
|
|
|
|
int
|
|
_PyLong_FormatWriter(_PyUnicodeWriter *writer,
|
|
PyObject *obj,
|
|
int base, int alternate)
|
|
{
|
|
if (base == 10)
|
|
return long_to_decimal_string_internal(obj, NULL, writer,
|
|
NULL, NULL);
|
|
else
|
|
return long_format_binary(obj, base, alternate, NULL, writer,
|
|
NULL, NULL);
|
|
}
|
|
|
|
char*
|
|
_PyLong_FormatBytesWriter(_PyBytesWriter *writer, char *str,
|
|
PyObject *obj,
|
|
int base, int alternate)
|
|
{
|
|
char *str2;
|
|
int res;
|
|
str2 = str;
|
|
if (base == 10)
|
|
res = long_to_decimal_string_internal(obj, NULL, NULL,
|
|
writer, &str2);
|
|
else
|
|
res = long_format_binary(obj, base, alternate, NULL, NULL,
|
|
writer, &str2);
|
|
if (res < 0)
|
|
return NULL;
|
|
assert(str2 != NULL);
|
|
return str2;
|
|
}
|
|
|
|
/* Table of digit values for 8-bit string -> integer conversion.
|
|
* '0' maps to 0, ..., '9' maps to 9.
|
|
* 'a' and 'A' map to 10, ..., 'z' and 'Z' map to 35.
|
|
* All other indices map to 37.
|
|
* Note that when converting a base B string, a char c is a legitimate
|
|
* base B digit iff _PyLong_DigitValue[Py_CHARPyLong_MASK(c)] < B.
|
|
*/
|
|
unsigned char _PyLong_DigitValue[256] = {
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 37, 37, 37, 37, 37, 37,
|
|
37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
|
|
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37,
|
|
37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
|
|
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
|
|
};
|
|
|
|
/* *str points to the first digit in a string of base `base` digits. base
|
|
* is a power of 2 (2, 4, 8, 16, or 32). *str is set to point to the first
|
|
* non-digit (which may be *str!). A normalized int is returned.
|
|
* The point to this routine is that it takes time linear in the number of
|
|
* string characters.
|
|
*
|
|
* Return values:
|
|
* -1 on syntax error (exception needs to be set, *res is untouched)
|
|
* 0 else (exception may be set, in that case *res is set to NULL)
|
|
*/
|
|
static int
|
|
long_from_binary_base(const char **str, int base, PyLongObject **res)
|
|
{
|
|
const char *p = *str;
|
|
const char *start = p;
|
|
char prev = 0;
|
|
int digits = 0;
|
|
int bits_per_char;
|
|
Py_ssize_t n;
|
|
PyLongObject *z;
|
|
twodigits accum;
|
|
int bits_in_accum;
|
|
digit *pdigit;
|
|
|
|
assert(base >= 2 && base <= 32 && (base & (base - 1)) == 0);
|
|
n = base;
|
|
for (bits_per_char = -1; n; ++bits_per_char) {
|
|
n >>= 1;
|
|
}
|
|
/* count digits and set p to end-of-string */
|
|
while (_PyLong_DigitValue[Py_CHARMASK(*p)] < base || *p == '_') {
|
|
if (*p == '_') {
|
|
if (prev == '_') {
|
|
*str = p - 1;
|
|
return -1;
|
|
}
|
|
} else {
|
|
++digits;
|
|
}
|
|
prev = *p;
|
|
++p;
|
|
}
|
|
if (prev == '_') {
|
|
/* Trailing underscore not allowed. */
|
|
*str = p - 1;
|
|
return -1;
|
|
}
|
|
|
|
*str = p;
|
|
/* n <- # of Python digits needed, = ceiling(n/PyLong_SHIFT). */
|
|
n = digits * bits_per_char + PyLong_SHIFT - 1;
|
|
if (n / bits_per_char < p - start) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"int string too large to convert");
|
|
*res = NULL;
|
|
return 0;
|
|
}
|
|
n = n / PyLong_SHIFT;
|
|
z = _PyLong_New(n);
|
|
if (z == NULL) {
|
|
*res = NULL;
|
|
return 0;
|
|
}
|
|
/* Read string from right, and fill in int from left; i.e.,
|
|
* from least to most significant in both.
|
|
*/
|
|
accum = 0;
|
|
bits_in_accum = 0;
|
|
pdigit = z->ob_digit;
|
|
while (--p >= start) {
|
|
int k;
|
|
if (*p == '_') {
|
|
continue;
|
|
}
|
|
k = (int)_PyLong_DigitValue[Py_CHARMASK(*p)];
|
|
assert(k >= 0 && k < base);
|
|
accum |= (twodigits)k << bits_in_accum;
|
|
bits_in_accum += bits_per_char;
|
|
if (bits_in_accum >= PyLong_SHIFT) {
|
|
*pdigit++ = (digit)(accum & PyLong_MASK);
|
|
assert(pdigit - z->ob_digit <= n);
|
|
accum >>= PyLong_SHIFT;
|
|
bits_in_accum -= PyLong_SHIFT;
|
|
assert(bits_in_accum < PyLong_SHIFT);
|
|
}
|
|
}
|
|
if (bits_in_accum) {
|
|
assert(bits_in_accum <= PyLong_SHIFT);
|
|
*pdigit++ = (digit)accum;
|
|
assert(pdigit - z->ob_digit <= n);
|
|
}
|
|
while (pdigit - z->ob_digit < n)
|
|
*pdigit++ = 0;
|
|
*res = long_normalize(z);
|
|
return 0;
|
|
}
|
|
|
|
/* Parses an int from a bytestring. Leading and trailing whitespace will be
|
|
* ignored.
|
|
*
|
|
* If successful, a PyLong object will be returned and 'pend' will be pointing
|
|
* to the first unused byte unless it's NULL.
|
|
*
|
|
* If unsuccessful, NULL will be returned.
|
|
*/
|
|
PyObject *
|
|
PyLong_FromString(const char *str, char **pend, int base)
|
|
{
|
|
int sign = 1, error_if_nonzero = 0;
|
|
const char *start, *orig_str = str;
|
|
PyLongObject *z = NULL;
|
|
PyObject *strobj;
|
|
Py_ssize_t slen;
|
|
|
|
if ((base != 0 && base < 2) || base > 36) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"int() arg 2 must be >= 2 and <= 36");
|
|
return NULL;
|
|
}
|
|
while (*str != '\0' && Py_ISSPACE(Py_CHARMASK(*str))) {
|
|
str++;
|
|
}
|
|
if (*str == '+') {
|
|
++str;
|
|
}
|
|
else if (*str == '-') {
|
|
++str;
|
|
sign = -1;
|
|
}
|
|
if (base == 0) {
|
|
if (str[0] != '0') {
|
|
base = 10;
|
|
}
|
|
else if (str[1] == 'x' || str[1] == 'X') {
|
|
base = 16;
|
|
}
|
|
else if (str[1] == 'o' || str[1] == 'O') {
|
|
base = 8;
|
|
}
|
|
else if (str[1] == 'b' || str[1] == 'B') {
|
|
base = 2;
|
|
}
|
|
else {
|
|
/* "old" (C-style) octal literal, now invalid.
|
|
it might still be zero though */
|
|
error_if_nonzero = 1;
|
|
base = 10;
|
|
}
|
|
}
|
|
if (str[0] == '0' &&
|
|
((base == 16 && (str[1] == 'x' || str[1] == 'X')) ||
|
|
(base == 8 && (str[1] == 'o' || str[1] == 'O')) ||
|
|
(base == 2 && (str[1] == 'b' || str[1] == 'B')))) {
|
|
str += 2;
|
|
/* One underscore allowed here. */
|
|
if (*str == '_') {
|
|
++str;
|
|
}
|
|
}
|
|
if (str[0] == '_') {
|
|
/* May not start with underscores. */
|
|
goto onError;
|
|
}
|
|
|
|
start = str;
|
|
if ((base & (base - 1)) == 0) {
|
|
int res = long_from_binary_base(&str, base, &z);
|
|
if (res < 0) {
|
|
/* Syntax error. */
|
|
goto onError;
|
|
}
|
|
}
|
|
else {
|
|
/***
|
|
Binary bases can be converted in time linear in the number of digits, because
|
|
Python's representation base is binary. Other bases (including decimal!) use
|
|
the simple quadratic-time algorithm below, complicated by some speed tricks.
|
|
|
|
First some math: the largest integer that can be expressed in N base-B digits
|
|
is B**N-1. Consequently, if we have an N-digit input in base B, the worst-
|
|
case number of Python digits needed to hold it is the smallest integer n s.t.
|
|
|
|
BASE**n-1 >= B**N-1 [or, adding 1 to both sides]
|
|
BASE**n >= B**N [taking logs to base BASE]
|
|
n >= log(B**N)/log(BASE) = N * log(B)/log(BASE)
|
|
|
|
The static array log_base_BASE[base] == log(base)/log(BASE) so we can compute
|
|
this quickly. A Python int with that much space is reserved near the start,
|
|
and the result is computed into it.
|
|
|
|
The input string is actually treated as being in base base**i (i.e., i digits
|
|
are processed at a time), where two more static arrays hold:
|
|
|
|
convwidth_base[base] = the largest integer i such that base**i <= BASE
|
|
convmultmax_base[base] = base ** convwidth_base[base]
|
|
|
|
The first of these is the largest i such that i consecutive input digits
|
|
must fit in a single Python digit. The second is effectively the input
|
|
base we're really using.
|
|
|
|
Viewing the input as a sequence <c0, c1, ..., c_n-1> of digits in base
|
|
convmultmax_base[base], the result is "simply"
|
|
|
|
(((c0*B + c1)*B + c2)*B + c3)*B + ... ))) + c_n-1
|
|
|
|
where B = convmultmax_base[base].
|
|
|
|
Error analysis: as above, the number of Python digits `n` needed is worst-
|
|
case
|
|
|
|
n >= N * log(B)/log(BASE)
|
|
|
|
where `N` is the number of input digits in base `B`. This is computed via
|
|
|
|
size_z = (Py_ssize_t)((scan - str) * log_base_BASE[base]) + 1;
|
|
|
|
below. Two numeric concerns are how much space this can waste, and whether
|
|
the computed result can be too small. To be concrete, assume BASE = 2**15,
|
|
which is the default (and it's unlikely anyone changes that).
|
|
|
|
Waste isn't a problem: provided the first input digit isn't 0, the difference
|
|
between the worst-case input with N digits and the smallest input with N
|
|
digits is about a factor of B, but B is small compared to BASE so at most
|
|
one allocated Python digit can remain unused on that count. If
|
|
N*log(B)/log(BASE) is mathematically an exact integer, then truncating that
|
|
and adding 1 returns a result 1 larger than necessary. However, that can't
|
|
happen: whenever B is a power of 2, long_from_binary_base() is called
|
|
instead, and it's impossible for B**i to be an integer power of 2**15 when
|
|
B is not a power of 2 (i.e., it's impossible for N*log(B)/log(BASE) to be
|
|
an exact integer when B is not a power of 2, since B**i has a prime factor
|
|
other than 2 in that case, but (2**15)**j's only prime factor is 2).
|
|
|
|
The computed result can be too small if the true value of N*log(B)/log(BASE)
|
|
is a little bit larger than an exact integer, but due to roundoff errors (in
|
|
computing log(B), log(BASE), their quotient, and/or multiplying that by N)
|
|
yields a numeric result a little less than that integer. Unfortunately, "how
|
|
close can a transcendental function get to an integer over some range?"
|
|
questions are generally theoretically intractable. Computer analysis via
|
|
continued fractions is practical: expand log(B)/log(BASE) via continued
|
|
fractions, giving a sequence i/j of "the best" rational approximations. Then
|
|
j*log(B)/log(BASE) is approximately equal to (the integer) i. This shows that
|
|
we can get very close to being in trouble, but very rarely. For example,
|
|
76573 is a denominator in one of the continued-fraction approximations to
|
|
log(10)/log(2**15), and indeed:
|
|
|
|
>>> log(10)/log(2**15)*76573
|
|
16958.000000654003
|
|
|
|
is very close to an integer. If we were working with IEEE single-precision,
|
|
rounding errors could kill us. Finding worst cases in IEEE double-precision
|
|
requires better-than-double-precision log() functions, and Tim didn't bother.
|
|
Instead the code checks to see whether the allocated space is enough as each
|
|
new Python digit is added, and copies the whole thing to a larger int if not.
|
|
This should happen extremely rarely, and in fact I don't have a test case
|
|
that triggers it(!). Instead the code was tested by artificially allocating
|
|
just 1 digit at the start, so that the copying code was exercised for every
|
|
digit beyond the first.
|
|
***/
|
|
twodigits c; /* current input character */
|
|
Py_ssize_t size_z;
|
|
int digits = 0;
|
|
int i;
|
|
int convwidth;
|
|
twodigits convmultmax, convmult;
|
|
digit *pz, *pzstop;
|
|
const char *scan, *lastdigit;
|
|
char prev = 0;
|
|
|
|
static double log_base_BASE[37] = {0.0e0,};
|
|
static int convwidth_base[37] = {0,};
|
|
static twodigits convmultmax_base[37] = {0,};
|
|
|
|
if (log_base_BASE[base] == 0.0) {
|
|
twodigits convmax = base;
|
|
int i = 1;
|
|
|
|
log_base_BASE[base] = (log((double)base) /
|
|
log((double)PyLong_BASE));
|
|
for (;;) {
|
|
twodigits next = convmax * base;
|
|
if (next > PyLong_BASE) {
|
|
break;
|
|
}
|
|
convmax = next;
|
|
++i;
|
|
}
|
|
convmultmax_base[base] = convmax;
|
|
assert(i > 0);
|
|
convwidth_base[base] = i;
|
|
}
|
|
|
|
/* Find length of the string of numeric characters. */
|
|
scan = str;
|
|
lastdigit = str;
|
|
|
|
while (_PyLong_DigitValue[Py_CHARMASK(*scan)] < base || *scan == '_') {
|
|
if (*scan == '_') {
|
|
if (prev == '_') {
|
|
/* Only one underscore allowed. */
|
|
str = lastdigit + 1;
|
|
goto onError;
|
|
}
|
|
}
|
|
else {
|
|
++digits;
|
|
lastdigit = scan;
|
|
}
|
|
prev = *scan;
|
|
++scan;
|
|
}
|
|
if (prev == '_') {
|
|
/* Trailing underscore not allowed. */
|
|
/* Set error pointer to first underscore. */
|
|
str = lastdigit + 1;
|
|
goto onError;
|
|
}
|
|
|
|
/* Create an int object that can contain the largest possible
|
|
* integer with this base and length. Note that there's no
|
|
* need to initialize z->ob_digit -- no slot is read up before
|
|
* being stored into.
|
|
*/
|
|
size_z = (Py_ssize_t)(digits * log_base_BASE[base]) + 1;
|
|
/* Uncomment next line to test exceedingly rare copy code */
|
|
/* size_z = 1; */
|
|
assert(size_z > 0);
|
|
z = _PyLong_New(size_z);
|
|
if (z == NULL) {
|
|
return NULL;
|
|
}
|
|
Py_SIZE(z) = 0;
|
|
|
|
/* `convwidth` consecutive input digits are treated as a single
|
|
* digit in base `convmultmax`.
|
|
*/
|
|
convwidth = convwidth_base[base];
|
|
convmultmax = convmultmax_base[base];
|
|
|
|
/* Work ;-) */
|
|
while (str < scan) {
|
|
if (*str == '_') {
|
|
str++;
|
|
continue;
|
|
}
|
|
/* grab up to convwidth digits from the input string */
|
|
c = (digit)_PyLong_DigitValue[Py_CHARMASK(*str++)];
|
|
for (i = 1; i < convwidth && str != scan; ++str) {
|
|
if (*str == '_') {
|
|
continue;
|
|
}
|
|
i++;
|
|
c = (twodigits)(c * base +
|
|
(int)_PyLong_DigitValue[Py_CHARMASK(*str)]);
|
|
assert(c < PyLong_BASE);
|
|
}
|
|
|
|
convmult = convmultmax;
|
|
/* Calculate the shift only if we couldn't get
|
|
* convwidth digits.
|
|
*/
|
|
if (i != convwidth) {
|
|
convmult = base;
|
|
for ( ; i > 1; --i) {
|
|
convmult *= base;
|
|
}
|
|
}
|
|
|
|
/* Multiply z by convmult, and add c. */
|
|
pz = z->ob_digit;
|
|
pzstop = pz + Py_SIZE(z);
|
|
for (; pz < pzstop; ++pz) {
|
|
c += (twodigits)*pz * convmult;
|
|
*pz = (digit)(c & PyLong_MASK);
|
|
c >>= PyLong_SHIFT;
|
|
}
|
|
/* carry off the current end? */
|
|
if (c) {
|
|
assert(c < PyLong_BASE);
|
|
if (Py_SIZE(z) < size_z) {
|
|
*pz = (digit)c;
|
|
++Py_SIZE(z);
|
|
}
|
|
else {
|
|
PyLongObject *tmp;
|
|
/* Extremely rare. Get more space. */
|
|
assert(Py_SIZE(z) == size_z);
|
|
tmp = _PyLong_New(size_z + 1);
|
|
if (tmp == NULL) {
|
|
Py_DECREF(z);
|
|
return NULL;
|
|
}
|
|
memcpy(tmp->ob_digit,
|
|
z->ob_digit,
|
|
sizeof(digit) * size_z);
|
|
Py_DECREF(z);
|
|
z = tmp;
|
|
z->ob_digit[size_z] = (digit)c;
|
|
++size_z;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (z == NULL) {
|
|
return NULL;
|
|
}
|
|
if (error_if_nonzero) {
|
|
/* reset the base to 0, else the exception message
|
|
doesn't make too much sense */
|
|
base = 0;
|
|
if (Py_SIZE(z) != 0) {
|
|
goto onError;
|
|
}
|
|
/* there might still be other problems, therefore base
|
|
remains zero here for the same reason */
|
|
}
|
|
if (str == start) {
|
|
goto onError;
|
|
}
|
|
if (sign < 0) {
|
|
Py_SIZE(z) = -(Py_SIZE(z));
|
|
}
|
|
while (*str && Py_ISSPACE(Py_CHARMASK(*str))) {
|
|
str++;
|
|
}
|
|
if (*str != '\0') {
|
|
goto onError;
|
|
}
|
|
long_normalize(z);
|
|
z = maybe_small_long(z);
|
|
if (z == NULL) {
|
|
return NULL;
|
|
}
|
|
if (pend != NULL) {
|
|
*pend = (char *)str;
|
|
}
|
|
return (PyObject *) z;
|
|
|
|
onError:
|
|
if (pend != NULL) {
|
|
*pend = (char *)str;
|
|
}
|
|
Py_XDECREF(z);
|
|
slen = strlen(orig_str) < 200 ? strlen(orig_str) : 200;
|
|
strobj = PyUnicode_FromStringAndSize(orig_str, slen);
|
|
if (strobj == NULL) {
|
|
return NULL;
|
|
}
|
|
PyErr_Format(PyExc_ValueError,
|
|
"invalid literal for int() with base %d: %.200R",
|
|
base, strobj);
|
|
Py_DECREF(strobj);
|
|
return NULL;
|
|
}
|
|
|
|
/* Since PyLong_FromString doesn't have a length parameter,
|
|
* check here for possible NULs in the string.
|
|
*
|
|
* Reports an invalid literal as a bytes object.
|
|
*/
|
|
PyObject *
|
|
_PyLong_FromBytes(const char *s, Py_ssize_t len, int base)
|
|
{
|
|
PyObject *result, *strobj;
|
|
char *end = NULL;
|
|
|
|
result = PyLong_FromString(s, &end, base);
|
|
if (end == NULL || (result != NULL && end == s + len))
|
|
return result;
|
|
Py_XDECREF(result);
|
|
strobj = PyBytes_FromStringAndSize(s, Py_MIN(len, 200));
|
|
if (strobj != NULL) {
|
|
PyErr_Format(PyExc_ValueError,
|
|
"invalid literal for int() with base %d: %.200R",
|
|
base, strobj);
|
|
Py_DECREF(strobj);
|
|
}
|
|
return NULL;
|
|
}
|
|
|
|
PyObject *
|
|
PyLong_FromUnicode(Py_UNICODE *u, Py_ssize_t length, int base)
|
|
{
|
|
PyObject *v, *unicode = PyUnicode_FromWideChar(u, length);
|
|
if (unicode == NULL)
|
|
return NULL;
|
|
v = PyLong_FromUnicodeObject(unicode, base);
|
|
Py_DECREF(unicode);
|
|
return v;
|
|
}
|
|
|
|
PyObject *
|
|
PyLong_FromUnicodeObject(PyObject *u, int base)
|
|
{
|
|
PyObject *result, *asciidig;
|
|
const char *buffer;
|
|
char *end = NULL;
|
|
Py_ssize_t buflen;
|
|
|
|
asciidig = _PyUnicode_TransformDecimalAndSpaceToASCII(u);
|
|
if (asciidig == NULL)
|
|
return NULL;
|
|
buffer = PyUnicode_AsUTF8AndSize(asciidig, &buflen);
|
|
if (buffer == NULL) {
|
|
Py_DECREF(asciidig);
|
|
if (!PyErr_ExceptionMatches(PyExc_UnicodeEncodeError))
|
|
return NULL;
|
|
}
|
|
else {
|
|
result = PyLong_FromString(buffer, &end, base);
|
|
if (end == NULL || (result != NULL && end == buffer + buflen)) {
|
|
Py_DECREF(asciidig);
|
|
return result;
|
|
}
|
|
Py_DECREF(asciidig);
|
|
Py_XDECREF(result);
|
|
}
|
|
PyErr_Format(PyExc_ValueError,
|
|
"invalid literal for int() with base %d: %.200R",
|
|
base, u);
|
|
return NULL;
|
|
}
|
|
|
|
/* forward */
|
|
static PyLongObject *x_divrem
|
|
(PyLongObject *, PyLongObject *, PyLongObject **);
|
|
static PyObject *long_long(PyObject *v);
|
|
|
|
/* Int division with remainder, top-level routine */
|
|
|
|
static int
|
|
long_divrem(PyLongObject *a, PyLongObject *b,
|
|
PyLongObject **pdiv, PyLongObject **prem)
|
|
{
|
|
Py_ssize_t size_a = Py_ABS(Py_SIZE(a)), size_b = Py_ABS(Py_SIZE(b));
|
|
PyLongObject *z;
|
|
|
|
if (size_b == 0) {
|
|
PyErr_SetString(PyExc_ZeroDivisionError,
|
|
"integer division or modulo by zero");
|
|
return -1;
|
|
}
|
|
if (size_a < size_b ||
|
|
(size_a == size_b &&
|
|
a->ob_digit[size_a-1] < b->ob_digit[size_b-1])) {
|
|
/* |a| < |b|. */
|
|
*prem = (PyLongObject *)long_long((PyObject *)a);
|
|
if (*prem == NULL) {
|
|
return -1;
|
|
}
|
|
Py_INCREF(_PyLong_Zero);
|
|
*pdiv = (PyLongObject*)_PyLong_Zero;
|
|
return 0;
|
|
}
|
|
if (size_b == 1) {
|
|
digit rem = 0;
|
|
z = divrem1(a, b->ob_digit[0], &rem);
|
|
if (z == NULL)
|
|
return -1;
|
|
*prem = (PyLongObject *) PyLong_FromLong((long)rem);
|
|
if (*prem == NULL) {
|
|
Py_DECREF(z);
|
|
return -1;
|
|
}
|
|
}
|
|
else {
|
|
z = x_divrem(a, b, prem);
|
|
if (z == NULL)
|
|
return -1;
|
|
}
|
|
/* Set the signs.
|
|
The quotient z has the sign of a*b;
|
|
the remainder r has the sign of a,
|
|
so a = b*z + r. */
|
|
if ((Py_SIZE(a) < 0) != (Py_SIZE(b) < 0)) {
|
|
_PyLong_Negate(&z);
|
|
if (z == NULL) {
|
|
Py_CLEAR(*prem);
|
|
return -1;
|
|
}
|
|
}
|
|
if (Py_SIZE(a) < 0 && Py_SIZE(*prem) != 0) {
|
|
_PyLong_Negate(prem);
|
|
if (*prem == NULL) {
|
|
Py_DECREF(z);
|
|
Py_CLEAR(*prem);
|
|
return -1;
|
|
}
|
|
}
|
|
*pdiv = maybe_small_long(z);
|
|
return 0;
|
|
}
|
|
|
|
/* Unsigned int division with remainder -- the algorithm. The arguments v1
|
|
and w1 should satisfy 2 <= Py_ABS(Py_SIZE(w1)) <= Py_ABS(Py_SIZE(v1)). */
|
|
|
|
static PyLongObject *
|
|
x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
|
|
{
|
|
PyLongObject *v, *w, *a;
|
|
Py_ssize_t i, k, size_v, size_w;
|
|
int d;
|
|
digit wm1, wm2, carry, q, r, vtop, *v0, *vk, *w0, *ak;
|
|
twodigits vv;
|
|
sdigit zhi;
|
|
stwodigits z;
|
|
|
|
/* We follow Knuth [The Art of Computer Programming, Vol. 2 (3rd
|
|
edn.), section 4.3.1, Algorithm D], except that we don't explicitly
|
|
handle the special case when the initial estimate q for a quotient
|
|
digit is >= PyLong_BASE: the max value for q is PyLong_BASE+1, and
|
|
that won't overflow a digit. */
|
|
|
|
/* allocate space; w will also be used to hold the final remainder */
|
|
size_v = Py_ABS(Py_SIZE(v1));
|
|
size_w = Py_ABS(Py_SIZE(w1));
|
|
assert(size_v >= size_w && size_w >= 2); /* Assert checks by div() */
|
|
v = _PyLong_New(size_v+1);
|
|
if (v == NULL) {
|
|
*prem = NULL;
|
|
return NULL;
|
|
}
|
|
w = _PyLong_New(size_w);
|
|
if (w == NULL) {
|
|
Py_DECREF(v);
|
|
*prem = NULL;
|
|
return NULL;
|
|
}
|
|
|
|
/* normalize: shift w1 left so that its top digit is >= PyLong_BASE/2.
|
|
shift v1 left by the same amount. Results go into w and v. */
|
|
d = PyLong_SHIFT - bits_in_digit(w1->ob_digit[size_w-1]);
|
|
carry = v_lshift(w->ob_digit, w1->ob_digit, size_w, d);
|
|
assert(carry == 0);
|
|
carry = v_lshift(v->ob_digit, v1->ob_digit, size_v, d);
|
|
if (carry != 0 || v->ob_digit[size_v-1] >= w->ob_digit[size_w-1]) {
|
|
v->ob_digit[size_v] = carry;
|
|
size_v++;
|
|
}
|
|
|
|
/* Now v->ob_digit[size_v-1] < w->ob_digit[size_w-1], so quotient has
|
|
at most (and usually exactly) k = size_v - size_w digits. */
|
|
k = size_v - size_w;
|
|
assert(k >= 0);
|
|
a = _PyLong_New(k);
|
|
if (a == NULL) {
|
|
Py_DECREF(w);
|
|
Py_DECREF(v);
|
|
*prem = NULL;
|
|
return NULL;
|
|
}
|
|
v0 = v->ob_digit;
|
|
w0 = w->ob_digit;
|
|
wm1 = w0[size_w-1];
|
|
wm2 = w0[size_w-2];
|
|
for (vk = v0+k, ak = a->ob_digit + k; vk-- > v0;) {
|
|
/* inner loop: divide vk[0:size_w+1] by w0[0:size_w], giving
|
|
single-digit quotient q, remainder in vk[0:size_w]. */
|
|
|
|
SIGCHECK({
|
|
Py_DECREF(a);
|
|
Py_DECREF(w);
|
|
Py_DECREF(v);
|
|
*prem = NULL;
|
|
return NULL;
|
|
});
|
|
|
|
/* estimate quotient digit q; may overestimate by 1 (rare) */
|
|
vtop = vk[size_w];
|
|
assert(vtop <= wm1);
|
|
vv = ((twodigits)vtop << PyLong_SHIFT) | vk[size_w-1];
|
|
q = (digit)(vv / wm1);
|
|
r = (digit)(vv - (twodigits)wm1 * q); /* r = vv % wm1 */
|
|
while ((twodigits)wm2 * q > (((twodigits)r << PyLong_SHIFT)
|
|
| vk[size_w-2])) {
|
|
--q;
|
|
r += wm1;
|
|
if (r >= PyLong_BASE)
|
|
break;
|
|
}
|
|
assert(q <= PyLong_BASE);
|
|
|
|
/* subtract q*w0[0:size_w] from vk[0:size_w+1] */
|
|
zhi = 0;
|
|
for (i = 0; i < size_w; ++i) {
|
|
/* invariants: -PyLong_BASE <= -q <= zhi <= 0;
|
|
-PyLong_BASE * q <= z < PyLong_BASE */
|
|
z = (sdigit)vk[i] + zhi -
|
|
(stwodigits)q * (stwodigits)w0[i];
|
|
vk[i] = (digit)z & PyLong_MASK;
|
|
zhi = (sdigit)Py_ARITHMETIC_RIGHT_SHIFT(stwodigits,
|
|
z, PyLong_SHIFT);
|
|
}
|
|
|
|
/* add w back if q was too large (this branch taken rarely) */
|
|
assert((sdigit)vtop + zhi == -1 || (sdigit)vtop + zhi == 0);
|
|
if ((sdigit)vtop + zhi < 0) {
|
|
carry = 0;
|
|
for (i = 0; i < size_w; ++i) {
|
|
carry += vk[i] + w0[i];
|
|
vk[i] = carry & PyLong_MASK;
|
|
carry >>= PyLong_SHIFT;
|
|
}
|
|
--q;
|
|
}
|
|
|
|
/* store quotient digit */
|
|
assert(q < PyLong_BASE);
|
|
*--ak = q;
|
|
}
|
|
|
|
/* unshift remainder; we reuse w to store the result */
|
|
carry = v_rshift(w0, v0, size_w, d);
|
|
assert(carry==0);
|
|
Py_DECREF(v);
|
|
|
|
*prem = long_normalize(w);
|
|
return long_normalize(a);
|
|
}
|
|
|
|
/* For a nonzero PyLong a, express a in the form x * 2**e, with 0.5 <=
|
|
abs(x) < 1.0 and e >= 0; return x and put e in *e. Here x is
|
|
rounded to DBL_MANT_DIG significant bits using round-half-to-even.
|
|
If a == 0, return 0.0 and set *e = 0. If the resulting exponent
|
|
e is larger than PY_SSIZE_T_MAX, raise OverflowError and return
|
|
-1.0. */
|
|
|
|
/* attempt to define 2.0**DBL_MANT_DIG as a compile-time constant */
|
|
#if DBL_MANT_DIG == 53
|
|
#define EXP2_DBL_MANT_DIG 9007199254740992.0
|
|
#else
|
|
#define EXP2_DBL_MANT_DIG (ldexp(1.0, DBL_MANT_DIG))
|
|
#endif
|
|
|
|
double
|
|
_PyLong_Frexp(PyLongObject *a, Py_ssize_t *e)
|
|
{
|
|
Py_ssize_t a_size, a_bits, shift_digits, shift_bits, x_size;
|
|
/* See below for why x_digits is always large enough. */
|
|
digit rem, x_digits[2 + (DBL_MANT_DIG + 1) / PyLong_SHIFT];
|
|
double dx;
|
|
/* Correction term for round-half-to-even rounding. For a digit x,
|
|
"x + half_even_correction[x & 7]" gives x rounded to the nearest
|
|
multiple of 4, rounding ties to a multiple of 8. */
|
|
static const int half_even_correction[8] = {0, -1, -2, 1, 0, -1, 2, 1};
|
|
|
|
a_size = Py_ABS(Py_SIZE(a));
|
|
if (a_size == 0) {
|
|
/* Special case for 0: significand 0.0, exponent 0. */
|
|
*e = 0;
|
|
return 0.0;
|
|
}
|
|
a_bits = bits_in_digit(a->ob_digit[a_size-1]);
|
|
/* The following is an overflow-free version of the check
|
|
"if ((a_size - 1) * PyLong_SHIFT + a_bits > PY_SSIZE_T_MAX) ..." */
|
|
if (a_size >= (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 &&
|
|
(a_size > (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 ||
|
|
a_bits > (PY_SSIZE_T_MAX - 1) % PyLong_SHIFT + 1))
|
|
goto overflow;
|
|
a_bits = (a_size - 1) * PyLong_SHIFT + a_bits;
|
|
|
|
/* Shift the first DBL_MANT_DIG + 2 bits of a into x_digits[0:x_size]
|
|
(shifting left if a_bits <= DBL_MANT_DIG + 2).
|
|
|
|
Number of digits needed for result: write // for floor division.
|
|
Then if shifting left, we end up using
|
|
|
|
1 + a_size + (DBL_MANT_DIG + 2 - a_bits) // PyLong_SHIFT
|
|
|
|
digits. If shifting right, we use
|
|
|
|
a_size - (a_bits - DBL_MANT_DIG - 2) // PyLong_SHIFT
|
|
|
|
digits. Using a_size = 1 + (a_bits - 1) // PyLong_SHIFT along with
|
|
the inequalities
|
|
|
|
m // PyLong_SHIFT + n // PyLong_SHIFT <= (m + n) // PyLong_SHIFT
|
|
m // PyLong_SHIFT - n // PyLong_SHIFT <=
|
|
1 + (m - n - 1) // PyLong_SHIFT,
|
|
|
|
valid for any integers m and n, we find that x_size satisfies
|
|
|
|
x_size <= 2 + (DBL_MANT_DIG + 1) // PyLong_SHIFT
|
|
|
|
in both cases.
|
|
*/
|
|
if (a_bits <= DBL_MANT_DIG + 2) {
|
|
shift_digits = (DBL_MANT_DIG + 2 - a_bits) / PyLong_SHIFT;
|
|
shift_bits = (DBL_MANT_DIG + 2 - a_bits) % PyLong_SHIFT;
|
|
x_size = 0;
|
|
while (x_size < shift_digits)
|
|
x_digits[x_size++] = 0;
|
|
rem = v_lshift(x_digits + x_size, a->ob_digit, a_size,
|
|
(int)shift_bits);
|
|
x_size += a_size;
|
|
x_digits[x_size++] = rem;
|
|
}
|
|
else {
|
|
shift_digits = (a_bits - DBL_MANT_DIG - 2) / PyLong_SHIFT;
|
|
shift_bits = (a_bits - DBL_MANT_DIG - 2) % PyLong_SHIFT;
|
|
rem = v_rshift(x_digits, a->ob_digit + shift_digits,
|
|
a_size - shift_digits, (int)shift_bits);
|
|
x_size = a_size - shift_digits;
|
|
/* For correct rounding below, we need the least significant
|
|
bit of x to be 'sticky' for this shift: if any of the bits
|
|
shifted out was nonzero, we set the least significant bit
|
|
of x. */
|
|
if (rem)
|
|
x_digits[0] |= 1;
|
|
else
|
|
while (shift_digits > 0)
|
|
if (a->ob_digit[--shift_digits]) {
|
|
x_digits[0] |= 1;
|
|
break;
|
|
}
|
|
}
|
|
assert(1 <= x_size && x_size <= (Py_ssize_t)Py_ARRAY_LENGTH(x_digits));
|
|
|
|
/* Round, and convert to double. */
|
|
x_digits[0] += half_even_correction[x_digits[0] & 7];
|
|
dx = x_digits[--x_size];
|
|
while (x_size > 0)
|
|
dx = dx * PyLong_BASE + x_digits[--x_size];
|
|
|
|
/* Rescale; make correction if result is 1.0. */
|
|
dx /= 4.0 * EXP2_DBL_MANT_DIG;
|
|
if (dx == 1.0) {
|
|
if (a_bits == PY_SSIZE_T_MAX)
|
|
goto overflow;
|
|
dx = 0.5;
|
|
a_bits += 1;
|
|
}
|
|
|
|
*e = a_bits;
|
|
return Py_SIZE(a) < 0 ? -dx : dx;
|
|
|
|
overflow:
|
|
/* exponent > PY_SSIZE_T_MAX */
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"huge integer: number of bits overflows a Py_ssize_t");
|
|
*e = 0;
|
|
return -1.0;
|
|
}
|
|
|
|
/* Get a C double from an int object. Rounds to the nearest double,
|
|
using the round-half-to-even rule in the case of a tie. */
|
|
|
|
double
|
|
PyLong_AsDouble(PyObject *v)
|
|
{
|
|
Py_ssize_t exponent;
|
|
double x;
|
|
|
|
if (v == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return -1.0;
|
|
}
|
|
if (!PyLong_Check(v)) {
|
|
PyErr_SetString(PyExc_TypeError, "an integer is required");
|
|
return -1.0;
|
|
}
|
|
if (Py_ABS(Py_SIZE(v)) <= 1) {
|
|
/* Fast path; single digit long (31 bits) will cast safely
|
|
to double. This improves performance of FP/long operations
|
|
by 20%.
|
|
*/
|
|
return (double)MEDIUM_VALUE((PyLongObject *)v);
|
|
}
|
|
x = _PyLong_Frexp((PyLongObject *)v, &exponent);
|
|
if ((x == -1.0 && PyErr_Occurred()) || exponent > DBL_MAX_EXP) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"int too large to convert to float");
|
|
return -1.0;
|
|
}
|
|
return ldexp(x, (int)exponent);
|
|
}
|
|
|
|
/* Methods */
|
|
|
|
static void
|
|
long_dealloc(PyObject *v)
|
|
{
|
|
Py_TYPE(v)->tp_free(v);
|
|
}
|
|
|
|
static int
|
|
long_compare(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
Py_ssize_t sign;
|
|
|
|
if (Py_SIZE(a) != Py_SIZE(b)) {
|
|
sign = Py_SIZE(a) - Py_SIZE(b);
|
|
}
|
|
else {
|
|
Py_ssize_t i = Py_ABS(Py_SIZE(a));
|
|
while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i])
|
|
;
|
|
if (i < 0)
|
|
sign = 0;
|
|
else {
|
|
sign = (sdigit)a->ob_digit[i] - (sdigit)b->ob_digit[i];
|
|
if (Py_SIZE(a) < 0)
|
|
sign = -sign;
|
|
}
|
|
}
|
|
return sign < 0 ? -1 : sign > 0 ? 1 : 0;
|
|
}
|
|
|
|
#define TEST_COND(cond) \
|
|
((cond) ? Py_True : Py_False)
|
|
|
|
static PyObject *
|
|
long_richcompare(PyObject *self, PyObject *other, int op)
|
|
{
|
|
int result;
|
|
PyObject *v;
|
|
CHECK_BINOP(self, other);
|
|
if (self == other)
|
|
result = 0;
|
|
else
|
|
result = long_compare((PyLongObject*)self, (PyLongObject*)other);
|
|
/* Convert the return value to a Boolean */
|
|
switch (op) {
|
|
case Py_EQ:
|
|
v = TEST_COND(result == 0);
|
|
break;
|
|
case Py_NE:
|
|
v = TEST_COND(result != 0);
|
|
break;
|
|
case Py_LE:
|
|
v = TEST_COND(result <= 0);
|
|
break;
|
|
case Py_GE:
|
|
v = TEST_COND(result >= 0);
|
|
break;
|
|
case Py_LT:
|
|
v = TEST_COND(result == -1);
|
|
break;
|
|
case Py_GT:
|
|
v = TEST_COND(result == 1);
|
|
break;
|
|
default:
|
|
PyErr_BadArgument();
|
|
return NULL;
|
|
}
|
|
Py_INCREF(v);
|
|
return v;
|
|
}
|
|
|
|
static Py_hash_t
|
|
long_hash(PyLongObject *v)
|
|
{
|
|
Py_uhash_t x;
|
|
Py_ssize_t i;
|
|
int sign;
|
|
|
|
i = Py_SIZE(v);
|
|
switch(i) {
|
|
case -1: return v->ob_digit[0]==1 ? -2 : -(sdigit)v->ob_digit[0];
|
|
case 0: return 0;
|
|
case 1: return v->ob_digit[0];
|
|
}
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -(i);
|
|
}
|
|
while (--i >= 0) {
|
|
/* Here x is a quantity in the range [0, _PyHASH_MODULUS); we
|
|
want to compute x * 2**PyLong_SHIFT + v->ob_digit[i] modulo
|
|
_PyHASH_MODULUS.
|
|
|
|
The computation of x * 2**PyLong_SHIFT % _PyHASH_MODULUS
|
|
amounts to a rotation of the bits of x. To see this, write
|
|
|
|
x * 2**PyLong_SHIFT = y * 2**_PyHASH_BITS + z
|
|
|
|
where y = x >> (_PyHASH_BITS - PyLong_SHIFT) gives the top
|
|
PyLong_SHIFT bits of x (those that are shifted out of the
|
|
original _PyHASH_BITS bits, and z = (x << PyLong_SHIFT) &
|
|
_PyHASH_MODULUS gives the bottom _PyHASH_BITS - PyLong_SHIFT
|
|
bits of x, shifted up. Then since 2**_PyHASH_BITS is
|
|
congruent to 1 modulo _PyHASH_MODULUS, y*2**_PyHASH_BITS is
|
|
congruent to y modulo _PyHASH_MODULUS. So
|
|
|
|
x * 2**PyLong_SHIFT = y + z (mod _PyHASH_MODULUS).
|
|
|
|
The right-hand side is just the result of rotating the
|
|
_PyHASH_BITS bits of x left by PyLong_SHIFT places; since
|
|
not all _PyHASH_BITS bits of x are 1s, the same is true
|
|
after rotation, so 0 <= y+z < _PyHASH_MODULUS and y + z is
|
|
the reduction of x*2**PyLong_SHIFT modulo
|
|
_PyHASH_MODULUS. */
|
|
x = ((x << PyLong_SHIFT) & _PyHASH_MODULUS) |
|
|
(x >> (_PyHASH_BITS - PyLong_SHIFT));
|
|
x += v->ob_digit[i];
|
|
if (x >= _PyHASH_MODULUS)
|
|
x -= _PyHASH_MODULUS;
|
|
}
|
|
x = x * sign;
|
|
if (x == (Py_uhash_t)-1)
|
|
x = (Py_uhash_t)-2;
|
|
return (Py_hash_t)x;
|
|
}
|
|
|
|
|
|
/* Add the absolute values of two integers. */
|
|
|
|
static PyLongObject *
|
|
x_add(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
Py_ssize_t size_a = Py_ABS(Py_SIZE(a)), size_b = Py_ABS(Py_SIZE(b));
|
|
PyLongObject *z;
|
|
Py_ssize_t i;
|
|
digit carry = 0;
|
|
|
|
/* Ensure a is the larger of the two: */
|
|
if (size_a < size_b) {
|
|
{ PyLongObject *temp = a; a = b; b = temp; }
|
|
{ Py_ssize_t size_temp = size_a;
|
|
size_a = size_b;
|
|
size_b = size_temp; }
|
|
}
|
|
z = _PyLong_New(size_a+1);
|
|
if (z == NULL)
|
|
return NULL;
|
|
for (i = 0; i < size_b; ++i) {
|
|
carry += a->ob_digit[i] + b->ob_digit[i];
|
|
z->ob_digit[i] = carry & PyLong_MASK;
|
|
carry >>= PyLong_SHIFT;
|
|
}
|
|
for (; i < size_a; ++i) {
|
|
carry += a->ob_digit[i];
|
|
z->ob_digit[i] = carry & PyLong_MASK;
|
|
carry >>= PyLong_SHIFT;
|
|
}
|
|
z->ob_digit[i] = carry;
|
|
return long_normalize(z);
|
|
}
|
|
|
|
/* Subtract the absolute values of two integers. */
|
|
|
|
static PyLongObject *
|
|
x_sub(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
Py_ssize_t size_a = Py_ABS(Py_SIZE(a)), size_b = Py_ABS(Py_SIZE(b));
|
|
PyLongObject *z;
|
|
Py_ssize_t i;
|
|
int sign = 1;
|
|
digit borrow = 0;
|
|
|
|
/* Ensure a is the larger of the two: */
|
|
if (size_a < size_b) {
|
|
sign = -1;
|
|
{ PyLongObject *temp = a; a = b; b = temp; }
|
|
{ Py_ssize_t size_temp = size_a;
|
|
size_a = size_b;
|
|
size_b = size_temp; }
|
|
}
|
|
else if (size_a == size_b) {
|
|
/* Find highest digit where a and b differ: */
|
|
i = size_a;
|
|
while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i])
|
|
;
|
|
if (i < 0)
|
|
return (PyLongObject *)PyLong_FromLong(0);
|
|
if (a->ob_digit[i] < b->ob_digit[i]) {
|
|
sign = -1;
|
|
{ PyLongObject *temp = a; a = b; b = temp; }
|
|
}
|
|
size_a = size_b = i+1;
|
|
}
|
|
z = _PyLong_New(size_a);
|
|
if (z == NULL)
|
|
return NULL;
|
|
for (i = 0; i < size_b; ++i) {
|
|
/* The following assumes unsigned arithmetic
|
|
works module 2**N for some N>PyLong_SHIFT. */
|
|
borrow = a->ob_digit[i] - b->ob_digit[i] - borrow;
|
|
z->ob_digit[i] = borrow & PyLong_MASK;
|
|
borrow >>= PyLong_SHIFT;
|
|
borrow &= 1; /* Keep only one sign bit */
|
|
}
|
|
for (; i < size_a; ++i) {
|
|
borrow = a->ob_digit[i] - borrow;
|
|
z->ob_digit[i] = borrow & PyLong_MASK;
|
|
borrow >>= PyLong_SHIFT;
|
|
borrow &= 1; /* Keep only one sign bit */
|
|
}
|
|
assert(borrow == 0);
|
|
if (sign < 0) {
|
|
Py_SIZE(z) = -Py_SIZE(z);
|
|
}
|
|
return long_normalize(z);
|
|
}
|
|
|
|
static PyObject *
|
|
long_add(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
PyLongObject *z;
|
|
|
|
CHECK_BINOP(a, b);
|
|
|
|
if (Py_ABS(Py_SIZE(a)) <= 1 && Py_ABS(Py_SIZE(b)) <= 1) {
|
|
return PyLong_FromLong(MEDIUM_VALUE(a) + MEDIUM_VALUE(b));
|
|
}
|
|
if (Py_SIZE(a) < 0) {
|
|
if (Py_SIZE(b) < 0) {
|
|
z = x_add(a, b);
|
|
if (z != NULL) {
|
|
/* x_add received at least one multiple-digit int,
|
|
and thus z must be a multiple-digit int.
|
|
That also means z is not an element of
|
|
small_ints, so negating it in-place is safe. */
|
|
assert(Py_REFCNT(z) == 1);
|
|
Py_SIZE(z) = -(Py_SIZE(z));
|
|
}
|
|
}
|
|
else
|
|
z = x_sub(b, a);
|
|
}
|
|
else {
|
|
if (Py_SIZE(b) < 0)
|
|
z = x_sub(a, b);
|
|
else
|
|
z = x_add(a, b);
|
|
}
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
static PyObject *
|
|
long_sub(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
PyLongObject *z;
|
|
|
|
CHECK_BINOP(a, b);
|
|
|
|
if (Py_ABS(Py_SIZE(a)) <= 1 && Py_ABS(Py_SIZE(b)) <= 1) {
|
|
return PyLong_FromLong(MEDIUM_VALUE(a) - MEDIUM_VALUE(b));
|
|
}
|
|
if (Py_SIZE(a) < 0) {
|
|
if (Py_SIZE(b) < 0)
|
|
z = x_sub(a, b);
|
|
else
|
|
z = x_add(a, b);
|
|
if (z != NULL) {
|
|
assert(Py_SIZE(z) == 0 || Py_REFCNT(z) == 1);
|
|
Py_SIZE(z) = -(Py_SIZE(z));
|
|
}
|
|
}
|
|
else {
|
|
if (Py_SIZE(b) < 0)
|
|
z = x_add(a, b);
|
|
else
|
|
z = x_sub(a, b);
|
|
}
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
/* Grade school multiplication, ignoring the signs.
|
|
* Returns the absolute value of the product, or NULL if error.
|
|
*/
|
|
static PyLongObject *
|
|
x_mul(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
PyLongObject *z;
|
|
Py_ssize_t size_a = Py_ABS(Py_SIZE(a));
|
|
Py_ssize_t size_b = Py_ABS(Py_SIZE(b));
|
|
Py_ssize_t i;
|
|
|
|
z = _PyLong_New(size_a + size_b);
|
|
if (z == NULL)
|
|
return NULL;
|
|
|
|
memset(z->ob_digit, 0, Py_SIZE(z) * sizeof(digit));
|
|
if (a == b) {
|
|
/* Efficient squaring per HAC, Algorithm 14.16:
|
|
* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
|
|
* Gives slightly less than a 2x speedup when a == b,
|
|
* via exploiting that each entry in the multiplication
|
|
* pyramid appears twice (except for the size_a squares).
|
|
*/
|
|
for (i = 0; i < size_a; ++i) {
|
|
twodigits carry;
|
|
twodigits f = a->ob_digit[i];
|
|
digit *pz = z->ob_digit + (i << 1);
|
|
digit *pa = a->ob_digit + i + 1;
|
|
digit *paend = a->ob_digit + size_a;
|
|
|
|
SIGCHECK({
|
|
Py_DECREF(z);
|
|
return NULL;
|
|
});
|
|
|
|
carry = *pz + f * f;
|
|
*pz++ = (digit)(carry & PyLong_MASK);
|
|
carry >>= PyLong_SHIFT;
|
|
assert(carry <= PyLong_MASK);
|
|
|
|
/* Now f is added in twice in each column of the
|
|
* pyramid it appears. Same as adding f<<1 once.
|
|
*/
|
|
f <<= 1;
|
|
while (pa < paend) {
|
|
carry += *pz + *pa++ * f;
|
|
*pz++ = (digit)(carry & PyLong_MASK);
|
|
carry >>= PyLong_SHIFT;
|
|
assert(carry <= (PyLong_MASK << 1));
|
|
}
|
|
if (carry) {
|
|
carry += *pz;
|
|
*pz++ = (digit)(carry & PyLong_MASK);
|
|
carry >>= PyLong_SHIFT;
|
|
}
|
|
if (carry)
|
|
*pz += (digit)(carry & PyLong_MASK);
|
|
assert((carry >> PyLong_SHIFT) == 0);
|
|
}
|
|
}
|
|
else { /* a is not the same as b -- gradeschool int mult */
|
|
for (i = 0; i < size_a; ++i) {
|
|
twodigits carry = 0;
|
|
twodigits f = a->ob_digit[i];
|
|
digit *pz = z->ob_digit + i;
|
|
digit *pb = b->ob_digit;
|
|
digit *pbend = b->ob_digit + size_b;
|
|
|
|
SIGCHECK({
|
|
Py_DECREF(z);
|
|
return NULL;
|
|
});
|
|
|
|
while (pb < pbend) {
|
|
carry += *pz + *pb++ * f;
|
|
*pz++ = (digit)(carry & PyLong_MASK);
|
|
carry >>= PyLong_SHIFT;
|
|
assert(carry <= PyLong_MASK);
|
|
}
|
|
if (carry)
|
|
*pz += (digit)(carry & PyLong_MASK);
|
|
assert((carry >> PyLong_SHIFT) == 0);
|
|
}
|
|
}
|
|
return long_normalize(z);
|
|
}
|
|
|
|
/* A helper for Karatsuba multiplication (k_mul).
|
|
Takes an int "n" and an integer "size" representing the place to
|
|
split, and sets low and high such that abs(n) == (high << size) + low,
|
|
viewing the shift as being by digits. The sign bit is ignored, and
|
|
the return values are >= 0.
|
|
Returns 0 on success, -1 on failure.
|
|
*/
|
|
static int
|
|
kmul_split(PyLongObject *n,
|
|
Py_ssize_t size,
|
|
PyLongObject **high,
|
|
PyLongObject **low)
|
|
{
|
|
PyLongObject *hi, *lo;
|
|
Py_ssize_t size_lo, size_hi;
|
|
const Py_ssize_t size_n = Py_ABS(Py_SIZE(n));
|
|
|
|
size_lo = Py_MIN(size_n, size);
|
|
size_hi = size_n - size_lo;
|
|
|
|
if ((hi = _PyLong_New(size_hi)) == NULL)
|
|
return -1;
|
|
if ((lo = _PyLong_New(size_lo)) == NULL) {
|
|
Py_DECREF(hi);
|
|
return -1;
|
|
}
|
|
|
|
memcpy(lo->ob_digit, n->ob_digit, size_lo * sizeof(digit));
|
|
memcpy(hi->ob_digit, n->ob_digit + size_lo, size_hi * sizeof(digit));
|
|
|
|
*high = long_normalize(hi);
|
|
*low = long_normalize(lo);
|
|
return 0;
|
|
}
|
|
|
|
static PyLongObject *k_lopsided_mul(PyLongObject *a, PyLongObject *b);
|
|
|
|
/* Karatsuba multiplication. Ignores the input signs, and returns the
|
|
* absolute value of the product (or NULL if error).
|
|
* See Knuth Vol. 2 Chapter 4.3.3 (Pp. 294-295).
|
|
*/
|
|
static PyLongObject *
|
|
k_mul(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
Py_ssize_t asize = Py_ABS(Py_SIZE(a));
|
|
Py_ssize_t bsize = Py_ABS(Py_SIZE(b));
|
|
PyLongObject *ah = NULL;
|
|
PyLongObject *al = NULL;
|
|
PyLongObject *bh = NULL;
|
|
PyLongObject *bl = NULL;
|
|
PyLongObject *ret = NULL;
|
|
PyLongObject *t1, *t2, *t3;
|
|
Py_ssize_t shift; /* the number of digits we split off */
|
|
Py_ssize_t i;
|
|
|
|
/* (ah*X+al)(bh*X+bl) = ah*bh*X*X + (ah*bl + al*bh)*X + al*bl
|
|
* Let k = (ah+al)*(bh+bl) = ah*bl + al*bh + ah*bh + al*bl
|
|
* Then the original product is
|
|
* ah*bh*X*X + (k - ah*bh - al*bl)*X + al*bl
|
|
* By picking X to be a power of 2, "*X" is just shifting, and it's
|
|
* been reduced to 3 multiplies on numbers half the size.
|
|
*/
|
|
|
|
/* We want to split based on the larger number; fiddle so that b
|
|
* is largest.
|
|
*/
|
|
if (asize > bsize) {
|
|
t1 = a;
|
|
a = b;
|
|
b = t1;
|
|
|
|
i = asize;
|
|
asize = bsize;
|
|
bsize = i;
|
|
}
|
|
|
|
/* Use gradeschool math when either number is too small. */
|
|
i = a == b ? KARATSUBA_SQUARE_CUTOFF : KARATSUBA_CUTOFF;
|
|
if (asize <= i) {
|
|
if (asize == 0)
|
|
return (PyLongObject *)PyLong_FromLong(0);
|
|
else
|
|
return x_mul(a, b);
|
|
}
|
|
|
|
/* If a is small compared to b, splitting on b gives a degenerate
|
|
* case with ah==0, and Karatsuba may be (even much) less efficient
|
|
* than "grade school" then. However, we can still win, by viewing
|
|
* b as a string of "big digits", each of width a->ob_size. That
|
|
* leads to a sequence of balanced calls to k_mul.
|
|
*/
|
|
if (2 * asize <= bsize)
|
|
return k_lopsided_mul(a, b);
|
|
|
|
/* Split a & b into hi & lo pieces. */
|
|
shift = bsize >> 1;
|
|
if (kmul_split(a, shift, &ah, &al) < 0) goto fail;
|
|
assert(Py_SIZE(ah) > 0); /* the split isn't degenerate */
|
|
|
|
if (a == b) {
|
|
bh = ah;
|
|
bl = al;
|
|
Py_INCREF(bh);
|
|
Py_INCREF(bl);
|
|
}
|
|
else if (kmul_split(b, shift, &bh, &bl) < 0) goto fail;
|
|
|
|
/* The plan:
|
|
* 1. Allocate result space (asize + bsize digits: that's always
|
|
* enough).
|
|
* 2. Compute ah*bh, and copy into result at 2*shift.
|
|
* 3. Compute al*bl, and copy into result at 0. Note that this
|
|
* can't overlap with #2.
|
|
* 4. Subtract al*bl from the result, starting at shift. This may
|
|
* underflow (borrow out of the high digit), but we don't care:
|
|
* we're effectively doing unsigned arithmetic mod
|
|
* BASE**(sizea + sizeb), and so long as the *final* result fits,
|
|
* borrows and carries out of the high digit can be ignored.
|
|
* 5. Subtract ah*bh from the result, starting at shift.
|
|
* 6. Compute (ah+al)*(bh+bl), and add it into the result starting
|
|
* at shift.
|
|
*/
|
|
|
|
/* 1. Allocate result space. */
|
|
ret = _PyLong_New(asize + bsize);
|
|
if (ret == NULL) goto fail;
|
|
#ifdef Py_DEBUG
|
|
/* Fill with trash, to catch reference to uninitialized digits. */
|
|
memset(ret->ob_digit, 0xDF, Py_SIZE(ret) * sizeof(digit));
|
|
#endif
|
|
|
|
/* 2. t1 <- ah*bh, and copy into high digits of result. */
|
|
if ((t1 = k_mul(ah, bh)) == NULL) goto fail;
|
|
assert(Py_SIZE(t1) >= 0);
|
|
assert(2*shift + Py_SIZE(t1) <= Py_SIZE(ret));
|
|
memcpy(ret->ob_digit + 2*shift, t1->ob_digit,
|
|
Py_SIZE(t1) * sizeof(digit));
|
|
|
|
/* Zero-out the digits higher than the ah*bh copy. */
|
|
i = Py_SIZE(ret) - 2*shift - Py_SIZE(t1);
|
|
if (i)
|
|
memset(ret->ob_digit + 2*shift + Py_SIZE(t1), 0,
|
|
i * sizeof(digit));
|
|
|
|
/* 3. t2 <- al*bl, and copy into the low digits. */
|
|
if ((t2 = k_mul(al, bl)) == NULL) {
|
|
Py_DECREF(t1);
|
|
goto fail;
|
|
}
|
|
assert(Py_SIZE(t2) >= 0);
|
|
assert(Py_SIZE(t2) <= 2*shift); /* no overlap with high digits */
|
|
memcpy(ret->ob_digit, t2->ob_digit, Py_SIZE(t2) * sizeof(digit));
|
|
|
|
/* Zero out remaining digits. */
|
|
i = 2*shift - Py_SIZE(t2); /* number of uninitialized digits */
|
|
if (i)
|
|
memset(ret->ob_digit + Py_SIZE(t2), 0, i * sizeof(digit));
|
|
|
|
/* 4 & 5. Subtract ah*bh (t1) and al*bl (t2). We do al*bl first
|
|
* because it's fresher in cache.
|
|
*/
|
|
i = Py_SIZE(ret) - shift; /* # digits after shift */
|
|
(void)v_isub(ret->ob_digit + shift, i, t2->ob_digit, Py_SIZE(t2));
|
|
Py_DECREF(t2);
|
|
|
|
(void)v_isub(ret->ob_digit + shift, i, t1->ob_digit, Py_SIZE(t1));
|
|
Py_DECREF(t1);
|
|
|
|
/* 6. t3 <- (ah+al)(bh+bl), and add into result. */
|
|
if ((t1 = x_add(ah, al)) == NULL) goto fail;
|
|
Py_DECREF(ah);
|
|
Py_DECREF(al);
|
|
ah = al = NULL;
|
|
|
|
if (a == b) {
|
|
t2 = t1;
|
|
Py_INCREF(t2);
|
|
}
|
|
else if ((t2 = x_add(bh, bl)) == NULL) {
|
|
Py_DECREF(t1);
|
|
goto fail;
|
|
}
|
|
Py_DECREF(bh);
|
|
Py_DECREF(bl);
|
|
bh = bl = NULL;
|
|
|
|
t3 = k_mul(t1, t2);
|
|
Py_DECREF(t1);
|
|
Py_DECREF(t2);
|
|
if (t3 == NULL) goto fail;
|
|
assert(Py_SIZE(t3) >= 0);
|
|
|
|
/* Add t3. It's not obvious why we can't run out of room here.
|
|
* See the (*) comment after this function.
|
|
*/
|
|
(void)v_iadd(ret->ob_digit + shift, i, t3->ob_digit, Py_SIZE(t3));
|
|
Py_DECREF(t3);
|
|
|
|
return long_normalize(ret);
|
|
|
|
fail:
|
|
Py_XDECREF(ret);
|
|
Py_XDECREF(ah);
|
|
Py_XDECREF(al);
|
|
Py_XDECREF(bh);
|
|
Py_XDECREF(bl);
|
|
return NULL;
|
|
}
|
|
|
|
/* (*) Why adding t3 can't "run out of room" above.
|
|
|
|
Let f(x) mean the floor of x and c(x) mean the ceiling of x. Some facts
|
|
to start with:
|
|
|
|
1. For any integer i, i = c(i/2) + f(i/2). In particular,
|
|
bsize = c(bsize/2) + f(bsize/2).
|
|
2. shift = f(bsize/2)
|
|
3. asize <= bsize
|
|
4. Since we call k_lopsided_mul if asize*2 <= bsize, asize*2 > bsize in this
|
|
routine, so asize > bsize/2 >= f(bsize/2) in this routine.
|
|
|
|
We allocated asize + bsize result digits, and add t3 into them at an offset
|
|
of shift. This leaves asize+bsize-shift allocated digit positions for t3
|
|
to fit into, = (by #1 and #2) asize + f(bsize/2) + c(bsize/2) - f(bsize/2) =
|
|
asize + c(bsize/2) available digit positions.
|
|
|
|
bh has c(bsize/2) digits, and bl at most f(size/2) digits. So bh+hl has
|
|
at most c(bsize/2) digits + 1 bit.
|
|
|
|
If asize == bsize, ah has c(bsize/2) digits, else ah has at most f(bsize/2)
|
|
digits, and al has at most f(bsize/2) digits in any case. So ah+al has at
|
|
most (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 1 bit.
|
|
|
|
The product (ah+al)*(bh+bl) therefore has at most
|
|
|
|
c(bsize/2) + (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits
|
|
|
|
and we have asize + c(bsize/2) available digit positions. We need to show
|
|
this is always enough. An instance of c(bsize/2) cancels out in both, so
|
|
the question reduces to whether asize digits is enough to hold
|
|
(asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits. If asize < bsize,
|
|
then we're asking whether asize digits >= f(bsize/2) digits + 2 bits. By #4,
|
|
asize is at least f(bsize/2)+1 digits, so this in turn reduces to whether 1
|
|
digit is enough to hold 2 bits. This is so since PyLong_SHIFT=15 >= 2. If
|
|
asize == bsize, then we're asking whether bsize digits is enough to hold
|
|
c(bsize/2) digits + 2 bits, or equivalently (by #1) whether f(bsize/2) digits
|
|
is enough to hold 2 bits. This is so if bsize >= 2, which holds because
|
|
bsize >= KARATSUBA_CUTOFF >= 2.
|
|
|
|
Note that since there's always enough room for (ah+al)*(bh+bl), and that's
|
|
clearly >= each of ah*bh and al*bl, there's always enough room to subtract
|
|
ah*bh and al*bl too.
|
|
*/
|
|
|
|
/* b has at least twice the digits of a, and a is big enough that Karatsuba
|
|
* would pay off *if* the inputs had balanced sizes. View b as a sequence
|
|
* of slices, each with a->ob_size digits, and multiply the slices by a,
|
|
* one at a time. This gives k_mul balanced inputs to work with, and is
|
|
* also cache-friendly (we compute one double-width slice of the result
|
|
* at a time, then move on, never backtracking except for the helpful
|
|
* single-width slice overlap between successive partial sums).
|
|
*/
|
|
static PyLongObject *
|
|
k_lopsided_mul(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
const Py_ssize_t asize = Py_ABS(Py_SIZE(a));
|
|
Py_ssize_t bsize = Py_ABS(Py_SIZE(b));
|
|
Py_ssize_t nbdone; /* # of b digits already multiplied */
|
|
PyLongObject *ret;
|
|
PyLongObject *bslice = NULL;
|
|
|
|
assert(asize > KARATSUBA_CUTOFF);
|
|
assert(2 * asize <= bsize);
|
|
|
|
/* Allocate result space, and zero it out. */
|
|
ret = _PyLong_New(asize + bsize);
|
|
if (ret == NULL)
|
|
return NULL;
|
|
memset(ret->ob_digit, 0, Py_SIZE(ret) * sizeof(digit));
|
|
|
|
/* Successive slices of b are copied into bslice. */
|
|
bslice = _PyLong_New(asize);
|
|
if (bslice == NULL)
|
|
goto fail;
|
|
|
|
nbdone = 0;
|
|
while (bsize > 0) {
|
|
PyLongObject *product;
|
|
const Py_ssize_t nbtouse = Py_MIN(bsize, asize);
|
|
|
|
/* Multiply the next slice of b by a. */
|
|
memcpy(bslice->ob_digit, b->ob_digit + nbdone,
|
|
nbtouse * sizeof(digit));
|
|
Py_SIZE(bslice) = nbtouse;
|
|
product = k_mul(a, bslice);
|
|
if (product == NULL)
|
|
goto fail;
|
|
|
|
/* Add into result. */
|
|
(void)v_iadd(ret->ob_digit + nbdone, Py_SIZE(ret) - nbdone,
|
|
product->ob_digit, Py_SIZE(product));
|
|
Py_DECREF(product);
|
|
|
|
bsize -= nbtouse;
|
|
nbdone += nbtouse;
|
|
}
|
|
|
|
Py_DECREF(bslice);
|
|
return long_normalize(ret);
|
|
|
|
fail:
|
|
Py_DECREF(ret);
|
|
Py_XDECREF(bslice);
|
|
return NULL;
|
|
}
|
|
|
|
static PyObject *
|
|
long_mul(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
PyLongObject *z;
|
|
|
|
CHECK_BINOP(a, b);
|
|
|
|
/* fast path for single-digit multiplication */
|
|
if (Py_ABS(Py_SIZE(a)) <= 1 && Py_ABS(Py_SIZE(b)) <= 1) {
|
|
stwodigits v = (stwodigits)(MEDIUM_VALUE(a)) * MEDIUM_VALUE(b);
|
|
return PyLong_FromLongLong((long long)v);
|
|
}
|
|
|
|
z = k_mul(a, b);
|
|
/* Negate if exactly one of the inputs is negative. */
|
|
if (((Py_SIZE(a) ^ Py_SIZE(b)) < 0) && z) {
|
|
_PyLong_Negate(&z);
|
|
if (z == NULL)
|
|
return NULL;
|
|
}
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
/* Fast modulo division for single-digit longs. */
|
|
static PyObject *
|
|
fast_mod(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
sdigit left = a->ob_digit[0];
|
|
sdigit right = b->ob_digit[0];
|
|
sdigit mod;
|
|
|
|
assert(Py_ABS(Py_SIZE(a)) == 1);
|
|
assert(Py_ABS(Py_SIZE(b)) == 1);
|
|
|
|
if (Py_SIZE(a) == Py_SIZE(b)) {
|
|
/* 'a' and 'b' have the same sign. */
|
|
mod = left % right;
|
|
}
|
|
else {
|
|
/* Either 'a' or 'b' is negative. */
|
|
mod = right - 1 - (left - 1) % right;
|
|
}
|
|
|
|
return PyLong_FromLong(mod * (sdigit)Py_SIZE(b));
|
|
}
|
|
|
|
/* Fast floor division for single-digit longs. */
|
|
static PyObject *
|
|
fast_floor_div(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
sdigit left = a->ob_digit[0];
|
|
sdigit right = b->ob_digit[0];
|
|
sdigit div;
|
|
|
|
assert(Py_ABS(Py_SIZE(a)) == 1);
|
|
assert(Py_ABS(Py_SIZE(b)) == 1);
|
|
|
|
if (Py_SIZE(a) == Py_SIZE(b)) {
|
|
/* 'a' and 'b' have the same sign. */
|
|
div = left / right;
|
|
}
|
|
else {
|
|
/* Either 'a' or 'b' is negative. */
|
|
div = -1 - (left - 1) / right;
|
|
}
|
|
|
|
return PyLong_FromLong(div);
|
|
}
|
|
|
|
/* The / and % operators are now defined in terms of divmod().
|
|
The expression a mod b has the value a - b*floor(a/b).
|
|
The long_divrem function gives the remainder after division of
|
|
|a| by |b|, with the sign of a. This is also expressed
|
|
as a - b*trunc(a/b), if trunc truncates towards zero.
|
|
Some examples:
|
|
a b a rem b a mod b
|
|
13 10 3 3
|
|
-13 10 -3 7
|
|
13 -10 3 -7
|
|
-13 -10 -3 -3
|
|
So, to get from rem to mod, we have to add b if a and b
|
|
have different signs. We then subtract one from the 'div'
|
|
part of the outcome to keep the invariant intact. */
|
|
|
|
/* Compute
|
|
* *pdiv, *pmod = divmod(v, w)
|
|
* NULL can be passed for pdiv or pmod, in which case that part of
|
|
* the result is simply thrown away. The caller owns a reference to
|
|
* each of these it requests (does not pass NULL for).
|
|
*/
|
|
static int
|
|
l_divmod(PyLongObject *v, PyLongObject *w,
|
|
PyLongObject **pdiv, PyLongObject **pmod)
|
|
{
|
|
PyLongObject *div, *mod;
|
|
|
|
if (Py_ABS(Py_SIZE(v)) == 1 && Py_ABS(Py_SIZE(w)) == 1) {
|
|
/* Fast path for single-digit longs */
|
|
div = NULL;
|
|
if (pdiv != NULL) {
|
|
div = (PyLongObject *)fast_floor_div(v, w);
|
|
if (div == NULL) {
|
|
return -1;
|
|
}
|
|
}
|
|
if (pmod != NULL) {
|
|
mod = (PyLongObject *)fast_mod(v, w);
|
|
if (mod == NULL) {
|
|
Py_XDECREF(div);
|
|
return -1;
|
|
}
|
|
*pmod = mod;
|
|
}
|
|
if (pdiv != NULL) {
|
|
/* We only want to set `*pdiv` when `*pmod` is
|
|
set successfully. */
|
|
*pdiv = div;
|
|
}
|
|
return 0;
|
|
}
|
|
if (long_divrem(v, w, &div, &mod) < 0)
|
|
return -1;
|
|
if ((Py_SIZE(mod) < 0 && Py_SIZE(w) > 0) ||
|
|
(Py_SIZE(mod) > 0 && Py_SIZE(w) < 0)) {
|
|
PyLongObject *temp;
|
|
temp = (PyLongObject *) long_add(mod, w);
|
|
Py_DECREF(mod);
|
|
mod = temp;
|
|
if (mod == NULL) {
|
|
Py_DECREF(div);
|
|
return -1;
|
|
}
|
|
temp = (PyLongObject *) long_sub(div, (PyLongObject *)_PyLong_One);
|
|
if (temp == NULL) {
|
|
Py_DECREF(mod);
|
|
Py_DECREF(div);
|
|
return -1;
|
|
}
|
|
Py_DECREF(div);
|
|
div = temp;
|
|
}
|
|
if (pdiv != NULL)
|
|
*pdiv = div;
|
|
else
|
|
Py_DECREF(div);
|
|
|
|
if (pmod != NULL)
|
|
*pmod = mod;
|
|
else
|
|
Py_DECREF(mod);
|
|
|
|
return 0;
|
|
}
|
|
|
|
static PyObject *
|
|
long_div(PyObject *a, PyObject *b)
|
|
{
|
|
PyLongObject *div;
|
|
|
|
CHECK_BINOP(a, b);
|
|
|
|
if (Py_ABS(Py_SIZE(a)) == 1 && Py_ABS(Py_SIZE(b)) == 1) {
|
|
return fast_floor_div((PyLongObject*)a, (PyLongObject*)b);
|
|
}
|
|
|
|
if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, NULL) < 0)
|
|
div = NULL;
|
|
return (PyObject *)div;
|
|
}
|
|
|
|
/* PyLong/PyLong -> float, with correctly rounded result. */
|
|
|
|
#define MANT_DIG_DIGITS (DBL_MANT_DIG / PyLong_SHIFT)
|
|
#define MANT_DIG_BITS (DBL_MANT_DIG % PyLong_SHIFT)
|
|
|
|
static PyObject *
|
|
long_true_divide(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b, *x;
|
|
Py_ssize_t a_size, b_size, shift, extra_bits, diff, x_size, x_bits;
|
|
digit mask, low;
|
|
int inexact, negate, a_is_small, b_is_small;
|
|
double dx, result;
|
|
|
|
CHECK_BINOP(v, w);
|
|
a = (PyLongObject *)v;
|
|
b = (PyLongObject *)w;
|
|
|
|
/*
|
|
Method in a nutshell:
|
|
|
|
0. reduce to case a, b > 0; filter out obvious underflow/overflow
|
|
1. choose a suitable integer 'shift'
|
|
2. use integer arithmetic to compute x = floor(2**-shift*a/b)
|
|
3. adjust x for correct rounding
|
|
4. convert x to a double dx with the same value
|
|
5. return ldexp(dx, shift).
|
|
|
|
In more detail:
|
|
|
|
0. For any a, a/0 raises ZeroDivisionError; for nonzero b, 0/b
|
|
returns either 0.0 or -0.0, depending on the sign of b. For a and
|
|
b both nonzero, ignore signs of a and b, and add the sign back in
|
|
at the end. Now write a_bits and b_bits for the bit lengths of a
|
|
and b respectively (that is, a_bits = 1 + floor(log_2(a)); likewise
|
|
for b). Then
|
|
|
|
2**(a_bits - b_bits - 1) < a/b < 2**(a_bits - b_bits + 1).
|
|
|
|
So if a_bits - b_bits > DBL_MAX_EXP then a/b > 2**DBL_MAX_EXP and
|
|
so overflows. Similarly, if a_bits - b_bits < DBL_MIN_EXP -
|
|
DBL_MANT_DIG - 1 then a/b underflows to 0. With these cases out of
|
|
the way, we can assume that
|
|
|
|
DBL_MIN_EXP - DBL_MANT_DIG - 1 <= a_bits - b_bits <= DBL_MAX_EXP.
|
|
|
|
1. The integer 'shift' is chosen so that x has the right number of
|
|
bits for a double, plus two or three extra bits that will be used
|
|
in the rounding decisions. Writing a_bits and b_bits for the
|
|
number of significant bits in a and b respectively, a
|
|
straightforward formula for shift is:
|
|
|
|
shift = a_bits - b_bits - DBL_MANT_DIG - 2
|
|
|
|
This is fine in the usual case, but if a/b is smaller than the
|
|
smallest normal float then it can lead to double rounding on an
|
|
IEEE 754 platform, giving incorrectly rounded results. So we
|
|
adjust the formula slightly. The actual formula used is:
|
|
|
|
shift = MAX(a_bits - b_bits, DBL_MIN_EXP) - DBL_MANT_DIG - 2
|
|
|
|
2. The quantity x is computed by first shifting a (left -shift bits
|
|
if shift <= 0, right shift bits if shift > 0) and then dividing by
|
|
b. For both the shift and the division, we keep track of whether
|
|
the result is inexact, in a flag 'inexact'; this information is
|
|
needed at the rounding stage.
|
|
|
|
With the choice of shift above, together with our assumption that
|
|
a_bits - b_bits >= DBL_MIN_EXP - DBL_MANT_DIG - 1, it follows
|
|
that x >= 1.
|
|
|
|
3. Now x * 2**shift <= a/b < (x+1) * 2**shift. We want to replace
|
|
this with an exactly representable float of the form
|
|
|
|
round(x/2**extra_bits) * 2**(extra_bits+shift).
|
|
|
|
For float representability, we need x/2**extra_bits <
|
|
2**DBL_MANT_DIG and extra_bits + shift >= DBL_MIN_EXP -
|
|
DBL_MANT_DIG. This translates to the condition:
|
|
|
|
extra_bits >= MAX(x_bits, DBL_MIN_EXP - shift) - DBL_MANT_DIG
|
|
|
|
To round, we just modify the bottom digit of x in-place; this can
|
|
end up giving a digit with value > PyLONG_MASK, but that's not a
|
|
problem since digits can hold values up to 2*PyLONG_MASK+1.
|
|
|
|
With the original choices for shift above, extra_bits will always
|
|
be 2 or 3. Then rounding under the round-half-to-even rule, we
|
|
round up iff the most significant of the extra bits is 1, and
|
|
either: (a) the computation of x in step 2 had an inexact result,
|
|
or (b) at least one other of the extra bits is 1, or (c) the least
|
|
significant bit of x (above those to be rounded) is 1.
|
|
|
|
4. Conversion to a double is straightforward; all floating-point
|
|
operations involved in the conversion are exact, so there's no
|
|
danger of rounding errors.
|
|
|
|
5. Use ldexp(x, shift) to compute x*2**shift, the final result.
|
|
The result will always be exactly representable as a double, except
|
|
in the case that it overflows. To avoid dependence on the exact
|
|
behaviour of ldexp on overflow, we check for overflow before
|
|
applying ldexp. The result of ldexp is adjusted for sign before
|
|
returning.
|
|
*/
|
|
|
|
/* Reduce to case where a and b are both positive. */
|
|
a_size = Py_ABS(Py_SIZE(a));
|
|
b_size = Py_ABS(Py_SIZE(b));
|
|
negate = (Py_SIZE(a) < 0) ^ (Py_SIZE(b) < 0);
|
|
if (b_size == 0) {
|
|
PyErr_SetString(PyExc_ZeroDivisionError,
|
|
"division by zero");
|
|
goto error;
|
|
}
|
|
if (a_size == 0)
|
|
goto underflow_or_zero;
|
|
|
|
/* Fast path for a and b small (exactly representable in a double).
|
|
Relies on floating-point division being correctly rounded; results
|
|
may be subject to double rounding on x86 machines that operate with
|
|
the x87 FPU set to 64-bit precision. */
|
|
a_is_small = a_size <= MANT_DIG_DIGITS ||
|
|
(a_size == MANT_DIG_DIGITS+1 &&
|
|
a->ob_digit[MANT_DIG_DIGITS] >> MANT_DIG_BITS == 0);
|
|
b_is_small = b_size <= MANT_DIG_DIGITS ||
|
|
(b_size == MANT_DIG_DIGITS+1 &&
|
|
b->ob_digit[MANT_DIG_DIGITS] >> MANT_DIG_BITS == 0);
|
|
if (a_is_small && b_is_small) {
|
|
double da, db;
|
|
da = a->ob_digit[--a_size];
|
|
while (a_size > 0)
|
|
da = da * PyLong_BASE + a->ob_digit[--a_size];
|
|
db = b->ob_digit[--b_size];
|
|
while (b_size > 0)
|
|
db = db * PyLong_BASE + b->ob_digit[--b_size];
|
|
result = da / db;
|
|
goto success;
|
|
}
|
|
|
|
/* Catch obvious cases of underflow and overflow */
|
|
diff = a_size - b_size;
|
|
if (diff > PY_SSIZE_T_MAX/PyLong_SHIFT - 1)
|
|
/* Extreme overflow */
|
|
goto overflow;
|
|
else if (diff < 1 - PY_SSIZE_T_MAX/PyLong_SHIFT)
|
|
/* Extreme underflow */
|
|
goto underflow_or_zero;
|
|
/* Next line is now safe from overflowing a Py_ssize_t */
|
|
diff = diff * PyLong_SHIFT + bits_in_digit(a->ob_digit[a_size - 1]) -
|
|
bits_in_digit(b->ob_digit[b_size - 1]);
|
|
/* Now diff = a_bits - b_bits. */
|
|
if (diff > DBL_MAX_EXP)
|
|
goto overflow;
|
|
else if (diff < DBL_MIN_EXP - DBL_MANT_DIG - 1)
|
|
goto underflow_or_zero;
|
|
|
|
/* Choose value for shift; see comments for step 1 above. */
|
|
shift = Py_MAX(diff, DBL_MIN_EXP) - DBL_MANT_DIG - 2;
|
|
|
|
inexact = 0;
|
|
|
|
/* x = abs(a * 2**-shift) */
|
|
if (shift <= 0) {
|
|
Py_ssize_t i, shift_digits = -shift / PyLong_SHIFT;
|
|
digit rem;
|
|
/* x = a << -shift */
|
|
if (a_size >= PY_SSIZE_T_MAX - 1 - shift_digits) {
|
|
/* In practice, it's probably impossible to end up
|
|
here. Both a and b would have to be enormous,
|
|
using close to SIZE_T_MAX bytes of memory each. */
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"intermediate overflow during division");
|
|
goto error;
|
|
}
|
|
x = _PyLong_New(a_size + shift_digits + 1);
|
|
if (x == NULL)
|
|
goto error;
|
|
for (i = 0; i < shift_digits; i++)
|
|
x->ob_digit[i] = 0;
|
|
rem = v_lshift(x->ob_digit + shift_digits, a->ob_digit,
|
|
a_size, -shift % PyLong_SHIFT);
|
|
x->ob_digit[a_size + shift_digits] = rem;
|
|
}
|
|
else {
|
|
Py_ssize_t shift_digits = shift / PyLong_SHIFT;
|
|
digit rem;
|
|
/* x = a >> shift */
|
|
assert(a_size >= shift_digits);
|
|
x = _PyLong_New(a_size - shift_digits);
|
|
if (x == NULL)
|
|
goto error;
|
|
rem = v_rshift(x->ob_digit, a->ob_digit + shift_digits,
|
|
a_size - shift_digits, shift % PyLong_SHIFT);
|
|
/* set inexact if any of the bits shifted out is nonzero */
|
|
if (rem)
|
|
inexact = 1;
|
|
while (!inexact && shift_digits > 0)
|
|
if (a->ob_digit[--shift_digits])
|
|
inexact = 1;
|
|
}
|
|
long_normalize(x);
|
|
x_size = Py_SIZE(x);
|
|
|
|
/* x //= b. If the remainder is nonzero, set inexact. We own the only
|
|
reference to x, so it's safe to modify it in-place. */
|
|
if (b_size == 1) {
|
|
digit rem = inplace_divrem1(x->ob_digit, x->ob_digit, x_size,
|
|
b->ob_digit[0]);
|
|
long_normalize(x);
|
|
if (rem)
|
|
inexact = 1;
|
|
}
|
|
else {
|
|
PyLongObject *div, *rem;
|
|
div = x_divrem(x, b, &rem);
|
|
Py_DECREF(x);
|
|
x = div;
|
|
if (x == NULL)
|
|
goto error;
|
|
if (Py_SIZE(rem))
|
|
inexact = 1;
|
|
Py_DECREF(rem);
|
|
}
|
|
x_size = Py_ABS(Py_SIZE(x));
|
|
assert(x_size > 0); /* result of division is never zero */
|
|
x_bits = (x_size-1)*PyLong_SHIFT+bits_in_digit(x->ob_digit[x_size-1]);
|
|
|
|
/* The number of extra bits that have to be rounded away. */
|
|
extra_bits = Py_MAX(x_bits, DBL_MIN_EXP - shift) - DBL_MANT_DIG;
|
|
assert(extra_bits == 2 || extra_bits == 3);
|
|
|
|
/* Round by directly modifying the low digit of x. */
|
|
mask = (digit)1 << (extra_bits - 1);
|
|
low = x->ob_digit[0] | inexact;
|
|
if ((low & mask) && (low & (3U*mask-1U)))
|
|
low += mask;
|
|
x->ob_digit[0] = low & ~(2U*mask-1U);
|
|
|
|
/* Convert x to a double dx; the conversion is exact. */
|
|
dx = x->ob_digit[--x_size];
|
|
while (x_size > 0)
|
|
dx = dx * PyLong_BASE + x->ob_digit[--x_size];
|
|
Py_DECREF(x);
|
|
|
|
/* Check whether ldexp result will overflow a double. */
|
|
if (shift + x_bits >= DBL_MAX_EXP &&
|
|
(shift + x_bits > DBL_MAX_EXP || dx == ldexp(1.0, (int)x_bits)))
|
|
goto overflow;
|
|
result = ldexp(dx, (int)shift);
|
|
|
|
success:
|
|
return PyFloat_FromDouble(negate ? -result : result);
|
|
|
|
underflow_or_zero:
|
|
return PyFloat_FromDouble(negate ? -0.0 : 0.0);
|
|
|
|
overflow:
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"integer division result too large for a float");
|
|
error:
|
|
return NULL;
|
|
}
|
|
|
|
static PyObject *
|
|
long_mod(PyObject *a, PyObject *b)
|
|
{
|
|
PyLongObject *mod;
|
|
|
|
CHECK_BINOP(a, b);
|
|
|
|
if (Py_ABS(Py_SIZE(a)) == 1 && Py_ABS(Py_SIZE(b)) == 1) {
|
|
return fast_mod((PyLongObject*)a, (PyLongObject*)b);
|
|
}
|
|
|
|
if (l_divmod((PyLongObject*)a, (PyLongObject*)b, NULL, &mod) < 0)
|
|
mod = NULL;
|
|
return (PyObject *)mod;
|
|
}
|
|
|
|
static PyObject *
|
|
long_divmod(PyObject *a, PyObject *b)
|
|
{
|
|
PyLongObject *div, *mod;
|
|
PyObject *z;
|
|
|
|
CHECK_BINOP(a, b);
|
|
|
|
if (l_divmod((PyLongObject*)a, (PyLongObject*)b, &div, &mod) < 0) {
|
|
return NULL;
|
|
}
|
|
z = PyTuple_New(2);
|
|
if (z != NULL) {
|
|
PyTuple_SetItem(z, 0, (PyObject *) div);
|
|
PyTuple_SetItem(z, 1, (PyObject *) mod);
|
|
}
|
|
else {
|
|
Py_DECREF(div);
|
|
Py_DECREF(mod);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
/* pow(v, w, x) */
|
|
static PyObject *
|
|
long_pow(PyObject *v, PyObject *w, PyObject *x)
|
|
{
|
|
PyLongObject *a, *b, *c; /* a,b,c = v,w,x */
|
|
int negativeOutput = 0; /* if x<0 return negative output */
|
|
|
|
PyLongObject *z = NULL; /* accumulated result */
|
|
Py_ssize_t i, j, k; /* counters */
|
|
PyLongObject *temp = NULL;
|
|
|
|
/* 5-ary values. If the exponent is large enough, table is
|
|
* precomputed so that table[i] == a**i % c for i in range(32).
|
|
*/
|
|
PyLongObject *table[32] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
|
|
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
|
|
|
|
/* a, b, c = v, w, x */
|
|
CHECK_BINOP(v, w);
|
|
a = (PyLongObject*)v; Py_INCREF(a);
|
|
b = (PyLongObject*)w; Py_INCREF(b);
|
|
if (PyLong_Check(x)) {
|
|
c = (PyLongObject *)x;
|
|
Py_INCREF(x);
|
|
}
|
|
else if (x == Py_None)
|
|
c = NULL;
|
|
else {
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
Py_RETURN_NOTIMPLEMENTED;
|
|
}
|
|
|
|
if (Py_SIZE(b) < 0) { /* if exponent is negative */
|
|
if (c) {
|
|
PyErr_SetString(PyExc_ValueError, "pow() 2nd argument "
|
|
"cannot be negative when 3rd argument specified");
|
|
goto Error;
|
|
}
|
|
else {
|
|
/* else return a float. This works because we know
|
|
that this calls float_pow() which converts its
|
|
arguments to double. */
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return PyFloat_Type.tp_as_number->nb_power(v, w, x);
|
|
}
|
|
}
|
|
|
|
if (c) {
|
|
/* if modulus == 0:
|
|
raise ValueError() */
|
|
if (Py_SIZE(c) == 0) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"pow() 3rd argument cannot be 0");
|
|
goto Error;
|
|
}
|
|
|
|
/* if modulus < 0:
|
|
negativeOutput = True
|
|
modulus = -modulus */
|
|
if (Py_SIZE(c) < 0) {
|
|
negativeOutput = 1;
|
|
temp = (PyLongObject *)_PyLong_Copy(c);
|
|
if (temp == NULL)
|
|
goto Error;
|
|
Py_DECREF(c);
|
|
c = temp;
|
|
temp = NULL;
|
|
_PyLong_Negate(&c);
|
|
if (c == NULL)
|
|
goto Error;
|
|
}
|
|
|
|
/* if modulus == 1:
|
|
return 0 */
|
|
if ((Py_SIZE(c) == 1) && (c->ob_digit[0] == 1)) {
|
|
z = (PyLongObject *)PyLong_FromLong(0L);
|
|
goto Done;
|
|
}
|
|
|
|
/* Reduce base by modulus in some cases:
|
|
1. If base < 0. Forcing the base non-negative makes things easier.
|
|
2. If base is obviously larger than the modulus. The "small
|
|
exponent" case later can multiply directly by base repeatedly,
|
|
while the "large exponent" case multiplies directly by base 31
|
|
times. It can be unboundedly faster to multiply by
|
|
base % modulus instead.
|
|
We could _always_ do this reduction, but l_divmod() isn't cheap,
|
|
so we only do it when it buys something. */
|
|
if (Py_SIZE(a) < 0 || Py_SIZE(a) > Py_SIZE(c)) {
|
|
if (l_divmod(a, c, NULL, &temp) < 0)
|
|
goto Error;
|
|
Py_DECREF(a);
|
|
a = temp;
|
|
temp = NULL;
|
|
}
|
|
}
|
|
|
|
/* At this point a, b, and c are guaranteed non-negative UNLESS
|
|
c is NULL, in which case a may be negative. */
|
|
|
|
z = (PyLongObject *)PyLong_FromLong(1L);
|
|
if (z == NULL)
|
|
goto Error;
|
|
|
|
/* Perform a modular reduction, X = X % c, but leave X alone if c
|
|
* is NULL.
|
|
*/
|
|
#define REDUCE(X) \
|
|
do { \
|
|
if (c != NULL) { \
|
|
if (l_divmod(X, c, NULL, &temp) < 0) \
|
|
goto Error; \
|
|
Py_XDECREF(X); \
|
|
X = temp; \
|
|
temp = NULL; \
|
|
} \
|
|
} while(0)
|
|
|
|
/* Multiply two values, then reduce the result:
|
|
result = X*Y % c. If c is NULL, skip the mod. */
|
|
#define MULT(X, Y, result) \
|
|
do { \
|
|
temp = (PyLongObject *)long_mul(X, Y); \
|
|
if (temp == NULL) \
|
|
goto Error; \
|
|
Py_XDECREF(result); \
|
|
result = temp; \
|
|
temp = NULL; \
|
|
REDUCE(result); \
|
|
} while(0)
|
|
|
|
if (Py_SIZE(b) <= FIVEARY_CUTOFF) {
|
|
/* Left-to-right binary exponentiation (HAC Algorithm 14.79) */
|
|
/* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf */
|
|
for (i = Py_SIZE(b) - 1; i >= 0; --i) {
|
|
digit bi = b->ob_digit[i];
|
|
|
|
for (j = (digit)1 << (PyLong_SHIFT-1); j != 0; j >>= 1) {
|
|
MULT(z, z, z);
|
|
if (bi & j)
|
|
MULT(z, a, z);
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
/* Left-to-right 5-ary exponentiation (HAC Algorithm 14.82) */
|
|
Py_INCREF(z); /* still holds 1L */
|
|
table[0] = z;
|
|
for (i = 1; i < 32; ++i)
|
|
MULT(table[i-1], a, table[i]);
|
|
|
|
for (i = Py_SIZE(b) - 1; i >= 0; --i) {
|
|
const digit bi = b->ob_digit[i];
|
|
|
|
for (j = PyLong_SHIFT - 5; j >= 0; j -= 5) {
|
|
const int index = (bi >> j) & 0x1f;
|
|
for (k = 0; k < 5; ++k)
|
|
MULT(z, z, z);
|
|
if (index)
|
|
MULT(z, table[index], z);
|
|
}
|
|
}
|
|
}
|
|
|
|
if (negativeOutput && (Py_SIZE(z) != 0)) {
|
|
temp = (PyLongObject *)long_sub(z, c);
|
|
if (temp == NULL)
|
|
goto Error;
|
|
Py_DECREF(z);
|
|
z = temp;
|
|
temp = NULL;
|
|
}
|
|
goto Done;
|
|
|
|
Error:
|
|
Py_CLEAR(z);
|
|
/* fall through */
|
|
Done:
|
|
if (Py_SIZE(b) > FIVEARY_CUTOFF) {
|
|
for (i = 0; i < 32; ++i)
|
|
Py_XDECREF(table[i]);
|
|
}
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
Py_XDECREF(c);
|
|
Py_XDECREF(temp);
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
static PyObject *
|
|
long_invert(PyLongObject *v)
|
|
{
|
|
/* Implement ~x as -(x+1) */
|
|
PyLongObject *x;
|
|
if (Py_ABS(Py_SIZE(v)) <=1)
|
|
return PyLong_FromLong(-(MEDIUM_VALUE(v)+1));
|
|
x = (PyLongObject *) long_add(v, (PyLongObject *)_PyLong_One);
|
|
if (x == NULL)
|
|
return NULL;
|
|
_PyLong_Negate(&x);
|
|
/* No need for maybe_small_long here, since any small
|
|
longs will have been caught in the Py_SIZE <= 1 fast path. */
|
|
return (PyObject *)x;
|
|
}
|
|
|
|
static PyObject *
|
|
long_neg(PyLongObject *v)
|
|
{
|
|
PyLongObject *z;
|
|
if (Py_ABS(Py_SIZE(v)) <= 1)
|
|
return PyLong_FromLong(-MEDIUM_VALUE(v));
|
|
z = (PyLongObject *)_PyLong_Copy(v);
|
|
if (z != NULL)
|
|
Py_SIZE(z) = -(Py_SIZE(v));
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
static PyObject *
|
|
long_abs(PyLongObject *v)
|
|
{
|
|
if (Py_SIZE(v) < 0)
|
|
return long_neg(v);
|
|
else
|
|
return long_long((PyObject *)v);
|
|
}
|
|
|
|
static int
|
|
long_bool(PyLongObject *v)
|
|
{
|
|
return Py_SIZE(v) != 0;
|
|
}
|
|
|
|
/* wordshift, remshift = divmod(shiftby, PyLong_SHIFT) */
|
|
static int
|
|
divmod_shift(PyLongObject *shiftby, Py_ssize_t *wordshift, digit *remshift)
|
|
{
|
|
assert(PyLong_Check((PyObject *)shiftby));
|
|
assert(Py_SIZE(shiftby) >= 0);
|
|
Py_ssize_t lshiftby = PyLong_AsSsize_t((PyObject *)shiftby);
|
|
if (lshiftby >= 0) {
|
|
*wordshift = lshiftby / PyLong_SHIFT;
|
|
*remshift = lshiftby % PyLong_SHIFT;
|
|
return 0;
|
|
}
|
|
/* PyLong_Check(shiftby) is true and Py_SIZE(shiftby) >= 0, so it must
|
|
be that PyLong_AsSsize_t raised an OverflowError. */
|
|
assert(PyErr_ExceptionMatches(PyExc_OverflowError));
|
|
PyErr_Clear();
|
|
PyLongObject *wordshift_obj = divrem1(shiftby, PyLong_SHIFT, remshift);
|
|
if (wordshift_obj == NULL) {
|
|
return -1;
|
|
}
|
|
*wordshift = PyLong_AsSsize_t((PyObject *)wordshift_obj);
|
|
Py_DECREF(wordshift_obj);
|
|
if (*wordshift >= 0 && *wordshift < PY_SSIZE_T_MAX / (Py_ssize_t)sizeof(digit)) {
|
|
return 0;
|
|
}
|
|
PyErr_Clear();
|
|
/* Clip the value. With such large wordshift the right shift
|
|
returns 0 and the left shift raises an error in _PyLong_New(). */
|
|
*wordshift = PY_SSIZE_T_MAX / sizeof(digit);
|
|
*remshift = 0;
|
|
return 0;
|
|
}
|
|
|
|
static PyObject *
|
|
long_rshift(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
PyLongObject *z = NULL;
|
|
Py_ssize_t newsize, wordshift, hishift, i, j;
|
|
digit loshift, lomask, himask;
|
|
|
|
CHECK_BINOP(a, b);
|
|
|
|
if (Py_SIZE(b) < 0) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"negative shift count");
|
|
return NULL;
|
|
}
|
|
|
|
if (Py_SIZE(a) < 0) {
|
|
/* Right shifting negative numbers is harder */
|
|
PyLongObject *a1, *a2;
|
|
a1 = (PyLongObject *) long_invert(a);
|
|
if (a1 == NULL)
|
|
return NULL;
|
|
a2 = (PyLongObject *) long_rshift(a1, b);
|
|
Py_DECREF(a1);
|
|
if (a2 == NULL)
|
|
return NULL;
|
|
z = (PyLongObject *) long_invert(a2);
|
|
Py_DECREF(a2);
|
|
}
|
|
else {
|
|
if (divmod_shift(b, &wordshift, &loshift) < 0)
|
|
return NULL;
|
|
newsize = Py_SIZE(a) - wordshift;
|
|
if (newsize <= 0)
|
|
return PyLong_FromLong(0);
|
|
hishift = PyLong_SHIFT - loshift;
|
|
lomask = ((digit)1 << hishift) - 1;
|
|
himask = PyLong_MASK ^ lomask;
|
|
z = _PyLong_New(newsize);
|
|
if (z == NULL)
|
|
return NULL;
|
|
for (i = 0, j = wordshift; i < newsize; i++, j++) {
|
|
z->ob_digit[i] = (a->ob_digit[j] >> loshift) & lomask;
|
|
if (i+1 < newsize)
|
|
z->ob_digit[i] |= (a->ob_digit[j+1] << hishift) & himask;
|
|
}
|
|
z = maybe_small_long(long_normalize(z));
|
|
}
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
static PyObject *
|
|
long_lshift(PyObject *v, PyObject *w)
|
|
{
|
|
/* This version due to Tim Peters */
|
|
PyLongObject *a = (PyLongObject*)v;
|
|
PyLongObject *b = (PyLongObject*)w;
|
|
PyLongObject *z = NULL;
|
|
Py_ssize_t oldsize, newsize, wordshift, i, j;
|
|
digit remshift;
|
|
twodigits accum;
|
|
|
|
CHECK_BINOP(a, b);
|
|
|
|
if (Py_SIZE(b) < 0) {
|
|
PyErr_SetString(PyExc_ValueError, "negative shift count");
|
|
return NULL;
|
|
}
|
|
if (Py_SIZE(a) == 0) {
|
|
return PyLong_FromLong(0);
|
|
}
|
|
|
|
if (divmod_shift(b, &wordshift, &remshift) < 0)
|
|
return NULL;
|
|
oldsize = Py_ABS(Py_SIZE(a));
|
|
newsize = oldsize + wordshift;
|
|
if (remshift)
|
|
++newsize;
|
|
z = _PyLong_New(newsize);
|
|
if (z == NULL)
|
|
return NULL;
|
|
if (Py_SIZE(a) < 0) {
|
|
assert(Py_REFCNT(z) == 1);
|
|
Py_SIZE(z) = -Py_SIZE(z);
|
|
}
|
|
for (i = 0; i < wordshift; i++)
|
|
z->ob_digit[i] = 0;
|
|
accum = 0;
|
|
for (i = wordshift, j = 0; j < oldsize; i++, j++) {
|
|
accum |= (twodigits)a->ob_digit[j] << remshift;
|
|
z->ob_digit[i] = (digit)(accum & PyLong_MASK);
|
|
accum >>= PyLong_SHIFT;
|
|
}
|
|
if (remshift)
|
|
z->ob_digit[newsize-1] = (digit)accum;
|
|
else
|
|
assert(!accum);
|
|
z = long_normalize(z);
|
|
return (PyObject *) maybe_small_long(z);
|
|
}
|
|
|
|
/* Compute two's complement of digit vector a[0:m], writing result to
|
|
z[0:m]. The digit vector a need not be normalized, but should not
|
|
be entirely zero. a and z may point to the same digit vector. */
|
|
|
|
static void
|
|
v_complement(digit *z, digit *a, Py_ssize_t m)
|
|
{
|
|
Py_ssize_t i;
|
|
digit carry = 1;
|
|
for (i = 0; i < m; ++i) {
|
|
carry += a[i] ^ PyLong_MASK;
|
|
z[i] = carry & PyLong_MASK;
|
|
carry >>= PyLong_SHIFT;
|
|
}
|
|
assert(carry == 0);
|
|
}
|
|
|
|
/* Bitwise and/xor/or operations */
|
|
|
|
static PyObject *
|
|
long_bitwise(PyLongObject *a,
|
|
char op, /* '&', '|', '^' */
|
|
PyLongObject *b)
|
|
{
|
|
int nega, negb, negz;
|
|
Py_ssize_t size_a, size_b, size_z, i;
|
|
PyLongObject *z;
|
|
|
|
/* Bitwise operations for negative numbers operate as though
|
|
on a two's complement representation. So convert arguments
|
|
from sign-magnitude to two's complement, and convert the
|
|
result back to sign-magnitude at the end. */
|
|
|
|
/* If a is negative, replace it by its two's complement. */
|
|
size_a = Py_ABS(Py_SIZE(a));
|
|
nega = Py_SIZE(a) < 0;
|
|
if (nega) {
|
|
z = _PyLong_New(size_a);
|
|
if (z == NULL)
|
|
return NULL;
|
|
v_complement(z->ob_digit, a->ob_digit, size_a);
|
|
a = z;
|
|
}
|
|
else
|
|
/* Keep reference count consistent. */
|
|
Py_INCREF(a);
|
|
|
|
/* Same for b. */
|
|
size_b = Py_ABS(Py_SIZE(b));
|
|
negb = Py_SIZE(b) < 0;
|
|
if (negb) {
|
|
z = _PyLong_New(size_b);
|
|
if (z == NULL) {
|
|
Py_DECREF(a);
|
|
return NULL;
|
|
}
|
|
v_complement(z->ob_digit, b->ob_digit, size_b);
|
|
b = z;
|
|
}
|
|
else
|
|
Py_INCREF(b);
|
|
|
|
/* Swap a and b if necessary to ensure size_a >= size_b. */
|
|
if (size_a < size_b) {
|
|
z = a; a = b; b = z;
|
|
size_z = size_a; size_a = size_b; size_b = size_z;
|
|
negz = nega; nega = negb; negb = negz;
|
|
}
|
|
|
|
/* JRH: The original logic here was to allocate the result value (z)
|
|
as the longer of the two operands. However, there are some cases
|
|
where the result is guaranteed to be shorter than that: AND of two
|
|
positives, OR of two negatives: use the shorter number. AND with
|
|
mixed signs: use the positive number. OR with mixed signs: use the
|
|
negative number.
|
|
*/
|
|
switch (op) {
|
|
case '^':
|
|
negz = nega ^ negb;
|
|
size_z = size_a;
|
|
break;
|
|
case '&':
|
|
negz = nega & negb;
|
|
size_z = negb ? size_a : size_b;
|
|
break;
|
|
case '|':
|
|
negz = nega | negb;
|
|
size_z = negb ? size_b : size_a;
|
|
break;
|
|
default:
|
|
PyErr_BadArgument();
|
|
return NULL;
|
|
}
|
|
|
|
/* We allow an extra digit if z is negative, to make sure that
|
|
the final two's complement of z doesn't overflow. */
|
|
z = _PyLong_New(size_z + negz);
|
|
if (z == NULL) {
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return NULL;
|
|
}
|
|
|
|
/* Compute digits for overlap of a and b. */
|
|
switch(op) {
|
|
case '&':
|
|
for (i = 0; i < size_b; ++i)
|
|
z->ob_digit[i] = a->ob_digit[i] & b->ob_digit[i];
|
|
break;
|
|
case '|':
|
|
for (i = 0; i < size_b; ++i)
|
|
z->ob_digit[i] = a->ob_digit[i] | b->ob_digit[i];
|
|
break;
|
|
case '^':
|
|
for (i = 0; i < size_b; ++i)
|
|
z->ob_digit[i] = a->ob_digit[i] ^ b->ob_digit[i];
|
|
break;
|
|
default:
|
|
PyErr_BadArgument();
|
|
return NULL;
|
|
}
|
|
|
|
/* Copy any remaining digits of a, inverting if necessary. */
|
|
if (op == '^' && negb)
|
|
for (; i < size_z; ++i)
|
|
z->ob_digit[i] = a->ob_digit[i] ^ PyLong_MASK;
|
|
else if (i < size_z)
|
|
memcpy(&z->ob_digit[i], &a->ob_digit[i],
|
|
(size_z-i)*sizeof(digit));
|
|
|
|
/* Complement result if negative. */
|
|
if (negz) {
|
|
Py_SIZE(z) = -(Py_SIZE(z));
|
|
z->ob_digit[size_z] = PyLong_MASK;
|
|
v_complement(z->ob_digit, z->ob_digit, size_z+1);
|
|
}
|
|
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *)maybe_small_long(long_normalize(z));
|
|
}
|
|
|
|
static PyObject *
|
|
long_and(PyObject *a, PyObject *b)
|
|
{
|
|
PyObject *c;
|
|
CHECK_BINOP(a, b);
|
|
c = long_bitwise((PyLongObject*)a, '&', (PyLongObject*)b);
|
|
return c;
|
|
}
|
|
|
|
static PyObject *
|
|
long_xor(PyObject *a, PyObject *b)
|
|
{
|
|
PyObject *c;
|
|
CHECK_BINOP(a, b);
|
|
c = long_bitwise((PyLongObject*)a, '^', (PyLongObject*)b);
|
|
return c;
|
|
}
|
|
|
|
static PyObject *
|
|
long_or(PyObject *a, PyObject *b)
|
|
{
|
|
PyObject *c;
|
|
CHECK_BINOP(a, b);
|
|
c = long_bitwise((PyLongObject*)a, '|', (PyLongObject*)b);
|
|
return c;
|
|
}
|
|
|
|
static PyObject *
|
|
long_long(PyObject *v)
|
|
{
|
|
if (PyLong_CheckExact(v))
|
|
Py_INCREF(v);
|
|
else
|
|
v = _PyLong_Copy((PyLongObject *)v);
|
|
return v;
|
|
}
|
|
|
|
PyObject *
|
|
_PyLong_GCD(PyObject *aarg, PyObject *barg)
|
|
{
|
|
PyLongObject *a, *b, *c = NULL, *d = NULL, *r;
|
|
stwodigits x, y, q, s, t, c_carry, d_carry;
|
|
stwodigits A, B, C, D, T;
|
|
int nbits, k;
|
|
Py_ssize_t size_a, size_b, alloc_a, alloc_b;
|
|
digit *a_digit, *b_digit, *c_digit, *d_digit, *a_end, *b_end;
|
|
|
|
a = (PyLongObject *)aarg;
|
|
b = (PyLongObject *)barg;
|
|
size_a = Py_SIZE(a);
|
|
size_b = Py_SIZE(b);
|
|
if (-2 <= size_a && size_a <= 2 && -2 <= size_b && size_b <= 2) {
|
|
Py_INCREF(a);
|
|
Py_INCREF(b);
|
|
goto simple;
|
|
}
|
|
|
|
/* Initial reduction: make sure that 0 <= b <= a. */
|
|
a = (PyLongObject *)long_abs(a);
|
|
if (a == NULL)
|
|
return NULL;
|
|
b = (PyLongObject *)long_abs(b);
|
|
if (b == NULL) {
|
|
Py_DECREF(a);
|
|
return NULL;
|
|
}
|
|
if (long_compare(a, b) < 0) {
|
|
r = a;
|
|
a = b;
|
|
b = r;
|
|
}
|
|
/* We now own references to a and b */
|
|
|
|
alloc_a = Py_SIZE(a);
|
|
alloc_b = Py_SIZE(b);
|
|
/* reduce until a fits into 2 digits */
|
|
while ((size_a = Py_SIZE(a)) > 2) {
|
|
nbits = bits_in_digit(a->ob_digit[size_a-1]);
|
|
/* extract top 2*PyLong_SHIFT bits of a into x, along with
|
|
corresponding bits of b into y */
|
|
size_b = Py_SIZE(b);
|
|
assert(size_b <= size_a);
|
|
if (size_b == 0) {
|
|
if (size_a < alloc_a) {
|
|
r = (PyLongObject *)_PyLong_Copy(a);
|
|
Py_DECREF(a);
|
|
}
|
|
else
|
|
r = a;
|
|
Py_DECREF(b);
|
|
Py_XDECREF(c);
|
|
Py_XDECREF(d);
|
|
return (PyObject *)r;
|
|
}
|
|
x = (((twodigits)a->ob_digit[size_a-1] << (2*PyLong_SHIFT-nbits)) |
|
|
((twodigits)a->ob_digit[size_a-2] << (PyLong_SHIFT-nbits)) |
|
|
(a->ob_digit[size_a-3] >> nbits));
|
|
|
|
y = ((size_b >= size_a - 2 ? b->ob_digit[size_a-3] >> nbits : 0) |
|
|
(size_b >= size_a - 1 ? (twodigits)b->ob_digit[size_a-2] << (PyLong_SHIFT-nbits) : 0) |
|
|
(size_b >= size_a ? (twodigits)b->ob_digit[size_a-1] << (2*PyLong_SHIFT-nbits) : 0));
|
|
|
|
/* inner loop of Lehmer's algorithm; A, B, C, D never grow
|
|
larger than PyLong_MASK during the algorithm. */
|
|
A = 1; B = 0; C = 0; D = 1;
|
|
for (k=0;; k++) {
|
|
if (y-C == 0)
|
|
break;
|
|
q = (x+(A-1))/(y-C);
|
|
s = B+q*D;
|
|
t = x-q*y;
|
|
if (s > t)
|
|
break;
|
|
x = y; y = t;
|
|
t = A+q*C; A = D; B = C; C = s; D = t;
|
|
}
|
|
|
|
if (k == 0) {
|
|
/* no progress; do a Euclidean step */
|
|
if (l_divmod(a, b, NULL, &r) < 0)
|
|
goto error;
|
|
Py_DECREF(a);
|
|
a = b;
|
|
b = r;
|
|
alloc_a = alloc_b;
|
|
alloc_b = Py_SIZE(b);
|
|
continue;
|
|
}
|
|
|
|
/*
|
|
a, b = A*b-B*a, D*a-C*b if k is odd
|
|
a, b = A*a-B*b, D*b-C*a if k is even
|
|
*/
|
|
if (k&1) {
|
|
T = -A; A = -B; B = T;
|
|
T = -C; C = -D; D = T;
|
|
}
|
|
if (c != NULL)
|
|
Py_SIZE(c) = size_a;
|
|
else if (Py_REFCNT(a) == 1) {
|
|
Py_INCREF(a);
|
|
c = a;
|
|
}
|
|
else {
|
|
alloc_a = size_a;
|
|
c = _PyLong_New(size_a);
|
|
if (c == NULL)
|
|
goto error;
|
|
}
|
|
|
|
if (d != NULL)
|
|
Py_SIZE(d) = size_a;
|
|
else if (Py_REFCNT(b) == 1 && size_a <= alloc_b) {
|
|
Py_INCREF(b);
|
|
d = b;
|
|
Py_SIZE(d) = size_a;
|
|
}
|
|
else {
|
|
alloc_b = size_a;
|
|
d = _PyLong_New(size_a);
|
|
if (d == NULL)
|
|
goto error;
|
|
}
|
|
a_end = a->ob_digit + size_a;
|
|
b_end = b->ob_digit + size_b;
|
|
|
|
/* compute new a and new b in parallel */
|
|
a_digit = a->ob_digit;
|
|
b_digit = b->ob_digit;
|
|
c_digit = c->ob_digit;
|
|
d_digit = d->ob_digit;
|
|
c_carry = 0;
|
|
d_carry = 0;
|
|
while (b_digit < b_end) {
|
|
c_carry += (A * *a_digit) - (B * *b_digit);
|
|
d_carry += (D * *b_digit++) - (C * *a_digit++);
|
|
*c_digit++ = (digit)(c_carry & PyLong_MASK);
|
|
*d_digit++ = (digit)(d_carry & PyLong_MASK);
|
|
c_carry >>= PyLong_SHIFT;
|
|
d_carry >>= PyLong_SHIFT;
|
|
}
|
|
while (a_digit < a_end) {
|
|
c_carry += A * *a_digit;
|
|
d_carry -= C * *a_digit++;
|
|
*c_digit++ = (digit)(c_carry & PyLong_MASK);
|
|
*d_digit++ = (digit)(d_carry & PyLong_MASK);
|
|
c_carry >>= PyLong_SHIFT;
|
|
d_carry >>= PyLong_SHIFT;
|
|
}
|
|
assert(c_carry == 0);
|
|
assert(d_carry == 0);
|
|
|
|
Py_INCREF(c);
|
|
Py_INCREF(d);
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
a = long_normalize(c);
|
|
b = long_normalize(d);
|
|
}
|
|
Py_XDECREF(c);
|
|
Py_XDECREF(d);
|
|
|
|
simple:
|
|
assert(Py_REFCNT(a) > 0);
|
|
assert(Py_REFCNT(b) > 0);
|
|
/* Issue #24999: use two shifts instead of ">> 2*PyLong_SHIFT" to avoid
|
|
undefined behaviour when LONG_MAX type is smaller than 60 bits */
|
|
#if LONG_MAX >> PyLong_SHIFT >> PyLong_SHIFT
|
|
/* a fits into a long, so b must too */
|
|
x = PyLong_AsLong((PyObject *)a);
|
|
y = PyLong_AsLong((PyObject *)b);
|
|
#elif PY_LLONG_MAX >> PyLong_SHIFT >> PyLong_SHIFT
|
|
x = PyLong_AsLongLong((PyObject *)a);
|
|
y = PyLong_AsLongLong((PyObject *)b);
|
|
#else
|
|
# error "_PyLong_GCD"
|
|
#endif
|
|
x = Py_ABS(x);
|
|
y = Py_ABS(y);
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
|
|
/* usual Euclidean algorithm for longs */
|
|
while (y != 0) {
|
|
t = y;
|
|
y = x % y;
|
|
x = t;
|
|
}
|
|
#if LONG_MAX >> PyLong_SHIFT >> PyLong_SHIFT
|
|
return PyLong_FromLong(x);
|
|
#elif PY_LLONG_MAX >> PyLong_SHIFT >> PyLong_SHIFT
|
|
return PyLong_FromLongLong(x);
|
|
#else
|
|
# error "_PyLong_GCD"
|
|
#endif
|
|
|
|
error:
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
Py_XDECREF(c);
|
|
Py_XDECREF(d);
|
|
return NULL;
|
|
}
|
|
|
|
static PyObject *
|
|
long_float(PyObject *v)
|
|
{
|
|
double result;
|
|
result = PyLong_AsDouble(v);
|
|
if (result == -1.0 && PyErr_Occurred())
|
|
return NULL;
|
|
return PyFloat_FromDouble(result);
|
|
}
|
|
|
|
static PyObject *
|
|
long_subtype_new(PyTypeObject *type, PyObject *x, PyObject *obase);
|
|
|
|
/*[clinic input]
|
|
@classmethod
|
|
int.__new__ as long_new
|
|
x: object(c_default="NULL") = 0
|
|
/
|
|
base as obase: object(c_default="NULL") = 10
|
|
[clinic start generated code]*/
|
|
|
|
static PyObject *
|
|
long_new_impl(PyTypeObject *type, PyObject *x, PyObject *obase)
|
|
/*[clinic end generated code: output=e47cfe777ab0f24c input=81c98f418af9eb6f]*/
|
|
{
|
|
Py_ssize_t base;
|
|
|
|
if (type != &PyLong_Type)
|
|
return long_subtype_new(type, x, obase); /* Wimp out */
|
|
if (x == NULL) {
|
|
if (obase != NULL) {
|
|
PyErr_SetString(PyExc_TypeError,
|
|
"int() missing string argument");
|
|
return NULL;
|
|
}
|
|
return PyLong_FromLong(0L);
|
|
}
|
|
if (obase == NULL)
|
|
return PyNumber_Long(x);
|
|
|
|
base = PyNumber_AsSsize_t(obase, NULL);
|
|
if (base == -1 && PyErr_Occurred())
|
|
return NULL;
|
|
if ((base != 0 && base < 2) || base > 36) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"int() base must be >= 2 and <= 36");
|
|
return NULL;
|
|
}
|
|
|
|
if (PyUnicode_Check(x))
|
|
return PyLong_FromUnicodeObject(x, (int)base);
|
|
else if (PyByteArray_Check(x) || PyBytes_Check(x)) {
|
|
char *string;
|
|
if (PyByteArray_Check(x))
|
|
string = PyByteArray_AS_STRING(x);
|
|
else
|
|
string = PyBytes_AS_STRING(x);
|
|
return _PyLong_FromBytes(string, Py_SIZE(x), (int)base);
|
|
}
|
|
else {
|
|
PyErr_SetString(PyExc_TypeError,
|
|
"int() can't convert non-string with explicit base");
|
|
return NULL;
|
|
}
|
|
}
|
|
|
|
/* Wimpy, slow approach to tp_new calls for subtypes of int:
|
|
first create a regular int from whatever arguments we got,
|
|
then allocate a subtype instance and initialize it from
|
|
the regular int. The regular int is then thrown away.
|
|
*/
|
|
static PyObject *
|
|
long_subtype_new(PyTypeObject *type, PyObject *x, PyObject *obase)
|
|
{
|
|
PyLongObject *tmp, *newobj;
|
|
Py_ssize_t i, n;
|
|
|
|
assert(PyType_IsSubtype(type, &PyLong_Type));
|
|
tmp = (PyLongObject *)long_new_impl(&PyLong_Type, x, obase);
|
|
if (tmp == NULL)
|
|
return NULL;
|
|
assert(PyLong_Check(tmp));
|
|
n = Py_SIZE(tmp);
|
|
if (n < 0)
|
|
n = -n;
|
|
newobj = (PyLongObject *)type->tp_alloc(type, n);
|
|
if (newobj == NULL) {
|
|
Py_DECREF(tmp);
|
|
return NULL;
|
|
}
|
|
assert(PyLong_Check(newobj));
|
|
Py_SIZE(newobj) = Py_SIZE(tmp);
|
|
for (i = 0; i < n; i++)
|
|
newobj->ob_digit[i] = tmp->ob_digit[i];
|
|
Py_DECREF(tmp);
|
|
return (PyObject *)newobj;
|
|
}
|
|
|
|
/*[clinic input]
|
|
int.__getnewargs__
|
|
[clinic start generated code]*/
|
|
|
|
static PyObject *
|
|
int___getnewargs___impl(PyObject *self)
|
|
/*[clinic end generated code: output=839a49de3f00b61b input=5904770ab1fb8c75]*/
|
|
{
|
|
return Py_BuildValue("(N)", _PyLong_Copy((PyLongObject *)self));
|
|
}
|
|
|
|
static PyObject *
|
|
long_get0(PyLongObject *v, void *context) {
|
|
return PyLong_FromLong(0L);
|
|
}
|
|
|
|
static PyObject *
|
|
long_get1(PyLongObject *v, void *context) {
|
|
return PyLong_FromLong(1L);
|
|
}
|
|
|
|
/*[clinic input]
|
|
int.__format__
|
|
|
|
format_spec: unicode
|
|
/
|
|
[clinic start generated code]*/
|
|
|
|
static PyObject *
|
|
int___format___impl(PyObject *self, PyObject *format_spec)
|
|
/*[clinic end generated code: output=b4929dee9ae18689 input=e31944a9b3e428b7]*/
|
|
{
|
|
_PyUnicodeWriter writer;
|
|
int ret;
|
|
|
|
_PyUnicodeWriter_Init(&writer);
|
|
ret = _PyLong_FormatAdvancedWriter(
|
|
&writer,
|
|
self,
|
|
format_spec, 0, PyUnicode_GET_LENGTH(format_spec));
|
|
if (ret == -1) {
|
|
_PyUnicodeWriter_Dealloc(&writer);
|
|
return NULL;
|
|
}
|
|
return _PyUnicodeWriter_Finish(&writer);
|
|
}
|
|
|
|
/* Return a pair (q, r) such that a = b * q + r, and
|
|
abs(r) <= abs(b)/2, with equality possible only if q is even.
|
|
In other words, q == a / b, rounded to the nearest integer using
|
|
round-half-to-even. */
|
|
|
|
PyObject *
|
|
_PyLong_DivmodNear(PyObject *a, PyObject *b)
|
|
{
|
|
PyLongObject *quo = NULL, *rem = NULL;
|
|
PyObject *twice_rem, *result, *temp;
|
|
int cmp, quo_is_odd, quo_is_neg;
|
|
|
|
/* Equivalent Python code:
|
|
|
|
def divmod_near(a, b):
|
|
q, r = divmod(a, b)
|
|
# round up if either r / b > 0.5, or r / b == 0.5 and q is odd.
|
|
# The expression r / b > 0.5 is equivalent to 2 * r > b if b is
|
|
# positive, 2 * r < b if b negative.
|
|
greater_than_half = 2*r > b if b > 0 else 2*r < b
|
|
exactly_half = 2*r == b
|
|
if greater_than_half or exactly_half and q % 2 == 1:
|
|
q += 1
|
|
r -= b
|
|
return q, r
|
|
|
|
*/
|
|
if (!PyLong_Check(a) || !PyLong_Check(b)) {
|
|
PyErr_SetString(PyExc_TypeError,
|
|
"non-integer arguments in division");
|
|
return NULL;
|
|
}
|
|
|
|
/* Do a and b have different signs? If so, quotient is negative. */
|
|
quo_is_neg = (Py_SIZE(a) < 0) != (Py_SIZE(b) < 0);
|
|
|
|
if (long_divrem((PyLongObject*)a, (PyLongObject*)b, &quo, &rem) < 0)
|
|
goto error;
|
|
|
|
/* compare twice the remainder with the divisor, to see
|
|
if we need to adjust the quotient and remainder */
|
|
twice_rem = long_lshift((PyObject *)rem, _PyLong_One);
|
|
if (twice_rem == NULL)
|
|
goto error;
|
|
if (quo_is_neg) {
|
|
temp = long_neg((PyLongObject*)twice_rem);
|
|
Py_DECREF(twice_rem);
|
|
twice_rem = temp;
|
|
if (twice_rem == NULL)
|
|
goto error;
|
|
}
|
|
cmp = long_compare((PyLongObject *)twice_rem, (PyLongObject *)b);
|
|
Py_DECREF(twice_rem);
|
|
|
|
quo_is_odd = Py_SIZE(quo) != 0 && ((quo->ob_digit[0] & 1) != 0);
|
|
if ((Py_SIZE(b) < 0 ? cmp < 0 : cmp > 0) || (cmp == 0 && quo_is_odd)) {
|
|
/* fix up quotient */
|
|
if (quo_is_neg)
|
|
temp = long_sub(quo, (PyLongObject *)_PyLong_One);
|
|
else
|
|
temp = long_add(quo, (PyLongObject *)_PyLong_One);
|
|
Py_DECREF(quo);
|
|
quo = (PyLongObject *)temp;
|
|
if (quo == NULL)
|
|
goto error;
|
|
/* and remainder */
|
|
if (quo_is_neg)
|
|
temp = long_add(rem, (PyLongObject *)b);
|
|
else
|
|
temp = long_sub(rem, (PyLongObject *)b);
|
|
Py_DECREF(rem);
|
|
rem = (PyLongObject *)temp;
|
|
if (rem == NULL)
|
|
goto error;
|
|
}
|
|
|
|
result = PyTuple_New(2);
|
|
if (result == NULL)
|
|
goto error;
|
|
|
|
/* PyTuple_SET_ITEM steals references */
|
|
PyTuple_SET_ITEM(result, 0, (PyObject *)quo);
|
|
PyTuple_SET_ITEM(result, 1, (PyObject *)rem);
|
|
return result;
|
|
|
|
error:
|
|
Py_XDECREF(quo);
|
|
Py_XDECREF(rem);
|
|
return NULL;
|
|
}
|
|
|
|
static PyObject *
|
|
long_round(PyObject *self, PyObject *args)
|
|
{
|
|
PyObject *o_ndigits=NULL, *temp, *result, *ndigits;
|
|
|
|
/* To round an integer m to the nearest 10**n (n positive), we make use of
|
|
* the divmod_near operation, defined by:
|
|
*
|
|
* divmod_near(a, b) = (q, r)
|
|
*
|
|
* where q is the nearest integer to the quotient a / b (the
|
|
* nearest even integer in the case of a tie) and r == a - q * b.
|
|
* Hence q * b = a - r is the nearest multiple of b to a,
|
|
* preferring even multiples in the case of a tie.
|
|
*
|
|
* So the nearest multiple of 10**n to m is:
|
|
*
|
|
* m - divmod_near(m, 10**n)[1].
|
|
*/
|
|
if (!PyArg_ParseTuple(args, "|O", &o_ndigits))
|
|
return NULL;
|
|
if (o_ndigits == NULL)
|
|
return long_long(self);
|
|
|
|
ndigits = PyNumber_Index(o_ndigits);
|
|
if (ndigits == NULL)
|
|
return NULL;
|
|
|
|
/* if ndigits >= 0 then no rounding is necessary; return self unchanged */
|
|
if (Py_SIZE(ndigits) >= 0) {
|
|
Py_DECREF(ndigits);
|
|
return long_long(self);
|
|
}
|
|
|
|
/* result = self - divmod_near(self, 10 ** -ndigits)[1] */
|
|
temp = long_neg((PyLongObject*)ndigits);
|
|
Py_DECREF(ndigits);
|
|
ndigits = temp;
|
|
if (ndigits == NULL)
|
|
return NULL;
|
|
|
|
result = PyLong_FromLong(10L);
|
|
if (result == NULL) {
|
|
Py_DECREF(ndigits);
|
|
return NULL;
|
|
}
|
|
|
|
temp = long_pow(result, ndigits, Py_None);
|
|
Py_DECREF(ndigits);
|
|
Py_DECREF(result);
|
|
result = temp;
|
|
if (result == NULL)
|
|
return NULL;
|
|
|
|
temp = _PyLong_DivmodNear(self, result);
|
|
Py_DECREF(result);
|
|
result = temp;
|
|
if (result == NULL)
|
|
return NULL;
|
|
|
|
temp = long_sub((PyLongObject *)self,
|
|
(PyLongObject *)PyTuple_GET_ITEM(result, 1));
|
|
Py_DECREF(result);
|
|
result = temp;
|
|
|
|
return result;
|
|
}
|
|
|
|
/*[clinic input]
|
|
int.__sizeof__ -> Py_ssize_t
|
|
|
|
Returns size in memory, in bytes.
|
|
[clinic start generated code]*/
|
|
|
|
static Py_ssize_t
|
|
int___sizeof___impl(PyObject *self)
|
|
/*[clinic end generated code: output=3303f008eaa6a0a5 input=9b51620c76fc4507]*/
|
|
{
|
|
Py_ssize_t res;
|
|
|
|
res = offsetof(PyLongObject, ob_digit) + Py_ABS(Py_SIZE(self))*sizeof(digit);
|
|
return res;
|
|
}
|
|
|
|
/*[clinic input]
|
|
int.bit_length
|
|
|
|
Number of bits necessary to represent self in binary.
|
|
|
|
>>> bin(37)
|
|
'0b100101'
|
|
>>> (37).bit_length()
|
|
6
|
|
[clinic start generated code]*/
|
|
|
|
static PyObject *
|
|
int_bit_length_impl(PyObject *self)
|
|
/*[clinic end generated code: output=fc1977c9353d6a59 input=e4eb7a587e849a32]*/
|
|
{
|
|
PyLongObject *result, *x, *y;
|
|
Py_ssize_t ndigits;
|
|
int msd_bits;
|
|
digit msd;
|
|
|
|
assert(self != NULL);
|
|
assert(PyLong_Check(self));
|
|
|
|
ndigits = Py_ABS(Py_SIZE(self));
|
|
if (ndigits == 0)
|
|
return PyLong_FromLong(0);
|
|
|
|
msd = ((PyLongObject *)self)->ob_digit[ndigits-1];
|
|
msd_bits = bits_in_digit(msd);
|
|
|
|
if (ndigits <= PY_SSIZE_T_MAX/PyLong_SHIFT)
|
|
return PyLong_FromSsize_t((ndigits-1)*PyLong_SHIFT + msd_bits);
|
|
|
|
/* expression above may overflow; use Python integers instead */
|
|
result = (PyLongObject *)PyLong_FromSsize_t(ndigits - 1);
|
|
if (result == NULL)
|
|
return NULL;
|
|
x = (PyLongObject *)PyLong_FromLong(PyLong_SHIFT);
|
|
if (x == NULL)
|
|
goto error;
|
|
y = (PyLongObject *)long_mul(result, x);
|
|
Py_DECREF(x);
|
|
if (y == NULL)
|
|
goto error;
|
|
Py_DECREF(result);
|
|
result = y;
|
|
|
|
x = (PyLongObject *)PyLong_FromLong((long)msd_bits);
|
|
if (x == NULL)
|
|
goto error;
|
|
y = (PyLongObject *)long_add(result, x);
|
|
Py_DECREF(x);
|
|
if (y == NULL)
|
|
goto error;
|
|
Py_DECREF(result);
|
|
result = y;
|
|
|
|
return (PyObject *)result;
|
|
|
|
error:
|
|
Py_DECREF(result);
|
|
return NULL;
|
|
}
|
|
|
|
#if 0
|
|
static PyObject *
|
|
long_is_finite(PyObject *v)
|
|
{
|
|
Py_RETURN_TRUE;
|
|
}
|
|
#endif
|
|
|
|
/*[clinic input]
|
|
int.to_bytes
|
|
|
|
length: Py_ssize_t
|
|
Length of bytes object to use. An OverflowError is raised if the
|
|
integer is not representable with the given number of bytes.
|
|
byteorder: unicode
|
|
The byte order used to represent the integer. If byteorder is 'big',
|
|
the most significant byte is at the beginning of the byte array. If
|
|
byteorder is 'little', the most significant byte is at the end of the
|
|
byte array. To request the native byte order of the host system, use
|
|
`sys.byteorder' as the byte order value.
|
|
*
|
|
signed as is_signed: bool = False
|
|
Determines whether two's complement is used to represent the integer.
|
|
If signed is False and a negative integer is given, an OverflowError
|
|
is raised.
|
|
|
|
Return an array of bytes representing an integer.
|
|
[clinic start generated code]*/
|
|
|
|
static PyObject *
|
|
int_to_bytes_impl(PyObject *self, Py_ssize_t length, PyObject *byteorder,
|
|
int is_signed)
|
|
/*[clinic end generated code: output=89c801df114050a3 input=ddac63f4c7bf414c]*/
|
|
{
|
|
int little_endian;
|
|
PyObject *bytes;
|
|
|
|
if (_PyUnicode_EqualToASCIIId(byteorder, &PyId_little))
|
|
little_endian = 1;
|
|
else if (_PyUnicode_EqualToASCIIId(byteorder, &PyId_big))
|
|
little_endian = 0;
|
|
else {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"byteorder must be either 'little' or 'big'");
|
|
return NULL;
|
|
}
|
|
|
|
if (length < 0) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"length argument must be non-negative");
|
|
return NULL;
|
|
}
|
|
|
|
bytes = PyBytes_FromStringAndSize(NULL, length);
|
|
if (bytes == NULL)
|
|
return NULL;
|
|
|
|
if (_PyLong_AsByteArray((PyLongObject *)self,
|
|
(unsigned char *)PyBytes_AS_STRING(bytes),
|
|
length, little_endian, is_signed) < 0) {
|
|
Py_DECREF(bytes);
|
|
return NULL;
|
|
}
|
|
|
|
return bytes;
|
|
}
|
|
|
|
/*[clinic input]
|
|
@classmethod
|
|
int.from_bytes
|
|
|
|
bytes as bytes_obj: object
|
|
Holds the array of bytes to convert. The argument must either
|
|
support the buffer protocol or be an iterable object producing bytes.
|
|
Bytes and bytearray are examples of built-in objects that support the
|
|
buffer protocol.
|
|
byteorder: unicode
|
|
The byte order used to represent the integer. If byteorder is 'big',
|
|
the most significant byte is at the beginning of the byte array. If
|
|
byteorder is 'little', the most significant byte is at the end of the
|
|
byte array. To request the native byte order of the host system, use
|
|
`sys.byteorder' as the byte order value.
|
|
*
|
|
signed as is_signed: bool = False
|
|
Indicates whether two's complement is used to represent the integer.
|
|
|
|
Return the integer represented by the given array of bytes.
|
|
[clinic start generated code]*/
|
|
|
|
static PyObject *
|
|
int_from_bytes_impl(PyTypeObject *type, PyObject *bytes_obj,
|
|
PyObject *byteorder, int is_signed)
|
|
/*[clinic end generated code: output=efc5d68e31f9314f input=cdf98332b6a821b0]*/
|
|
{
|
|
int little_endian;
|
|
PyObject *long_obj, *bytes;
|
|
|
|
if (_PyUnicode_EqualToASCIIId(byteorder, &PyId_little))
|
|
little_endian = 1;
|
|
else if (_PyUnicode_EqualToASCIIId(byteorder, &PyId_big))
|
|
little_endian = 0;
|
|
else {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"byteorder must be either 'little' or 'big'");
|
|
return NULL;
|
|
}
|
|
|
|
bytes = PyObject_Bytes(bytes_obj);
|
|
if (bytes == NULL)
|
|
return NULL;
|
|
|
|
long_obj = _PyLong_FromByteArray(
|
|
(unsigned char *)PyBytes_AS_STRING(bytes), Py_SIZE(bytes),
|
|
little_endian, is_signed);
|
|
Py_DECREF(bytes);
|
|
|
|
if (type != &PyLong_Type) {
|
|
Py_SETREF(long_obj, PyObject_CallFunctionObjArgs((PyObject *)type,
|
|
long_obj, NULL));
|
|
}
|
|
|
|
return long_obj;
|
|
}
|
|
|
|
static PyMethodDef long_methods[] = {
|
|
{"conjugate", (PyCFunction)long_long, METH_NOARGS,
|
|
"Returns self, the complex conjugate of any int."},
|
|
INT_BIT_LENGTH_METHODDEF
|
|
#if 0
|
|
{"is_finite", (PyCFunction)long_is_finite, METH_NOARGS,
|
|
"Returns always True."},
|
|
#endif
|
|
INT_TO_BYTES_METHODDEF
|
|
INT_FROM_BYTES_METHODDEF
|
|
{"__trunc__", (PyCFunction)long_long, METH_NOARGS,
|
|
"Truncating an Integral returns itself."},
|
|
{"__floor__", (PyCFunction)long_long, METH_NOARGS,
|
|
"Flooring an Integral returns itself."},
|
|
{"__ceil__", (PyCFunction)long_long, METH_NOARGS,
|
|
"Ceiling of an Integral returns itself."},
|
|
{"__round__", (PyCFunction)long_round, METH_VARARGS,
|
|
"Rounding an Integral returns itself.\n"
|
|
"Rounding with an ndigits argument also returns an integer."},
|
|
INT___GETNEWARGS___METHODDEF
|
|
INT___FORMAT___METHODDEF
|
|
INT___SIZEOF___METHODDEF
|
|
{NULL, NULL} /* sentinel */
|
|
};
|
|
|
|
static PyGetSetDef long_getset[] = {
|
|
{"real",
|
|
(getter)long_long, (setter)NULL,
|
|
"the real part of a complex number",
|
|
NULL},
|
|
{"imag",
|
|
(getter)long_get0, (setter)NULL,
|
|
"the imaginary part of a complex number",
|
|
NULL},
|
|
{"numerator",
|
|
(getter)long_long, (setter)NULL,
|
|
"the numerator of a rational number in lowest terms",
|
|
NULL},
|
|
{"denominator",
|
|
(getter)long_get1, (setter)NULL,
|
|
"the denominator of a rational number in lowest terms",
|
|
NULL},
|
|
{NULL} /* Sentinel */
|
|
};
|
|
|
|
PyDoc_STRVAR(long_doc,
|
|
"int([x]) -> integer\n\
|
|
int(x, base=10) -> integer\n\
|
|
\n\
|
|
Convert a number or string to an integer, or return 0 if no arguments\n\
|
|
are given. If x is a number, return x.__int__(). For floating point\n\
|
|
numbers, this truncates towards zero.\n\
|
|
\n\
|
|
If x is not a number or if base is given, then x must be a string,\n\
|
|
bytes, or bytearray instance representing an integer literal in the\n\
|
|
given base. The literal can be preceded by '+' or '-' and be surrounded\n\
|
|
by whitespace. The base defaults to 10. Valid bases are 0 and 2-36.\n\
|
|
Base 0 means to interpret the base from the string as an integer literal.\n\
|
|
>>> int('0b100', base=0)\n\
|
|
4");
|
|
|
|
static PyNumberMethods long_as_number = {
|
|
(binaryfunc)long_add, /*nb_add*/
|
|
(binaryfunc)long_sub, /*nb_subtract*/
|
|
(binaryfunc)long_mul, /*nb_multiply*/
|
|
long_mod, /*nb_remainder*/
|
|
long_divmod, /*nb_divmod*/
|
|
long_pow, /*nb_power*/
|
|
(unaryfunc)long_neg, /*nb_negative*/
|
|
(unaryfunc)long_long, /*tp_positive*/
|
|
(unaryfunc)long_abs, /*tp_absolute*/
|
|
(inquiry)long_bool, /*tp_bool*/
|
|
(unaryfunc)long_invert, /*nb_invert*/
|
|
long_lshift, /*nb_lshift*/
|
|
(binaryfunc)long_rshift, /*nb_rshift*/
|
|
long_and, /*nb_and*/
|
|
long_xor, /*nb_xor*/
|
|
long_or, /*nb_or*/
|
|
long_long, /*nb_int*/
|
|
0, /*nb_reserved*/
|
|
long_float, /*nb_float*/
|
|
0, /* nb_inplace_add */
|
|
0, /* nb_inplace_subtract */
|
|
0, /* nb_inplace_multiply */
|
|
0, /* nb_inplace_remainder */
|
|
0, /* nb_inplace_power */
|
|
0, /* nb_inplace_lshift */
|
|
0, /* nb_inplace_rshift */
|
|
0, /* nb_inplace_and */
|
|
0, /* nb_inplace_xor */
|
|
0, /* nb_inplace_or */
|
|
long_div, /* nb_floor_divide */
|
|
long_true_divide, /* nb_true_divide */
|
|
0, /* nb_inplace_floor_divide */
|
|
0, /* nb_inplace_true_divide */
|
|
long_long, /* nb_index */
|
|
};
|
|
|
|
PyTypeObject PyLong_Type = {
|
|
PyVarObject_HEAD_INIT(&PyType_Type, 0)
|
|
"int", /* tp_name */
|
|
offsetof(PyLongObject, ob_digit), /* tp_basicsize */
|
|
sizeof(digit), /* tp_itemsize */
|
|
long_dealloc, /* tp_dealloc */
|
|
0, /* tp_print */
|
|
0, /* tp_getattr */
|
|
0, /* tp_setattr */
|
|
0, /* tp_reserved */
|
|
long_to_decimal_string, /* tp_repr */
|
|
&long_as_number, /* tp_as_number */
|
|
0, /* tp_as_sequence */
|
|
0, /* tp_as_mapping */
|
|
(hashfunc)long_hash, /* tp_hash */
|
|
0, /* tp_call */
|
|
long_to_decimal_string, /* tp_str */
|
|
PyObject_GenericGetAttr, /* tp_getattro */
|
|
0, /* tp_setattro */
|
|
0, /* tp_as_buffer */
|
|
Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE |
|
|
Py_TPFLAGS_LONG_SUBCLASS, /* tp_flags */
|
|
long_doc, /* tp_doc */
|
|
0, /* tp_traverse */
|
|
0, /* tp_clear */
|
|
long_richcompare, /* tp_richcompare */
|
|
0, /* tp_weaklistoffset */
|
|
0, /* tp_iter */
|
|
0, /* tp_iternext */
|
|
long_methods, /* tp_methods */
|
|
0, /* tp_members */
|
|
long_getset, /* tp_getset */
|
|
0, /* tp_base */
|
|
0, /* tp_dict */
|
|
0, /* tp_descr_get */
|
|
0, /* tp_descr_set */
|
|
0, /* tp_dictoffset */
|
|
0, /* tp_init */
|
|
0, /* tp_alloc */
|
|
long_new, /* tp_new */
|
|
PyObject_Del, /* tp_free */
|
|
};
|
|
|
|
static PyTypeObject Int_InfoType;
|
|
|
|
PyDoc_STRVAR(int_info__doc__,
|
|
"sys.int_info\n\
|
|
\n\
|
|
A struct sequence that holds information about Python's\n\
|
|
internal representation of integers. The attributes are read only.");
|
|
|
|
static PyStructSequence_Field int_info_fields[] = {
|
|
{"bits_per_digit", "size of a digit in bits"},
|
|
{"sizeof_digit", "size in bytes of the C type used to represent a digit"},
|
|
{NULL, NULL}
|
|
};
|
|
|
|
static PyStructSequence_Desc int_info_desc = {
|
|
"sys.int_info", /* name */
|
|
int_info__doc__, /* doc */
|
|
int_info_fields, /* fields */
|
|
2 /* number of fields */
|
|
};
|
|
|
|
PyObject *
|
|
PyLong_GetInfo(void)
|
|
{
|
|
PyObject* int_info;
|
|
int field = 0;
|
|
int_info = PyStructSequence_New(&Int_InfoType);
|
|
if (int_info == NULL)
|
|
return NULL;
|
|
PyStructSequence_SET_ITEM(int_info, field++,
|
|
PyLong_FromLong(PyLong_SHIFT));
|
|
PyStructSequence_SET_ITEM(int_info, field++,
|
|
PyLong_FromLong(sizeof(digit)));
|
|
if (PyErr_Occurred()) {
|
|
Py_CLEAR(int_info);
|
|
return NULL;
|
|
}
|
|
return int_info;
|
|
}
|
|
|
|
int
|
|
_PyLong_Init(void)
|
|
{
|
|
#if NSMALLNEGINTS + NSMALLPOSINTS > 0
|
|
int ival, size;
|
|
PyLongObject *v = small_ints;
|
|
|
|
for (ival = -NSMALLNEGINTS; ival < NSMALLPOSINTS; ival++, v++) {
|
|
size = (ival < 0) ? -1 : ((ival == 0) ? 0 : 1);
|
|
if (Py_TYPE(v) == &PyLong_Type) {
|
|
/* The element is already initialized, most likely
|
|
* the Python interpreter was initialized before.
|
|
*/
|
|
Py_ssize_t refcnt;
|
|
PyObject* op = (PyObject*)v;
|
|
|
|
refcnt = Py_REFCNT(op) < 0 ? 0 : Py_REFCNT(op);
|
|
_Py_NewReference(op);
|
|
/* _Py_NewReference sets the ref count to 1 but
|
|
* the ref count might be larger. Set the refcnt
|
|
* to the original refcnt + 1 */
|
|
Py_REFCNT(op) = refcnt + 1;
|
|
assert(Py_SIZE(op) == size);
|
|
assert(v->ob_digit[0] == (digit)abs(ival));
|
|
}
|
|
else {
|
|
(void)PyObject_INIT(v, &PyLong_Type);
|
|
}
|
|
Py_SIZE(v) = size;
|
|
v->ob_digit[0] = (digit)abs(ival);
|
|
}
|
|
#endif
|
|
_PyLong_Zero = PyLong_FromLong(0);
|
|
if (_PyLong_Zero == NULL)
|
|
return 0;
|
|
_PyLong_One = PyLong_FromLong(1);
|
|
if (_PyLong_One == NULL)
|
|
return 0;
|
|
|
|
/* initialize int_info */
|
|
if (Int_InfoType.tp_name == NULL) {
|
|
if (PyStructSequence_InitType2(&Int_InfoType, &int_info_desc) < 0)
|
|
return 0;
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
void
|
|
PyLong_Fini(void)
|
|
{
|
|
/* Integers are currently statically allocated. Py_DECREF is not
|
|
needed, but Python must forget about the reference or multiple
|
|
reinitializations will fail. */
|
|
Py_CLEAR(_PyLong_One);
|
|
Py_CLEAR(_PyLong_Zero);
|
|
#if NSMALLNEGINTS + NSMALLPOSINTS > 0
|
|
int i;
|
|
PyLongObject *v = small_ints;
|
|
for (i = 0; i < NSMALLNEGINTS + NSMALLPOSINTS; i++, v++) {
|
|
_Py_DEC_REFTOTAL;
|
|
_Py_ForgetReference((PyObject*)v);
|
|
}
|
|
#endif
|
|
}
|