| /* Long (arbitrary precision) integer object implementation */ |
| |
| /* XXX The functional organization of this file is terrible */ |
| |
| #include "Python.h" |
| #include "pycore_bitutils.h" // _Py_popcount32() |
| #include "pycore_interp.h" // _PY_NSMALLPOSINTS |
| #include "pycore_long.h" // __PyLong_GetSmallInt_internal() |
| #include "pycore_object.h" // _PyObject_InitVar() |
| #include "pycore_pystate.h" // _Py_IsMainInterpreter() |
| #include "longintrepr.h" |
| |
| #include <float.h> |
| #include <ctype.h> |
| #include <stddef.h> |
| |
| #include "clinic/longobject.c.h" |
| /*[clinic input] |
| class int "PyObject *" "&PyLong_Type" |
| [clinic start generated code]*/ |
| /*[clinic end generated code: output=da39a3ee5e6b4b0d input=ec0275e3422a36e3]*/ |
| |
| #define NSMALLNEGINTS _PY_NSMALLNEGINTS |
| #define NSMALLPOSINTS _PY_NSMALLPOSINTS |
| |
| _Py_IDENTIFIER(little); |
| _Py_IDENTIFIER(big); |
| |
| /* convert a PyLong of size 1, 0 or -1 to an sdigit */ |
| #define MEDIUM_VALUE(x) (assert(-1 <= Py_SIZE(x) && Py_SIZE(x) <= 1), \ |
| Py_SIZE(x) < 0 ? -(sdigit)(x)->ob_digit[0] : \ |
| (Py_SIZE(x) == 0 ? (sdigit)0 : \ |
| (sdigit)(x)->ob_digit[0])) |
| |
| #define IS_SMALL_INT(ival) (-NSMALLNEGINTS <= (ival) && (ival) < NSMALLPOSINTS) |
| #define IS_SMALL_UINT(ival) ((ival) < NSMALLPOSINTS) |
| |
| static PyObject * |
| get_small_int(sdigit ival) |
| { |
| assert(IS_SMALL_INT(ival)); |
| PyObject *v = __PyLong_GetSmallInt_internal(ival); |
| Py_INCREF(v); |
| return v; |
| } |
| |
| static PyLongObject * |
| maybe_small_long(PyLongObject *v) |
| { |
| if (v && Py_ABS(Py_SIZE(v)) <= 1) { |
| sdigit ival = MEDIUM_VALUE(v); |
| if (IS_SMALL_INT(ival)) { |
| Py_DECREF(v); |
| return (PyLongObject *)get_small_int(ival); |
| } |
| } |
| return v; |
| } |
| |
| /* If a freshly-allocated int is already shared, it must |
| be a small integer, so negating it must go to PyLong_FromLong */ |
| Py_LOCAL_INLINE(void) |
| _PyLong_Negate(PyLongObject **x_p) |
| { |
| PyLongObject *x; |
| |
| x = (PyLongObject *)*x_p; |
| if (Py_REFCNT(x) == 1) { |
| Py_SET_SIZE(x, -Py_SIZE(x)); |
| return; |
| } |
| |
| *x_p = (PyLongObject *)PyLong_FromLong(-MEDIUM_VALUE(x)); |
| Py_DECREF(x); |
| } |
| |
| /* For int multiplication, use the O(N**2) school algorithm unless |
| * both operands contain more than KARATSUBA_CUTOFF digits (this |
| * being an internal Python int digit, in base BASE). |
| */ |
| #define KARATSUBA_CUTOFF 70 |
| #define KARATSUBA_SQUARE_CUTOFF (2 * KARATSUBA_CUTOFF) |
| |
| /* For exponentiation, use the binary left-to-right algorithm |
| * unless the exponent contains more than FIVEARY_CUTOFF digits. |
| * In that case, do 5 bits at a time. The potential drawback is that |
| * a table of 2**5 intermediate results is computed. |
| */ |
| #define FIVEARY_CUTOFF 8 |
| |
| #define SIGCHECK(PyTryBlock) \ |
| do { \ |
| if (PyErr_CheckSignals()) PyTryBlock \ |
| } while(0) |
| |
| /* Normalize (remove leading zeros from) an int object. |
| Doesn't attempt to free the storage--in most cases, due to the nature |
| of the algorithms used, this could save at most be one word anyway. */ |
| |
| static PyLongObject * |
| long_normalize(PyLongObject *v) |
| { |
| Py_ssize_t j = Py_ABS(Py_SIZE(v)); |
| Py_ssize_t i = j; |
| |
| while (i > 0 && v->ob_digit[i-1] == 0) |
| --i; |
| if (i != j) { |
| Py_SET_SIZE(v, (Py_SIZE(v) < 0) ? -(i) : i); |
| } |
| return v; |
| } |
| |
| /* Allocate a new int object with size digits. |
| Return NULL and set exception if we run out of memory. */ |
| |
| #define MAX_LONG_DIGITS \ |
| ((PY_SSIZE_T_MAX - offsetof(PyLongObject, ob_digit))/sizeof(digit)) |
| |
| PyLongObject * |
| _PyLong_New(Py_ssize_t size) |
| { |
| PyLongObject *result; |
| /* Number of bytes needed is: offsetof(PyLongObject, ob_digit) + |
| sizeof(digit)*size. Previous incarnations of this code used |
| sizeof(PyVarObject) instead of the offsetof, but this risks being |
| incorrect in the presence of padding between the PyVarObject header |
| and the digits. */ |
| if (size > (Py_ssize_t)MAX_LONG_DIGITS) { |
| PyErr_SetString(PyExc_OverflowError, |
| "too many digits in integer"); |
| return NULL; |
| } |
| result = PyObject_Malloc(offsetof(PyLongObject, ob_digit) + |
| size*sizeof(digit)); |
| if (!result) { |
| PyErr_NoMemory(); |
| return NULL; |
| } |
| _PyObject_InitVar((PyVarObject*)result, &PyLong_Type, size); |
| return result; |
| } |
| |
| PyObject * |
| _PyLong_Copy(PyLongObject *src) |
| { |
| PyLongObject *result; |
| Py_ssize_t i; |
| |
| assert(src != NULL); |
| i = Py_SIZE(src); |
| if (i < 0) |
| i = -(i); |
| if (i < 2) { |
| sdigit ival = MEDIUM_VALUE(src); |
| if (IS_SMALL_INT(ival)) { |
| return get_small_int(ival); |
| } |
| } |
| result = _PyLong_New(i); |
| if (result != NULL) { |
| Py_SET_SIZE(result, Py_SIZE(src)); |
| while (--i >= 0) { |
| result->ob_digit[i] = src->ob_digit[i]; |
| } |
| } |
| return (PyObject *)result; |
| } |
| |
| /* Create a new int object from a C long int */ |
| |
| PyObject * |
| PyLong_FromLong(long ival) |
| { |
| PyLongObject *v; |
| unsigned long abs_ival; |
| unsigned long t; /* unsigned so >> doesn't propagate sign bit */ |
| int ndigits = 0; |
| int sign; |
| |
| if (IS_SMALL_INT(ival)) { |
| return get_small_int((sdigit)ival); |
| } |
| |
| if (ival < 0) { |
| /* negate: can't write this as abs_ival = -ival since that |
| invokes undefined behaviour when ival is LONG_MIN */ |
| abs_ival = 0U-(unsigned long)ival; |
| sign = -1; |
| } |
| else { |
| abs_ival = (unsigned long)ival; |
| sign = ival == 0 ? 0 : 1; |
| } |
| |
| /* Fast path for single-digit ints */ |
| if (!(abs_ival >> PyLong_SHIFT)) { |
| v = _PyLong_New(1); |
| if (v) { |
| Py_SET_SIZE(v, sign); |
| v->ob_digit[0] = Py_SAFE_DOWNCAST( |
| abs_ival, unsigned long, digit); |
| } |
| return (PyObject*)v; |
| } |
| |
| #if PyLong_SHIFT==15 |
| /* 2 digits */ |
| if (!(abs_ival >> 2*PyLong_SHIFT)) { |
| v = _PyLong_New(2); |
| if (v) { |
| Py_SET_SIZE(v, 2 * sign); |
| v->ob_digit[0] = Py_SAFE_DOWNCAST( |
| abs_ival & PyLong_MASK, unsigned long, digit); |
| v->ob_digit[1] = Py_SAFE_DOWNCAST( |
| abs_ival >> PyLong_SHIFT, unsigned long, digit); |
| } |
| return (PyObject*)v; |
| } |
| #endif |
| |
| /* Larger numbers: loop to determine number of digits */ |
| t = abs_ival; |
| while (t) { |
| ++ndigits; |
| t >>= PyLong_SHIFT; |
| } |
| v = _PyLong_New(ndigits); |
| if (v != NULL) { |
| digit *p = v->ob_digit; |
| Py_SET_SIZE(v, ndigits * sign); |
| t = abs_ival; |
| while (t) { |
| *p++ = Py_SAFE_DOWNCAST( |
| t & PyLong_MASK, unsigned long, digit); |
| t >>= PyLong_SHIFT; |
| } |
| } |
| return (PyObject *)v; |
| } |
| |
| #define PYLONG_FROM_UINT(INT_TYPE, ival) \ |
| do { \ |
| if (IS_SMALL_UINT(ival)) { \ |
| return get_small_int((sdigit)(ival)); \ |
| } \ |
| /* Count the number of Python digits. */ \ |
| Py_ssize_t ndigits = 0; \ |
| INT_TYPE t = (ival); \ |
| while (t) { \ |
| ++ndigits; \ |
| t >>= PyLong_SHIFT; \ |
| } \ |
| PyLongObject *v = _PyLong_New(ndigits); \ |
| if (v == NULL) { \ |
| return NULL; \ |
| } \ |
| digit *p = v->ob_digit; \ |
| while ((ival)) { \ |
| *p++ = (digit)((ival) & PyLong_MASK); \ |
| (ival) >>= PyLong_SHIFT; \ |
| } \ |
| return (PyObject *)v; \ |
| } while(0) |
| |
| /* Create a new int object from a C unsigned long int */ |
| |
| PyObject * |
| PyLong_FromUnsignedLong(unsigned long ival) |
| { |
| PYLONG_FROM_UINT(unsigned long, ival); |
| } |
| |
| /* Create a new int object from a C unsigned long long int. */ |
| |
| PyObject * |
| PyLong_FromUnsignedLongLong(unsigned long long ival) |
| { |
| PYLONG_FROM_UINT(unsigned long long, ival); |
| } |
| |
| /* Create a new int object from a C size_t. */ |
| |
| PyObject * |
| PyLong_FromSize_t(size_t ival) |
| { |
| PYLONG_FROM_UINT(size_t, ival); |
| } |
| |
| /* Create a new int object from a C double */ |
| |
| PyObject * |
| PyLong_FromDouble(double dval) |
| { |
| /* Try to get out cheap if this fits in a long. When a finite value of real |
| * floating type is converted to an integer type, the value is truncated |
| * toward zero. If the value of the integral part cannot be represented by |
| * the integer type, the behavior is undefined. Thus, we must check that |
| * value is in range (LONG_MIN - 1, LONG_MAX + 1). If a long has more bits |
| * of precision than a double, casting LONG_MIN - 1 to double may yield an |
| * approximation, but LONG_MAX + 1 is a power of two and can be represented |
| * as double exactly (assuming FLT_RADIX is 2 or 16), so for simplicity |
| * check against [-(LONG_MAX + 1), LONG_MAX + 1). |
| */ |
| const double int_max = (unsigned long)LONG_MAX + 1; |
| if (-int_max < dval && dval < int_max) { |
| return PyLong_FromLong((long)dval); |
| } |
| |
| PyLongObject *v; |
| double frac; |
| int i, ndig, expo, neg; |
| neg = 0; |
| if (Py_IS_INFINITY(dval)) { |
| PyErr_SetString(PyExc_OverflowError, |
| "cannot convert float infinity to integer"); |
| return NULL; |
| } |
| if (Py_IS_NAN(dval)) { |
| PyErr_SetString(PyExc_ValueError, |
| "cannot convert float NaN to integer"); |
| return NULL; |
| } |
| if (dval < 0.0) { |
| neg = 1; |
| dval = -dval; |
| } |
| frac = frexp(dval, &expo); /* dval = frac*2**expo; 0.0 <= frac < 1.0 */ |
| assert(expo > 0); |
| ndig = (expo-1) / PyLong_SHIFT + 1; /* Number of 'digits' in result */ |
| v = _PyLong_New(ndig); |
| if (v == NULL) |
| return NULL; |
| frac = ldexp(frac, (expo-1) % PyLong_SHIFT + 1); |
| for (i = ndig; --i >= 0; ) { |
| digit bits = (digit)frac; |
| v->ob_digit[i] = bits; |
| frac = frac - (double)bits; |
| frac = ldexp(frac, PyLong_SHIFT); |
| } |
| if (neg) { |
| Py_SET_SIZE(v, -(Py_SIZE(v))); |
| } |
| return (PyObject *)v; |
| } |
| |
| /* Checking for overflow in PyLong_AsLong is a PITA since C doesn't define |
| * anything about what happens when a signed integer operation overflows, |
| * and some compilers think they're doing you a favor by being "clever" |
| * then. The bit pattern for the largest positive signed long is |
| * (unsigned long)LONG_MAX, and for the smallest negative signed long |
| * it is abs(LONG_MIN), which we could write -(unsigned long)LONG_MIN. |
| * However, some other compilers warn about applying unary minus to an |
| * unsigned operand. Hence the weird "0-". |
| */ |
| #define PY_ABS_LONG_MIN (0-(unsigned long)LONG_MIN) |
| #define PY_ABS_SSIZE_T_MIN (0-(size_t)PY_SSIZE_T_MIN) |
| |
| /* Get a C long int from an int object or any object that has an __index__ |
| 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 |
| PyLong_AsLongAndOverflow(PyObject *vv, int *overflow) |
| { |
| /* This version by Tim Peters */ |
| PyLongObject *v; |
| unsigned long x, prev; |
| long res; |
| Py_ssize_t i; |
| int sign; |
| int do_decref = 0; /* if PyNumber_Index was called */ |
| |
| *overflow = 0; |
| if (vv == NULL) { |
| PyErr_BadInternalCall(); |
| return -1; |
| } |
| |
| if (PyLong_Check(vv)) { |
| v = (PyLongObject *)vv; |
| } |
| else { |
| v = (PyLongObject *)_PyNumber_Index(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_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 __index__ |
| 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 __index__ |
| 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 = (PyLongObject *)_PyNumber_Index(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); |
| } |
| |
| static int |
| bit_length_digit(digit x) |
| { |
| Py_BUILD_ASSERT(PyLong_SHIFT <= sizeof(unsigned long) * 8); |
| return _Py_bit_length((unsigned long)x); |
| } |
| |
| 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 = bit_length_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_SET_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)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; |
| |
| if (IS_SMALL_INT(ival)) { |
| return get_small_int((sdigit)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_SET_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 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; |
| |
| if (IS_SMALL_INT(ival)) { |
| return get_small_int((sdigit)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_SET_SIZE(v, negative ? -ndigits : ndigits); |
| t = abs_ival; |
| while (t) { |
| *p++ = (digit)(t & PyLong_MASK); |
| t >>= PyLong_SHIFT; |
| } |
| } |
| return (PyObject *)v; |
| } |
| |
| /* Get a C long long int from an int object or any object that has an |
| __index__ 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 PyNumber_Index was called */ |
| |
| if (vv == NULL) { |
| PyErr_BadInternalCall(); |
| return -1; |
| } |
| |
| if (PyLong_Check(vv)) { |
| v = (PyLongObject *)vv; |
| } |
| else { |
| v = (PyLongObject *)_PyNumber_Index(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 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 long)-1; |
| } |
| |
| if (PyLong_Check(op)) { |
| return _PyLong_AsUnsignedLongLongMask(op); |
| } |
| |
| lo = (PyLongObject *)_PyNumber_Index(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 |
| __index__ 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 PyNumber_Index was called */ |
| |
| *overflow = 0; |
| if (vv == NULL) { |
| PyErr_BadInternalCall(); |
| return -1; |
| } |
| |
| if (PyLong_Check(vv)) { |
| v = (PyLongObject *)vv; |
| } |
| else { |
| v = (PyLongObject *)_PyNumber_Index(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)LLONG_MAX) { |
| res = (long long)x * sign; |
| } |
| else if (sign < 0 && x == PY_ABS_LLONG_MIN) { |
| res = LLONG_MIN; |
| } |
| else { |
| *overflow = sign; |
| /* res is already set to -1 */ |
| } |
| } |
| exit: |
| if (do_decref) { |
| Py_DECREF(v); |
| } |
| return res; |
| } |
| |
| int |
| _PyLong_UnsignedShort_Converter(PyObject *obj, void *ptr) |
| { |
| unsigned long uval; |
| |
| if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { |
| PyErr_SetString(PyExc_ValueError, "value must be positive"); |
| return 0; |
| } |
| uval = PyLong_AsUnsignedLong(obj); |
| if (uval == (unsigned long)-1 && PyErr_Occurred()) |
| return 0; |
| if (uval > USHRT_MAX) { |
| PyErr_SetString(PyExc_OverflowError, |
| "Python int too large for C unsigned short"); |
| return 0; |
| } |
| |
| *(unsigned short *)ptr = Py_SAFE_DOWNCAST(uval, unsigned long, unsigned short); |
| return 1; |
| } |
| |
| int |
| _PyLong_UnsignedInt_Converter(PyObject *obj, void *ptr) |
| { |
| unsigned long uval; |
| |
| if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { |
| PyErr_SetString(PyExc_ValueError, "value must be positive"); |
| return 0; |
| } |
| uval = PyLong_AsUnsignedLong(obj); |
| if (uval == (unsigned long)-1 && PyErr_Occurred()) |
| return 0; |
| if (uval > UINT_MAX) { |
| PyErr_SetString(PyExc_OverflowError, |
| "Python int too large for C unsigned int"); |
| return 0; |
| } |
| |
| *(unsigned int *)ptr = Py_SAFE_DOWNCAST(uval, unsigned long, unsigned int); |
| return 1; |
| } |
| |
| int |
| _PyLong_UnsignedLong_Converter(PyObject *obj, void *ptr) |
| { |
| unsigned long uval; |
| |
| if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { |
| PyErr_SetString(PyExc_ValueError, "value must be positive"); |
| return 0; |
| } |
| uval = PyLong_AsUnsignedLong(obj); |
| if (uval == (unsigned long)-1 && PyErr_Occurred()) |
| return 0; |
| |
| *(unsigned long *)ptr = uval; |
| return 1; |
| } |
| |
| int |
| _PyLong_UnsignedLongLong_Converter(PyObject *obj, void *ptr) |
| { |
| unsigned long long uval; |
| |
| if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { |
| PyErr_SetString(PyExc_ValueError, "value must be positive"); |
| return 0; |
| } |
| uval = PyLong_AsUnsignedLongLong(obj); |
| if (uval == (unsigned long long)-1 && PyErr_Occurred()) |
| return 0; |
| |
| *(unsigned long long *)ptr = uval; |
| return 1; |
| } |
| |
| int |
| _PyLong_Size_t_Converter(PyObject *obj, void *ptr) |
| { |
| size_t uval; |
| |
| if (PyLong_Check(obj) && _PyLong_Sign(obj) < 0) { |
| PyErr_SetString(PyExc_ValueError, "value must be positive"); |
| return 0; |
| } |
| uval = PyLong_AsSize_t(obj); |
| if (uval == (size_t)-1 && PyErr_Occurred()) |
| return 0; |
| |
| *(size_t *)ptr = uval; |
| return 1; |
| } |
| |
| |
| #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: |
| Py_UNREACHABLE(); |
| } |
| |
| /* 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 + |
| bit_length_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; |
| Py_ssize_t 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 <- the number of Python digits needed, |
| = ceiling((digits * bits_per_char) / PyLong_SHIFT). */ |
| if (digits > (PY_SSIZE_T_MAX - (PyLong_SHIFT - 1)) / bits_per_char) { |
| PyErr_SetString(PyExc_ValueError, |
| "int string too large to convert"); |
| *res = NULL; |
| return 0; |
| } |
| n = (digits * bits_per_char + PyLong_SHIFT - 1) / 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(*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; |
| Py_ssize_t 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. |
| */ |
| double fsize_z = (double)digits * log_base_BASE[base] + 1.0; |
| if (fsize_z > (double)MAX_LONG_DIGITS) { |
| /* The same exception as in _PyLong_New(). */ |
| PyErr_SetString(PyExc_OverflowError, |
| "too many digits in integer"); |
| return NULL; |
| } |
| size_z = (Py_ssize_t)fsize_z; |
| /* 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_SET_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_SET_SIZE(z, Py_SIZE(z) + 1); |
| } |
| 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_SET_SIZE(z, -(Py_SIZE(z))); |
| } |
| while (*str && Py_ISSPACE(*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_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; |
| assert(PyUnicode_IS_ASCII(asciidig)); |
| /* Simply get a pointer to existing ASCII characters. */ |
| buffer = PyUnicode_AsUTF8AndSize(asciidig, &buflen); |
| assert(buffer != NULL); |
| |
| 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; |
| } |
| PyObject *zero = _PyLong_GetZero(); |
| Py_INCREF(zero); |
| *pdiv = (PyLongObject*)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 - bit_length_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; |
| digit x_digits[2 + (DBL_MANT_DIG + 1) / PyLong_SHIFT] = {0,}; |
| 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 = bit_length_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 = shift_digits; |
| 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 */ |
| |
| /* if a < b, return a negative number |
| if a == b, return 0 |
| if a > b, return a positive number */ |
| |
| static Py_ssize_t |
| long_compare(PyLongObject *a, PyLongObject *b) |
| { |
| Py_ssize_t sign = Py_SIZE(a) - Py_SIZE(b); |
| if (sign == 0) { |
| Py_ssize_t i = Py_ABS(Py_SIZE(a)); |
| sdigit diff = 0; |
| while (--i >= 0) { |
| diff = (sdigit) a->ob_digit[i] - (sdigit) b->ob_digit[i]; |
| if (diff) { |
| break; |
| } |
| } |
| sign = Py_SIZE(a) < 0 ? -diff : diff; |
| } |
| return sign; |
| } |
| |
| static PyObject * |
| long_richcompare(PyObject *self, PyObject *other, int op) |
| { |
| Py_ssize_t result; |
| CHECK_BINOP(self, other); |
| if (self == other) |
| result = 0; |
| else |
| result = long_compare((PyLongObject*)self, (PyLongObject*)other); |
| Py_RETURN_RICHCOMPARE(result, 0, op); |
| } |
| |
| 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_SET_SIZE(z, -Py_SIZE(z)); |
| } |
| return maybe_small_long(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_SET_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(b, a); |
| } |
| else { |
| z = x_add(a, b); |
| if (z != NULL) { |
| assert(Py_SIZE(z) == 0 || Py_REFCNT(z) == 1); |
| Py_SET_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_SET_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_GetOne()); |
| 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 + bit_length_digit(a->ob_digit[a_size - 1]) - |
| bit_length_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+bit_length_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_SET_ITEM(z, 0, (PyObject *) div); |
| PyTuple_SET_ITEM(z, 1, (PyObject *) mod); |
| } |
| else { |
| Py_DECREF(div); |
| Py_DECREF(mod); |
| } |
| return z; |
| } |
| |
| |
| /* Compute an inverse to a modulo n, or raise ValueError if a is not |
| invertible modulo n. Assumes n is positive. The inverse returned |
| is whatever falls out of the extended Euclidean algorithm: it may |
| be either positive or negative, but will be smaller than n in |
| absolute value. |
| |
| Pure Python equivalent for long_invmod: |
| |
| def invmod(a, n): |
| b, c = 1, 0 |
| while n: |
| q, r = divmod(a, n) |
| a, b, c, n = n, c, b - q*c, r |
| |
| # at this point a is the gcd of the original inputs |
| if a == 1: |
| return b |
| raise ValueError("Not invertible") |
| */ |
| |
| static PyLongObject * |
| long_invmod(PyLongObject *a, PyLongObject *n) |
| { |
| PyLongObject *b, *c; |
| |
| /* Should only ever be called for positive n */ |
| assert(Py_SIZE(n) > 0); |
| |
| b = (PyLongObject *)PyLong_FromLong(1L); |
| if (b == NULL) { |
| return NULL; |
| } |
| c = (PyLongObject *)PyLong_FromLong(0L); |
| if (c == NULL) { |
| Py_DECREF(b); |
| return NULL; |
| } |
| Py_INCREF(a); |
| Py_INCREF(n); |
| |
| /* references now owned: a, b, c, n */ |
| while (Py_SIZE(n) != 0) { |
| PyLongObject *q, *r, *s, *t; |
| |
| if (l_divmod(a, n, &q, &r) == -1) { |
| goto Error; |
| } |
| Py_DECREF(a); |
| a = n; |
| n = r; |
| t = (PyLongObject *)long_mul(q, c); |
| Py_DECREF(q); |
| if (t == NULL) { |
| goto Error; |
| } |
| s = (PyLongObject *)long_sub(b, t); |
| Py_DECREF(t); |
| if (s == NULL) { |
| goto Error; |
| } |
| Py_DECREF(b); |
| b = c; |
| c = s; |
| } |
| /* references now owned: a, b, c, n */ |
| |
| Py_DECREF(c); |
| Py_DECREF(n); |
| if (long_compare(a, (PyLongObject *)_PyLong_GetOne())) { |
| /* a != 1; we don't have an inverse. */ |
| Py_DECREF(a); |
| Py_DECREF(b); |
| PyErr_SetString(PyExc_ValueError, |
| "base is not invertible for the given modulus"); |
| return NULL; |
| } |
| else { |
| /* a == 1; b gives an inverse modulo n */ |
| Py_DECREF(a); |
| return b; |
| } |
| |
| Error: |
| Py_DECREF(a); |
| Py_DECREF(b); |
| Py_DECREF(c); |
| Py_DECREF(n); |
| return NULL; |
| } |
| |
| |
| /* 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 && c == NULL) { |
| /* if exponent is negative and there's no modulus: |
| 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; |
| } |
| |
| /* if exponent is negative, negate the exponent and |
| replace the base with a modular inverse */ |
| if (Py_SIZE(b) < 0) { |
| temp = (PyLongObject *)_PyLong_Copy(b); |
| if (temp == NULL) |
| goto Error; |
| Py_DECREF(b); |
| b = temp; |
| temp = NULL; |
| _PyLong_Negate(&b); |
| if (b == NULL) |
| goto Error; |
| |
| temp = long_invmod(a, c); |
| if (temp == NULL) |
| goto Error; |
| Py_DECREF(a); |
| a = temp; |
| } |
| |
| /* 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_GetOne()); |
| 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_SET_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(PyObject *shiftby, Py_ssize_t *wordshift, digit *remshift) |
| { |
| assert(PyLong_Check(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((PyLongObject *)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_rshift1(PyLongObject *a, Py_ssize_t wordshift, digit remshift) |
| { |
| PyLongObject *z = NULL; |
| Py_ssize_t newsize, hishift, i, j; |
| digit lomask, himask; |
| |
| 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_rshift1(a1, wordshift, remshift); |
| Py_DECREF(a1); |
| if (a2 == NULL) |
| return NULL; |
| z = (PyLongObject *) long_invert(a2); |
| Py_DECREF(a2); |
| } |
| else { |
| newsize = Py_SIZE(a) - wordshift; |
| if (newsize <= 0) |
| return PyLong_FromLong(0); |
| hishift = PyLong_SHIFT - remshift; |
| 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] >> remshift) & 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_rshift(PyObject *a, PyObject *b) |
| { |
| Py_ssize_t wordshift; |
| digit remshift; |
| |
| 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; |
| return long_rshift1((PyLongObject *)a, wordshift, remshift); |
| } |
| |
| /* Return a >> shiftby. */ |
| PyObject * |
| _PyLong_Rshift(PyObject *a, size_t shiftby) |
| { |
| Py_ssize_t wordshift; |
| digit remshift; |
| |
| assert(PyLong_Check(a)); |
| if (Py_SIZE(a) == 0) { |
| return PyLong_FromLong(0); |
| } |
| wordshift = shiftby / PyLong_SHIFT; |
| remshift = shiftby % PyLong_SHIFT; |
| return long_rshift1((PyLongObject *)a, wordshift, remshift); |
| } |
| |
| static PyObject * |
| long_lshift1(PyLongObject *a, Py_ssize_t wordshift, digit remshift) |
| { |
| /* This version due to Tim Peters */ |
| PyLongObject *z = NULL; |
| Py_ssize_t oldsize, newsize, i, j; |
| twodigits accum; |
| |
| 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_SET_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); |
| } |
| |
| static PyObject * |
| long_lshift(PyObject *a, PyObject *b) |
| { |
| Py_ssize_t wordshift; |
| digit remshift; |
| |
| 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; |
| return long_lshift1((PyLongObject *)a, wordshift, remshift); |
| } |
| |
| /* Return a << shiftby. */ |
| PyObject * |
| _PyLong_Lshift(PyObject *a, size_t shiftby) |
| { |
| Py_ssize_t wordshift; |
| digit remshift; |
| |
| assert(PyLong_Check(a)); |
| if (Py_SIZE(a) == 0) { |
| return PyLong_FromLong(0); |
| } |
| wordshift = shiftby / PyLong_SHIFT; |
| remshift = shiftby % PyLong_SHIFT; |
| return long_lshift1((PyLongObject *)a, wordshift, remshift); |
| } |
| |
| /* 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: |
| Py_UNREACHABLE(); |
| } |
| |
| /* 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: |
| Py_UNREACHABLE(); |
| } |
| |
| /* 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_SET_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 = bit_length_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_SET_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_SET_SIZE(d, size_a); |
| } |
| else if (Py_REFCNT(b) == 1 && size_a <= alloc_b) { |
| Py_INCREF(b); |
| d = b; |
| Py_SET_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 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 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, or 0"); |
| return NULL; |
| } |
| |
| if (PyUnicode_Check(x)) |
| return PyLong_FromUnicodeObject(x, (int)base); |
| else if (PyByteArray_Check(x) || PyBytes_Check(x)) { |
| const 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_SET_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(PyObject *Py_UNUSED(self), void *Py_UNUSED(context)) |
| { |
| return PyLong_FromLong(0L); |
| } |
| |
| static PyObject * |
| long_get1(PyObject *Py_UNUSED(self), void *Py_UNUSED(ignored)) |
| { |
| 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 quo_is_odd, quo_is_neg; |
| Py_ssize_t cmp; |
| |
| /* 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 */ |
| PyObject *one = _PyLong_GetOne(); // borrowed reference |
| twice_rem = long_lshift((PyObject *)rem, 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 *)one); |
| else |
| temp = long_add(quo, (PyLongObject *)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; |
| } |
| |
| /*[clinic input] |
| int.__round__ |
| |
| ndigits as o_ndigits: object = NULL |
| / |
| |
| Rounding an Integral returns itself. |
| |
| Rounding with an ndigits argument also returns an integer. |
| [clinic start generated code]*/ |
| |
| static PyObject * |
| int___round___impl(PyObject *self, PyObject *o_ndigits) |
| /*[clinic end generated code: output=954fda6b18875998 input=1614cf23ec9e18c3]*/ |
| { |
| PyObject *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 (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 = bit_length_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; |
| } |
| |
| static int |
| popcount_digit(digit d) |
| { |
| // digit can be larger than uint32_t, but only PyLong_SHIFT bits |
| // of it will be ever used. |
| Py_BUILD_ASSERT(PyLong_SHIFT <= 32); |
| return _Py_popcount32((uint32_t)d); |
| } |
| |
| /*[clinic input] |
| int.bit_count |
| |
| Number of ones in the binary representation of the absolute value of self. |
| |
| Also known as the population count. |
| |
| >>> bin(13) |
| '0b1101' |
| >>> (13).bit_count() |
| 3 |
| [clinic start generated code]*/ |
| |
| static PyObject * |
| int_bit_count_impl(PyObject *self) |
| /*[clinic end generated code: output=2e571970daf1e5c3 input=7e0adef8e8ccdf2e]*/ |
| { |
| assert(self != NULL); |
| assert(PyLong_Check(self)); |
| |
| PyLongObject *z = (PyLongObject *)self; |
| Py_ssize_t ndigits = Py_ABS(Py_SIZE(z)); |
| Py_ssize_t bit_count = 0; |
| |
| /* Each digit has up to PyLong_SHIFT ones, so the accumulated bit count |
| from the first PY_SSIZE_T_MAX/PyLong_SHIFT digits can't overflow a |
| Py_ssize_t. */ |
| Py_ssize_t ndigits_fast = Py_MIN(ndigits, PY_SSIZE_T_MAX/PyLong_SHIFT); |
| for (Py_ssize_t i = 0; i < ndigits_fast; i++) { |
| bit_count += popcount_digit(z->ob_digit[i]); |
| } |
| |
| PyObject *result = PyLong_FromSsize_t(bit_count); |
| if (result == NULL) { |
| return NULL; |
| } |
| |
| /* Use Python integers if bit_count would overflow. */ |
| for (Py_ssize_t i = ndigits_fast; i < ndigits; i++) { |
| PyObject *x = PyLong_FromLong(popcount_digit(z->ob_digit[i])); |
| if (x == NULL) { |
| goto error; |
| } |
| PyObject *y = long_add((PyLongObject *)result, (PyLongObject *)x); |
| Py_DECREF(x); |
| if (y == NULL) { |
| goto error; |
| } |
| Py_DECREF(result); |
| result = y; |
| } |
| |
| return result; |
| |
| error: |
| Py_DECREF(result); |
| return NULL; |
| } |
| |
| /*[clinic input] |
| int.as_integer_ratio |
| |
| Return integer ratio. |
| |
| Return a pair of integers, whose ratio is exactly equal to the original int |
| and with a positive denominator. |
| |
| >>> (10).as_integer_ratio() |
| (10, 1) |
| >>> (-10).as_integer_ratio() |
| (-10, 1) |
| >>> (0).as_integer_ratio() |
| (0, 1) |
| [clinic start generated code]*/ |
| |
| static PyObject * |
| int_as_integer_ratio_impl(PyObject *self) |
| /*[clinic end generated code: output=e60803ae1cc8621a input=55ce3058e15de393]*/ |
| { |
| PyObject *ratio_tuple; |
| PyObject *numerator = long_long(self); |
| if (numerator == NULL) { |
| return NULL; |
| } |
| ratio_tuple = PyTuple_Pack(2, numerator, _PyLong_GetOne()); |
| Py_DECREF(numerator); |
| return ratio_tuple; |
| } |
| |
| /*[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 (long_obj != NULL && type != &PyLong_Type) { |
| Py_SETREF(long_obj, PyObject_CallOneArg((PyObject *)type, long_obj)); |
| } |
| |
| return long_obj; |
| } |
| |
| static PyObject * |
| long_long_meth(PyObject *self, PyObject *Py_UNUSED(ignored)) |
| { |
| return long_long(self); |
| } |
| |
| static PyMethodDef long_methods[] = { |
| {"conjugate", long_long_meth, METH_NOARGS, |
| "Returns self, the complex conjugate of any int."}, |
| INT_BIT_LENGTH_METHODDEF |
| INT_BIT_COUNT_METHODDEF |
| INT_TO_BYTES_METHODDEF |
| INT_FROM_BYTES_METHODDEF |
| INT_AS_INTEGER_RATIO_METHODDEF |
| {"__trunc__", long_long_meth, METH_NOARGS, |
| "Truncating an Integral returns itself."}, |
| {"__floor__", long_long_meth, METH_NOARGS, |
| "Flooring an Integral returns itself."}, |
| {"__ceil__", long_long_meth, METH_NOARGS, |
| "Ceiling of an Integral returns itself."}, |
| INT___ROUND___METHODDEF |
| INT___GETNEWARGS___METHODDEF |
| INT___FORMAT___METHODDEF |
| INT___SIZEOF___METHODDEF |
| {NULL, NULL} /* sentinel */ |
| }; |
| |
| static PyGetSetDef long_getset[] = { |
| {"real", |
| (getter)long_long_meth, (setter)NULL, |
| "the real part of a complex number", |
| NULL}, |
| {"imag", |
| long_get0, (setter)NULL, |
| "the imaginary part of a complex number", |
| NULL}, |
| {"numerator", |
| (getter)long_long_meth, (setter)NULL, |
| "the numerator of a rational number in lowest terms", |
| NULL}, |
| {"denominator", |
| 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*/ |
| long_long, /*tp_positive*/ |
| (unaryfunc)long_abs, /*tp_absolute*/ |
| (inquiry)long_bool, /*tp_bool*/ |
| (unaryfunc)long_invert, /*nb_invert*/ |
| long_lshift, /*nb_lshift*/ |
| 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 */ |
| 0, /* tp_dealloc */ |
| 0, /* tp_vectorcall_offset */ |
| 0, /* tp_getattr */ |
| 0, /* tp_setattr */ |
| 0, /* tp_as_async */ |
| 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 */ |
| 0, /* 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 named tuple 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(PyThreadState *tstate) |
| { |
| for (Py_ssize_t i=0; i < NSMALLNEGINTS + NSMALLPOSINTS; i++) { |
| sdigit ival = (sdigit)i - NSMALLNEGINTS; |
| int size = (ival < 0) ? -1 : ((ival == 0) ? 0 : 1); |
| |
| PyLongObject *v = _PyLong_New(1); |
| if (!v) { |
| return -1; |
| } |
| |
| Py_SET_SIZE(v, size); |
| v->ob_digit[0] = (digit)abs(ival); |
| |
| tstate->interp->small_ints[i] = v; |
| } |
| |
| if (_Py_IsMainInterpreter(tstate)) { |
| /* 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(PyThreadState *tstate) |
| { |
| for (Py_ssize_t i = 0; i < NSMALLNEGINTS + NSMALLPOSINTS; i++) { |
| Py_CLEAR(tstate->interp->small_ints[i]); |
| } |
| } |