| /*********************************************************** |
| Copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam, |
| The Netherlands. |
| |
| All Rights Reserved |
| |
| Permission to use, copy, modify, and distribute this software and its |
| documentation for any purpose and without fee is hereby granted, |
| provided that the above copyright notice appear in all copies and that |
| both that copyright notice and this permission notice appear in |
| supporting documentation, and that the names of Stichting Mathematisch |
| Centrum or CWI or Corporation for National Research Initiatives or |
| CNRI not be used in advertising or publicity pertaining to |
| distribution of the software without specific, written prior |
| permission. |
| |
| While CWI is the initial source for this software, a modified version |
| is made available by the Corporation for National Research Initiatives |
| (CNRI) at the Internet address ftp://ftp.python.org. |
| |
| STICHTING MATHEMATISCH CENTRUM AND CNRI DISCLAIM ALL WARRANTIES WITH |
| REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF |
| MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH |
| CENTRUM OR CNRI BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL |
| DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR |
| PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER |
| TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR |
| PERFORMANCE OF THIS SOFTWARE. |
| |
| ******************************************************************/ |
| |
| /* Long (arbitrary precision) integer object implementation */ |
| |
| /* XXX The functional organization of this file is terrible */ |
| |
| #include "Python.h" |
| #include "longintrepr.h" |
| #include "mymath.h" |
| |
| #include <assert.h> |
| #include <ctype.h> |
| |
| #define ABS(x) ((x) < 0 ? -(x) : (x)) |
| |
| /* Forward */ |
| static PyLongObject *long_normalize Py_PROTO((PyLongObject *)); |
| static PyLongObject *mul1 Py_PROTO((PyLongObject *, wdigit)); |
| static PyLongObject *muladd1 Py_PROTO((PyLongObject *, wdigit, wdigit)); |
| static PyLongObject *divrem1 Py_PROTO((PyLongObject *, wdigit, digit *)); |
| static PyObject *long_format Py_PROTO((PyObject *aa, int base)); |
| |
| static int ticker; /* XXX Could be shared with ceval? */ |
| |
| #define SIGCHECK(PyTryBlock) \ |
| if (--ticker < 0) { \ |
| ticker = 100; \ |
| if (PyErr_CheckSignals()) { PyTryBlock; } \ |
| } |
| |
| /* Normalize (remove leading zeros from) a long 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(v) |
| register PyLongObject *v; |
| { |
| int j = ABS(v->ob_size); |
| register int i = j; |
| |
| while (i > 0 && v->ob_digit[i-1] == 0) |
| --i; |
| if (i != j) |
| v->ob_size = (v->ob_size < 0) ? -(i) : i; |
| return v; |
| } |
| |
| /* Allocate a new long int object with size digits. |
| Return NULL and set exception if we run out of memory. */ |
| |
| PyLongObject * |
| _PyLong_New(size) |
| int size; |
| { |
| return PyObject_NEW_VAR(PyLongObject, &PyLong_Type, size); |
| } |
| |
| /* Create a new long int object from a C long int */ |
| |
| PyObject * |
| PyLong_FromLong(ival) |
| long ival; |
| { |
| /* Assume a C long fits in at most 5 'digits' */ |
| /* Works on both 32- and 64-bit machines */ |
| PyLongObject *v = _PyLong_New(5); |
| if (v != NULL) { |
| unsigned long t = ival; |
| int i; |
| if (ival < 0) { |
| t = -ival; |
| v->ob_size = -(v->ob_size); |
| } |
| for (i = 0; i < 5; i++) { |
| v->ob_digit[i] = (digit) (t & MASK); |
| t >>= SHIFT; |
| } |
| v = long_normalize(v); |
| } |
| return (PyObject *)v; |
| } |
| |
| /* Create a new long int object from a C unsigned long int */ |
| |
| PyObject * |
| PyLong_FromUnsignedLong(ival) |
| unsigned long ival; |
| { |
| /* Assume a C long fits in at most 5 'digits' */ |
| /* Works on both 32- and 64-bit machines */ |
| PyLongObject *v = _PyLong_New(5); |
| if (v != NULL) { |
| unsigned long t = ival; |
| int i; |
| for (i = 0; i < 5; i++) { |
| v->ob_digit[i] = (digit) (t & MASK); |
| t >>= SHIFT; |
| } |
| v = long_normalize(v); |
| } |
| return (PyObject *)v; |
| } |
| |
| /* Create a new long int object from a C double */ |
| |
| PyObject * |
| #ifdef MPW |
| PyLong_FromDouble(double dval) |
| #else |
| PyLong_FromDouble(dval) |
| double dval; |
| #endif /* MPW */ |
| { |
| PyLongObject *v; |
| double frac; |
| int i, ndig, expo, neg; |
| neg = 0; |
| if (dval < 0.0) { |
| neg = 1; |
| dval = -dval; |
| } |
| frac = frexp(dval, &expo); /* dval = frac*2**expo; 0.0 <= frac < 1.0 */ |
| if (expo <= 0) |
| return PyLong_FromLong(0L); |
| ndig = (expo-1) / SHIFT + 1; /* Number of 'digits' in result */ |
| v = _PyLong_New(ndig); |
| if (v == NULL) |
| return NULL; |
| frac = ldexp(frac, (expo-1) % SHIFT + 1); |
| for (i = ndig; --i >= 0; ) { |
| long bits = (long)frac; |
| v->ob_digit[i] = (digit) bits; |
| frac = frac - (double)bits; |
| frac = ldexp(frac, SHIFT); |
| } |
| if (neg) |
| v->ob_size = -(v->ob_size); |
| return (PyObject *)v; |
| } |
| |
| /* Get a C long int from a long int object. |
| Returns -1 and sets an error condition if overflow occurs. */ |
| |
| long |
| PyLong_AsLong(vv) |
| PyObject *vv; |
| { |
| register PyLongObject *v; |
| long x, prev; |
| int i, sign; |
| |
| if (vv == NULL || !PyLong_Check(vv)) { |
| PyErr_BadInternalCall(); |
| return -1; |
| } |
| v = (PyLongObject *)vv; |
| i = v->ob_size; |
| sign = 1; |
| x = 0; |
| if (i < 0) { |
| sign = -1; |
| i = -(i); |
| } |
| while (--i >= 0) { |
| prev = x; |
| x = (x << SHIFT) + v->ob_digit[i]; |
| if ((x >> SHIFT) != prev) { |
| PyErr_SetString(PyExc_OverflowError, |
| "long int too long to convert"); |
| return -1; |
| } |
| } |
| return x * sign; |
| } |
| |
| /* Get a C long int from a long int object. |
| Returns -1 and sets an error condition if overflow occurs. */ |
| |
| unsigned long |
| PyLong_AsUnsignedLong(vv) |
| PyObject *vv; |
| { |
| register PyLongObject *v; |
| unsigned long x, prev; |
| int i; |
| |
| if (vv == NULL || !PyLong_Check(vv)) { |
| PyErr_BadInternalCall(); |
| return (unsigned long) -1; |
| } |
| v = (PyLongObject *)vv; |
| i = v->ob_size; |
| x = 0; |
| if (i < 0) { |
| PyErr_SetString(PyExc_OverflowError, |
| "can't convert negative value to unsigned long"); |
| return (unsigned long) -1; |
| } |
| while (--i >= 0) { |
| prev = x; |
| x = (x << SHIFT) + v->ob_digit[i]; |
| if ((x >> SHIFT) != prev) { |
| PyErr_SetString(PyExc_OverflowError, |
| "long int too long to convert"); |
| return (unsigned long) -1; |
| } |
| } |
| return x; |
| } |
| |
| /* Get a C double from a long int object. */ |
| |
| double |
| PyLong_AsDouble(vv) |
| PyObject *vv; |
| { |
| register PyLongObject *v; |
| double x; |
| double multiplier = (double) (1L << SHIFT); |
| int i, sign; |
| |
| if (vv == NULL || !PyLong_Check(vv)) { |
| PyErr_BadInternalCall(); |
| return -1; |
| } |
| v = (PyLongObject *)vv; |
| i = v->ob_size; |
| sign = 1; |
| x = 0.0; |
| if (i < 0) { |
| sign = -1; |
| i = -(i); |
| } |
| while (--i >= 0) { |
| x = x*multiplier + (double)v->ob_digit[i]; |
| } |
| return x * sign; |
| } |
| |
| /* Multiply by a single digit, ignoring the sign. */ |
| |
| static PyLongObject * |
| mul1(a, n) |
| PyLongObject *a; |
| wdigit n; |
| { |
| return muladd1(a, n, (digit)0); |
| } |
| |
| /* Multiply by a single digit and add a single digit, ignoring the sign. */ |
| |
| static PyLongObject * |
| muladd1(a, n, extra) |
| PyLongObject *a; |
| wdigit n; |
| wdigit extra; |
| { |
| int size_a = ABS(a->ob_size); |
| PyLongObject *z = _PyLong_New(size_a+1); |
| twodigits carry = extra; |
| int i; |
| |
| if (z == NULL) |
| return NULL; |
| for (i = 0; i < size_a; ++i) { |
| carry += (twodigits)a->ob_digit[i] * n; |
| z->ob_digit[i] = (digit) (carry & MASK); |
| carry >>= SHIFT; |
| } |
| z->ob_digit[i] = (digit) carry; |
| return long_normalize(z); |
| } |
| |
| /* Divide a long 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(a, n, prem) |
| PyLongObject *a; |
| wdigit n; |
| digit *prem; |
| { |
| int size = ABS(a->ob_size); |
| PyLongObject *z; |
| int i; |
| twodigits rem = 0; |
| |
| assert(n > 0 && n <= MASK); |
| z = _PyLong_New(size); |
| if (z == NULL) |
| return NULL; |
| for (i = size; --i >= 0; ) { |
| rem = (rem << SHIFT) + a->ob_digit[i]; |
| z->ob_digit[i] = (digit) (rem/n); |
| rem %= n; |
| } |
| *prem = (digit) rem; |
| return long_normalize(z); |
| } |
| |
| /* Convert a long int object to a string, using a given conversion base. |
| Return a string object. |
| If base is 8 or 16, add the proper prefix '0' or '0x'. |
| External linkage: used in bltinmodule.c by hex() and oct(). */ |
| |
| static PyObject * |
| long_format(aa, base) |
| PyObject *aa; |
| int base; |
| { |
| register PyLongObject *a = (PyLongObject *)aa; |
| PyStringObject *str; |
| int i; |
| int size_a = ABS(a->ob_size); |
| char *p; |
| int bits; |
| char sign = '\0'; |
| |
| if (a == NULL || !PyLong_Check(a)) { |
| PyErr_BadInternalCall(); |
| return NULL; |
| } |
| assert(base >= 2 && base <= 36); |
| |
| /* Compute a rough upper bound for the length of the string */ |
| i = base; |
| bits = 0; |
| while (i > 1) { |
| ++bits; |
| i >>= 1; |
| } |
| i = 6 + (size_a*SHIFT + bits-1) / bits; |
| str = (PyStringObject *) PyString_FromStringAndSize((char *)0, i); |
| if (str == NULL) |
| return NULL; |
| p = PyString_AS_STRING(str) + i; |
| *p = '\0'; |
| *--p = 'L'; |
| if (a->ob_size < 0) |
| sign = '-'; |
| |
| Py_INCREF(a); |
| do { |
| digit rem; |
| PyLongObject *temp = divrem1(a, (digit)base, &rem); |
| if (temp == NULL) { |
| Py_DECREF(a); |
| Py_DECREF(str); |
| return NULL; |
| } |
| if (rem < 10) |
| rem += '0'; |
| else |
| rem += 'A'-10; |
| assert(p > PyString_AS_STRING(str)); |
| *--p = (char) rem; |
| Py_DECREF(a); |
| a = temp; |
| SIGCHECK({ |
| Py_DECREF(a); |
| Py_DECREF(str); |
| return NULL; |
| }) |
| } while (ABS(a->ob_size) != 0); |
| Py_DECREF(a); |
| if (base == 8) { |
| if (size_a != 0) |
| *--p = '0'; |
| } |
| else if (base == 16) { |
| *--p = 'x'; |
| *--p = '0'; |
| } |
| else if (base != 10) { |
| *--p = '#'; |
| *--p = '0' + base%10; |
| if (base > 10) |
| *--p = '0' + base/10; |
| } |
| if (sign) |
| *--p = sign; |
| if (p != PyString_AS_STRING(str)) { |
| char *q = PyString_AS_STRING(str); |
| assert(p > q); |
| do { |
| } while ((*q++ = *p++) != '\0'); |
| q--; |
| _PyString_Resize((PyObject **)&str, |
| (int) (q - PyString_AS_STRING(str))); |
| } |
| return (PyObject *)str; |
| } |
| |
| #if 0 |
| /* Convert a string to a long int object, in a given base. |
| Base zero implies a default depending on the number. |
| External linkage: used in compile.c and stropmodule.c. */ |
| |
| PyObject * |
| long_scan(str, base) |
| char *str; |
| int base; |
| { |
| return PyLong_FromString(str, (char **)NULL, base); |
| } |
| #endif |
| |
| PyObject * |
| PyLong_FromString(str, pend, base) |
| char *str; |
| char **pend; |
| int base; |
| { |
| int sign = 1; |
| PyLongObject *z; |
| |
| if ((base != 0 && base < 2) || base > 36) { |
| PyErr_SetString(PyExc_ValueError, |
| "invalid base for long literal"); |
| return NULL; |
| } |
| while (*str != '\0' && isspace(Py_CHARMASK(*str))) |
| str++; |
| if (*str == '+') |
| ++str; |
| else if (*str == '-') { |
| ++str; |
| sign = -1; |
| } |
| while (*str != '\0' && isspace(Py_CHARMASK(*str))) |
| str++; |
| if (base == 0) { |
| if (str[0] != '0') |
| base = 10; |
| else if (str[1] == 'x' || str[1] == 'X') |
| base = 16; |
| else |
| base = 8; |
| } |
| if (base == 16 && str[0] == '0' && (str[1] == 'x' || str[1] == 'X')) |
| str += 2; |
| z = _PyLong_New(0); |
| for ( ; z != NULL; ++str) { |
| int k = -1; |
| PyLongObject *temp; |
| |
| if (*str <= '9') |
| k = *str - '0'; |
| else if (*str >= 'a') |
| k = *str - 'a' + 10; |
| else if (*str >= 'A') |
| k = *str - 'A' + 10; |
| if (k < 0 || k >= base) |
| break; |
| temp = muladd1(z, (digit)base, (digit)k); |
| Py_DECREF(z); |
| z = temp; |
| } |
| if (sign < 0 && z != NULL && z->ob_size != 0) |
| z->ob_size = -(z->ob_size); |
| if (pend) |
| *pend = str; |
| return (PyObject *) z; |
| } |
| |
| static PyLongObject *x_divrem |
| Py_PROTO((PyLongObject *, PyLongObject *, PyLongObject **)); |
| static PyObject *long_pos Py_PROTO((PyLongObject *)); |
| static int long_divrem Py_PROTO((PyLongObject *, PyLongObject *, |
| PyLongObject **, PyLongObject **)); |
| |
| /* Long division with remainder, top-level routine */ |
| |
| static int |
| long_divrem(a, b, pdiv, prem) |
| PyLongObject *a, *b; |
| PyLongObject **pdiv; |
| PyLongObject **prem; |
| { |
| int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size); |
| PyLongObject *z; |
| |
| if (size_b == 0) { |
| PyErr_SetString(PyExc_ZeroDivisionError, "long division or modulo"); |
| 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|. */ |
| *pdiv = _PyLong_New(0); |
| Py_INCREF(a); |
| *prem = (PyLongObject *) a; |
| 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); |
| } |
| 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 ((a->ob_size < 0) != (b->ob_size < 0)) |
| z->ob_size = -(z->ob_size); |
| if (a->ob_size < 0 && (*prem)->ob_size != 0) |
| (*prem)->ob_size = -((*prem)->ob_size); |
| *pdiv = z; |
| return 0; |
| } |
| |
| /* Unsigned long division with remainder -- the algorithm */ |
| |
| static PyLongObject * |
| x_divrem(v1, w1, prem) |
| PyLongObject *v1, *w1; |
| PyLongObject **prem; |
| { |
| int size_v = ABS(v1->ob_size), size_w = ABS(w1->ob_size); |
| digit d = (digit) ((twodigits)BASE / (w1->ob_digit[size_w-1] + 1)); |
| PyLongObject *v = mul1(v1, d); |
| PyLongObject *w = mul1(w1, d); |
| PyLongObject *a; |
| int j, k; |
| |
| if (v == NULL || w == NULL) { |
| Py_XDECREF(v); |
| Py_XDECREF(w); |
| return NULL; |
| } |
| |
| assert(size_v >= size_w && size_w > 1); /* Assert checks by div() */ |
| assert(v->ob_refcnt == 1); /* Since v will be used as accumulator! */ |
| assert(size_w == ABS(w->ob_size)); /* That's how d was calculated */ |
| |
| size_v = ABS(v->ob_size); |
| a = _PyLong_New(size_v - size_w + 1); |
| |
| for (j = size_v, k = a->ob_size-1; a != NULL && k >= 0; --j, --k) { |
| digit vj = (j >= size_v) ? 0 : v->ob_digit[j]; |
| twodigits q; |
| stwodigits carry = 0; |
| int i; |
| |
| SIGCHECK({ |
| Py_DECREF(a); |
| a = NULL; |
| break; |
| }) |
| if (vj == w->ob_digit[size_w-1]) |
| q = MASK; |
| else |
| q = (((twodigits)vj << SHIFT) + v->ob_digit[j-1]) / |
| w->ob_digit[size_w-1]; |
| |
| while (w->ob_digit[size_w-2]*q > |
| (( |
| ((twodigits)vj << SHIFT) |
| + v->ob_digit[j-1] |
| - q*w->ob_digit[size_w-1] |
| ) << SHIFT) |
| + v->ob_digit[j-2]) |
| --q; |
| |
| for (i = 0; i < size_w && i+k < size_v; ++i) { |
| twodigits z = w->ob_digit[i] * q; |
| digit zz = (digit) (z >> SHIFT); |
| carry += v->ob_digit[i+k] - z |
| + ((twodigits)zz << SHIFT); |
| v->ob_digit[i+k] = carry & MASK; |
| carry = (carry >> SHIFT) - zz; |
| } |
| |
| if (i+k < size_v) { |
| carry += v->ob_digit[i+k]; |
| v->ob_digit[i+k] = 0; |
| } |
| |
| if (carry == 0) |
| a->ob_digit[k] = (digit) q; |
| else { |
| assert(carry == -1); |
| a->ob_digit[k] = (digit) q-1; |
| carry = 0; |
| for (i = 0; i < size_w && i+k < size_v; ++i) { |
| carry += v->ob_digit[i+k] + w->ob_digit[i]; |
| v->ob_digit[i+k] = carry & MASK; |
| carry >>= SHIFT; |
| } |
| } |
| } /* for j, k */ |
| |
| if (a == NULL) |
| *prem = NULL; |
| else { |
| a = long_normalize(a); |
| *prem = divrem1(v, d, &d); |
| /* d receives the (unused) remainder */ |
| if (*prem == NULL) { |
| Py_DECREF(a); |
| a = NULL; |
| } |
| } |
| Py_DECREF(v); |
| Py_DECREF(w); |
| return a; |
| } |
| |
| /* Methods */ |
| |
| /* Forward */ |
| static void long_dealloc Py_PROTO((PyObject *)); |
| static PyObject *long_repr Py_PROTO((PyObject *)); |
| static int long_compare Py_PROTO((PyLongObject *, PyLongObject *)); |
| static long long_hash Py_PROTO((PyLongObject *)); |
| |
| static PyObject *long_add Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_sub Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_mul Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_div Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_mod Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_divmod Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_pow |
| Py_PROTO((PyLongObject *, PyLongObject *, PyLongObject *)); |
| static PyObject *long_neg Py_PROTO((PyLongObject *)); |
| static PyObject *long_pos Py_PROTO((PyLongObject *)); |
| static PyObject *long_abs Py_PROTO((PyLongObject *)); |
| static int long_nonzero Py_PROTO((PyLongObject *)); |
| static PyObject *long_invert Py_PROTO((PyLongObject *)); |
| static PyObject *long_lshift Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_rshift Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_and Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_xor Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyObject *long_or Py_PROTO((PyLongObject *, PyLongObject *)); |
| |
| static void |
| long_dealloc(v) |
| PyObject *v; |
| { |
| PyMem_DEL(v); |
| } |
| |
| static PyObject * |
| long_repr(v) |
| PyObject *v; |
| { |
| return long_format(v, 10); |
| } |
| |
| static int |
| long_compare(a, b) |
| PyLongObject *a, *b; |
| { |
| int sign; |
| |
| if (a->ob_size != b->ob_size) { |
| if (ABS(a->ob_size) == 0 && ABS(b->ob_size) == 0) |
| sign = 0; |
| else |
| sign = a->ob_size - b->ob_size; |
| } |
| else { |
| int i = ABS(a->ob_size); |
| while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i]) |
| ; |
| if (i < 0) |
| sign = 0; |
| else { |
| sign = (int)a->ob_digit[i] - (int)b->ob_digit[i]; |
| if (a->ob_size < 0) |
| sign = -sign; |
| } |
| } |
| return sign < 0 ? -1 : sign > 0 ? 1 : 0; |
| } |
| |
| static long |
| long_hash(v) |
| PyLongObject *v; |
| { |
| long x; |
| int i, sign; |
| |
| /* This is designed so that Python ints and longs with the |
| same value hash to the same value, otherwise comparisons |
| of mapping keys will turn out weird */ |
| i = v->ob_size; |
| sign = 1; |
| x = 0; |
| if (i < 0) { |
| sign = -1; |
| i = -(i); |
| } |
| while (--i >= 0) { |
| /* Force a 32-bit circular shift */ |
| x = ((x << SHIFT) & ~MASK) | ((x >> (32-SHIFT)) & MASK); |
| x += v->ob_digit[i]; |
| } |
| x = x * sign; |
| if (x == -1) |
| x = -2; |
| return x; |
| } |
| |
| |
| /* Add the absolute values of two long integers. */ |
| |
| static PyLongObject *x_add Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyLongObject * |
| x_add(a, b) |
| PyLongObject *a, *b; |
| { |
| int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size); |
| PyLongObject *z; |
| int i; |
| digit carry = 0; |
| |
| /* Ensure a is the larger of the two: */ |
| if (size_a < size_b) { |
| { PyLongObject *temp = a; a = b; b = temp; } |
| { int 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 & MASK; |
| /* The following assumes unsigned shifts don't |
| propagate the sign bit. */ |
| carry >>= SHIFT; |
| } |
| for (; i < size_a; ++i) { |
| carry += a->ob_digit[i]; |
| z->ob_digit[i] = carry & MASK; |
| carry >>= SHIFT; |
| } |
| z->ob_digit[i] = carry; |
| return long_normalize(z); |
| } |
| |
| /* Subtract the absolute values of two integers. */ |
| |
| static PyLongObject *x_sub Py_PROTO((PyLongObject *, PyLongObject *)); |
| static PyLongObject * |
| x_sub(a, b) |
| PyLongObject *a, *b; |
| { |
| int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size); |
| PyLongObject *z; |
| int 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; } |
| { int 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 _PyLong_New(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>SHIFT. */ |
| borrow = a->ob_digit[i] - b->ob_digit[i] - borrow; |
| z->ob_digit[i] = borrow & MASK; |
| borrow >>= SHIFT; |
| borrow &= 1; /* Keep only one sign bit */ |
| } |
| for (; i < size_a; ++i) { |
| borrow = a->ob_digit[i] - borrow; |
| z->ob_digit[i] = borrow & MASK; |
| borrow >>= SHIFT; |
| } |
| assert(borrow == 0); |
| if (sign < 0) |
| z->ob_size = -(z->ob_size); |
| return long_normalize(z); |
| } |
| |
| static PyObject * |
| long_add(a, b) |
| PyLongObject *a; |
| PyLongObject *b; |
| { |
| PyLongObject *z; |
| |
| if (a->ob_size < 0) { |
| if (b->ob_size < 0) { |
| z = x_add(a, b); |
| if (z != NULL && z->ob_size != 0) |
| z->ob_size = -(z->ob_size); |
| } |
| else |
| z = x_sub(b, a); |
| } |
| else { |
| if (b->ob_size < 0) |
| z = x_sub(a, b); |
| else |
| z = x_add(a, b); |
| } |
| return (PyObject *)z; |
| } |
| |
| static PyObject * |
| long_sub(a, b) |
| PyLongObject *a; |
| PyLongObject *b; |
| { |
| PyLongObject *z; |
| |
| if (a->ob_size < 0) { |
| if (b->ob_size < 0) |
| z = x_sub(a, b); |
| else |
| z = x_add(a, b); |
| if (z != NULL && z->ob_size != 0) |
| z->ob_size = -(z->ob_size); |
| } |
| else { |
| if (b->ob_size < 0) |
| z = x_add(a, b); |
| else |
| z = x_sub(a, b); |
| } |
| return (PyObject *)z; |
| } |
| |
| static PyObject * |
| long_mul(a, b) |
| PyLongObject *a; |
| PyLongObject *b; |
| { |
| int size_a; |
| int size_b; |
| PyLongObject *z; |
| int i; |
| |
| size_a = ABS(a->ob_size); |
| size_b = ABS(b->ob_size); |
| z = _PyLong_New(size_a + size_b); |
| if (z == NULL) |
| return NULL; |
| for (i = 0; i < z->ob_size; ++i) |
| z->ob_digit[i] = 0; |
| for (i = 0; i < size_a; ++i) { |
| twodigits carry = 0; |
| twodigits f = a->ob_digit[i]; |
| int j; |
| |
| SIGCHECK({ |
| Py_DECREF(z); |
| return NULL; |
| }) |
| for (j = 0; j < size_b; ++j) { |
| carry += z->ob_digit[i+j] + b->ob_digit[j] * f; |
| z->ob_digit[i+j] = (digit) (carry & MASK); |
| carry >>= SHIFT; |
| } |
| for (; carry != 0; ++j) { |
| assert(i+j < z->ob_size); |
| carry += z->ob_digit[i+j]; |
| z->ob_digit[i+j] = (digit) (carry & MASK); |
| carry >>= SHIFT; |
| } |
| } |
| if (a->ob_size < 0) |
| z->ob_size = -(z->ob_size); |
| if (b->ob_size < 0) |
| z->ob_size = -(z->ob_size); |
| return (PyObject *) long_normalize(z); |
| } |
| |
| /* 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. */ |
| |
| static int l_divmod Py_PROTO((PyLongObject *, PyLongObject *, |
| PyLongObject **, PyLongObject **)); |
| static int |
| l_divmod(v, w, pdiv, pmod) |
| PyLongObject *v; |
| PyLongObject *w; |
| PyLongObject **pdiv; |
| PyLongObject **pmod; |
| { |
| PyLongObject *div, *mod; |
| |
| if (long_divrem(v, w, &div, &mod) < 0) |
| return -1; |
| if ((mod->ob_size < 0 && w->ob_size > 0) || |
| (mod->ob_size > 0 && w->ob_size < 0)) { |
| PyLongObject *temp; |
| PyLongObject *one; |
| temp = (PyLongObject *) long_add(mod, w); |
| Py_DECREF(mod); |
| mod = temp; |
| if (mod == NULL) { |
| Py_DECREF(div); |
| return -1; |
| } |
| one = (PyLongObject *) PyLong_FromLong(1L); |
| if (one == NULL || |
| (temp = (PyLongObject *) long_sub(div, one)) == NULL) { |
| Py_DECREF(mod); |
| Py_DECREF(div); |
| Py_XDECREF(one); |
| return -1; |
| } |
| Py_DECREF(one); |
| Py_DECREF(div); |
| div = temp; |
| } |
| *pdiv = div; |
| *pmod = mod; |
| return 0; |
| } |
| |
| static PyObject * |
| long_div(v, w) |
| PyLongObject *v; |
| PyLongObject *w; |
| { |
| PyLongObject *div, *mod; |
| if (l_divmod(v, w, &div, &mod) < 0) |
| return NULL; |
| Py_DECREF(mod); |
| return (PyObject *)div; |
| } |
| |
| static PyObject * |
| long_mod(v, w) |
| PyLongObject *v; |
| PyLongObject *w; |
| { |
| PyLongObject *div, *mod; |
| if (l_divmod(v, w, &div, &mod) < 0) |
| return NULL; |
| Py_DECREF(div); |
| return (PyObject *)mod; |
| } |
| |
| static PyObject * |
| long_divmod(v, w) |
| PyLongObject *v; |
| PyLongObject *w; |
| { |
| PyObject *z; |
| PyLongObject *div, *mod; |
| if (l_divmod(v, w, &div, &mod) < 0) |
| return NULL; |
| z = PyTuple_New(2); |
| if (z != NULL) { |
| PyTuple_SetItem(z, 0, (PyObject *) div); |
| PyTuple_SetItem(z, 1, (PyObject *) mod); |
| } |
| else { |
| Py_DECREF(div); |
| Py_DECREF(mod); |
| } |
| return z; |
| } |
| |
| static PyObject * |
| long_pow(a, b, c) |
| PyLongObject *a; |
| PyLongObject *b; |
| PyLongObject *c; |
| { |
| PyLongObject *z, *div, *mod; |
| int size_b, i; |
| |
| size_b = b->ob_size; |
| if (size_b < 0) { |
| PyErr_SetString(PyExc_ValueError, |
| "long integer to the negative power"); |
| return NULL; |
| } |
| z = (PyLongObject *)PyLong_FromLong(1L); |
| Py_INCREF(a); |
| for (i = 0; i < size_b; ++i) { |
| digit bi = b->ob_digit[i]; |
| int j; |
| |
| for (j = 0; j < SHIFT; ++j) { |
| PyLongObject *temp; |
| |
| if (bi & 1) { |
| temp = (PyLongObject *)long_mul(z, a); |
| Py_DECREF(z); |
| if ((PyObject*)c!=Py_None && temp!=NULL) { |
| l_divmod(temp, c, &div, &mod); |
| Py_XDECREF(div); |
| Py_DECREF(temp); |
| temp = mod; |
| } |
| z = temp; |
| if (z == NULL) |
| break; |
| } |
| bi >>= 1; |
| if (bi == 0 && i+1 == size_b) |
| break; |
| temp = (PyLongObject *)long_mul(a, a); |
| Py_DECREF(a); |
| if ((PyObject*)c!=Py_None && temp!=NULL) { |
| l_divmod(temp, c, &div, &mod); |
| Py_XDECREF(div); |
| Py_DECREF(temp); |
| temp = mod; |
| } |
| a = temp; |
| if (a == NULL) { |
| Py_DECREF(z); |
| z = NULL; |
| break; |
| } |
| } |
| if (a == NULL || z == NULL) |
| break; |
| } |
| Py_XDECREF(a); |
| if ((PyObject*)c!=Py_None && z!=NULL) { |
| l_divmod(z, c, &div, &mod); |
| Py_XDECREF(div); |
| Py_DECREF(z); |
| z=mod; |
| } |
| return (PyObject *)z; |
| } |
| |
| static PyObject * |
| long_invert(v) |
| PyLongObject *v; |
| { |
| /* Implement ~x as -(x+1) */ |
| PyLongObject *x; |
| PyLongObject *w; |
| w = (PyLongObject *)PyLong_FromLong(1L); |
| if (w == NULL) |
| return NULL; |
| x = (PyLongObject *) long_add(v, w); |
| Py_DECREF(w); |
| if (x == NULL) |
| return NULL; |
| if (x->ob_size != 0) |
| x->ob_size = -(x->ob_size); |
| return (PyObject *)x; |
| } |
| |
| static PyObject * |
| long_pos(v) |
| PyLongObject *v; |
| { |
| Py_INCREF(v); |
| return (PyObject *)v; |
| } |
| |
| static PyObject * |
| long_neg(v) |
| PyLongObject *v; |
| { |
| PyLongObject *z; |
| int i, n; |
| n = ABS(v->ob_size); |
| if (n == 0) { |
| /* -0 == 0 */ |
| Py_INCREF(v); |
| return (PyObject *) v; |
| } |
| z = _PyLong_New(ABS(n)); |
| if (z == NULL) |
| return NULL; |
| for (i = 0; i < n; i++) |
| z->ob_digit[i] = v->ob_digit[i]; |
| z->ob_size = -(v->ob_size); |
| return (PyObject *)z; |
| } |
| |
| static PyObject * |
| long_abs(v) |
| PyLongObject *v; |
| { |
| if (v->ob_size < 0) |
| return long_neg(v); |
| else { |
| Py_INCREF(v); |
| return (PyObject *)v; |
| } |
| } |
| |
| static int |
| long_nonzero(v) |
| PyLongObject *v; |
| { |
| return ABS(v->ob_size) != 0; |
| } |
| |
| static PyObject * |
| long_rshift(a, b) |
| PyLongObject *a; |
| PyLongObject *b; |
| { |
| PyLongObject *z; |
| long shiftby; |
| int newsize, wordshift, loshift, hishift, i, j; |
| digit lomask, himask; |
| |
| if (a->ob_size < 0) { |
| /* Right shifting negative numbers is harder */ |
| PyLongObject *a1, *a2, *a3; |
| a1 = (PyLongObject *) long_invert(a); |
| if (a1 == NULL) return NULL; |
| a2 = (PyLongObject *) long_rshift(a1, b); |
| Py_DECREF(a1); |
| if (a2 == NULL) return NULL; |
| a3 = (PyLongObject *) long_invert(a2); |
| Py_DECREF(a2); |
| return (PyObject *) a3; |
| } |
| |
| shiftby = PyLong_AsLong((PyObject *)b); |
| if (shiftby == -1L && PyErr_Occurred()) |
| return NULL; |
| if (shiftby < 0) { |
| PyErr_SetString(PyExc_ValueError, "negative shift count"); |
| return NULL; |
| } |
| wordshift = shiftby / SHIFT; |
| newsize = ABS(a->ob_size) - wordshift; |
| if (newsize <= 0) { |
| z = _PyLong_New(0); |
| return (PyObject *)z; |
| } |
| loshift = shiftby % SHIFT; |
| hishift = SHIFT - loshift; |
| lomask = ((digit)1 << hishift) - 1; |
| himask = MASK ^ lomask; |
| z = _PyLong_New(newsize); |
| if (z == NULL) |
| return NULL; |
| if (a->ob_size < 0) |
| z->ob_size = -(z->ob_size); |
| for (i = 0, j = wordshift; i < newsize; i++, j++) { |
| z->ob_digit[i] = (a->ob_digit[j] >> loshift) & lomask; |
| if (i+1 < newsize) |
| z->ob_digit[i] |= |
| (a->ob_digit[j+1] << hishift) & himask; |
| } |
| return (PyObject *) long_normalize(z); |
| } |
| |
| static PyObject * |
| long_lshift(a, b) |
| PyLongObject *a; |
| PyLongObject *b; |
| { |
| /* This version due to Tim Peters */ |
| PyLongObject *z; |
| long shiftby; |
| int oldsize, newsize, wordshift, remshift, i, j; |
| twodigits accum; |
| |
| shiftby = PyLong_AsLong((PyObject *)b); |
| if (shiftby == -1L && PyErr_Occurred()) |
| return NULL; |
| if (shiftby < 0) { |
| PyErr_SetString(PyExc_ValueError, "negative shift count"); |
| return NULL; |
| } |
| if ((long)(int)shiftby != shiftby) { |
| PyErr_SetString(PyExc_ValueError, |
| "outrageous left shift count"); |
| return NULL; |
| } |
| /* wordshift, remshift = divmod(shiftby, SHIFT) */ |
| wordshift = (int)shiftby / SHIFT; |
| remshift = (int)shiftby - wordshift * SHIFT; |
| |
| oldsize = ABS(a->ob_size); |
| newsize = oldsize + wordshift; |
| if (remshift) |
| ++newsize; |
| z = _PyLong_New(newsize); |
| if (z == NULL) |
| return NULL; |
| if (a->ob_size < 0) |
| z->ob_size = -(z->ob_size); |
| for (i = 0; i < wordshift; i++) |
| z->ob_digit[i] = 0; |
| accum = 0; |
| for (i = wordshift, j = 0; j < oldsize; i++, j++) { |
| accum |= a->ob_digit[j] << remshift; |
| z->ob_digit[i] = (digit)(accum & MASK); |
| accum >>= SHIFT; |
| } |
| if (remshift) |
| z->ob_digit[newsize-1] = (digit)accum; |
| else |
| assert(!accum); |
| return (PyObject *) long_normalize(z); |
| } |
| |
| |
| /* Bitwise and/xor/or operations */ |
| |
| #define MAX(x, y) ((x) < (y) ? (y) : (x)) |
| #define MIN(x, y) ((x) > (y) ? (y) : (x)) |
| |
| static PyObject *long_bitwise Py_PROTO((PyLongObject *, int, PyLongObject *)); |
| static PyObject * |
| long_bitwise(a, op, b) |
| PyLongObject *a; |
| int op; /* '&', '|', '^' */ |
| PyLongObject *b; |
| { |
| digit maska, maskb; /* 0 or MASK */ |
| int negz; |
| int size_a, size_b, size_z; |
| PyLongObject *z; |
| int i; |
| digit diga, digb; |
| PyObject *v; |
| |
| if (a->ob_size < 0) { |
| a = (PyLongObject *) long_invert(a); |
| maska = MASK; |
| } |
| else { |
| Py_INCREF(a); |
| maska = 0; |
| } |
| if (b->ob_size < 0) { |
| b = (PyLongObject *) long_invert(b); |
| maskb = MASK; |
| } |
| else { |
| Py_INCREF(b); |
| maskb = 0; |
| } |
| |
| size_a = a->ob_size; |
| size_b = b->ob_size; |
| size_z = MAX(size_a, size_b); |
| z = _PyLong_New(size_z); |
| if (a == NULL || b == NULL || z == NULL) { |
| Py_XDECREF(a); |
| Py_XDECREF(b); |
| Py_XDECREF(z); |
| return NULL; |
| } |
| |
| negz = 0; |
| switch (op) { |
| case '^': |
| if (maska != maskb) { |
| maska ^= MASK; |
| negz = -1; |
| } |
| break; |
| case '&': |
| if (maska && maskb) { |
| op = '|'; |
| maska ^= MASK; |
| maskb ^= MASK; |
| negz = -1; |
| } |
| break; |
| case '|': |
| if (maska || maskb) { |
| op = '&'; |
| maska ^= MASK; |
| maskb ^= MASK; |
| negz = -1; |
| } |
| break; |
| } |
| |
| for (i = 0; i < size_z; ++i) { |
| diga = (i < size_a ? a->ob_digit[i] : 0) ^ maska; |
| digb = (i < size_b ? b->ob_digit[i] : 0) ^ maskb; |
| switch (op) { |
| case '&': z->ob_digit[i] = diga & digb; break; |
| case '|': z->ob_digit[i] = diga | digb; break; |
| case '^': z->ob_digit[i] = diga ^ digb; break; |
| } |
| } |
| |
| Py_DECREF(a); |
| Py_DECREF(b); |
| z = long_normalize(z); |
| if (negz == 0) |
| return (PyObject *) z; |
| v = long_invert(z); |
| Py_DECREF(z); |
| return v; |
| } |
| |
| static PyObject * |
| long_and(a, b) |
| PyLongObject *a; |
| PyLongObject *b; |
| { |
| return long_bitwise(a, '&', b); |
| } |
| |
| static PyObject * |
| long_xor(a, b) |
| PyLongObject *a; |
| PyLongObject *b; |
| { |
| return long_bitwise(a, '^', b); |
| } |
| |
| static PyObject * |
| long_or(a, b) |
| PyLongObject *a; |
| PyLongObject *b; |
| { |
| return long_bitwise(a, '|', b); |
| } |
| |
| static int |
| long_coerce(pv, pw) |
| PyObject **pv; |
| PyObject **pw; |
| { |
| if (PyInt_Check(*pw)) { |
| *pw = PyLong_FromLong(PyInt_AsLong(*pw)); |
| Py_INCREF(*pv); |
| return 0; |
| } |
| return 1; /* Can't do it */ |
| } |
| |
| static PyObject * |
| long_int(v) |
| PyObject *v; |
| { |
| long x; |
| x = PyLong_AsLong(v); |
| if (PyErr_Occurred()) |
| return NULL; |
| return PyInt_FromLong(x); |
| } |
| |
| static PyObject * |
| long_long(v) |
| PyObject *v; |
| { |
| Py_INCREF(v); |
| return v; |
| } |
| |
| static PyObject * |
| long_float(v) |
| PyObject *v; |
| { |
| double result; |
| PyFPE_START_PROTECT("long_float", return 0) |
| result = PyLong_AsDouble(v); |
| PyFPE_END_PROTECT(result) |
| return PyFloat_FromDouble(result); |
| } |
| |
| static PyObject * |
| long_oct(v) |
| PyObject *v; |
| { |
| return long_format(v, 8); |
| } |
| |
| static PyObject * |
| long_hex(v) |
| PyObject *v; |
| { |
| return long_format(v, 16); |
| } |
| |
| |
| #define UF (unaryfunc) |
| #define BF (binaryfunc) |
| #define TF (ternaryfunc) |
| #define IF (inquiry) |
| |
| static PyNumberMethods long_as_number = { |
| BF long_add, /*nb_add*/ |
| BF long_sub, /*nb_subtract*/ |
| BF long_mul, /*nb_multiply*/ |
| BF long_div, /*nb_divide*/ |
| BF long_mod, /*nb_remainder*/ |
| BF long_divmod, /*nb_divmod*/ |
| TF long_pow, /*nb_power*/ |
| UF long_neg, /*nb_negative*/ |
| UF long_pos, /*tp_positive*/ |
| UF long_abs, /*tp_absolute*/ |
| IF long_nonzero,/*tp_nonzero*/ |
| UF long_invert, /*nb_invert*/ |
| BF long_lshift, /*nb_lshift*/ |
| BF long_rshift, /*nb_rshift*/ |
| BF long_and, /*nb_and*/ |
| BF long_xor, /*nb_xor*/ |
| BF long_or, /*nb_or*/ |
| (int (*) Py_FPROTO((PyObject **, PyObject **))) |
| (coercion)long_coerce, /*nb_coerce*/ |
| UF long_int, /*nb_int*/ |
| UF long_long, /*nb_long*/ |
| UF long_float, /*nb_float*/ |
| UF long_oct, /*nb_oct*/ |
| UF long_hex, /*nb_hex*/ |
| }; |
| |
| PyTypeObject PyLong_Type = { |
| PyObject_HEAD_INIT(&PyType_Type) |
| 0, |
| "long int", |
| sizeof(PyLongObject) - sizeof(digit), |
| sizeof(digit), |
| (destructor)long_dealloc, /*tp_dealloc*/ |
| 0, /*tp_print*/ |
| 0, /*tp_getattr*/ |
| 0, /*tp_setattr*/ |
| (int (*) Py_FPROTO((PyObject *, PyObject *))) |
| (cmpfunc)long_compare, /*tp_compare*/ |
| (reprfunc)long_repr, /*tp_repr*/ |
| &long_as_number,/*tp_as_number*/ |
| 0, /*tp_as_sequence*/ |
| 0, /*tp_as_mapping*/ |
| (long (*) Py_FPROTO((PyObject *))) |
| (hashfunc)long_hash, /*tp_hash*/ |
| }; |