/*********************************************************** 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. ******************************************************************/ /* Integer object implementation */ #include "Python.h" #include #ifdef HAVE_LIMITS_H #include #endif #ifndef LONG_MAX #define LONG_MAX 0X7FFFFFFFL #endif #ifndef LONG_MIN #define LONG_MIN (-LONG_MAX-1) #endif #ifndef CHAR_BIT #define CHAR_BIT 8 #endif #ifndef LONG_BIT #define LONG_BIT (CHAR_BIT * sizeof(long)) #endif long PyInt_GetMax() { return LONG_MAX; /* To initialize sys.maxint */ } /* Standard Booleans */ PyIntObject _Py_ZeroStruct = { PyObject_HEAD_INIT(&PyInt_Type) 0 }; PyIntObject _Py_TrueStruct = { PyObject_HEAD_INIT(&PyInt_Type) 1 }; static PyObject * err_ovf(msg) char *msg; { PyErr_SetString(PyExc_OverflowError, msg); return NULL; } /* Integers are quite normal objects, to make object handling uniform. (Using odd pointers to represent integers would save much space but require extra checks for this special case throughout the code.) Since, a typical Python program spends much of its time allocating and deallocating integers, these operations should be very fast. Therefore we use a dedicated allocation scheme with a much lower overhead (in space and time) than straight malloc(): a simple dedicated free list, filled when necessary with memory from malloc(). */ #define BLOCK_SIZE 1000 /* 1K less typical malloc overhead */ #define BHEAD_SIZE 8 /* Enough for a 64-bit pointer */ #define N_INTOBJECTS ((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyIntObject)) #define PyMem_MALLOC malloc #define PyMem_FREE free struct _intblock { struct _intblock *next; PyIntObject objects[N_INTOBJECTS]; }; typedef struct _intblock PyIntBlock; static PyIntBlock *block_list = NULL; static PyIntObject *free_list = NULL; static PyIntObject * fill_free_list() { PyIntObject *p, *q; p = (PyIntObject *)PyMem_MALLOC(sizeof(PyIntBlock)); if (p == NULL) return (PyIntObject *)PyErr_NoMemory(); ((PyIntBlock *)p)->next = block_list; block_list = (PyIntBlock *)p; p = &((PyIntBlock *)p)->objects[0]; q = p + N_INTOBJECTS; while (--q > p) q->ob_type = (struct _typeobject *)(q-1); q->ob_type = NULL; return p + N_INTOBJECTS - 1; } #ifndef NSMALLPOSINTS #define NSMALLPOSINTS 100 #endif #ifndef NSMALLNEGINTS #define NSMALLNEGINTS 1 #endif #if NSMALLNEGINTS + NSMALLPOSINTS > 0 /* References to small integers are saved in this array so that they can be shared. The integers that are saved are those in the range -NSMALLNEGINTS (inclusive) to NSMALLPOSINTS (not inclusive). */ static PyIntObject *small_ints[NSMALLNEGINTS + NSMALLPOSINTS]; #endif #ifdef COUNT_ALLOCS int quick_int_allocs, quick_neg_int_allocs; #endif PyObject * PyInt_FromLong(ival) long ival; { register PyIntObject *v; #if NSMALLNEGINTS + NSMALLPOSINTS > 0 if (-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS && (v = small_ints[ival + NSMALLNEGINTS]) != NULL) { Py_INCREF(v); #ifdef COUNT_ALLOCS if (ival >= 0) quick_int_allocs++; else quick_neg_int_allocs++; #endif return (PyObject *) v; } #endif if (free_list == NULL) { if ((free_list = fill_free_list()) == NULL) return NULL; } v = free_list; free_list = (PyIntObject *)v->ob_type; v->ob_type = &PyInt_Type; v->ob_ival = ival; _Py_NewReference((PyObject *)v); #if NSMALLNEGINTS + NSMALLPOSINTS > 0 if (-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS) { /* save this one for a following allocation */ Py_INCREF(v); small_ints[ival + NSMALLNEGINTS] = v; } #endif return (PyObject *) v; } static void int_dealloc(v) PyIntObject *v; { v->ob_type = (struct _typeobject *)free_list; free_list = v; } long PyInt_AsLong(op) register PyObject *op; { PyNumberMethods *nb; PyIntObject *io; long val; if (op && PyInt_Check(op)) return PyInt_AS_LONG((PyIntObject*) op); if (op == NULL || (nb = op->ob_type->tp_as_number) == NULL || nb->nb_int == NULL) { PyErr_BadArgument(); return -1; } io = (PyIntObject*) (*nb->nb_int) (op); if (io == NULL) return -1; if (!PyInt_Check(io)) { PyErr_SetString(PyExc_TypeError, "nb_int should return int object"); return -1; } val = PyInt_AS_LONG(io); Py_DECREF(io); return val; } PyObject * PyInt_FromString(s, pend, base) char *s; char **pend; int base; { char *end; long x; char buffer[256]; /* For errors */ if ((base != 0 && base < 2) || base > 36) { PyErr_SetString(PyExc_ValueError, "invalid base for int()"); return NULL; } while (*s && isspace(Py_CHARMASK(*s))) s++; errno = 0; if (base == 0 && s[0] == '0') x = (long) PyOS_strtoul(s, &end, base); else x = PyOS_strtol(s, &end, base); if (end == s || !isalnum(end[-1])) goto bad; while (*end && isspace(Py_CHARMASK(*end))) end++; if (*end != '\0') { bad: sprintf(buffer, "invalid literal for int(): %.200s", s); PyErr_SetString(PyExc_ValueError, buffer); return NULL; } else if (errno != 0) { sprintf(buffer, "int() literal too large: %.200s", s); PyErr_SetString(PyExc_ValueError, buffer); return NULL; } if (pend) *pend = end; return PyInt_FromLong(x); } /* Methods */ /* ARGSUSED */ static int int_print(v, fp, flags) PyIntObject *v; FILE *fp; int flags; /* Not used but required by interface */ { fprintf(fp, "%ld", v->ob_ival); return 0; } static PyObject * int_repr(v) PyIntObject *v; { char buf[20]; sprintf(buf, "%ld", v->ob_ival); return PyString_FromString(buf); } static int int_compare(v, w) PyIntObject *v, *w; { register long i = v->ob_ival; register long j = w->ob_ival; return (i < j) ? -1 : (i > j) ? 1 : 0; } static long int_hash(v) PyIntObject *v; { /* XXX If this is changed, you also need to change the way Python's long, float and complex types are hashed. */ long x = v -> ob_ival; if (x == -1) x = -2; return x; } static PyObject * int_add(v, w) PyIntObject *v; PyIntObject *w; { register long a, b, x; a = v->ob_ival; b = w->ob_ival; x = a + b; if ((x^a) < 0 && (x^b) < 0) return err_ovf("integer addition"); return PyInt_FromLong(x); } static PyObject * int_sub(v, w) PyIntObject *v; PyIntObject *w; { register long a, b, x; a = v->ob_ival; b = w->ob_ival; x = a - b; if ((x^a) < 0 && (x^~b) < 0) return err_ovf("integer subtraction"); return PyInt_FromLong(x); } /* Integer overflow checking used to be done using a double, but on 64 bit machines (where both long and double are 64 bit) this fails because the double doesn't have enouvg precision. John Tromp suggests the following algorithm: Suppose again we normalize a and b to be nonnegative. Let ah and al (bh and bl) be the high and low 32 bits of a (b, resp.). Now we test ah and bh against zero and get essentially 3 possible outcomes. 1) both ah and bh > 0 : then report overflow 2) both ah and bh = 0 : then compute a*b and report overflow if it comes out negative 3) ah > 0 and bh = 0 : compute ah*bl and report overflow if it's >= 2^31 compute al*bl and report overflow if it's negative add (ah*bl)<<32 to al*bl and report overflow if it's negative In case of no overflow the result is then negated if necessary. The majority of cases will be 2), in which case this method is the same as what I suggested before. If multiplication is expensive enough, then the other method is faster on case 3), but also more work to program, so I guess the above is the preferred solution. */ static PyObject * int_mul(v, w) PyIntObject *v; PyIntObject *w; { long a, b, ah, bh, x, y; int s = 1; a = v->ob_ival; b = w->ob_ival; ah = a >> (LONG_BIT/2); bh = b >> (LONG_BIT/2); /* Quick test for common case: two small positive ints */ if (ah == 0 && bh == 0) { x = a*b; if (x < 0) goto bad; return PyInt_FromLong(x); } /* Arrange that a >= b >= 0 */ if (a < 0) { a = -a; if (a < 0) { /* Largest negative */ if (b == 0 || b == 1) { x = a*b; goto ok; } else goto bad; } s = -s; ah = a >> (LONG_BIT/2); } if (b < 0) { b = -b; if (b < 0) { /* Largest negative */ if (a == 0 || (a == 1 && s == 1)) { x = a*b; goto ok; } else goto bad; } s = -s; bh = b >> (LONG_BIT/2); } /* 1) both ah and bh > 0 : then report overflow */ if (ah != 0 && bh != 0) goto bad; /* 2) both ah and bh = 0 : then compute a*b and report overflow if it comes out negative */ if (ah == 0 && bh == 0) { x = a*b; if (x < 0) goto bad; return PyInt_FromLong(x*s); } if (a < b) { /* Swap */ x = a; a = b; b = x; ah = bh; /* bh not used beyond this point */ } /* 3) ah > 0 and bh = 0 : compute ah*bl and report overflow if it's >= 2^31 compute al*bl and report overflow if it's negative add (ah*bl)<<32 to al*bl and report overflow if it's negative (NB b == bl in this case, and we make a = al) */ y = ah*b; if (y >= (1L << (LONG_BIT/2 - 1))) goto bad; a &= (1L << (LONG_BIT/2)) - 1; x = a*b; if (x < 0) goto bad; x += y << (LONG_BIT/2); if (x < 0) goto bad; ok: return PyInt_FromLong(x * s); bad: return err_ovf("integer multiplication"); } static int i_divmod(x, y, p_xdivy, p_xmody) register PyIntObject *x, *y; long *p_xdivy, *p_xmody; { long xi = x->ob_ival; long yi = y->ob_ival; long xdivy, xmody; if (yi == 0) { PyErr_SetString(PyExc_ZeroDivisionError, "integer division or modulo"); return -1; } if (yi < 0) { if (xi < 0) { if (yi == -1 && -xi < 0) { /* most negative / -1 */ err_ovf("integer division"); return -1; } xdivy = -xi / -yi; } else xdivy = - (xi / -yi); } else { if (xi < 0) xdivy = - (-xi / yi); else xdivy = xi / yi; } xmody = xi - xdivy*yi; if ((xmody < 0 && yi > 0) || (xmody > 0 && yi < 0)) { xmody += yi; xdivy -= 1; } *p_xdivy = xdivy; *p_xmody = xmody; return 0; } static PyObject * int_div(x, y) PyIntObject *x; PyIntObject *y; { long d, m; if (i_divmod(x, y, &d, &m) < 0) return NULL; return PyInt_FromLong(d); } static PyObject * int_mod(x, y) PyIntObject *x; PyIntObject *y; { long d, m; if (i_divmod(x, y, &d, &m) < 0) return NULL; return PyInt_FromLong(m); } static PyObject * int_divmod(x, y) PyIntObject *x; PyIntObject *y; { long d, m; if (i_divmod(x, y, &d, &m) < 0) return NULL; return Py_BuildValue("(ll)", d, m); } static PyObject * int_pow(v, w, z) PyIntObject *v; PyIntObject *w; PyIntObject *z; { #if 1 register long iv, iw, iz=0, ix, temp, prev; iv = v->ob_ival; iw = w->ob_ival; if (iw < 0) { PyErr_SetString(PyExc_ValueError, "integer to the negative power"); return NULL; } if ((PyObject *)z != Py_None) { iz = z->ob_ival; if (iz == 0) { PyErr_SetString(PyExc_ValueError, "pow(x, y, z) with z==0"); return NULL; } } /* * XXX: The original exponentiation code stopped looping * when temp hit zero; this code will continue onwards * unnecessarily, but at least it won't cause any errors. * Hopefully the speed improvement from the fast exponentiation * will compensate for the slight inefficiency. * XXX: Better handling of overflows is desperately needed. */ temp = iv; ix = 1; while (iw > 0) { prev = ix; /* Save value for overflow check */ if (iw & 1) { ix = ix*temp; if (temp == 0) break; /* Avoid ix / 0 */ if (ix / temp != prev) return err_ovf("integer exponentiation"); } iw >>= 1; /* Shift exponent down by 1 bit */ if (iw==0) break; prev = temp; temp *= temp; /* Square the value of temp */ if (prev!=0 && temp/prev!=prev) return err_ovf("integer exponentiation"); if (iz) { /* If we did a multiplication, perform a modulo */ ix = ix % iz; temp = temp % iz; } } if (iz) { PyObject *t1, *t2; long int div, mod; t1=PyInt_FromLong(ix); t2=PyInt_FromLong(iz); if (t1==NULL || t2==NULL || i_divmod((PyIntObject *)t1, (PyIntObject *)t2, &div, &mod)<0) { Py_XDECREF(t1); Py_XDECREF(t2); return(NULL); } Py_DECREF(t1); Py_DECREF(t2); ix=mod; } return PyInt_FromLong(ix); #else register long iv, iw, ix; iv = v->ob_ival; iw = w->ob_ival; if (iw < 0) { PyErr_SetString(PyExc_ValueError, "integer to the negative power"); return NULL; } if ((PyObject *)z != Py_None) { PyErr_SetString(PyExc_TypeError, "pow(int, int, int) not yet supported"); return NULL; } ix = 1; while (--iw >= 0) { long prev = ix; ix = ix * iv; if (iv == 0) break; /* 0 to some power -- avoid ix / 0 */ if (ix / iv != prev) return err_ovf("integer exponentiation"); } return PyInt_FromLong(ix); #endif } static PyObject * int_neg(v) PyIntObject *v; { register long a, x; a = v->ob_ival; x = -a; if (a < 0 && x < 0) return err_ovf("integer negation"); return PyInt_FromLong(x); } static PyObject * int_pos(v) PyIntObject *v; { Py_INCREF(v); return (PyObject *)v; } static PyObject * int_abs(v) PyIntObject *v; { if (v->ob_ival >= 0) return int_pos(v); else return int_neg(v); } static int int_nonzero(v) PyIntObject *v; { return v->ob_ival != 0; } static PyObject * int_invert(v) PyIntObject *v; { return PyInt_FromLong(~v->ob_ival); } static PyObject * int_lshift(v, w) PyIntObject *v; PyIntObject *w; { register long a, b; a = v->ob_ival; b = w->ob_ival; if (b < 0) { PyErr_SetString(PyExc_ValueError, "negative shift count"); return NULL; } if (a == 0 || b == 0) { Py_INCREF(v); return (PyObject *) v; } if (b >= LONG_BIT) { return PyInt_FromLong(0L); } a = (unsigned long)a << b; return PyInt_FromLong(a); } static PyObject * int_rshift(v, w) PyIntObject *v; PyIntObject *w; { register long a, b; a = v->ob_ival; b = w->ob_ival; if (b < 0) { PyErr_SetString(PyExc_ValueError, "negative shift count"); return NULL; } if (a == 0 || b == 0) { Py_INCREF(v); return (PyObject *) v; } if (b >= LONG_BIT) { if (a < 0) a = -1; else a = 0; } else { if (a < 0) a = ~( ~(unsigned long)a >> b ); else a = (unsigned long)a >> b; } return PyInt_FromLong(a); } static PyObject * int_and(v, w) PyIntObject *v; PyIntObject *w; { register long a, b; a = v->ob_ival; b = w->ob_ival; return PyInt_FromLong(a & b); } static PyObject * int_xor(v, w) PyIntObject *v; PyIntObject *w; { register long a, b; a = v->ob_ival; b = w->ob_ival; return PyInt_FromLong(a ^ b); } static PyObject * int_or(v, w) PyIntObject *v; PyIntObject *w; { register long a, b; a = v->ob_ival; b = w->ob_ival; return PyInt_FromLong(a | b); } static PyObject * int_int(v) PyIntObject *v; { Py_INCREF(v); return (PyObject *)v; } static PyObject * int_long(v) PyIntObject *v; { return PyLong_FromLong((v -> ob_ival)); } static PyObject * int_float(v) PyIntObject *v; { return PyFloat_FromDouble((double)(v -> ob_ival)); } static PyObject * int_oct(v) PyIntObject *v; { char buf[100]; long x = v -> ob_ival; if (x == 0) strcpy(buf, "0"); else sprintf(buf, "0%lo", x); return PyString_FromString(buf); } static PyObject * int_hex(v) PyIntObject *v; { char buf[100]; long x = v -> ob_ival; sprintf(buf, "0x%lx", x); return PyString_FromString(buf); } static PyNumberMethods int_as_number = { (binaryfunc)int_add, /*nb_add*/ (binaryfunc)int_sub, /*nb_subtract*/ (binaryfunc)int_mul, /*nb_multiply*/ (binaryfunc)int_div, /*nb_divide*/ (binaryfunc)int_mod, /*nb_remainder*/ (binaryfunc)int_divmod, /*nb_divmod*/ (ternaryfunc)int_pow, /*nb_power*/ (unaryfunc)int_neg, /*nb_negative*/ (unaryfunc)int_pos, /*nb_positive*/ (unaryfunc)int_abs, /*nb_absolute*/ (inquiry)int_nonzero, /*nb_nonzero*/ (unaryfunc)int_invert, /*nb_invert*/ (binaryfunc)int_lshift, /*nb_lshift*/ (binaryfunc)int_rshift, /*nb_rshift*/ (binaryfunc)int_and, /*nb_and*/ (binaryfunc)int_xor, /*nb_xor*/ (binaryfunc)int_or, /*nb_or*/ 0, /*nb_coerce*/ (unaryfunc)int_int, /*nb_int*/ (unaryfunc)int_long, /*nb_long*/ (unaryfunc)int_float, /*nb_float*/ (unaryfunc)int_oct, /*nb_oct*/ (unaryfunc)int_hex, /*nb_hex*/ }; PyTypeObject PyInt_Type = { PyObject_HEAD_INIT(&PyType_Type) 0, "int", sizeof(PyIntObject), 0, (destructor)int_dealloc, /*tp_dealloc*/ (printfunc)int_print, /*tp_print*/ 0, /*tp_getattr*/ 0, /*tp_setattr*/ (cmpfunc)int_compare, /*tp_compare*/ (reprfunc)int_repr, /*tp_repr*/ &int_as_number, /*tp_as_number*/ 0, /*tp_as_sequence*/ 0, /*tp_as_mapping*/ (hashfunc)int_hash, /*tp_hash*/ }; void PyInt_Fini() { PyIntObject *p; PyIntBlock *list, *next; int i; int bc, bf; /* block count, number of freed blocks */ int irem, isum; /* remaining unfreed ints per block, total */ #if NSMALLNEGINTS + NSMALLPOSINTS > 0 PyIntObject **q; i = NSMALLNEGINTS + NSMALLPOSINTS; q = small_ints; while (--i >= 0) { Py_XDECREF(*q); *q++ = NULL; } #endif bc = 0; bf = 0; isum = 0; list = block_list; block_list = NULL; free_list = NULL; while (list != NULL) { bc++; irem = 0; for (i = 0, p = &list->objects[0]; i < N_INTOBJECTS; i++, p++) { if (PyInt_Check(p) && p->ob_refcnt != 0) irem++; } next = list->next; if (irem) { list->next = block_list; block_list = list; for (i = 0, p = &list->objects[0]; i < N_INTOBJECTS; i++, p++) { if (!PyInt_Check(p) || p->ob_refcnt == 0) { p->ob_type = (struct _typeobject *) free_list; free_list = p; } #if NSMALLNEGINTS + NSMALLPOSINTS > 0 else if (-NSMALLNEGINTS <= p->ob_ival && p->ob_ival < NSMALLPOSINTS && small_ints[p->ob_ival + NSMALLNEGINTS] == NULL) { Py_INCREF(p); small_ints[p->ob_ival + NSMALLNEGINTS] = p; } #endif } } else { PyMem_FREE(list); bf++; } isum += irem; list = next; } if (!Py_VerboseFlag) return; fprintf(stderr, "# cleanup ints"); if (!isum) { fprintf(stderr, "\n"); } else { fprintf(stderr, ": %d unfreed int%s in %d out of %d block%s\n", isum, isum == 1 ? "" : "s", bc - bf, bc, bc == 1 ? "" : "s"); } if (Py_VerboseFlag > 1) { list = block_list; while (list != NULL) { for (i = 0, p = &list->objects[0]; i < N_INTOBJECTS; i++, p++) { if (PyInt_Check(p) && p->ob_refcnt != 0) fprintf(stderr, "# \n", (long)p, p->ob_refcnt, p->ob_ival); } list = list->next; } } }