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- /***********************************************************
- Copyright 1991, 1992, 1993, 1994 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 not be used in advertising or publicity pertaining to
- distribution of the software without specific, written prior permission.
-
- STICHTING MATHEMATISCH CENTRUM DISCLAIMS ALL WARRANTIES WITH REGARD TO
- THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
- FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH CENTRUM 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 "allobjects.h"
- #include "modsupport.h"
-
- #ifdef HAVE_LIMITS_H
- #include <limits.h>
- #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
- getmaxint()
- {
- return LONG_MAX; /* To initialize sys.maxint */
- }
-
- /* Standard Booleans */
-
- intobject FalseObject = {
- OB_HEAD_INIT(&Inttype)
- 0
- };
-
- intobject TrueObject = {
- OB_HEAD_INIT(&Inttype)
- 1
- };
-
- static object *
- err_ovf(msg)
- char *msg;
- {
- err_setstr(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 N_INTOBJECTS (BLOCK_SIZE / sizeof(intobject))
-
- static intobject *
- fill_free_list()
- {
- intobject *p, *q;
- p = NEW(intobject, N_INTOBJECTS);
- if (p == NULL)
- return (intobject *)err_nomem();
- q = p + N_INTOBJECTS;
- while (--q > p)
- *(intobject **)q = q-1;
- *(intobject **)q = NULL;
- return p + N_INTOBJECTS - 1;
- }
-
- static intobject *free_list = NULL;
- #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 intobject *small_ints[NSMALLNEGINTS + NSMALLPOSINTS];
- #endif
- #ifdef COUNT_ALLOCS
- int quick_int_allocs, quick_neg_int_allocs;
- #endif
-
- object *
- newintobject(ival)
- long ival;
- {
- register intobject *v;
- #if NSMALLNEGINTS + NSMALLPOSINTS > 0
- if (-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS &&
- (v = small_ints[ival + NSMALLNEGINTS]) != NULL) {
- INCREF(v);
- #ifdef COUNT_ALLOCS
- if (ival >= 0)
- quick_int_allocs++;
- else
- quick_neg_int_allocs++;
- #endif
- return (object *) v;
- }
- #endif
- if (free_list == NULL) {
- if ((free_list = fill_free_list()) == NULL)
- return NULL;
- }
- v = free_list;
- free_list = *(intobject **)free_list;
- v->ob_type = &Inttype;
- v->ob_ival = ival;
- NEWREF(v);
- #if NSMALLNEGINTS + NSMALLPOSINTS > 0
- if (-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS) {
- /* save this one for a following allocation */
- INCREF(v);
- small_ints[ival + NSMALLNEGINTS] = v;
- }
- #endif
- return (object *) v;
- }
-
- static void
- int_dealloc(v)
- intobject *v;
- {
- *(intobject **)v = free_list;
- free_list = v;
- }
-
- long
- getintvalue(op)
- register object *op;
- {
- number_methods *nb;
- intobject *io;
- long val;
-
- if (op && is_intobject(op))
- return GETINTVALUE((intobject*) op);
-
- if (op == NULL || (nb = op->ob_type->tp_as_number) == NULL ||
- nb->nb_int == NULL) {
- err_badarg();
- return -1;
- }
-
- io = (intobject*) (*nb->nb_int) (op);
- if (io == NULL)
- return -1;
- if (!is_intobject(io)) {
- err_setstr(TypeError, "nb_int should return int object");
- return -1;
- }
-
- val = GETINTVALUE(io);
- DECREF(io);
-
- return val;
- }
-
- /* Methods */
-
- /* ARGSUSED */
- static int
- int_print(v, fp, flags)
- intobject *v;
- FILE *fp;
- int flags; /* Not used but required by interface */
- {
- fprintf(fp, "%ld", v->ob_ival);
- return 0;
- }
-
- static object *
- int_repr(v)
- intobject *v;
- {
- char buf[20];
- sprintf(buf, "%ld", v->ob_ival);
- return newstringobject(buf);
- }
-
- static int
- int_compare(v, w)
- intobject *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)
- intobject *v;
- {
- long x = v -> ob_ival;
- if (x == -1)
- x = -2;
- return x;
- }
-
- static object *
- int_add(v, w)
- intobject *v;
- intobject *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 newintobject(x);
- }
-
- static object *
- int_sub(v, w)
- intobject *v;
- intobject *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 newintobject(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 object *
- int_mul(v, w)
- intobject *v;
- intobject *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 newintobject(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 newintobject(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)))
- 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 newintobject(x * s);
-
- bad:
- return err_ovf("integer multiplication");
- }
-
- static int
- i_divmod(x, y, p_xdivy, p_xmody)
- register intobject *x, *y;
- long *p_xdivy, *p_xmody;
- {
- long xi = x->ob_ival;
- long yi = y->ob_ival;
- long xdivy, xmody;
-
- if (yi == 0) {
- err_setstr(ZeroDivisionError, "integer division or modulo");
- return -1;
- }
- if (yi < 0) {
- if (xi < 0)
- 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 object *
- int_div(x, y)
- intobject *x;
- intobject *y;
- {
- long d, m;
- if (i_divmod(x, y, &d, &m) < 0)
- return NULL;
- return newintobject(d);
- }
-
- static object *
- int_mod(x, y)
- intobject *x;
- intobject *y;
- {
- long d, m;
- if (i_divmod(x, y, &d, &m) < 0)
- return NULL;
- return newintobject(m);
- }
-
- static object *
- int_divmod(x, y)
- intobject *x;
- intobject *y;
- {
- object *v, *v0, *v1;
- long d, m;
- if (i_divmod(x, y, &d, &m) < 0)
- return NULL;
- return mkvalue("(ll)", d, m);
- }
-
- static object *
- int_pow(v, w, z)
- intobject *v;
- intobject *w;
- intobject *z;
- {
- #if 1
- register long iv, iw, iz, ix, temp, prev;
- int zset = 0;
- iv = v->ob_ival;
- iw = w->ob_ival;
- if (iw < 0) {
- err_setstr(ValueError, "integer to the negative power");
- return NULL;
- }
- if ((object *)z != None) {
- iz = z->ob_ival;
- zset = 1;
- }
- /*
- * 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 pow()");
- }
- 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 pow()");
- if (zset) {
- /* If we did a multiplication, perform a modulo */
- ix = ix % iz;
- temp = temp % iz;
- }
- }
- if (zset) {
- object *t1, *t2;
- long int div, mod;
- t1=newintobject(ix);
- t2=newintobject(iz);
- if (t1==NULL || t2==NULL ||
- i_divmod((intobject *)t1, (intobject *)t2, &div, &mod)<0) {
- XDECREF(t1);
- XDECREF(t2);
- return(NULL);
- }
- ix=mod;
- }
- return newintobject(ix);
- #else
- register long iv, iw, ix;
- iv = v->ob_ival;
- iw = w->ob_ival;
- if (iw < 0) {
- err_setstr(ValueError, "integer to the negative power");
- return NULL;
- }
- if ((object *)z != None) {
- err_setstr(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 pow()");
- }
- return newintobject(ix);
- #endif
- }
-
- static object *
- int_neg(v)
- intobject *v;
- {
- register long a, x;
- a = v->ob_ival;
- x = -a;
- if (a < 0 && x < 0)
- return err_ovf("integer negation");
- return newintobject(x);
- }
-
- static object *
- int_pos(v)
- intobject *v;
- {
- INCREF(v);
- return (object *)v;
- }
-
- static object *
- int_abs(v)
- intobject *v;
- {
- if (v->ob_ival >= 0)
- return int_pos(v);
- else
- return int_neg(v);
- }
-
- static int
- int_nonzero(v)
- intobject *v;
- {
- return v->ob_ival != 0;
- }
-
- static object *
- int_invert(v)
- intobject *v;
- {
- return newintobject(~v->ob_ival);
- }
-
- static object *
- int_lshift(v, w)
- intobject *v;
- intobject *w;
- {
- register long a, b;
- a = v->ob_ival;
- b = w->ob_ival;
- if (b < 0) {
- err_setstr(ValueError, "negative shift count");
- return NULL;
- }
- if (a == 0 || b == 0) {
- INCREF(v);
- return (object *) v;
- }
- if (b >= LONG_BIT) {
- return newintobject(0L);
- }
- a = (unsigned long)a << b;
- return newintobject(a);
- }
-
- static object *
- int_rshift(v, w)
- intobject *v;
- intobject *w;
- {
- register long a, b;
- a = v->ob_ival;
- b = w->ob_ival;
- if (b < 0) {
- err_setstr(ValueError, "negative shift count");
- return NULL;
- }
- if (a == 0 || b == 0) {
- INCREF(v);
- return (object *) 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 newintobject(a);
- }
-
- static object *
- int_and(v, w)
- intobject *v;
- intobject *w;
- {
- register long a, b;
- a = v->ob_ival;
- b = w->ob_ival;
- return newintobject(a & b);
- }
-
- static object *
- int_xor(v, w)
- intobject *v;
- intobject *w;
- {
- register long a, b;
- a = v->ob_ival;
- b = w->ob_ival;
- return newintobject(a ^ b);
- }
-
- static object *
- int_or(v, w)
- intobject *v;
- intobject *w;
- {
- register long a, b;
- a = v->ob_ival;
- b = w->ob_ival;
- return newintobject(a | b);
- }
-
- static object *
- int_int(v)
- intobject *v;
- {
- INCREF(v);
- return (object *)v;
- }
-
- static object *
- int_long(v)
- intobject *v;
- {
- return newlongobject((v -> ob_ival));
- }
-
- static object *
- int_float(v)
- intobject *v;
- {
- return newfloatobject((double)(v -> ob_ival));
- }
-
- static object *
- int_oct(v)
- intobject *v;
- {
- char buf[20];
- long x = v -> ob_ival;
- if (x == 0)
- strcpy(buf, "0");
- else if (x > 0)
- sprintf(buf, "0%lo", x);
- else
- sprintf(buf, "-0%lo", -x);
- return newstringobject(buf);
- }
-
- static object *
- int_hex(v)
- intobject *v;
- {
- char buf[20];
- long x = v -> ob_ival;
- if (x >= 0)
- sprintf(buf, "0x%lx", x);
- else
- sprintf(buf, "-0x%lx", -x);
- return newstringobject(buf);
- }
-
- static number_methods 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*/
- };
-
- typeobject Inttype = {
- OB_HEAD_INIT(&Typetype)
- 0,
- "int",
- sizeof(intobject),
- 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*/
- };
-