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e6eefc2231
coercion is now completely generic. * ceval.c: for instances, don't coerce for + and *; * reverses arguments if left one is non-instance numeric and right one sequence.
1312 lines
27 KiB
C
1312 lines
27 KiB
C
/***********************************************************
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Copyright 1991, 1992 by Stichting Mathematisch Centrum, Amsterdam, The
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Netherlands.
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All Rights Reserved
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Permission to use, copy, modify, and distribute this software and its
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documentation for any purpose and without fee is hereby granted,
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provided that the above copyright notice appear in all copies and that
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both that copyright notice and this permission notice appear in
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supporting documentation, and that the names of Stichting Mathematisch
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Centrum or CWI not be used in advertising or publicity pertaining to
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distribution of the software without specific, written prior permission.
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STICHTING MATHEMATISCH CENTRUM DISCLAIMS ALL WARRANTIES WITH REGARD TO
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THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
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FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH CENTRUM BE LIABLE
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FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT
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OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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******************************************************************/
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/* Long (arbitrary precision) integer object implementation */
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/* XXX The functional organization of this file is terrible */
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#include "allobjects.h"
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#include "intrcheck.h"
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#include "longintrepr.h"
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#include <math.h>
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#include <assert.h>
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#define ABS(x) ((x) < 0 ? -(x) : (x))
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/* Forward */
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static longobject *long_normalize PROTO((longobject *));
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static longobject *mul1 PROTO((longobject *, wdigit));
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static longobject *muladd1 PROTO((longobject *, wdigit, wdigit));
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static longobject *divrem1 PROTO((longobject *, wdigit, digit *));
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static int ticker; /* XXX Could be shared with ceval? */
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#define INTRCHECK(block) \
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if (--ticker < 0) { \
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ticker = 100; \
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if (intrcheck()) { block; } \
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}
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/* Normalize (remove leading zeros from) a long int object.
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Doesn't attempt to free the storage--in most cases, due to the nature
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of the algorithms used, this could save at most be one word anyway. */
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static longobject *
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long_normalize(v)
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register longobject *v;
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{
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int j = ABS(v->ob_size);
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register int i = j;
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while (i > 0 && v->ob_digit[i-1] == 0)
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--i;
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if (i != j)
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v->ob_size = (v->ob_size < 0) ? -(i) : i;
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return v;
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}
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/* Allocate a new long int object with size digits.
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Return NULL and set exception if we run out of memory. */
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longobject *
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alloclongobject(size)
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int size;
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{
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return NEWVAROBJ(longobject, &Longtype, size);
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}
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/* Create a new long int object from a C long int */
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object *
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newlongobject(ival)
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long ival;
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{
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/* Assume a C long fits in at most 3 'digits' */
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longobject *v = alloclongobject(3);
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if (v != NULL) {
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if (ival < 0) {
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ival = -ival;
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v->ob_size = -(v->ob_size);
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}
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v->ob_digit[0] = ival & MASK;
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v->ob_digit[1] = (ival >> SHIFT) & MASK;
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v->ob_digit[2] = (ival >> (2*SHIFT)) & MASK;
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v = long_normalize(v);
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}
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return (object *)v;
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}
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/* Create a new long int object from a C double */
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object *
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dnewlongobject(dval)
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double dval;
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{
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longobject *v;
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double frac;
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int i, ndig, expo, neg;
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neg = 0;
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if (dval < 0.0) {
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neg = 1;
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dval = -dval;
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}
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frac = frexp(dval, &expo); /* dval = frac*2**expo; 0.0 <= frac < 1.0 */
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if (expo <= 0)
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return newlongobject(0L);
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ndig = (expo-1) / SHIFT + 1; /* Number of 'digits' in result */
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v = alloclongobject(ndig);
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if (v == NULL)
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return NULL;
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frac = ldexp(frac, (expo-1) % SHIFT + 1);
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for (i = ndig; --i >= 0; ) {
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long bits = (long)frac;
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v->ob_digit[i] = bits;
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frac = frac - (double)bits;
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frac = ldexp(frac, SHIFT);
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}
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if (neg)
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v->ob_size = -(v->ob_size);
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return (object *)v;
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}
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/* Get a C long int from a long int object.
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Returns -1 and sets an error condition if overflow occurs. */
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long
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getlongvalue(vv)
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object *vv;
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{
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register longobject *v;
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long x, prev;
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int i, sign;
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if (vv == NULL || !is_longobject(vv)) {
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err_badcall();
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return -1;
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}
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v = (longobject *)vv;
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i = v->ob_size;
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sign = 1;
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x = 0;
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if (i < 0) {
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sign = -1;
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i = -(i);
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}
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while (--i >= 0) {
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prev = x;
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x = (x << SHIFT) + v->ob_digit[i];
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if ((x >> SHIFT) != prev) {
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err_setstr(ValueError,
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"long int too long to convert");
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return -1;
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}
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}
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return x * sign;
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}
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/* Get a C double from a long int object. No overflow check. */
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double
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dgetlongvalue(vv)
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object *vv;
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{
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register longobject *v;
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double x;
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double multiplier = (double) (1L << SHIFT);
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int i, sign;
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if (vv == NULL || !is_longobject(vv)) {
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err_badcall();
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return -1;
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}
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v = (longobject *)vv;
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i = v->ob_size;
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sign = 1;
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x = 0.0;
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if (i < 0) {
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sign = -1;
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i = -(i);
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}
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while (--i >= 0) {
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x = x*multiplier + v->ob_digit[i];
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}
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return x * sign;
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}
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/* Multiply by a single digit, ignoring the sign. */
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static longobject *
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mul1(a, n)
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longobject *a;
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wdigit n;
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{
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return muladd1(a, n, (digit)0);
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}
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/* Multiply by a single digit and add a single digit, ignoring the sign. */
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static longobject *
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muladd1(a, n, extra)
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longobject *a;
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wdigit n;
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wdigit extra;
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{
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int size_a = ABS(a->ob_size);
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longobject *z = alloclongobject(size_a+1);
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twodigits carry = extra;
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int i;
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if (z == NULL)
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return NULL;
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for (i = 0; i < size_a; ++i) {
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carry += (twodigits)a->ob_digit[i] * n;
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z->ob_digit[i] = carry & MASK;
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carry >>= SHIFT;
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}
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z->ob_digit[i] = carry;
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return long_normalize(z);
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}
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/* Divide a long integer by a digit, returning both the quotient
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(as function result) and the remainder (through *prem).
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The sign of a is ignored; n should not be zero. */
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static longobject *
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divrem1(a, n, prem)
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longobject *a;
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wdigit n;
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digit *prem;
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{
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int size = ABS(a->ob_size);
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longobject *z;
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int i;
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twodigits rem = 0;
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assert(n > 0 && n <= MASK);
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z = alloclongobject(size);
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if (z == NULL)
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return NULL;
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for (i = size; --i >= 0; ) {
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rem = (rem << SHIFT) + a->ob_digit[i];
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z->ob_digit[i] = rem/n;
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rem %= n;
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}
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*prem = rem;
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return long_normalize(z);
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}
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/* Convert a long int object to a string, using a given conversion base.
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Return a string object.
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If base is 8 or 16, add the proper prefix '0' or '0x'.
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External linkage: used in bltinmodule.c by hex() and oct(). */
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object *
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long_format(aa, base)
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object *aa;
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int base;
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{
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register longobject *a = (longobject *)aa;
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stringobject *str;
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int i;
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int size_a = ABS(a->ob_size);
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char *p;
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int bits;
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char sign = '\0';
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if (a == NULL || !is_longobject(a)) {
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err_badcall();
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return NULL;
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}
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assert(base >= 2 && base <= 36);
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/* Compute a rough upper bound for the length of the string */
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i = base;
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bits = 0;
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while (i > 1) {
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++bits;
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i >>= 1;
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}
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i = 6 + (size_a*SHIFT + bits-1) / bits;
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str = (stringobject *) newsizedstringobject((char *)0, i);
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if (str == NULL)
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return NULL;
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p = GETSTRINGVALUE(str) + i;
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*p = '\0';
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*--p = 'L';
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if (a->ob_size < 0)
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sign = '-';
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INCREF(a);
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do {
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digit rem;
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longobject *temp = divrem1(a, (digit)base, &rem);
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if (temp == NULL) {
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DECREF(a);
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DECREF(str);
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return NULL;
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}
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if (rem < 10)
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rem += '0';
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else
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rem += 'A'-10;
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assert(p > GETSTRINGVALUE(str));
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*--p = rem;
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DECREF(a);
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a = temp;
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INTRCHECK({
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DECREF(a);
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DECREF(str);
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err_set(KeyboardInterrupt);
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return NULL;
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})
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} while (ABS(a->ob_size) != 0);
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DECREF(a);
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if (base == 8)
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*--p = '0';
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else if (base == 16) {
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*--p = 'x';
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*--p = '0';
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}
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else if (base != 10) {
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*--p = '#';
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*--p = '0' + base%10;
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if (base > 10)
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*--p = '0' + base/10;
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}
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if (sign)
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*--p = sign;
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if (p != GETSTRINGVALUE(str)) {
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char *q = GETSTRINGVALUE(str);
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assert(p > q);
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do {
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} while ((*q++ = *p++) != '\0');
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q--;
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resizestring((object **)&str, (int) (q - GETSTRINGVALUE(str)));
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}
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return (object *)str;
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}
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/* Convert a string to a long int object, in a given base.
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Base zero implies a default depending on the number.
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External linkage: used in compile.c for literals. */
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object *
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long_scan(str, base)
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char *str;
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int base;
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{
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int sign = 1;
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longobject *z;
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assert(base == 0 || base >= 2 && base <= 36);
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if (*str == '+')
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++str;
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else if (*str == '-') {
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++str;
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sign = -1;
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}
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if (base == 0) {
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if (str[0] != '0')
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base = 10;
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else if (str[1] == 'x' || str[1] == 'X')
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base = 16;
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else
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base = 8;
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}
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if (base == 16 && str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
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str += 2;
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z = alloclongobject(0);
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for ( ; z != NULL; ++str) {
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int k = -1;
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longobject *temp;
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if (*str <= '9')
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k = *str - '0';
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else if (*str >= 'a')
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k = *str - 'a' + 10;
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else if (*str >= 'A')
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k = *str - 'A' + 10;
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if (k < 0 || k >= base)
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break;
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temp = muladd1(z, (digit)base, (digit)k);
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DECREF(z);
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z = temp;
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}
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if (sign < 0 && z != NULL && z->ob_size != 0)
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z->ob_size = -(z->ob_size);
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return (object *) z;
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}
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static longobject *x_divrem PROTO((longobject *, longobject *, longobject **));
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static object *long_pos PROTO((longobject *));
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static long_divrem PROTO((longobject *, longobject *,
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longobject **, longobject **));
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/* Long division with remainder, top-level routine */
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static int
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long_divrem(a, b, pdiv, prem)
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longobject *a, *b;
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longobject **pdiv;
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longobject **prem;
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{
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int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size);
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longobject *z;
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if (size_b == 0) {
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err_setstr(ZeroDivisionError, "long division or modulo");
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return -1;
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}
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if (size_a < size_b ||
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size_a == size_b &&
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a->ob_digit[size_a-1] < b->ob_digit[size_b-1]) {
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/* |a| < |b|. */
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*pdiv = alloclongobject(0);
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INCREF(a);
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*prem = (longobject *) a;
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return 0;
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}
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if (size_b == 1) {
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digit rem = 0;
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z = divrem1(a, b->ob_digit[0], &rem);
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if (z == NULL)
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return -1;
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*prem = (longobject *) newlongobject((long)rem);
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}
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else {
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z = x_divrem(a, b, prem);
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if (z == NULL)
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return -1;
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}
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/* Set the signs.
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The quotient z has the sign of a*b;
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the remainder r has the sign of a,
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so a = b*z + r. */
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if ((a->ob_size < 0) != (b->ob_size < 0))
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z->ob_size = -(z->ob_size);
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if (a->ob_size < 0 && (*prem)->ob_size != 0)
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(*prem)->ob_size = -((*prem)->ob_size);
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*pdiv = z;
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return 0;
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}
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|
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/* Unsigned long division with remainder -- the algorithm */
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static longobject *
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x_divrem(v1, w1, prem)
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longobject *v1, *w1;
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longobject **prem;
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{
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int size_v = ABS(v1->ob_size), size_w = ABS(w1->ob_size);
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digit d = (twodigits)BASE / (w1->ob_digit[size_w-1] + 1);
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longobject *v = mul1(v1, d);
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longobject *w = mul1(w1, d);
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longobject *a;
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int j, k;
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if (v == NULL || w == NULL) {
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XDECREF(v);
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XDECREF(w);
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return NULL;
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}
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assert(size_v >= size_w && size_w > 1); /* Assert checks by div() */
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assert(v->ob_refcnt == 1); /* Since v will be used as accumulator! */
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assert(size_w == ABS(w->ob_size)); /* That's how d was calculated */
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size_v = ABS(v->ob_size);
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a = alloclongobject(size_v - size_w + 1);
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for (j = size_v, k = a->ob_size-1; a != NULL && k >= 0; --j, --k) {
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digit vj = (j >= size_v) ? 0 : v->ob_digit[j];
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twodigits q;
|
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stwodigits carry = 0;
|
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int i;
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INTRCHECK({
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DECREF(a);
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a = NULL;
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err_set(KeyboardInterrupt);
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break;
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})
|
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if (vj == w->ob_digit[size_w-1])
|
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q = MASK;
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else
|
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q = (((twodigits)vj << SHIFT) + v->ob_digit[j-1]) /
|
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w->ob_digit[size_w-1];
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|
|
while (w->ob_digit[size_w-2]*q >
|
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((
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((twodigits)vj << SHIFT)
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+ v->ob_digit[j-1]
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- q*w->ob_digit[size_w-1]
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) << SHIFT)
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+ v->ob_digit[j-2])
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--q;
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for (i = 0; i < size_w && i+k < size_v; ++i) {
|
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twodigits z = w->ob_digit[i] * q;
|
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digit zz = z >> SHIFT;
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carry += v->ob_digit[i+k] - z + ((twodigits)zz << SHIFT);
|
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v->ob_digit[i+k] = carry & MASK;
|
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carry = (carry >> SHIFT) - zz;
|
|
}
|
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|
|
if (i+k < size_v) {
|
|
carry += v->ob_digit[i+k];
|
|
v->ob_digit[i+k] = 0;
|
|
}
|
|
|
|
if (carry == 0)
|
|
a->ob_digit[k] = q;
|
|
else {
|
|
assert(carry == -1);
|
|
a->ob_digit[k] = q-1;
|
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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) {
|
|
a = long_normalize(a);
|
|
*prem = divrem1(v, d, &d);
|
|
/* d receives the (unused) remainder */
|
|
if (*prem == NULL) {
|
|
DECREF(a);
|
|
a = NULL;
|
|
}
|
|
}
|
|
DECREF(v);
|
|
DECREF(w);
|
|
return a;
|
|
}
|
|
|
|
/* Methods */
|
|
|
|
/* Forward */
|
|
static void long_dealloc PROTO((object *));
|
|
static int long_print PROTO((object *, FILE *, int));
|
|
static object *long_repr PROTO((object *));
|
|
static int long_compare PROTO((longobject *, longobject *));
|
|
|
|
static object *long_add PROTO((longobject *, longobject *));
|
|
static object *long_sub PROTO((longobject *, longobject *));
|
|
static object *long_mul PROTO((longobject *, longobject *));
|
|
static object *long_div PROTO((longobject *, longobject *));
|
|
static object *long_mod PROTO((longobject *, longobject *));
|
|
static object *long_divmod PROTO((longobject *, longobject *));
|
|
static object *long_pow PROTO((longobject *, longobject *));
|
|
static object *long_neg PROTO((longobject *));
|
|
static object *long_pos PROTO((longobject *));
|
|
static object *long_abs PROTO((longobject *));
|
|
static int long_nonzero PROTO((longobject *));
|
|
static object *long_invert PROTO((longobject *));
|
|
static object *long_lshift PROTO((longobject *, longobject *));
|
|
static object *long_rshift PROTO((longobject *, longobject *));
|
|
static object *long_and PROTO((longobject *, longobject *));
|
|
static object *long_xor PROTO((longobject *, longobject *));
|
|
static object *long_or PROTO((longobject *, longobject *));
|
|
|
|
static void
|
|
long_dealloc(v)
|
|
object *v;
|
|
{
|
|
DEL(v);
|
|
}
|
|
|
|
/* ARGSUSED */
|
|
static int
|
|
long_print(v, fp, flags)
|
|
object *v;
|
|
FILE *fp;
|
|
int flags; /* Not used but required by interface */
|
|
{
|
|
stringobject *str = (stringobject *) long_format(v, 10);
|
|
if (str == NULL)
|
|
return -1;
|
|
fprintf(fp, "%s", GETSTRINGVALUE(str));
|
|
DECREF(str);
|
|
return 0;
|
|
}
|
|
|
|
static object *
|
|
long_repr(v)
|
|
object *v;
|
|
{
|
|
return long_format(v, 10);
|
|
}
|
|
|
|
static int
|
|
long_compare(a, b)
|
|
longobject *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];
|
|
}
|
|
return sign < 0 ? -1 : sign > 0 ? 1 : 0;
|
|
}
|
|
|
|
/* Add the absolute values of two long integers. */
|
|
|
|
static longobject *x_add PROTO((longobject *, longobject *));
|
|
static longobject *
|
|
x_add(a, b)
|
|
longobject *a, *b;
|
|
{
|
|
int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size);
|
|
longobject *z;
|
|
int i;
|
|
digit carry = 0;
|
|
|
|
/* Ensure a is the larger of the two: */
|
|
if (size_a < size_b) {
|
|
{ longobject *temp = a; a = b; b = temp; }
|
|
{ int size_temp = size_a; size_a = size_b; size_b = size_temp; }
|
|
}
|
|
z = alloclongobject(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 longobject *x_sub PROTO((longobject *, longobject *));
|
|
static longobject *
|
|
x_sub(a, b)
|
|
longobject *a, *b;
|
|
{
|
|
int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size);
|
|
longobject *z;
|
|
int i;
|
|
int sign = 1;
|
|
digit borrow = 0;
|
|
|
|
/* Ensure a is the larger of the two: */
|
|
if (size_a < size_b) {
|
|
sign = -1;
|
|
{ longobject *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 alloclongobject(0);
|
|
if (a->ob_digit[i] < b->ob_digit[i]) {
|
|
sign = -1;
|
|
{ longobject *temp = a; a = b; b = temp; }
|
|
}
|
|
size_a = size_b = i+1;
|
|
}
|
|
z = alloclongobject(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 object *
|
|
long_add(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
longobject *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 (object *)z;
|
|
}
|
|
|
|
static object *
|
|
long_sub(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
longobject *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 (object *)z;
|
|
}
|
|
|
|
static object *
|
|
long_mul(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
int size_a;
|
|
int size_b;
|
|
longobject *z;
|
|
int i;
|
|
|
|
size_a = ABS(a->ob_size);
|
|
size_b = ABS(b->ob_size);
|
|
z = alloclongobject(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;
|
|
|
|
INTRCHECK({
|
|
DECREF(z);
|
|
err_set(KeyboardInterrupt);
|
|
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] = 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] = 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 (object *) 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 PROTO((longobject *, longobject *,
|
|
longobject **, longobject **));
|
|
static int
|
|
l_divmod(v, w, pdiv, pmod)
|
|
longobject *v;
|
|
longobject *w;
|
|
longobject **pdiv;
|
|
longobject **pmod;
|
|
{
|
|
longobject *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) {
|
|
longobject *temp;
|
|
longobject *one;
|
|
temp = (longobject *) long_add(mod, w);
|
|
DECREF(mod);
|
|
mod = temp;
|
|
if (mod == NULL) {
|
|
DECREF(div);
|
|
return -1;
|
|
}
|
|
one = (longobject *) newlongobject(1L);
|
|
if (one == NULL ||
|
|
(temp = (longobject *) long_sub(div, one)) == NULL) {
|
|
DECREF(mod);
|
|
DECREF(div);
|
|
return -1;
|
|
}
|
|
DECREF(div);
|
|
div = temp;
|
|
}
|
|
*pdiv = div;
|
|
*pmod = mod;
|
|
return 0;
|
|
}
|
|
|
|
static object *
|
|
long_div(v, w)
|
|
longobject *v;
|
|
longobject *w;
|
|
{
|
|
longobject *div, *mod;
|
|
if (l_divmod(v, w, &div, &mod) < 0)
|
|
return NULL;
|
|
DECREF(mod);
|
|
return (object *)div;
|
|
}
|
|
|
|
static object *
|
|
long_mod(v, w)
|
|
longobject *v;
|
|
longobject *w;
|
|
{
|
|
longobject *div, *mod;
|
|
if (l_divmod(v, w, &div, &mod) < 0)
|
|
return NULL;
|
|
DECREF(div);
|
|
return (object *)mod;
|
|
}
|
|
|
|
static object *
|
|
long_divmod(v, w)
|
|
longobject *v;
|
|
longobject *w;
|
|
{
|
|
object *z;
|
|
longobject *div, *mod;
|
|
if (l_divmod(v, w, &div, &mod) < 0)
|
|
return NULL;
|
|
z = newtupleobject(2);
|
|
if (z != NULL) {
|
|
settupleitem(z, 0, (object *) div);
|
|
settupleitem(z, 1, (object *) mod);
|
|
}
|
|
else {
|
|
DECREF(div);
|
|
DECREF(mod);
|
|
}
|
|
return z;
|
|
}
|
|
|
|
static object *
|
|
long_pow(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
longobject *z;
|
|
int size_b, i;
|
|
|
|
size_b = b->ob_size;
|
|
if (size_b < 0) {
|
|
err_setstr(ValueError, "long integer to the negative power");
|
|
return NULL;
|
|
}
|
|
|
|
z = (longobject *)newlongobject(1L);
|
|
|
|
INCREF(a);
|
|
for (i = 0; i < size_b; ++i) {
|
|
digit bi = b->ob_digit[i];
|
|
int j;
|
|
|
|
for (j = 0; j < SHIFT; ++j) {
|
|
longobject *temp;
|
|
|
|
if (bi & 1) {
|
|
temp = (longobject *)long_mul(z, a);
|
|
DECREF(z);
|
|
z = temp;
|
|
if (z == NULL)
|
|
break;
|
|
}
|
|
bi >>= 1;
|
|
if (bi == 0 && i+1 == size_b)
|
|
break;
|
|
temp = (longobject *)long_mul(a, a);
|
|
DECREF(a);
|
|
a = temp;
|
|
if (a == NULL) {
|
|
DECREF(z);
|
|
z = NULL;
|
|
break;
|
|
}
|
|
}
|
|
if (a == NULL)
|
|
break;
|
|
}
|
|
XDECREF(a);
|
|
return (object *)z;
|
|
}
|
|
|
|
static object *
|
|
long_invert(v)
|
|
longobject *v;
|
|
{
|
|
/* Implement ~x as -(x+1) */
|
|
longobject *x;
|
|
longobject *w;
|
|
w = (longobject *)newlongobject(1L);
|
|
if (w == NULL)
|
|
return NULL;
|
|
x = (longobject *) long_add(v, w);
|
|
DECREF(w);
|
|
if (x == NULL)
|
|
return NULL;
|
|
if (x->ob_size != 0)
|
|
x->ob_size = -(x->ob_size);
|
|
return (object *)x;
|
|
}
|
|
|
|
static object *
|
|
long_pos(v)
|
|
longobject *v;
|
|
{
|
|
INCREF(v);
|
|
return (object *)v;
|
|
}
|
|
|
|
static object *
|
|
long_neg(v)
|
|
longobject *v;
|
|
{
|
|
longobject *z;
|
|
int i, n;
|
|
n = ABS(v->ob_size);
|
|
if (n == 0) {
|
|
/* -0 == 0 */
|
|
INCREF(v);
|
|
return (object *) v;
|
|
}
|
|
z = alloclongobject(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 (object *)z;
|
|
}
|
|
|
|
static object *
|
|
long_abs(v)
|
|
longobject *v;
|
|
{
|
|
if (v->ob_size < 0)
|
|
return long_neg(v);
|
|
else {
|
|
INCREF(v);
|
|
return (object *)v;
|
|
}
|
|
}
|
|
|
|
static int
|
|
long_nonzero(v)
|
|
longobject *v;
|
|
{
|
|
return ABS(v->ob_size) != 0;
|
|
}
|
|
|
|
static object *
|
|
long_rshift(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
longobject *z;
|
|
long shiftby;
|
|
int newsize, wordshift, loshift, hishift, i, j;
|
|
digit lomask, himask;
|
|
|
|
if (a->ob_size < 0) {
|
|
/* Right shifting negative numbers is harder */
|
|
longobject *a1, *a2, *a3;
|
|
a1 = (longobject *) long_invert(a);
|
|
if (a1 == NULL) return NULL;
|
|
a2 = (longobject *) long_rshift(a1, b);
|
|
DECREF(a1);
|
|
if (a2 == NULL) return NULL;
|
|
a3 = (longobject *) long_invert(a2);
|
|
DECREF(a2);
|
|
return (object *) a3;
|
|
}
|
|
|
|
shiftby = getlongvalue((object *)b);
|
|
if (shiftby == -1L && err_occurred())
|
|
return NULL;
|
|
if (shiftby < 0) {
|
|
err_setstr(ValueError, "negative shift count");
|
|
return NULL;
|
|
}
|
|
wordshift = shiftby / SHIFT;
|
|
newsize = ABS(a->ob_size) - wordshift;
|
|
if (newsize <= 0) {
|
|
z = alloclongobject(0);
|
|
return (object *)z;
|
|
}
|
|
loshift = shiftby % SHIFT;
|
|
hishift = SHIFT - loshift;
|
|
lomask = ((digit)1 << hishift) - 1;
|
|
himask = MASK ^ lomask;
|
|
z = alloclongobject(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 (object *) long_normalize(z);
|
|
}
|
|
|
|
static object *
|
|
long_lshift(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
longobject *z;
|
|
long shiftby;
|
|
int newsize, wordshift, loshift, hishift, i, j;
|
|
digit lomask, himask;
|
|
|
|
shiftby = getlongvalue((object *)b);
|
|
if (shiftby == -1L && err_occurred())
|
|
return NULL;
|
|
if (shiftby < 0) {
|
|
err_setstr(ValueError, "negative shift count");
|
|
return NULL;
|
|
}
|
|
if (shiftby > MASK) {
|
|
err_setstr(ValueError, "outrageous left shift count");
|
|
return NULL;
|
|
}
|
|
if (shiftby % SHIFT == 0) {
|
|
wordshift = shiftby / SHIFT;
|
|
loshift = 0;
|
|
hishift = SHIFT;
|
|
newsize = ABS(a->ob_size) + wordshift;
|
|
lomask = MASK;
|
|
himask = 0;
|
|
}
|
|
else {
|
|
wordshift = shiftby / SHIFT + 1;
|
|
loshift = SHIFT - shiftby%SHIFT;
|
|
hishift = shiftby % SHIFT;
|
|
newsize = ABS(a->ob_size) + wordshift;
|
|
lomask = ((digit)1 << hishift) - 1;
|
|
himask = MASK ^ lomask;
|
|
}
|
|
z = alloclongobject(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;
|
|
for (i = wordshift, j = 0; i < newsize; i++, j++) {
|
|
if (i > 0)
|
|
z->ob_digit[i-1] |=
|
|
(a->ob_digit[j] << hishift) & himask;
|
|
z->ob_digit[i] =
|
|
(a->ob_digit[j] >> loshift) & lomask;
|
|
}
|
|
return (object *) 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 object *long_bitwise PROTO((longobject *, int, longobject *));
|
|
static object *
|
|
long_bitwise(a, op, b)
|
|
longobject *a;
|
|
int op; /* '&', '|', '^' */
|
|
longobject *b;
|
|
{
|
|
digit maska, maskb; /* 0 or MASK */
|
|
int negz;
|
|
int size_a, size_b, size_z;
|
|
longobject *z;
|
|
int i;
|
|
digit diga, digb;
|
|
object *v;
|
|
|
|
if (a->ob_size < 0) {
|
|
a = (longobject *) long_invert(a);
|
|
maska = MASK;
|
|
}
|
|
else {
|
|
INCREF(a);
|
|
maska = 0;
|
|
}
|
|
if (b->ob_size < 0) {
|
|
b = (longobject *) long_invert(b);
|
|
maskb = MASK;
|
|
}
|
|
else {
|
|
INCREF(b);
|
|
maskb = 0;
|
|
}
|
|
|
|
size_a = a->ob_size;
|
|
size_b = b->ob_size;
|
|
size_z = MAX(size_a, size_b);
|
|
z = alloclongobject(size_z);
|
|
if (a == NULL || b == NULL || z == NULL) {
|
|
XDECREF(a);
|
|
XDECREF(b);
|
|
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;
|
|
}
|
|
}
|
|
|
|
DECREF(a);
|
|
DECREF(b);
|
|
z = long_normalize(z);
|
|
if (negz == 0)
|
|
return (object *) z;
|
|
v = long_invert(z);
|
|
DECREF(z);
|
|
return v;
|
|
}
|
|
|
|
static object *
|
|
long_and(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
return long_bitwise(a, '&', b);
|
|
}
|
|
|
|
static object *
|
|
long_xor(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
return long_bitwise(a, '^', b);
|
|
}
|
|
|
|
static object *
|
|
long_or(a, b)
|
|
longobject *a;
|
|
longobject *b;
|
|
{
|
|
return long_bitwise(a, '|', b);
|
|
}
|
|
|
|
int
|
|
long_coerce(pv, pw)
|
|
object **pv;
|
|
object **pw;
|
|
{
|
|
if (is_intobject(*pw)) {
|
|
*pw = newlongobject(getintvalue(*pw));
|
|
INCREF(*pv);
|
|
return 0;
|
|
}
|
|
return 1; /* Can't do it */
|
|
}
|
|
|
|
#define UF (object* (*) FPROTO((object *))) /* Unary function */
|
|
#define BF (object* (*) FPROTO((object *, object *))) /* Binary function */
|
|
#define IF (int (*) FPROTO((object *))) /* Int function */
|
|
|
|
static number_methods 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*/
|
|
BF 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 (*) FPROTO((object **, object **)))
|
|
long_coerce, /*nb_coerce*/
|
|
};
|
|
|
|
typeobject Longtype = {
|
|
OB_HEAD_INIT(&Typetype)
|
|
0,
|
|
"long int",
|
|
sizeof(longobject) - sizeof(digit),
|
|
sizeof(digit),
|
|
long_dealloc, /*tp_dealloc*/
|
|
long_print, /*tp_print*/
|
|
0, /*tp_getattr*/
|
|
0, /*tp_setattr*/
|
|
(int (*) FPROTO((object *, object *)))
|
|
long_compare, /*tp_compare*/
|
|
long_repr, /*tp_repr*/
|
|
&long_as_number,/*tp_as_number*/
|
|
0, /*tp_as_sequence*/
|
|
0, /*tp_as_mapping*/
|
|
};
|