rev 557 - in trunk: include/prothon src
SVN User <[email protected]> Thu, 27 May 2004 15:24:16 -0400
| Newsgroups | gmane.comp.lang.prothon.cvs |
|---|---|
| Message-ID | <[email protected]> |
Author: mark
Date: 2004-05-27 15:24:13 -0400 (Thu, 27 May 2004)
New Revision: 557
Added:
trunk/src/builtins-bigint.c
Modified:
trunk/include/prothon/prothon.h
trunk/src/src.vcproj
Log:
started work on bigints, build is VERY boken and will be for the next day or so unless you remove builtins-bigint.c
Modified: trunk/include/prothon/prothon.h
===================================================================
--- trunk/include/prothon/prothon.h 2004-05-27 05:03:24 UTC (rev 556)
+++ trunk/include/prothon/prothon.h 2004-05-27 19:24:13 UTC (rev 557)
@@ -133,6 +133,8 @@
# define max(a,b) (((a)<(b)) ? (b) : (a))
#undef exch
#define exch(a,b) (tmp=a, a=b, b=tmp)
+#undef abs
+#define abs(x) ((x) < 0 ? -(x) : (x))
// neg key value means entry is deleted
#define ENTRY_DELETED -1
Added: trunk/src/builtins-bigint.c
===================================================================
--- trunk/src/builtins-bigint.c 2004-05-27 05:03:24 UTC (rev 556)
+++ trunk/src/builtins-bigint.c 2004-05-27 19:24:13 UTC (rev 557)
@@ -0,0 +1,2950 @@
+/* ====================================================================
+ * The Prothon License Agreement, Version 1.1
+ *
+ * Copyright (c) 2004 Hahn Creative Applications, http://hahnca.com.
+ * All rights reserved.
+ *
+ * 1. This LICENSE AGREEMENT is between Hahn Creative Applications ("HCA"),
+ * and the Individual or Organization ("Licensee") accessing and otherwise
+ * using Prothon software in source or binary form and its associated
+ * documentation.
+ *
+ * 2. Subject to the terms and conditions of this License Agreement, HCA
+ * hereby grants Licensee a nonexclusive, royalty-free, world-wide license
+ * to reproduce, analyze, test, perform and/or display publicly, prepare
+ * derivative works, distribute, and otherwise use Prothon alone or in any
+ * derivative version, provided, however, that HCA's License Agreement and
+ * HCA's notice of copyright, i.e., "Copyright (c) 2004 Hahn Creative
+ * Applications; All Rights Reserved" are retained in Prothon alone or
+ * in any derivative version prepared by Licensee.
+ *
+ * 3. In the event Licensee prepares a derivative work that is based on or
+ * incorporates Prothon or any part thereof, and wants to make the
+ * derivative work available to others as provided herein, then Licensee
+ * hereby agrees to include in any such work a brief summary of the
+ * changes made to Prothon.
+ *
+ * 4. HCA is making Prothon available to Licensee on an "AS IS" basis.
+ * HCA MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED. BY WAY
+ * OF EXAMPLE, BUT NOT LIMITATION, HCA MAKES NO AND DISCLAIMS ANY
+ * REPRESENTATION OR WARRANTY OF MERCHANTABILITY OR FITNESS FOR ANY
+ * PARTICULAR PURPOSE OR THAT THE USE OF PROTHON WILL NOT INFRINGE ANY
+ * THIRD PARTY RIGHTS.
+ *
+ * 5. HCA SHALL NOT BE LIABLE TO LICENSEE OR ANY OTHER USERS OF PROTHON
+ * FOR ANY INCIDENTAL, SPECIAL, OR CONSEQUENTIAL DAMAGES OR LOSS AS A
+ * RESULT OF MODIFYING, DISTRIBUTING, OR OTHERWISE USING PROTHON, OR ANY
+ * DERIVATIVE THEREOF, EVEN IF ADVISED OF THE POSSIBILITY THEREOF.
+ *
+ * 6. This License Agreement will automatically terminate upon a material
+ * breach of its terms and conditions.
+ *
+ * 7. Nothing in this License Agreement shall be deemed to create any
+ * relationship of agency, partnership, or joint venture between HCA and
+ * Licensee. This License Agreement does not grant permission to use HCA
+ * trademarks or trade name in a trademark sense to endorse or promote
+ * products or services of Licensee, or any third party.
+ *
+ * 8. By copying, installing or otherwise using Prothon, Licensee agrees
+ * to be bound by the terms and conditions of this License Agreement.
+ * ====================================================================
+ */
+
+// builtins-bigint.c
+// copied from python/python/dist/src/Objects/longobject.c
+// and heavily modified for use in Prothon
+
+#include <prothon/prothon.h>
+
+/* Long (arbitrary precision) integer object implementation */
+
+/* For long multiplication, use the O(N**2) school algorithm unless
+ * both operands contain more than KARATSUBA_CUTOFF digits (this
+ * being an internal Python long digit, in base BASE).
+ */
+#define KARATSUBA_CUTOFF 35
+#define SHIFT 15
+typedef u16_t wdigit;
+
+/* Forward */
+static obj_p long_normalize(obj_p);
+static obj_p mul1(obj_p, wdigit);
+static obj_p muladd1(obj_p, wdigit, wdigit);
+static obj_p divrem1(obj_p, digit, digit *);
+static obj_p long_format(obj_p aa, int base, int addL);
+
+/* Normalize (remove leading zeros from) a 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 obj_p long_normalize(register obj_p 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. */
+
+obj_p
+_PyLong_New(int size)
+{
+ return PyObject_NEW_VAR(PyLongObject, &PyLong_Type, size);
+}
+
+obj_p
+_PyLong_Copy(obj_p src)
+{
+ obj_p result;
+ int i;
+
+ assert(src != NULL);
+ i = src->ob_size;
+ if (i < 0)
+ i = -(i);
+ result = _PyLong_New(i);
+ if (result != NULL) {
+ result->ob_size = src->ob_size;
+ while (--i >= 0)
+ result->ob_digit[i] = src->ob_digit[i];
+ }
+ return (obj_p)result;
+}
+
+/* Create a new long int object from a C long int */
+
+obj_p
+PyLong_FromLong(long ival)
+{
+ obj_p v;
+ unsigned long t; /* unsigned so >> doesn't propagate sign bit */
+ int ndigits = 0;
+ int negative = 0;
+
+ if (ival < 0) {
+ ival = -ival;
+ negative = 1;
+ }
+
+ /* Count the number of Python digits.
+ We used to pick 5 ("big enough for anything"), but that's a
+ waste of time and space given that 5*15 = 75 bits are rarely
+ needed. */
+ t = (unsigned long)ival;
+ while (t) {
+ ++ndigits;
+ t >>= SHIFT;
+ }
+ v = _PyLong_New(ndigits);
+ if (v != NULL) {
+ digit *p = v->ob_digit;
+ v->ob_size = negative ? -ndigits : ndigits;
+ t = (unsigned long)ival;
+ while (t) {
+ *p++ = (digit)(t & MASK);
+ t >>= SHIFT;
+ }
+ }
+ return (obj_p)v;
+}
+
+/* Create a new long int object from a C unsigned long int */
+
+obj_p
+PyLong_FromUnsignedLong(unsigned long ival)
+{
+ obj_p v;
+ unsigned long t;
+ int ndigits = 0;
+
+ /* Count the number of Python digits. */
+ t = (unsigned long)ival;
+ while (t) {
+ ++ndigits;
+ t >>= SHIFT;
+ }
+ v = _PyLong_New(ndigits);
+ if (v != NULL) {
+ digit *p = v->ob_digit;
+ v->ob_size = ndigits;
+ while (ival) {
+ *p++ = (digit)(ival & MASK);
+ ival >>= SHIFT;
+ }
+ }
+ return (obj_p)v;
+}
+
+/* Create a new long int object from a C double */
+
+obj_p
+PyLong_FromDouble(double dval)
+{
+ obj_p v;
+ double frac;
+ int i, ndig, expo, neg;
+ neg = 0;
+ if (Py_IS_INFINITY(dval)) {
+ PyErr_SetString(PyExc_OverflowError,
+ "cannot convert float infinity to long");
+ return NULL;
+ }
+ 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 (obj_p)v;
+}
+
+/* Get a C long int from a long int object.
+ Returns -1 and sets an error condition if overflow occurs. */
+
+long
+PyLong_AsLong(obj_p vv)
+{
+ /* This version by Tim Peters */
+ register obj_p v;
+ unsigned long x, prev;
+ int i, sign;
+
+ if (vv == NULL || !PyLong_Check(vv)) {
+ if (vv != NULL && PyInt_Check(vv))
+ return PyInt_AsLong(vv);
+ PyErr_BadInternalCall();
+ return -1;
+ }
+ v = (obj_p)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)
+ goto overflow;
+ }
+ /* Haven't lost any bits, but if the sign bit is set we're in
+ * trouble *unless* this is the min negative number. So,
+ * trouble iff sign bit set && (positive || some bit set other
+ * than the sign bit).
+ */
+ if ((long)x < 0 && (sign > 0 || (x << 1) != 0))
+ goto overflow;
+ return (long)x * sign;
+
+ overflow:
+ PyErr_SetString(PyExc_OverflowError,
+ "long int too large to convert to int");
+ return -1;
+}
+
+/* Get a C unsigned long int from a long int object.
+ Returns -1 and sets an error condition if overflow occurs. */
+
+unsigned long
+PyLong_AsUnsignedLong(obj_p vv)
+{
+ register obj_p v;
+ unsigned long x, prev;
+ int i;
+
+ if (vv == NULL || !PyLong_Check(vv)) {
+ PyErr_BadInternalCall();
+ return (unsigned long) -1;
+ }
+ v = (obj_p)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 large to convert");
+ return (unsigned long) -1;
+ }
+ }
+ return x;
+}
+
+/* Get a C unsigned long int from a long int object, ignoring the high bits.
+ Returns -1 and sets an error condition if an error occurs. */
+
+unsigned long
+PyLong_AsUnsignedLongMask(obj_p vv)
+{
+ register obj_p v;
+ unsigned long x;
+ int i, sign;
+
+ if (vv == NULL || !PyLong_Check(vv)) {
+ PyErr_BadInternalCall();
+ return (unsigned long) -1;
+ }
+ v = (obj_p)vv;
+ i = v->ob_size;
+ sign = 1;
+ x = 0;
+ if (i < 0) {
+ sign = -1;
+ i = -i;
+ }
+ while (--i >= 0) {
+ x = (x << SHIFT) + v->ob_digit[i];
+ }
+ return x * sign;
+}
+
+int
+_PyLong_Sign(obj_p vv)
+{
+ obj_p v = (obj_p)vv;
+
+ assert(v != NULL);
+ assert(PyLong_Check(v));
+
+ return v->ob_size == 0 ? 0 : (v->ob_size < 0 ? -1 : 1);
+}
+
+size_t
+_PyLong_NumBits(obj_p vv)
+{
+ obj_p v = (obj_p)vv;
+ size_t result = 0;
+ int ndigits;
+
+ assert(v != NULL);
+ assert(PyLong_Check(v));
+ ndigits = abs(v->ob_size);
+ assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
+ if (ndigits > 0) {
+ digit msd = v->ob_digit[ndigits - 1];
+
+ result = (ndigits - 1) * SHIFT;
+ if (result / SHIFT != (size_t)ndigits - 1)
+ goto Overflow;
+ do {
+ ++result;
+ if (result == 0)
+ goto Overflow;
+ msd >>= 1;
+ } while (msd);
+ }
+ return result;
+
+Overflow:
+ PyErr_SetString(PyExc_OverflowError, "long has too many bits "
+ "to express in a platform size_t");
+ return (size_t)-1;
+}
+
+obj_p
+_PyLong_FromByteArray(const unsigned char* bytes, size_t n,
+ int little_endian, int is_signed)
+{
+ const unsigned char* pstartbyte;/* LSB of bytes */
+ int incr; /* direction to move pstartbyte */
+ const unsigned char* pendbyte; /* MSB of bytes */
+ size_t numsignificantbytes; /* number of bytes that matter */
+ size_t ndigits; /* number of Python long digits */
+ PyLongObject* v; /* result */
+ int idigit = 0; /* next free index in v->ob_digit */
+
+ if (n == 0)
+ return PyLong_FromLong(0L);
+
+ if (little_endian) {
+ pstartbyte = bytes;
+ pendbyte = bytes + n - 1;
+ incr = 1;
+ }
+ else {
+ pstartbyte = bytes + n - 1;
+ pendbyte = bytes;
+ incr = -1;
+ }
+
+ if (is_signed)
+ is_signed = *pendbyte >= 0x80;
+
+ /* Compute numsignificantbytes. This consists of finding the most
+ significant byte. Leading 0 bytes are insignficant if the number
+ is positive, and leading 0xff bytes if negative. */
+ {
+ size_t i;
+ const unsigned char* p = pendbyte;
+ const int pincr = -incr; /* search MSB to LSB */
+ const unsigned char insignficant = is_signed ? 0xff : 0x00;
+
+ for (i = 0; i < n; ++i, p += pincr) {
+ if (*p != insignficant)
+ break;
+ }
+ numsignificantbytes = n - i;
+ /* 2's-comp is a bit tricky here, e.g. 0xff00 == -0x0100, so
+ actually has 2 significant bytes. OTOH, 0xff0001 ==
+ -0x00ffff, so we wouldn't *need* to bump it there; but we
+ do for 0xffff = -0x0001. To be safe without bothering to
+ check every case, bump it regardless. */
+ if (is_signed && numsignificantbytes < n)
+ ++numsignificantbytes;
+ }
+
+ /* How many Python long digits do we need? We have
+ 8*numsignificantbytes bits, and each Python long digit has SHIFT
+ bits, so it's the ceiling of the quotient. */
+ ndigits = (numsignificantbytes * 8 + SHIFT - 1) / SHIFT;
+ if (ndigits > (size_t)INT_MAX)
+ return PyErr_NoMemory();
+ v = _PyLong_New((int)ndigits);
+ if (v == NULL)
+ return NULL;
+
+ /* Copy the bits over. The tricky parts are computing 2's-comp on
+ the fly for signed numbers, and dealing with the mismatch between
+ 8-bit bytes and (probably) 15-bit Python digits.*/
+ {
+ size_t i;
+ twodigits carry = 1; /* for 2's-comp calculation */
+ twodigits accum = 0; /* sliding register */
+ unsigned int accumbits = 0; /* number of bits in accum */
+ const unsigned char* p = pstartbyte;
+
+ for (i = 0; i < numsignificantbytes; ++i, p += incr) {
+ twodigits thisbyte = *p;
+ /* Compute correction for 2's comp, if needed. */
+ if (is_signed) {
+ thisbyte = (0xff ^ thisbyte) + carry;
+ carry = thisbyte >> 8;
+ thisbyte &= 0xff;
+ }
+ /* Because we're going LSB to MSB, thisbyte is
+ more significant than what's already in accum,
+ so needs to be prepended to accum. */
+ accum |= thisbyte << accumbits;
+ accumbits += 8;
+ if (accumbits >= SHIFT) {
+ /* There's enough to fill a Python digit. */
+ assert(idigit < (int)ndigits);
+ v->ob_digit[idigit] = (digit)(accum & MASK);
+ ++idigit;
+ accum >>= SHIFT;
+ accumbits -= SHIFT;
+ assert(accumbits < SHIFT);
+ }
+ }
+ assert(accumbits < SHIFT);
+ if (accumbits) {
+ assert(idigit < (int)ndigits);
+ v->ob_digit[idigit] = (digit)accum;
+ ++idigit;
+ }
+ }
+
+ v->ob_size = is_signed ? -idigit : idigit;
+ return (obj_p)long_normalize(v);
+}
+
+int
+_PyLong_AsByteArray(PyLongObject* v,
+ unsigned char* bytes, size_t n,
+ int little_endian, int is_signed)
+{
+ int i; /* index into v->ob_digit */
+ int ndigits; /* |v->ob_size| */
+ twodigits accum; /* sliding register */
+ unsigned int accumbits; /* # bits in accum */
+ int do_twos_comp; /* store 2's-comp? is_signed and v < 0 */
+ twodigits carry; /* for computing 2's-comp */
+ size_t j; /* # bytes filled */
+ unsigned char* p; /* pointer to next byte in bytes */
+ int pincr; /* direction to move p */
+
+ assert(v != NULL && PyLong_Check(v));
+
+ if (v->ob_size < 0) {
+ ndigits = -(v->ob_size);
+ if (!is_signed) {
+ PyErr_SetString(PyExc_TypeError,
+ "can't convert negative long to unsigned");
+ return -1;
+ }
+ do_twos_comp = 1;
+ }
+ else {
+ ndigits = v->ob_size;
+ do_twos_comp = 0;
+ }
+
+ if (little_endian) {
+ p = bytes;
+ pincr = 1;
+ }
+ else {
+ p = bytes + n - 1;
+ pincr = -1;
+ }
+
+ /* Copy over all the Python digits.
+ It's crucial that every Python digit except for the MSD contribute
+ exactly SHIFT bits to the total, so first assert that the long is
+ normalized. */
+ assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
+ j = 0;
+ accum = 0;
+ accumbits = 0;
+ carry = do_twos_comp ? 1 : 0;
+ for (i = 0; i < ndigits; ++i) {
+ twodigits thisdigit = v->ob_digit[i];
+ if (do_twos_comp) {
+ thisdigit = (thisdigit ^ MASK) + carry;
+ carry = thisdigit >> SHIFT;
+ thisdigit &= MASK;
+ }
+ /* Because we're going LSB to MSB, thisdigit is more
+ significant than what's already in accum, so needs to be
+ prepended to accum. */
+ accum |= thisdigit << accumbits;
+ accumbits += SHIFT;
+
+ /* The most-significant digit may be (probably is) at least
+ partly empty. */
+ if (i == ndigits - 1) {
+ /* Count # of sign bits -- they needn't be stored,
+ * although for signed conversion we need later to
+ * make sure at least one sign bit gets stored.
+ * First shift conceptual sign bit to real sign bit.
+ */
+ stwodigits s = (stwodigits)(thisdigit <<
+ (8*sizeof(stwodigits) - SHIFT));
+ unsigned int nsignbits = 0;
+ while ((s < 0) == do_twos_comp && nsignbits < SHIFT) {
+ ++nsignbits;
+ s <<= 1;
+ }
+ accumbits -= nsignbits;
+ }
+
+ /* Store as many bytes as possible. */
+ while (accumbits >= 8) {
+ if (j >= n)
+ goto Overflow;
+ ++j;
+ *p = (unsigned char)(accum & 0xff);
+ p += pincr;
+ accumbits -= 8;
+ accum >>= 8;
+ }
+ }
+
+ /* Store the straggler (if any). */
+ assert(accumbits < 8);
+ assert(carry == 0); /* else do_twos_comp and *every* digit was 0 */
+ if (accumbits > 0) {
+ if (j >= n)
+ goto Overflow;
+ ++j;
+ if (do_twos_comp) {
+ /* Fill leading bits of the byte with sign bits
+ (appropriately pretending that the long had an
+ infinite supply of sign bits). */
+ accum |= (~(twodigits)0) << accumbits;
+ }
+ *p = (unsigned char)(accum & 0xff);
+ p += pincr;
+ }
+ else if (j == n && n > 0 && is_signed) {
+ /* The main loop filled the byte array exactly, so the code
+ just above didn't get to ensure there's a sign bit, and the
+ loop below wouldn't add one either. Make sure a sign bit
+ exists. */
+ unsigned char msb = *(p - pincr);
+ int sign_bit_set = msb >= 0x80;
+ assert(accumbits == 0);
+ if (sign_bit_set == do_twos_comp)
+ return 0;
+ else
+ goto Overflow;
+ }
+
+ /* Fill remaining bytes with copies of the sign bit. */
+ {
+ unsigned char signbyte = do_twos_comp ? 0xffU : 0U;
+ for ( ; j < n; ++j, p += pincr)
+ *p = signbyte;
+ }
+
+ return 0;
+
+Overflow:
+ PyErr_SetString(PyExc_OverflowError, "long too big to convert");
+ return -1;
+
+}
+
+double
+_PyLong_AsScaledDouble(obj_p vv, int *exponent)
+{
+/* NBITS_WANTED should be > the number of bits in a double's precision,
+ but small enough so that 2**NBITS_WANTED is within the normal double
+ range. nbitsneeded is set to 1 less than that because the most-significant
+ Python digit contains at least 1 significant bit, but we don't want to
+ bother counting them (catering to the worst case cheaply).
+
+ 57 is one more than VAX-D double precision; I (Tim) don't know of a double
+ format with more precision than that; it's 1 larger so that we add in at
+ least one round bit to stand in for the ignored least-significant bits.
+*/
+#define NBITS_WANTED 57
+ obj_p v;
+ double x;
+ const double multiplier = (double)(1L << SHIFT);
+ int i, sign;
+ int nbitsneeded;
+
+ if (vv == NULL || !PyLong_Check(vv)) {
+ PyErr_BadInternalCall();
+ return -1;
+ }
+ v = (obj_p)vv;
+ i = v->ob_size;
+ sign = 1;
+ if (i < 0) {
+ sign = -1;
+ i = -(i);
+ }
+ else if (i == 0) {
+ *exponent = 0;
+ return 0.0;
+ }
+ --i;
+ x = (double)v->ob_digit[i];
+ nbitsneeded = NBITS_WANTED - 1;
+ /* Invariant: i Python digits remain unaccounted for. */
+ while (i > 0 && nbitsneeded > 0) {
+ --i;
+ x = x * multiplier + (double)v->ob_digit[i];
+ nbitsneeded -= SHIFT;
+ }
+ /* There are i digits we didn't shift in. Pretending they're all
+ zeroes, the true value is x * 2**(i*SHIFT). */
+ *exponent = i;
+ assert(x > 0.0);
+ return x * sign;
+#undef NBITS_WANTED
+}
+
+/* Get a C double from a long int object. */
+
+double
+PyLong_AsDouble(obj_p vv)
+{
+ int e;
+ double x;
+
+ if (vv == NULL || !PyLong_Check(vv)) {
+ PyErr_BadInternalCall();
+ return -1;
+ }
+ x = _PyLong_AsScaledDouble(vv, &e);
+ if (x == -1.0 && PyErr_Occurred())
+ return -1.0;
+ if (e > INT_MAX / SHIFT)
+ goto overflow;
+ errno = 0;
+ x = ldexp(x, e * SHIFT);
+ if (Py_OVERFLOWED(x))
+ goto overflow;
+ return x;
+
+overflow:
+ PyErr_SetString(PyExc_OverflowError,
+ "long int too large to convert to float");
+ return -1.0;
+}
+
+/* Create a new long (or int) object from a C pointer */
+
+obj_p
+PyLong_FromVoidPtr(void *p)
+{
+#if SIZEOF_VOID_P <= SIZEOF_LONG
+ return PyInt_FromLong((long)p);
+#else
+
+#ifndef HAVE_LONG_LONG
+# error "PyLong_FromVoidPtr: sizeof(void*) > sizeof(long), but no long long"
+#endif
+#if SIZEOF_LONG_LONG < SIZEOF_VOID_P
+# error "PyLong_FromVoidPtr: sizeof(PY_LONG_LONG) < sizeof(void*)"
+#endif
+ /* optimize null pointers */
+ if (p == NULL)
+ return PyInt_FromLong(0);
+ return PyLong_FromLongLong((PY_LONG_LONG)p);
+
+#endif /* SIZEOF_VOID_P <= SIZEOF_LONG */
+}
+
+/* Get a C pointer from a long object (or an int object in some cases) */
+
+void *
+PyLong_AsVoidPtr(obj_p vv)
+{
+ /* This function will allow int or long objects. If vv is neither,
+ then the PyLong_AsLong*() functions will raise the exception:
+ PyExc_SystemError, "bad argument to internal function"
+ */
+#if SIZEOF_VOID_P <= SIZEOF_LONG
+ long x;
+
+ if (PyInt_Check(vv))
+ x = PyInt_AS_LONG(vv);
+ else
+ x = PyLong_AsLong(vv);
+#else
+
+#ifndef HAVE_LONG_LONG
+# error "PyLong_AsVoidPtr: sizeof(void*) > sizeof(long), but no long long"
+#endif
+#if SIZEOF_LONG_LONG < SIZEOF_VOID_P
+# error "PyLong_AsVoidPtr: sizeof(PY_LONG_LONG) < sizeof(void*)"
+#endif
+ PY_LONG_LONG x;
+
+ if (PyInt_Check(vv))
+ x = PyInt_AS_LONG(vv);
+ else
+ x = PyLong_AsLongLong(vv);
+
+#endif /* SIZEOF_VOID_P <= SIZEOF_LONG */
+
+ if (x == -1 && PyErr_Occurred())
+ return NULL;
+ return (void *)x;
+}
+
+#ifdef HAVE_LONG_LONG
+
+/* Initial PY_LONG_LONG support by Chris Herborth ([email protected]), later
+ * rewritten to use the newer PyLong_{As,From}ByteArray API.
+ */
+
+#define IS_LITTLE_ENDIAN (int)*(unsigned char*)&one
+
+/* Create a new long int object from a C PY_LONG_LONG int. */
+
+obj_p
+PyLong_FromLongLong(PY_LONG_LONG ival)
+{
+ PY_LONG_LONG bytes = ival;
+ int one = 1;
+ return _PyLong_FromByteArray(
+ (unsigned char *)&bytes,
+ SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 1);
+}
+
+/* Create a new long int object from a C unsigned PY_LONG_LONG int. */
+
+obj_p
+PyLong_FromUnsignedLongLong(unsigned PY_LONG_LONG ival)
+{
+ unsigned PY_LONG_LONG bytes = ival;
+ int one = 1;
+ return _PyLong_FromByteArray(
+ (unsigned char *)&bytes,
+ SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 0);
+}
+
+/* Get a C PY_LONG_LONG int from a long int object.
+ Return -1 and set an error if overflow occurs. */
+
+PY_LONG_LONG
+PyLong_AsLongLong(obj_p vv)
+{
+ PY_LONG_LONG bytes;
+ int one = 1;
+ int res;
+
+ if (vv == NULL) {
+ PyErr_BadInternalCall();
+ return -1;
+ }
+ if (!PyLong_Check(vv)) {
+ if (PyInt_Check(vv))
+ return (PY_LONG_LONG)PyInt_AsLong(vv);
+ PyErr_BadInternalCall();
+ return -1;
+ }
+
+ res = _PyLong_AsByteArray(
+ (obj_p)vv, (unsigned char *)&bytes,
+ SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 1);
+
+ /* Plan 9 can't handle PY_LONG_LONG in ? : expressions */
+ if (res < 0)
+ return (PY_LONG_LONG)-1;
+ else
+ return bytes;
+}
+
+/* Get a C unsigned PY_LONG_LONG int from a long int object.
+ Return -1 and set an error if overflow occurs. */
+
+unsigned PY_LONG_LONG
+PyLong_AsUnsignedLongLong(obj_p vv)
+{
+ unsigned PY_LONG_LONG bytes;
+ int one = 1;
+ int res;
+
+ if (vv == NULL || !PyLong_Check(vv)) {
+ PyErr_BadInternalCall();
+ return -1;
+ }
+
+ res = _PyLong_AsByteArray(
+ (obj_p)vv, (unsigned char *)&bytes,
+ SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 0);
+
+ /* Plan 9 can't handle PY_LONG_LONG in ? : expressions */
+ if (res < 0)
+ return (unsigned PY_LONG_LONG)res;
+ else
+ return bytes;
+}
+
+/* Get a C unsigned long int from a long int object, ignoring the high bits.
+ Returns -1 and sets an error condition if an error occurs. */
+
+unsigned PY_LONG_LONG
+PyLong_AsUnsignedLongLongMask(obj_p vv)
+{
+ register obj_p v;
+ unsigned PY_LONG_LONG x;
+ int i, sign;
+
+ if (vv == NULL || !PyLong_Check(vv)) {
+ PyErr_BadInternalCall();
+ return (unsigned long) -1;
+ }
+ v = (obj_p)vv;
+ i = v->ob_size;
+ sign = 1;
+ x = 0;
+ if (i < 0) {
+ sign = -1;
+ i = -i;
+ }
+ while (--i >= 0) {
+ x = (x << SHIFT) + v->ob_digit[i];
+ }
+ return x * sign;
+}
+#undef IS_LITTLE_ENDIAN
+
+#endif /* HAVE_LONG_LONG */
+
+
+static int
+convert_binop(obj_p v, obj_p w, obj_p *a, obj_p *b) {
+ if (PyLong_Check(v)) {
+ *a = (obj_p) v;
+ Py_INCREF(v);
+ }
+ else if (PyInt_Check(v)) {
+ *a = (obj_p) PyLong_FromLong(PyInt_AS_LONG(v));
+ }
+ else {
+ return 0;
+ }
+ if (PyLong_Check(w)) {
+ *b = (obj_p) w;
+ Py_INCREF(w);
+ }
+ else if (PyInt_Check(w)) {
+ *b = (obj_p) PyLong_FromLong(PyInt_AS_LONG(w));
+ }
+ else {
+ Py_DECREF(*a);
+ return 0;
+ }
+ return 1;
+}
+
+#define CONVERT_BINOP(v, w, a, b) \
+ if (!convert_binop(v, w, a, b)) { \
+ Py_INCREF(Py_NotImplemented); \
+ return Py_NotImplemented; \
+ }
+
+/* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required. x[0:n]
+ * is modified in place, by adding y to it. Carries are propagated as far as
+ * x[m-1], and the remaining carry (0 or 1) is returned.
+ */
+static digit
+v_iadd(digit *x, int m, digit *y, int n)
+{
+ int i;
+ digit carry = 0;
+
+ assert(m >= n);
+ for (i = 0; i < n; ++i) {
+ carry += x[i] + y[i];
+ x[i] = carry & MASK;
+ carry >>= SHIFT;
+ assert((carry & 1) == carry);
+ }
+ for (; carry && i < m; ++i) {
+ carry += x[i];
+ x[i] = carry & MASK;
+ carry >>= SHIFT;
+ assert((carry & 1) == carry);
+ }
+ return carry;
+}
+
+/* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required. x[0:n]
+ * is modified in place, by subtracting y from it. Borrows are propagated as
+ * far as x[m-1], and the remaining borrow (0 or 1) is returned.
+ */
+static digit
+v_isub(digit *x, int m, digit *y, int n)
+{
+ int i;
+ digit borrow = 0;
+
+ assert(m >= n);
+ for (i = 0; i < n; ++i) {
+ borrow = x[i] - y[i] - borrow;
+ x[i] = borrow & MASK;
+ borrow >>= SHIFT;
+ borrow &= 1; /* keep only 1 sign bit */
+ }
+ for (; borrow && i < m; ++i) {
+ borrow = x[i] - borrow;
+ x[i] = borrow & MASK;
+ borrow >>= SHIFT;
+ borrow &= 1;
+ }
+ return borrow;
+}
+
+/* Multiply by a single digit, ignoring the sign. */
+
+static obj_p
+mul1(obj_p a, wdigit n)
+{
+ return muladd1(a, n, (digit)0);
+}
+
+/* Multiply by a single digit and add a single digit, ignoring the sign. */
+
+static obj_p
+muladd1(obj_p a, wdigit n, wdigit extra)
+{
+ int size_a = abs(a->ob_size);
+ obj_p 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 long pin, w/ size digits, by non-zero digit n, storing quotient
+ in pout, and returning the remainder. pin and pout point at the LSD.
+ It's OK for pin == pout on entry, which saves oodles of mallocs/frees in
+ long_format, but that should be done with great care since longs are
+ immutable. */
+
+static digit
+inplace_divrem1(digit *pout, digit *pin, int size, digit n)
+{
+ twodigits rem = 0;
+
+ assert(n > 0 && n <= MASK);
+ pin += size;
+ pout += size;
+ while (--size >= 0) {
+ digit hi;
+ rem = (rem << SHIFT) + *--pin;
+ *--pout = hi = (digit)(rem / n);
+ rem -= hi * n;
+ }
+ return (digit)rem;
+}
+
+/* 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 obj_p
+divrem1(obj_p a, digit n, digit *prem)
+{
+ const int size = abs(a->ob_size);
+ obj_p z;
+
+ assert(n > 0 && n <= MASK);
+ z = _PyLong_New(size);
+ if (z == NULL)
+ return NULL;
+ *prem = inplace_divrem1(z->ob_digit, a->ob_digit, size, n);
+ return long_normalize(z);
+}
+
+/* Convert 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'. */
+
+static obj_p
+long_format(obj_p aa, int base, int addL)
+{
+ register obj_p a = (obj_p)aa;
+ PyStringObject *str;
+ int i;
+ const 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 = 5 + (addL ? 1 : 0) + (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';
+ if (addL)
+ *--p = 'L';
+ if (a->ob_size < 0)
+ sign = '-';
+
+ if (a->ob_size == 0) {
+ *--p = '0';
+ }
+ else if ((base & (base - 1)) == 0) {
+ /* JRH: special case for power-of-2 bases */
+ twodigits accum = 0;
+ int accumbits = 0; /* # of bits in accum */
+ int basebits = 1; /* # of bits in base-1 */
+ i = base;
+ while ((i >>= 1) > 1)
+ ++basebits;
+
+ for (i = 0; i < size_a; ++i) {
+ accum |= (twodigits)a->ob_digit[i] << accumbits;
+ accumbits += SHIFT;
+ assert(accumbits >= basebits);
+ do {
+ char cdigit = (char)(accum & (base - 1));
+ cdigit += (cdigit < 10) ? '0' : 'A'-10;
+ assert(p > PyString_AS_STRING(str));
+ *--p = cdigit;
+ accumbits -= basebits;
+ accum >>= basebits;
+ } while (i < size_a-1 ? accumbits >= basebits :
+ accum > 0);
+ }
+ }
+ else {
+ /* Not 0, and base not a power of 2. Divide repeatedly by
+ base, but for speed use the highest power of base that
+ fits in a digit. */
+ int size = size_a;
+ digit *pin = a->ob_digit;
+ obj_p scratch;
+ /* powbasw <- largest power of base that fits in a digit. */
+ digit powbase = base; /* powbase == base ** power */
+ int power = 1;
+ for (;;) {
+ unsigned long newpow = powbase * (unsigned long)base;
+ if (newpow >> SHIFT) /* doesn't fit in a digit */
+ break;
+ powbase = (digit)newpow;
+ ++power;
+ }
+
+ /* Get a scratch area for repeated division. */
+ scratch = _PyLong_New(size);
+ if (scratch == NULL) {
+ Py_DECREF(str);
+ return NULL;
+ }
+
+ /* Repeatedly divide by powbase. */
+ do {
+ int ntostore = power;
+ digit rem = inplace_divrem1(scratch->ob_digit,
+ pin, size, powbase);
+ pin = scratch->ob_digit; /* no need to use a again */
+ if (pin[size - 1] == 0)
+ --size;
+ SIGCHECK({
+ Py_DECREF(scratch);
+ Py_DECREF(str);
+ return NULL;
+ })
+
+ /* Break rem into digits. */
+ assert(ntostore > 0);
+ do {
+ digit nextrem = (digit)(rem / base);
+ char c = (char)(rem - nextrem * base);
+ assert(p > PyString_AS_STRING(str));
+ c += (c < 10) ? '0' : 'A'-10;
+ *--p = c;
+ rem = nextrem;
+ --ntostore;
+ /* Termination is a bit delicate: must not
+ store leading zeroes, so must get out if
+ remaining quotient and rem are both 0. */
+ } while (ntostore && (size || rem));
+ } while (size != 0);
+ Py_DECREF(scratch);
+ }
+
+ 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((obj_p *)&str,
+ (int) (q - PyString_AS_STRING(str)));
+ }
+ return (obj_p)str;
+}
+
+/* *str points to the first digit in a string of base base digits. base
+ * is a power of 2 (2, 4, 8, 16, or 32). *str is set to point to the first
+ * non-digit (which may be *str!). A normalized long is returned.
+ * The point to this routine is that it takes time linear in the number of
+ * string characters.
+ */
+static obj_p
+long_from_binary_base(char **str, int base)
+{
+ char *p = *str;
+ char *start = p;
+ int bits_per_char;
+ int n;
+ obj_p z;
+ twodigits accum;
+ int bits_in_accum;
+ digit *pdigit;
+
+ assert(base >= 2 && base <= 32 && (base & (base - 1)) == 0);
+ n = base;
+ for (bits_per_char = -1; n; ++bits_per_char)
+ n >>= 1;
+ /* n <- total # of bits needed, while setting p to end-of-string */
+ n = 0;
+ for (;;) {
+ int k = -1;
+ char ch = *p;
+
+ if (ch <= '9')
+ k = ch - '0';
+ else if (ch >= 'a')
+ k = ch - 'a' + 10;
+ else if (ch >= 'A')
+ k = ch - 'A' + 10;
+ if (k < 0 || k >= base)
+ break;
+ ++p;
+ }
+ *str = p;
+ n = (p - start) * bits_per_char;
+ if (n / bits_per_char != p - start) {
+ PyErr_SetString(PyExc_ValueError,
+ "long string too large to convert");
+ return NULL;
+ }
+ /* n <- # of Python digits needed, = ceiling(n/SHIFT). */
+ n = (n + SHIFT - 1) / SHIFT;
+ z = _PyLong_New(n);
+ if (z == NULL)
+ return NULL;
+ /* Read string from right, and fill in long from left; i.e.,
+ * from least to most significant in both.
+ */
+ accum = 0;
+ bits_in_accum = 0;
+ pdigit = z->ob_digit;
+ while (--p >= start) {
+ int k;
+ char ch = *p;
+
+ if (ch <= '9')
+ k = ch - '0';
+ else if (ch >= 'a')
+ k = ch - 'a' + 10;
+ else {
+ assert(ch >= 'A');
+ k = ch - 'A' + 10;
+ }
+ assert(k >= 0 && k < base);
+ accum |= (twodigits)(k << bits_in_accum);
+ bits_in_accum += bits_per_char;
+ if (bits_in_accum >= SHIFT) {
+ *pdigit++ = (digit)(accum & MASK);
+ assert(pdigit - z->ob_digit <= n);
+ accum >>= SHIFT;
+ bits_in_accum -= SHIFT;
+ assert(bits_in_accum < SHIFT);
+ }
+ }
+ if (bits_in_accum) {
+ assert(bits_in_accum <= SHIFT);
+ *pdigit++ = (digit)accum;
+ assert(pdigit - z->ob_digit <= n);
+ }
+ while (pdigit - z->ob_digit < n)
+ *pdigit++ = 0;
+ return long_normalize(z);
+}
+
+obj_p
+PyLong_FromString(char *str, char **pend, int base)
+{
+ int sign = 1;
+ char *start, *orig_str = str;
+ obj_p z;
+
+ if ((base != 0 && base < 2) || base > 36) {
+ PyErr_SetString(PyExc_ValueError,
+ "long() arg 2 must be >= 2 and <= 36");
+ 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;
+ start = str;
+ if ((base & (base - 1)) == 0)
+ z = long_from_binary_base(&str, base);
+ else {
+ z = _PyLong_New(0);
+ for ( ; z != NULL; ++str) {
+ int k = -1;
+ obj_p 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 (z == NULL)
+ return NULL;
+ if (str == start)
+ goto onError;
+ if (sign < 0 && z != NULL && z->ob_size != 0)
+ z->ob_size = -(z->ob_size);
+ if (*str == 'L' || *str == 'l')
+ str++;
+ while (*str && isspace(Py_CHARMASK(*str)))
+ str++;
+ if (*str != '\0')
+ goto onError;
+ if (pend)
+ *pend = str;
+ return (obj_p) z;
+
+ onError:
+ PyErr_Format(PyExc_ValueError,
+ "invalid literal for long(): %.200s", orig_str);
+ Py_XDECREF(z);
+ return NULL;
+}
+
+#ifdef Py_USING_UNICODE
+obj_p
+PyLong_FromUnicode(Py_UNICODE *u, int length, int base)
+{
+ obj_p result;
+ char *buffer = PyMem_MALLOC(length+1);
+
+ if (buffer == NULL)
+ return NULL;
+
+ if (PyUnicode_EncodeDecimal(u, length, buffer, NULL)) {
+ PyMem_FREE(buffer);
+ return NULL;
+ }
+ result = PyLong_FromString(buffer, NULL, base);
+ PyMem_FREE(buffer);
+ return result;
+}
+#endif
+
+/* forward */
+static obj_p x_divrem
+ (obj_p, obj_p, obj_p *);
+static obj_p long_pos(obj_p);
+static int long_divrem(obj_p, obj_p,
+ obj_p *, obj_p *);
+
+/* Long division with remainder, top-level routine */
+
+static int
+long_divrem(obj_p a, obj_p b,
+ obj_p *pdiv, obj_p *prem)
+{
+ int size_a = abs(a->ob_size), size_b = abs(b->ob_size);
+ obj_p z;
+
+ if (size_b == 0) {
+ PyErr_SetString(PyExc_ZeroDivisionError,
+ "long division or modulo by zero");
+ return -1;
+ }
+ if (size_a < size_b ||
+ (size_a == size_b &&
+ a->ob_digit[size_a-1] < b->ob_digit[size_b-1])) {
+ /* |a| < |b|. */
+ *pdiv = _PyLong_New(0);
+ Py_INCREF(a);
+ *prem = (obj_p) a;
+ return 0;
+ }
+ if (size_b == 1) {
+ digit rem = 0;
+ z = divrem1(a, b->ob_digit[0], &rem);
+ if (z == NULL)
+ return -1;
+ *prem = (obj_p) 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 obj_p
+x_divrem(obj_p v1, obj_p w1, obj_p *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));
+ obj_p v = mul1(v1, d);
+ obj_p w = mul1(w1, d);
+ obj_p 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] = (digit)(carry & MASK);
+ carry = Py_ARITHMETIC_RIGHT_SHIFT(BASE_TWODIGITS_TYPE,
+ carry, SHIFT);
+ carry -= 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] = (digit)(carry & MASK);
+ carry = Py_ARITHMETIC_RIGHT_SHIFT(
+ BASE_TWODIGITS_TYPE,
+ 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 */
+
+static void
+long_dealloc(obj_p v)
+{
+ v->ob_type->tp_free(v);
+}
+
+static obj_p
+long_repr(obj_p v)
+{
+ return long_format(v, 10, 1);
+}
+
+static obj_p
+long_str(obj_p v)
+{
+ return long_format(v, 10, 0);
+}
+
+static int
+long_compare(obj_p a, obj_p 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(obj_p 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);
+ }
+#define LONG_BIT_SHIFT (8*sizeof(long) - SHIFT)
+ while (--i >= 0) {
+ /* Force a native long #-bits (32 or 64) circular shift */
+ x = ((x << SHIFT) & ~MASK) | ((x >> LONG_BIT_SHIFT) & MASK);
+ x += v->ob_digit[i];
+ }
+#undef LONG_BIT_SHIFT
+ x = x * sign;
+ if (x == -1)
+ x = -2;
+ return x;
+}
+
+
+/* Add the absolute values of two long integers. */
+
+static obj_p
+x_add(obj_p a, obj_p b)
+{
+ int size_a = abs(a->ob_size), size_b = abs(b->ob_size);
+ obj_p z;
+ int i;
+ digit carry = 0;
+
+ /* Ensure a is the larger of the two: */
+ if (size_a < size_b) {
+ { obj_p 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;
+ 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 obj_p
+x_sub(obj_p a, obj_p b)
+{
+ int size_a = abs(a->ob_size), size_b = abs(b->ob_size);
+ obj_p z;
+ int i;
+ int sign = 1;
+ digit borrow = 0;
+
+ /* Ensure a is the larger of the two: */
+ if (size_a < size_b) {
+ sign = -1;
+ { obj_p 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;
+ { obj_p 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;
+ borrow &= 1; /* Keep only one sign bit */
+ }
+ assert(borrow == 0);
+ if (sign < 0)
+ z->ob_size = -(z->ob_size);
+ return long_normalize(z);
+}
+
+static obj_p
+long_add(obj_p v, obj_p w)
+{
+ obj_p a, *b, *z;
+
+ CONVERT_BINOP((obj_p)v, (obj_p)w, &a, &b);
+
+ 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);
+ }
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return (obj_p)z;
+}
+
+static obj_p
+long_sub(obj_p v, obj_p w)
+{
+ obj_p a, *b, *z;
+
+ CONVERT_BINOP((obj_p)v, (obj_p)w, &a, &b);
+
+ 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);
+ }
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return (obj_p)z;
+}
+
+/* Grade school multiplication, ignoring the signs.
+ * Returns the absolute value of the product, or NULL if error.
+ */
+static obj_p
+x_mul(obj_p a, obj_p b)
+{
+ obj_p z;
+ int size_a = abs(a->ob_size);
+ int size_b = abs(b->ob_size);
+ int i;
+
+ z = _PyLong_New(size_a + size_b);
+ if (z == NULL)
+ return NULL;
+
+ memset(z->ob_digit, 0, z->ob_size * sizeof(digit));
+ for (i = 0; i < size_a; ++i) {
+ twodigits carry = 0;
+ twodigits f = a->ob_digit[i];
+ int j;
+ digit *pz = z->ob_digit + i;
+
+ SIGCHECK({
+ Py_DECREF(z);
+ return NULL;
+ })
+ for (j = 0; j < size_b; ++j) {
+ carry += *pz + b->ob_digit[j] * f;
+ *pz++ = (digit) (carry & MASK);
+ carry >>= SHIFT;
+ }
+ for (; carry != 0; ++j) {
+ assert(i+j < z->ob_size);
+ carry += *pz;
+ *pz++ = (digit) (carry & MASK);
+ carry >>= SHIFT;
+ }
+ }
+ return long_normalize(z);
+}
+
+/* A helper for Karatsuba multiplication (k_mul).
+ Takes a long "n" and an integer "size" representing the place to
+ split, and sets low and high such that abs(n) == (high << size) + low,
+ viewing the shift as being by digits. The sign bit is ignored, and
+ the return values are >= 0.
+ Returns 0 on success, -1 on failure.
+*/
+static int
+kmul_split(obj_p n, int size, obj_p *high, obj_p *low)
+{
+ obj_p hi, *lo;
+ int size_lo, size_hi;
+ const int size_n = abs(n->ob_size);
+
+ size_lo = MIN(size_n, size);
+ size_hi = size_n - size_lo;
+
+ if ((hi = _PyLong_New(size_hi)) == NULL)
+ return -1;
+ if ((lo = _PyLong_New(size_lo)) == NULL) {
+ Py_DECREF(hi);
+ return -1;
+ }
+
+ memcpy(lo->ob_digit, n->ob_digit, size_lo * sizeof(digit));
+ memcpy(hi->ob_digit, n->ob_digit + size_lo, size_hi * sizeof(digit));
+
+ *high = long_normalize(hi);
+ *low = long_normalize(lo);
+ return 0;
+}
+
+static obj_p k_lopsided_mul(obj_p a, obj_p b);
+
+/* Karatsuba multiplication. Ignores the input signs, and returns the
+ * absolute value of the product (or NULL if error).
+ * See Knuth Vol. 2 Chapter 4.3.3 (Pp. 294-295).
+ */
+static obj_p
+k_mul(obj_p a, obj_p b)
+{
+ int asize = abs(a->ob_size);
+ int bsize = abs(b->ob_size);
+ obj_p ah = NULL;
+ obj_p al = NULL;
+ obj_p bh = NULL;
+ obj_p bl = NULL;
+ obj_p ret = NULL;
+ obj_p t1, *t2, *t3;
+ int shift; /* the number of digits we split off */
+ int i;
+
+ /* (ah*X+al)(bh*X+bl) = ah*bh*X*X + (ah*bl + al*bh)*X + al*bl
+ * Let k = (ah+al)*(bh+bl) = ah*bl + al*bh + ah*bh + al*bl
+ * Then the original product is
+ * ah*bh*X*X + (k - ah*bh - al*bl)*X + al*bl
+ * By picking X to be a power of 2, "*X" is just shifting, and it's
+ * been reduced to 3 multiplies on numbers half the size.
+ */
+
+ /* We want to split based on the larger number; fiddle so that b
+ * is largest.
+ */
+ if (asize > bsize) {
+ t1 = a;
+ a = b;
+ b = t1;
+
+ i = asize;
+ asize = bsize;
+ bsize = i;
+ }
+
+ /* Use gradeschool math when either number is too small. */
+ if (asize <= KARATSUBA_CUTOFF) {
+ if (asize == 0)
+ return _PyLong_New(0);
+ else
+ return x_mul(a, b);
+ }
+
+ /* If a is small compared to b, splitting on b gives a degenerate
+ * case with ah==0, and Karatsuba may be (even much) less efficient
+ * than "grade school" then. However, we can still win, by viewing
+ * b as a string of "big digits", each of width a->ob_size. That
+ * leads to a sequence of balanced calls to k_mul.
+ */
+ if (2 * asize <= bsize)
+ return k_lopsided_mul(a, b);
+
+ /* Split a & b into hi & lo pieces. */
+ shift = bsize >> 1;
+ if (kmul_split(a, shift, &ah, &al) < 0) goto fail;
+ assert(ah->ob_size > 0); /* the split isn't degenerate */
+
+ if (kmul_split(b, shift, &bh, &bl) < 0) goto fail;
+
+ /* The plan:
+ * 1. Allocate result space (asize + bsize digits: that's always
+ * enough).
+ * 2. Compute ah*bh, and copy into result at 2*shift.
+ * 3. Compute al*bl, and copy into result at 0. Note that this
+ * can't overlap with #2.
+ * 4. Subtract al*bl from the result, starting at shift. This may
+ * underflow (borrow out of the high digit), but we don't care:
+ * we're effectively doing unsigned arithmetic mod
+ * BASE**(sizea + sizeb), and so long as the *final* result fits,
+ * borrows and carries out of the high digit can be ignored.
+ * 5. Subtract ah*bh from the result, starting at shift.
+ * 6. Compute (ah+al)*(bh+bl), and add it into the result starting
+ * at shift.
+ */
+
+ /* 1. Allocate result space. */
+ ret = _PyLong_New(asize + bsize);
+ if (ret == NULL) goto fail;
+#ifdef Py_DEBUG
+ /* Fill with trash, to catch reference to uninitialized digits. */
+ memset(ret->ob_digit, 0xDF, ret->ob_size * sizeof(digit));
+#endif
+
+ /* 2. t1 <- ah*bh, and copy into high digits of result. */
+ if ((t1 = k_mul(ah, bh)) == NULL) goto fail;
+ assert(t1->ob_size >= 0);
+ assert(2*shift + t1->ob_size <= ret->ob_size);
+ memcpy(ret->ob_digit + 2*shift, t1->ob_digit,
+ t1->ob_size * sizeof(digit));
+
+ /* Zero-out the digits higher than the ah*bh copy. */
+ i = ret->ob_size - 2*shift - t1->ob_size;
+ if (i)
+ memset(ret->ob_digit + 2*shift + t1->ob_size, 0,
+ i * sizeof(digit));
+
+ /* 3. t2 <- al*bl, and copy into the low digits. */
+ if ((t2 = k_mul(al, bl)) == NULL) {
+ Py_DECREF(t1);
+ goto fail;
+ }
+ assert(t2->ob_size >= 0);
+ assert(t2->ob_size <= 2*shift); /* no overlap with high digits */
+ memcpy(ret->ob_digit, t2->ob_digit, t2->ob_size * sizeof(digit));
+
+ /* Zero out remaining digits. */
+ i = 2*shift - t2->ob_size; /* number of uninitialized digits */
+ if (i)
+ memset(ret->ob_digit + t2->ob_size, 0, i * sizeof(digit));
+
+ /* 4 & 5. Subtract ah*bh (t1) and al*bl (t2). We do al*bl first
+ * because it's fresher in cache.
+ */
+ i = ret->ob_size - shift; /* # digits after shift */
+ (void)v_isub(ret->ob_digit + shift, i, t2->ob_digit, t2->ob_size);
+ Py_DECREF(t2);
+
+ (void)v_isub(ret->ob_digit + shift, i, t1->ob_digit, t1->ob_size);
+ Py_DECREF(t1);
+
+ /* 6. t3 <- (ah+al)(bh+bl), and add into result. */
+ if ((t1 = x_add(ah, al)) == NULL) goto fail;
+ Py_DECREF(ah);
+ Py_DECREF(al);
+ ah = al = NULL;
+
+ if ((t2 = x_add(bh, bl)) == NULL) {
+ Py_DECREF(t1);
+ goto fail;
+ }
+ Py_DECREF(bh);
+ Py_DECREF(bl);
+ bh = bl = NULL;
+
+ t3 = k_mul(t1, t2);
+ Py_DECREF(t1);
+ Py_DECREF(t2);
+ if (t3 == NULL) goto fail;
+ assert(t3->ob_size >= 0);
+
+ /* Add t3. It's not obvious why we can't run out of room here.
+ * See the (*) comment after this function.
+ */
+ (void)v_iadd(ret->ob_digit + shift, i, t3->ob_digit, t3->ob_size);
+ Py_DECREF(t3);
+
+ return long_normalize(ret);
+
+ fail:
+ Py_XDECREF(ret);
+ Py_XDECREF(ah);
+ Py_XDECREF(al);
+ Py_XDECREF(bh);
+ Py_XDECREF(bl);
+ return NULL;
+}
+
+/* (*) Why adding t3 can't "run out of room" above.
+
+Let f(x) mean the floor of x and c(x) mean the ceiling of x. Some facts
+to start with:
+
+1. For any integer i, i = c(i/2) + f(i/2). In particular,
+ bsize = c(bsize/2) + f(bsize/2).
+2. shift = f(bsize/2)
+3. asize <= bsize
+4. Since we call k_lopsided_mul if asize*2 <= bsize, asize*2 > bsize in this
+ routine, so asize > bsize/2 >= f(bsize/2) in this routine.
+
+We allocated asize + bsize result digits, and add t3 into them at an offset
+of shift. This leaves asize+bsize-shift allocated digit positions for t3
+to fit into, = (by #1 and #2) asize + f(bsize/2) + c(bsize/2) - f(bsize/2) =
+asize + c(bsize/2) available digit positions.
+
+bh has c(bsize/2) digits, and bl at most f(size/2) digits. So bh+hl has
+at most c(bsize/2) digits + 1 bit.
+
+If asize == bsize, ah has c(bsize/2) digits, else ah has at most f(bsize/2)
+digits, and al has at most f(bsize/2) digits in any case. So ah+al has at
+most (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 1 bit.
+
+The product (ah+al)*(bh+bl) therefore has at most
+
+ c(bsize/2) + (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits
+
+and we have asize + c(bsize/2) available digit positions. We need to show
+this is always enough. An instance of c(bsize/2) cancels out in both, so
+the question reduces to whether asize digits is enough to hold
+(asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits. If asize < bsize,
+then we're asking whether asize digits >= f(bsize/2) digits + 2 bits. By #4,
+asize is at least f(bsize/2)+1 digits, so this in turn reduces to whether 1
+digit is enough to hold 2 bits. This is so since SHIFT=15 >= 2. If
+asize == bsize, then we're asking whether bsize digits is enough to hold
+c(bsize/2) digits + 2 bits, or equivalently (by #1) whether f(bsize/2) digits
+is enough to hold 2 bits. This is so if bsize >= 2, which holds because
+bsize >= KARATSUBA_CUTOFF >= 2.
+
+Note that since there's always enough room for (ah+al)*(bh+bl), and that's
+clearly >= each of ah*bh and al*bl, there's always enough room to subtract
+ah*bh and al*bl too.
+*/
+
+/* b has at least twice the digits of a, and a is big enough that Karatsuba
+ * would pay off *if* the inputs had balanced sizes. View b as a sequence
+ * of slices, each with a->ob_size digits, and multiply the slices by a,
+ * one at a time. This gives k_mul balanced inputs to work with, and is
+ * also cache-friendly (we compute one double-width slice of the result
+ * at a time, then move on, never bactracking except for the helpful
+ * single-width slice overlap between successive partial sums).
+ */
+static obj_p
+k_lopsided_mul(obj_p a, obj_p b)
+{
+ const int asize = abs(a->ob_size);
+ int bsize = abs(b->ob_size);
+ int nbdone; /* # of b digits already multiplied */
+ obj_p ret;
+ obj_p bslice = NULL;
+
+ assert(asize > KARATSUBA_CUTOFF);
+ assert(2 * asize <= bsize);
+
+ /* Allocate result space, and zero it out. */
+ ret = _PyLong_New(asize + bsize);
+ if (ret == NULL)
+ return NULL;
+ memset(ret->ob_digit, 0, ret->ob_size * sizeof(digit));
+
+ /* Successive slices of b are copied into bslice. */
+ bslice = _PyLong_New(asize);
+ if (bslice == NULL)
+ goto fail;
+
+ nbdone = 0;
+ while (bsize > 0) {
+ obj_p product;
+ const int nbtouse = MIN(bsize, asize);
+
+ /* Multiply the next slice of b by a. */
+ memcpy(bslice->ob_digit, b->ob_digit + nbdone,
+ nbtouse * sizeof(digit));
+ bslice->ob_size = nbtouse;
+ product = k_mul(a, bslice);
+ if (product == NULL)
+ goto fail;
+
+ /* Add into result. */
+ (void)v_iadd(ret->ob_digit + nbdone, ret->ob_size - nbdone,
+ product->ob_digit, product->ob_size);
+ Py_DECREF(product);
+
+ bsize -= nbtouse;
+ nbdone += nbtouse;
+ }
+
+ Py_DECREF(bslice);
+ return long_normalize(ret);
+
+ fail:
+ Py_DECREF(ret);
+ Py_XDECREF(bslice);
+ return NULL;
+}
+
+static obj_p
+long_mul(obj_p v, obj_p w)
+{
+ obj_p a, *b, *z;
+
+ if (!convert_binop((obj_p)v, (obj_p)w, &a, &b)) {
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ z = k_mul(a, b);
+ /* Negate if exactly one of the inputs is negative. */
+ if (((a->ob_size ^ b->ob_size) < 0) && z)
+ z->ob_size = -(z->ob_size);
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return (obj_p)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(obj_p v, obj_p w,
+ obj_p *pdiv, obj_p *pmod)
+{
+ obj_p 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)) {
+ obj_p temp;
+ obj_p one;
+ temp = (obj_p) long_add(mod, w);
+ Py_DECREF(mod);
+ mod = temp;
+ if (mod == NULL) {
+ Py_DECREF(div);
+ return -1;
+ }
+ one = (obj_p) PyLong_FromLong(1L);
+ if (one == NULL ||
+ (temp = (obj_p) 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 obj_p
+long_div(obj_p v, obj_p w)
+{
+ obj_p a, *b, *div, *mod;
+
+ CONVERT_BINOP(v, w, &a, &b);
+
+ if (l_divmod(a, b, &div, &mod) < 0) {
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return NULL;
+ }
+ Py_DECREF(a);
+ Py_DECREF(b);
+ Py_DECREF(mod);
+ return (obj_p)div;
+}
+
+static obj_p
+long_classic_div(obj_p v, obj_p w)
+{
+ obj_p a, *b, *div, *mod;
+
+ CONVERT_BINOP(v, w, &a, &b);
+
+ if (Py_DivisionWarningFlag &&
+ PyErr_Warn(PyExc_DeprecationWarning, "classic long division") < 0)
+ div = NULL;
+ else if (l_divmod(a, b, &div, &mod) < 0)
+ div = NULL;
+ else
+ Py_DECREF(mod);
+
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return (obj_p)div;
+}
+
+static obj_p
+long_true_divide(obj_p v, obj_p w)
+{
+ obj_p a, *b;
+ double ad, bd;
+ int aexp, bexp, failed;
+
+ CONVERT_BINOP(v, w, &a, &b);
+ ad = _PyLong_AsScaledDouble((obj_p)a, &aexp);
+ bd = _PyLong_AsScaledDouble((obj_p)b, &bexp);
+ failed = (ad == -1.0 || bd == -1.0) && PyErr_Occurred();
+ Py_DECREF(a);
+ Py_DECREF(b);
+ if (failed)
+ return NULL;
+
+ if (bd == 0.0) {
+ PyErr_SetString(PyExc_ZeroDivisionError,
+ "long division or modulo by zero");
+ return NULL;
+ }
+
+ /* True value is very close to ad/bd * 2**(SHIFT*(aexp-bexp)) */
+ ad /= bd; /* overflow/underflow impossible here */
+ aexp -= bexp;
+ if (aexp > INT_MAX / SHIFT)
+ goto overflow;
+ else if (aexp < -(INT_MAX / SHIFT))
+ return PyFloat_FromDouble(0.0); /* underflow to 0 */
+ errno = 0;
+ ad = ldexp(ad, aexp * SHIFT);
+ if (Py_OVERFLOWED(ad)) /* ignore underflow to 0.0 */
+ goto overflow;
+ return PyFloat_FromDouble(ad);
+
+overflow:
+ PyErr_SetString(PyExc_OverflowError,
+ "long/long too large for a float");
+ return NULL;
+
+}
+
+static obj_p
+long_mod(obj_p v, obj_p w)
+{
+ obj_p a, *b, *div, *mod;
+
+ CONVERT_BINOP(v, w, &a, &b);
+
+ if (l_divmod(a, b, &div, &mod) < 0) {
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return NULL;
+ }
+ Py_DECREF(a);
+ Py_DECREF(b);
+ Py_DECREF(div);
+ return (obj_p)mod;
+}
+
+static obj_p
+long_divmod(obj_p v, obj_p w)
+{
+ obj_p a, *b, *div, *mod;
+ obj_p z;
+
+ CONVERT_BINOP(v, w, &a, &b);
+
+ if (l_divmod(a, b, &div, &mod) < 0) {
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return NULL;
+ }
+ z = PyTuple_New(2);
+ if (z != NULL) {
+ PyTuple_SetItem(z, 0, (obj_p) div);
+ PyTuple_SetItem(z, 1, (obj_p) mod);
+ }
+ else {
+ Py_DECREF(div);
+ Py_DECREF(mod);
+ }
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return z;
+}
+
+static obj_p
+long_pow(obj_p v, obj_p w, obj_p x)
+{
+ obj_p a, *b;
+ obj_p c;
+ obj_p z, *div, *mod;
+ int size_b, i;
+
+ CONVERT_BINOP(v, w, &a, &b);
+ if (PyLong_Check(x) || Py_None == x) {
+ c = x;
+ Py_INCREF(x);
+ }
+ else if (PyInt_Check(x)) {
+ c = PyLong_FromLong(PyInt_AS_LONG(x));
+ }
+ else {
+ Py_DECREF(a);
+ Py_DECREF(b);
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ if (c != Py_None && ((obj_p)c)->ob_size == 0) {
+ PyErr_SetString(PyExc_ValueError,
+ "pow() 3rd argument cannot be 0");
+ z = NULL;
+ goto error;
+ }
+
+ size_b = b->ob_size;
+ if (size_b < 0) {
+ Py_DECREF(a);
+ Py_DECREF(b);
+ Py_DECREF(c);
+ if (x != Py_None) {
+ PyErr_SetString(PyExc_TypeError, "pow() 2nd argument "
+ "cannot be negative when 3rd argument specified");
+ return NULL;
+ }
+ /* Return a float. This works because we know that
+ this calls float_pow() which converts its
+ arguments to double. */
+ return PyFloat_Type.tp_as_number->nb_power(v, w, x);
+ }
+ z = (obj_p)PyLong_FromLong(1L);
+ for (i = 0; i < size_b; ++i) {
+ digit bi = b->ob_digit[i];
+ int j;
+
+ for (j = 0; j < SHIFT; ++j) {
+ obj_p temp;
+
+ if (bi & 1) {
+ temp = (obj_p)long_mul(z, a);
+ Py_DECREF(z);
+ if (c!=Py_None && temp!=NULL) {
+ if (l_divmod(temp,(obj_p)c,
+ &div,&mod) < 0) {
+ Py_DECREF(temp);
+ z = NULL;
+ goto error;
+ }
+ 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 = (obj_p)long_mul(a, a);
+ Py_DECREF(a);
+ if (c!=Py_None && temp!=NULL) {
+ if (l_divmod(temp, (obj_p)c, &div,
+ &mod) < 0) {
+ Py_DECREF(temp);
+ z = NULL;
+ goto error;
+ }
+ 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;
+ }
+ if (c!=Py_None && z!=NULL) {
+ if (l_divmod(z, (obj_p)c, &div, &mod) < 0) {
+ Py_DECREF(z);
+ z = NULL;
+ }
+ else {
+ Py_XDECREF(div);
+ Py_DECREF(z);
+ z = mod;
+ }
+ }
+ error:
+ Py_XDECREF(a);
+ Py_DECREF(b);
+ Py_DECREF(c);
+ return (obj_p)z;
+}
+
+static obj_p
+long_invert(obj_p v)
+{
+ /* Implement ~x as -(x+1) */
+ obj_p x;
+ obj_p w;
+ w = (obj_p)PyLong_FromLong(1L);
+ if (w == NULL)
+ return NULL;
+ x = (obj_p) long_add(v, w);
+ Py_DECREF(w);
+ if (x == NULL)
+ return NULL;
+ x->ob_size = -(x->ob_size);
+ return (obj_p)x;
+}
+
+static obj_p
+long_pos(obj_p v)
+{
+ if (PyLong_CheckExact(v)) {
+ Py_INCREF(v);
+ return (obj_p)v;
+ }
+ else
+ return _PyLong_Copy(v);
+}
+
+static obj_p
+long_neg(obj_p v)
+{
+ obj_p z;
+ if (v->ob_size == 0 && PyLong_CheckExact(v)) {
+ /* -0 == 0 */
+ Py_INCREF(v);
+ return (obj_p) v;
+ }
+ z = (obj_p)_PyLong_Copy(v);
+ if (z != NULL)
+ z->ob_size = -(v->ob_size);
+ return (obj_p)z;
+}
+
+static obj_p
+long_abs(obj_p v)
+{
+ if (v->ob_size < 0)
+ return long_neg(v);
+ else
+ return long_pos(v);
+}
+
+static int
+long_nonzero(obj_p v)
+{
+ return abs(v->ob_size) != 0;
+}
+
+static obj_p
+long_rshift(obj_p v, obj_p w)
+{
+ obj_p a, *b;
+ obj_p z = NULL;
+ long shiftby;
+ int newsize, wordshift, loshift, hishift, i, j;
+ digit lomask, himask;
+
+ CONVERT_BINOP((obj_p)v, (obj_p)w, &a, &b);
+
+ if (a->ob_size < 0) {
+ /* Right shifting negative numbers is harder */
+ obj_p a1, *a2;
+ a1 = (obj_p) long_invert(a);
+ if (a1 == NULL)
+ goto rshift_error;
+ a2 = (obj_p) long_rshift(a1, b);
+ Py_DECREF(a1);
+ if (a2 == NULL)
+ goto rshift_error;
+ z = (obj_p) long_invert(a2);
+ Py_DECREF(a2);
+ }
+ else {
+
+ shiftby = PyLong_AsLong((obj_p)b);
+ if (shiftby == -1L && PyErr_Occurred())
+ goto rshift_error;
+ if (shiftby < 0) {
+ PyErr_SetString(PyExc_ValueError,
+ "negative shift count");
+ goto rshift_error;
+ }
+ wordshift = shiftby / SHIFT;
+ newsize = abs(a->ob_size) - wordshift;
+ if (newsize <= 0) {
+ z = _PyLong_New(0);
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return (obj_p)z;
+ }
+ loshift = shiftby % SHIFT;
+ hishift = SHIFT - loshift;
+ lomask = ((digit)1 << hishift) - 1;
+ himask = MASK ^ lomask;
+ z = _PyLong_New(newsize);
+ if (z == NULL)
+ goto rshift_error;
+ 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;
+ }
+ z = long_normalize(z);
+ }
+rshift_error:
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return (obj_p) z;
+
+}
+
+static obj_p
+long_lshift(obj_p v, obj_p w)
+{
+ /* This version due to Tim Peters */
+ obj_p a, *b;
+ obj_p z = NULL;
+ long shiftby;
+ int oldsize, newsize, wordshift, remshift, i, j;
+ twodigits accum;
+
+ CONVERT_BINOP(v, w, &a, &b);
+
+ shiftby = PyLong_AsLong((obj_p)b);
+ if (shiftby == -1L && PyErr_Occurred())
+ goto lshift_error;
+ if (shiftby < 0) {
+ PyErr_SetString(PyExc_ValueError, "negative shift count");
+ goto lshift_error;
+ }
+ if ((long)(int)shiftby != shiftby) {
+ PyErr_SetString(PyExc_ValueError,
+ "outrageous left shift count");
+ goto lshift_error;
+ }
+ /* 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)
+ goto lshift_error;
+ 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 |= (twodigits)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);
+ z = long_normalize(z);
+lshift_error:
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return (obj_p) z;
+}
+
+
+/* Bitwise and/xor/or operations */
+
+static obj_p
+long_bitwise(obj_p a,
+ int op, /* '&', '|', '^' */
+ obj_p b)
+{
+ digit maska, maskb; /* 0 or MASK */
+ int negz;
+ int size_a, size_b, size_z;
+ obj_p z;
+ int i;
+ digit diga, digb;
+ obj_p v;
+
+ if (a->ob_size < 0) {
+ a = (obj_p) long_invert(a);
+ maska = MASK;
+ }
+ else {
+ Py_INCREF(a);
+ maska = 0;
+ }
+ if (b->ob_size < 0) {
+ b = (obj_p) long_invert(b);
+ maskb = MASK;
+ }
+ else {
+ Py_INCREF(b);
+ maskb = 0;
+ }
+
+ 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;
+ }
+
+ /* JRH: The original logic here was to allocate the result value (z)
+ as the longer of the two operands. However, there are some cases
+ where the result is guaranteed to be shorter than that: AND of two
+ positives, OR of two negatives: use the shorter number. AND with
+ mixed signs: use the positive number. OR with mixed signs: use the
+ negative number. After the transformations above, op will be '&'
+ iff one of these cases applies, and mask will be non-0 for operands
+ whose length should be ignored.
+ */
+
+ size_a = a->ob_size;
+ size_b = b->ob_size;
+ size_z = op == '&'
+ ? (maska
+ ? size_b
+ : (maskb ? size_a : MIN(size_a, size_b)))
+ : 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;
+ }
+
+ 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 (obj_p) z;
+ v = long_invert(z);
+ Py_DECREF(z);
+ return v;
+}
+
+static obj_p
+long_and(obj_p v, obj_p w)
+{
+ obj_p a, *b;
+ obj_p c;
+ CONVERT_BINOP(v, w, &a, &b);
+ c = long_bitwise(a, '&', b);
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return c;
+}
+
+static obj_p
+long_xor(obj_p v, obj_p w)
+{
+ obj_p a, *b;
+ obj_p c;
+ CONVERT_BINOP(v, w, &a, &b);
+ c = long_bitwise(a, '^', b);
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return c;
+}
+
+static obj_p
+long_or(obj_p v, obj_p w)
+{
+ obj_p a, *b;
+ obj_p c;
+ CONVERT_BINOP(v, w, &a, &b);
+ c = long_bitwise(a, '|', b);
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return c;
+}
+
+static int
+long_coerce(obj_p *pv, obj_p *pw)
+{
+ if (PyInt_Check(*pw)) {
+ *pw = PyLong_FromLong(PyInt_AS_LONG(*pw));
+ Py_INCREF(*pv);
+ return 0;
+ }
+ else if (PyLong_Check(*pw)) {
+ Py_INCREF(*pv);
+ Py_INCREF(*pw);
+ return 0;
+ }
+ return 1; /* Can't do it */
+}
+
+static obj_p
+long_long(obj_p v)
+{
+ Py_INCREF(v);
+ return v;
+}
+
+static obj_p
+long_int(obj_p v)
+{
+ long x;
+ x = PyLong_AsLong(v);
+ if (PyErr_Occurred()) {
+ if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
+ PyErr_Clear();
+ if (PyLong_CheckExact(v)) {
+ Py_INCREF(v);
+ return v;
+ }
+ else
+ return _PyLong_Copy((obj_p)v);
+ }
+ else
+ return NULL;
+ }
+ return PyInt_FromLong(x);
+}
+
+static obj_p
+long_float(obj_p v)
+{
+ double result;
+ result = PyLong_AsDouble(v);
+ if (result == -1.0 && PyErr_Occurred())
+ return NULL;
+ return PyFloat_FromDouble(result);
+}
+
+static obj_p
+long_oct(obj_p v)
+{
+ return long_format(v, 8, 1);
+}
+
+static obj_p
+long_hex(obj_p v)
+{
+ return long_format(v, 16, 1);
+}
+
+static obj_p
+long_subtype_new(PyTypeObject *type, obj_p args, obj_p kwds);
+
+static obj_p
+long_new(PyTypeObject *type, obj_p args, obj_p kwds)
+{
+ obj_p x = NULL;
+ int base = -909; /* unlikely! */
+ static char *kwlist[] = {"x", "base", 0};
+
+ if (type != &PyLong_Type)
+ return long_subtype_new(type, args, kwds); /* Wimp out */
+ if (!PyArg_ParseTupleAndKeywords(args, kwds, "|Oi:long", kwlist,
+ &x, &base))
+ return NULL;
+ if (x == NULL)
+ return PyLong_FromLong(0L);
+ if (base == -909)
+ return PyNumber_Long(x);
+ else if (PyString_Check(x))
+ return PyLong_FromString(PyString_AS_STRING(x), NULL, base);
+#ifdef Py_USING_UNICODE
+ else if (PyUnicode_Check(x))
+ return PyLong_FromUnicode(PyUnicode_AS_UNICODE(x),
+ PyUnicode_GET_SIZE(x),
+ base);
+#endif
+ else {
+ PyErr_SetString(PyExc_TypeError,
+ "long() can't convert non-string with explicit base");
+ return NULL;
+ }
+}
+
+/* Wimpy, slow approach to tp_new calls for subtypes of long:
+ first create a regular long from whatever arguments we got,
+ then allocate a subtype instance and initialize it from
+ the regular long. The regular long is then thrown away.
+*/
+static obj_p
+long_subtype_new(PyTypeObject *type, obj_p args, obj_p kwds)
+{
+ obj_p tmp, *new;
+ int i, n;
+
+ assert(PyType_IsSubtype(type, &PyLong_Type));
+ tmp = (obj_p)long_new(&PyLong_Type, args, kwds);
+ if (tmp == NULL)
+ return NULL;
+ assert(PyLong_CheckExact(tmp));
+ n = tmp->ob_size;
+ if (n < 0)
+ n = -n;
+ new = (obj_p)type->tp_alloc(type, n);
+ if (new == NULL) {
+ Py_DECREF(tmp);
+ return NULL;
+ }
+ assert(PyLong_Check(new));
+ new->ob_size = tmp->ob_size;
+ for (i = 0; i < n; i++)
+ new->ob_digit[i] = tmp->ob_digit[i];
+ Py_DECREF(tmp);
+ return (obj_p)new;
+}
+
+static obj_p
+long_getnewargs(obj_p v)
+{
+ return Py_BuildValue("(N)", _PyLong_Copy(v));
+}
+
+static PyMethodDef long_methods[] = {
+ {"__getnewargs__", (PyCFunction)long_getnewargs, METH_NOARGS},
+ {NULL, NULL} /* sentinel */
+};
+
+PyDoc_STRVAR(long_doc,
+"long(x[, base]) -> integer\n\
+\n\
+Convert a string or number to a long integer, if possible. A floating\n\
+point argument will be truncated towards zero (this does not include a\n\
+string representation of a floating point number!) When converting a\n\
+string, use the optional base. It is an error to supply a base when\n\
+converting a non-string.");
+
+static PyNumberMethods long_as_number = {
+ (binaryfunc) long_add, /*nb_add*/
+ (binaryfunc) long_sub, /*nb_subtract*/
+ (binaryfunc) long_mul, /*nb_multiply*/
+ (binaryfunc) long_classic_div, /*nb_divide*/
+ (binaryfunc) long_mod, /*nb_remainder*/
+ (binaryfunc) long_divmod, /*nb_divmod*/
+ (ternaryfunc) long_pow, /*nb_power*/
+ (unaryfunc) long_neg, /*nb_negative*/
+ (unaryfunc) long_pos, /*tp_positive*/
+ (unaryfunc) long_abs, /*tp_absolute*/
+ (inquiry) long_nonzero, /*tp_nonzero*/
+ (unaryfunc) long_invert, /*nb_invert*/
+ (binaryfunc) long_lshift, /*nb_lshift*/
+ (binaryfunc) long_rshift, /*nb_rshift*/
+ (binaryfunc) long_and, /*nb_and*/
+ (binaryfunc) long_xor, /*nb_xor*/
+ (binaryfunc) long_or, /*nb_or*/
+ (coercion) long_coerce, /*nb_coerce*/
+ (unaryfunc) long_int, /*nb_int*/
+ (unaryfunc) long_long, /*nb_long*/
+ (unaryfunc) long_float, /*nb_float*/
+ (unaryfunc) long_oct, /*nb_oct*/
+ (unaryfunc) long_hex, /*nb_hex*/
+ 0, /* nb_inplace_add */
+ 0, /* nb_inplace_subtract */
+ 0, /* nb_inplace_multiply */
+ 0, /* nb_inplace_divide */
+ 0, /* nb_inplace_remainder */
+ 0, /* nb_inplace_power */
+ 0, /* nb_inplace_lshift */
+ 0, /* nb_inplace_rshift */
+ 0, /* nb_inplace_and */
+ 0, /* nb_inplace_xor */
+ 0, /* nb_inplace_or */
+ (binaryfunc)long_div, /* nb_floor_divide */
+ long_true_divide, /* nb_true_divide */
+ 0, /* nb_inplace_floor_divide */
+ 0, /* nb_inplace_true_divide */
+};
+
+PyTypeObject PyLong_Type = {
+ PyObject_HEAD_INIT(&PyType_Type)
+ 0, /* ob_size */
+ "long", /* tp_name */
+ sizeof(PyLongObject) - sizeof(digit), /* tp_basicsize */
+ sizeof(digit), /* tp_itemsize */
+ (destructor)long_dealloc, /* tp_dealloc */
+ 0, /* tp_print */
+ 0, /* tp_getattr */
+ 0, /* tp_setattr */
+ (cmpfunc)long_compare, /* tp_compare */
+ (reprfunc)long_repr, /* tp_repr */
+ &long_as_number, /* tp_as_number */
+ 0, /* tp_as_sequence */
+ 0, /* tp_as_mapping */
+ (hashfunc)long_hash, /* tp_hash */
+ 0, /* tp_call */
+ (reprfunc)long_str, /* tp_str */
+ PyObject_GenericGetAttr, /* tp_getattro */
+ 0, /* tp_setattro */
+ 0, /* tp_as_buffer */
+ Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
+ Py_TPFLAGS_BASETYPE, /* tp_flags */
+ long_doc, /* tp_doc */
+ 0, /* tp_traverse */
+ 0, /* tp_clear */
+ 0, /* tp_richcompare */
+ 0, /* tp_weaklistoffset */
+ 0, /* tp_iter */
+ 0, /* tp_iternext */
+ long_methods, /* tp_methods */
+ 0, /* tp_members */
+ 0, /* tp_getset */
+ 0, /* tp_base */
+ 0, /* tp_dict */
+ 0, /* tp_descr_get */
+ 0, /* tp_descr_set */
+ 0, /* tp_dictoffset */
+ 0, /* tp_init */
+ 0, /* tp_alloc */
+ long_new, /* tp_new */
+ PyObject_Del, /* tp_free */
+};
+
Modified: trunk/src/src.vcproj
===================================================================
--- trunk/src/src.vcproj 2004-05-27 05:03:24 UTC (rev 556)
+++ trunk/src/src.vcproj 2004-05-27 19:24:13 UTC (rev 557)
@@ -137,6 +137,9 @@
RelativePath=".\builtins-attrdict.c">
</File>
<File
+ RelativePath=".\builtins-bigint.c">
+ </File>
+ <File
RelativePath=".\builtins-core.c">
</File>
<File