--- /dev/null
+/* poly.c
+ * Greg Cook, 9/Apr/2015
+ */
+
+/* CRC RevEng, an arbitrary-precision CRC calculator and algorithm finder
+ * Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015 Gregory Cook
+ *
+ * This file is part of CRC RevEng.
+ *
+ * CRC RevEng is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * CRC RevEng is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with CRC RevEng. If not, see <http://www.gnu.org/licenses/>.
+ */
+
+/* 2015-04-03: added direct mode to strtop()
+ * 2014-01-11: added LOFS(), RNDUP()
+ * 2013-09-16: SIZE(), IDX(), OFS() macros bitshift if BMP_POF2
+ * 2013-02-07: conditional non-2^n fix, pmpar() return mask constant type
+ * 2013-01-17: fixed pfirst(), plast() for non-2^n BMP_BIT
+ * 2012-07-16: added pident()
+ * 2012-05-23: added pmpar()
+ * 2012-03-03: internal lookup tables stored better
+ * 2012-03-02: fixed full-width masking in filtop()
+ * 2011-09-06: added prevch()
+ * 2011-08-27: fixed zero test in piter()
+ * 2011-01-17: fixed ANSI C warnings, uses bmp_t type
+ * 2011-01-15: palloc() and praloc() gracefully handle lengths slightly
+ * less than ULONG_MAX
+ * 2011-01-15: strtop() error on invalid argument. pkchop() special case
+ * when argument all zeroes
+ * 2011-01-14: added pkchop()
+ * 2011-01-04: fixed bogus final length calculation in wide pcrc()
+ * 2011-01-02: faster, more robust prcp()
+ * 2011-01-01: commented functions, full const declarations, all-LUT rev()
+ * 2010-12-26: renamed CRC RevEng
+ * 2010-12-18: removed pmods(), finished pcrc(), added piter()
+ * 2010-12-17: roughed out pcrc(). difficult, etiam aberat musa heri :(
+ * 2010-12-15: added psnorm(), psncmp(); optimised pnorm(); fix to praloc()
+ * 2010-12-14: strtop() resets count between passes
+ * 2010-12-12: added pright()
+ * 2010-12-11: filtop won't read more than length bits
+ * 2010-12-10: finished filtop. 26 public functions
+ * 2010-12-05: finished strtop, pxsubs; unit tests
+ * 2010-12-02: project started
+ */
+
+/* Note: WELL-FORMED poly_t objects have a valid bitmap pointer pointing
+ * to a malloc()-ed array of at least as many bits as stated in its
+ * length field. Any poly_t with a length of 0 is also a WELL-FORMED
+ * poly_t (whatever value the bitmap pointer has.)
+ * All poly_t objects passed to and from functions must be WELL-FORMED
+ * unless otherwise stated.
+ *
+ * CLEAN (or CANONICAL) poly_t objects are WELL-FORMED objects in which
+ * all spare bits in the bitmap word containing the last bit are zero.
+ * (Any excess allocated words will not be accessed.)
+ *
+ * SEMI-NORMALISED poly_t objects are CLEAN objects in which the last
+ * bit, at position (length - 1), is one.
+ *
+ * NORMALISED poly_t objects are SEMI-NORMALISED objects in which the
+ * first bit is one.
+ *
+ * pfree() should be called on every poly_t object (including
+ * those returned by functions) after its last use.
+ * As always, free() should be called on every malloc()-ed string after
+ * its last use.
+ */
+
+#include <limits.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include "reveng.h"
+
+static bmp_t getwrd(const poly_t poly, unsigned long iter);
+static bmp_t rev(bmp_t accu, int bits);
+static void prhex(char **spp, bmp_t bits, int flags, int bperhx);
+
+static const poly_t pzero = PZERO;
+
+/* word number (0..m-1) of var'th bit (0..n-1) */
+#if BMP_POF2 >= 5
+# define IDX(var) ((var) >> BMP_POF2)
+#else
+# define IDX(var) ((var) / BMP_BIT)
+#endif
+
+/* size of polynomial with var bits */
+#if BMP_POF2 >= 5
+# define SIZE(var) ((BMP_BIT - 1UL + (var)) >> BMP_POF2)
+#else
+# define SIZE(var) ((BMP_BIT - 1UL + (var)) / BMP_BIT)
+#endif
+
+/* polynomial length rounded up to BMP_BIT */
+#ifdef BMP_POF2
+# define RNDUP(var) (~(BMP_BIT - 1UL) & (BMP_BIT - 1UL + (var)))
+#else
+# define RNDUP(var) ((BMP_BIT - (var) % BMP_BIT) % BMP_BIT + (var))
+#endif
+
+/* bit offset (0..BMP_BIT-1, 0 = LSB) of var'th bit (0..n-1) */
+#ifdef BMP_POF2
+# define OFS(var) ((int) ((BMP_BIT - 1UL) & ~(var)))
+#else
+# define OFS(var) ((int) (BMP_BIT - 1UL - (var) % BMP_BIT))
+#endif
+
+/* bit offset (0..BMP_BIT-1, 0 = MSB) of var'th bit (0..n-1) */
+#ifdef BMP_POF2
+# define LOFS(var) ((int) ((BMP_BIT - 1UL) & (var)))
+#else
+# define LOFS(var) ((int) ((var) % BMP_BIT))
+#endif
+
+poly_t
+filtop(FILE *input, unsigned long length, int flags, int bperhx) {
+ /* reads binary data from input into a poly_t until EOF or until
+ * length bits are read. Characters are read until
+ * ceil(bperhx / CHAR_BIT) bits are collected; if P_LTLBYT is
+ * set in flags then the first character contains the LSB,
+ * otherwise the last one does. The least significant bperhx
+ * bits are taken, reflected (if P_REFIN) and appended to the
+ * result, then more characters are read. The maximum number of
+ * characters read is
+ * floor(length / bperhx) * ceil(bperhx / * CHAR_BIT).
+ * The returned poly_t is CLEAN.
+ */
+
+ bmp_t accu = BMP_C(0);
+ bmp_t mask = bperhx == BMP_BIT ? ~BMP_C(0) : (BMP_C(1) << bperhx) - BMP_C(1);
+ unsigned long iter = 0UL, idx;
+ int cmask = ~(~0 << CHAR_BIT), c;
+ int count = 0, ofs;
+ poly_t poly = PZERO;
+ if(bperhx == 0) return(poly);
+
+ length -= length % bperhx;
+ palloc(&poly, length); /* >= 0 */
+
+ while(iter < length && (c = fgetc(input)) != EOF) {
+ if(flags & P_LTLBYT)
+ accu |= (bmp_t) (c & cmask) << count;
+ else
+ accu = (accu << CHAR_BIT) | (bmp_t) (c & cmask);
+ count += CHAR_BIT;
+ if(count >= bperhx) {
+ /* the low bperhx bits of accu contain bits of the poly.*/
+ iter += bperhx;
+ count = 0;
+ if(flags & P_REFIN)
+ accu = rev(accu, bperhx);
+ accu &= mask;
+
+ /* iter >= bperhx > 0 */
+ idx = IDX(iter - 1UL);
+ ofs = OFS(iter - 1UL);
+ poly.bitmap[idx] |= accu << ofs;
+ if(ofs + bperhx > BMP_BIT) {
+ poly.bitmap[idx-1] |= accu >> (BMP_BIT - ofs);
+ }
+ accu = BMP_C(0); /* only needed for P_LTLBYT */
+ }
+ }
+ praloc(&poly, iter);
+ return(poly);
+}
+
+poly_t
+strtop(const char *string, int flags, int bperhx) {
+ /* Converts a hex or character string to a poly_t.
+ * Each character is converted to a hex nibble yielding 4 bits
+ * unless P_DIRECT, when each character yields CHAR_BIT bits.
+ * Nibbles and characters are accumulated left-to-right
+ * unless P_DIRECT && P_LTLBYT, when they are accumulated
+ * right-to-left without reflection.
+ * As soon as at least bperhx bits are accumulated, the
+ * rightmost bperhx bits are reflected (if P_REFIN)
+ * and appended to the poly. When !P_DIRECT:
+ * bperhx=8 reads hex nibbles in pairs
+ * bperhx=7 reads hex nibbles in pairs and discards
+ * b3 of first nibble
+ * bperhx=4 reads hex nibbles singly
+ * bperhx=3 reads octal
+ * bperhx=1 reads longhand binary
+ * in theory if !P_REFIN, bperhx can be any multiple of 4
+ * with equal effect
+ * The returned poly_t is CLEAN.
+ */
+
+ /* make two passes, one to determine the poly size
+ * one to populate the bitmap
+ */
+ unsigned long length = 1UL, idx;
+ bmp_t accu;
+ bmp_t mask = bperhx == BMP_BIT ? ~BMP_C(0) : (BMP_C(1) << bperhx) - BMP_C(1);
+ int pass, count, ofs;
+ int cmask = ~(~0 << CHAR_BIT), c;
+ const char *s;
+
+ poly_t poly = PZERO;
+ if(bperhx > BMP_BIT || bperhx <= 0 || string == NULL || *string == '\0')
+ return(poly);
+
+ for(pass=0; pass<2 && length > 0UL; ++pass) {
+ s = string;
+ length = 0UL;
+ count = 0;
+ accu = BMP_C(0);
+ while((c = *s++)) {
+ if(flags & P_DIRECT) {
+ if(flags & P_LTLBYT)
+ accu |= (bmp_t) (c & cmask) << count;
+ else
+ accu = (accu << CHAR_BIT) | (bmp_t) (c & cmask);
+ count += CHAR_BIT;
+ } else {
+ if(c == ' ' || c == '\t' || c == '\r' || c == '\n') continue;
+ accu <<= 4;
+ count += 4;
+ switch(c) {
+ case '0':
+ case '1':
+ case '2':
+ case '3':
+ case '4':
+ case '5':
+ case '6':
+ case '7':
+ case '8':
+ case '9':
+ accu |= (bmp_t) c - '0';
+ break;
+ case 'A':
+ case 'a':
+ accu |= BMP_C(0xa);
+ break;
+ case 'B':
+ case 'b':
+ accu |= BMP_C(0xb);
+ break;
+ case 'C':
+ case 'c':
+ accu |= BMP_C(0xc);
+ break;
+ case 'D':
+ case 'd':
+ accu |= BMP_C(0xd);
+ break;
+ case 'E':
+ case 'e':
+ accu |= BMP_C(0xe);
+ break;
+ case 'F':
+ case 'f':
+ accu |= BMP_C(0xf);
+ break;
+ default:
+ uerror("invalid character in hexadecimal argument");
+ }
+ }
+
+ if(count >= bperhx) {
+ /* the low bperhx bits of accu contain bits of the poly.
+ * in pass 0, increment length by bperhx.
+ * in pass 1, put the low bits of accu into the bitmap. */
+ length += bperhx;
+ count = 0;
+ if(pass == 1) {
+ if(flags & P_REFIN)
+ accu = rev(accu, bperhx);
+ accu &= mask;
+
+ /* length >= bperhx > 0 */
+ idx = IDX(length - 1);
+ ofs = OFS(length - 1);
+ poly.bitmap[idx] |= accu << ofs;
+ if(ofs + bperhx > BMP_BIT)
+ poly.bitmap[idx-1] |= accu >> (BMP_BIT - ofs);
+ accu = BMP_C(0); /* only needed for P_LTLBYT */
+ }
+ }
+ }
+ if(pass == 0) palloc(&poly, length);
+ }
+ return(poly);
+}
+
+char *
+ptostr(const poly_t poly, int flags, int bperhx) {
+ /* Returns a malloc()-ed string containing a hexadecimal
+ * representation of poly. See phxsubs().
+ */
+ return(pxsubs(poly, flags, bperhx, 0UL, poly.length));
+}
+
+char *
+pxsubs(const poly_t poly, int flags, int bperhx, unsigned long start, unsigned long end) {
+ /* Returns a malloc()-ed string containing a hexadecimal
+ * representation of a portion of poly, from bit offset start to
+ * (end - 1) inclusive. The output is grouped into words of
+ * bperhx bits each. If P_RTJUST then the first word is padded
+ * with zeroes at the MSB end to make a whole number of words,
+ * otherwise the last word is padded at the LSB end. After
+ * justification the bperhx bits of each word are reversed (if
+ * P_REFOUT) and printed as a hex sequence, with words
+ * optionally separated by spaces (P_SPACE).
+ * If end exceeds the length of poly then zero bits are appended
+ * to make up the difference, in which case poly must be CLEAN.
+ */
+ char *string, *sptr;
+ unsigned long size, iter;
+ bmp_t accu;
+ bmp_t mask = bperhx == BMP_BIT ? ~BMP_C(0) : (BMP_C(1) << bperhx) - BMP_C(1);
+ int cperhx, part;
+
+ if(bperhx <= 0 || bperhx > BMP_BIT) return(NULL);
+
+ if(start > poly.length) start = poly.length;
+ if(end > poly.length) end = poly.length;
+ if(end < start) end = start;
+
+ cperhx = (bperhx + 3) >> 2;
+ if(flags & P_SPACE) ++cperhx;
+
+ size = (end - start + bperhx - 1UL) / bperhx;
+ size *= cperhx;
+ if(!size || ~flags & P_SPACE) ++size; /* for trailing null */
+
+ if(!(sptr = string = (char *) malloc(size)))
+ uerror("cannot allocate memory for string");
+
+ size = end - start;
+ part = (int) size % bperhx;
+ if(part && flags & P_RTJUST) {
+ iter = start + part;
+ accu = getwrd(poly, iter - 1UL) & ((BMP_C(1) << part) - BMP_C(1));
+ if(flags & P_REFOUT)
+ /* best to reverse over bperhx rather than part, I think
+ * e.g. converting a 7-bit poly to 8-bit little-endian hex
+ */
+ accu = rev(accu, bperhx);
+ prhex(&sptr, accu, flags, bperhx);
+ if(flags & P_SPACE && size > iter) *sptr++ = ' ';
+ } else {
+ iter = start;
+ }
+
+ while((iter+=bperhx) <= end) {
+ accu = getwrd(poly, iter - 1UL) & mask;
+ if(flags & P_REFOUT)
+ accu = rev(accu, bperhx);
+ prhex(&sptr, accu, flags, bperhx);
+ if(flags & P_SPACE && size > iter) *sptr++ = ' ';
+ }
+
+ if(part && ~flags & P_RTJUST) {
+ accu = getwrd(poly, end - 1UL);
+ if(flags & P_REFOUT)
+ accu = rev(accu, part);
+ else
+ accu = accu << (bperhx - part) & mask;
+ prhex(&sptr, accu, flags, bperhx);
+ }
+ *sptr = '\0';
+ return(string);
+}
+
+poly_t
+pclone(const poly_t poly) {
+ /* Returns a freestanding copy of poly. Does not clean poly or
+ * the result.
+ */
+ poly_t clone = PZERO;
+
+ pcpy(&clone, poly);
+ return(clone);
+}
+
+void
+pcpy(poly_t *dest, const poly_t src) {
+ /* Assigns (copies) src into dest. Does not clean src or dest.
+ */
+ unsigned long iter, idx;
+
+ praloc(dest, src.length);
+ for(iter=0UL, idx=0UL; iter < src.length; iter += BMP_BIT, ++idx)
+ dest->bitmap[idx] = src.bitmap[idx];
+}
+
+void
+pcanon(poly_t *poly) {
+ /* Converts poly into a CLEAN object by freeing unused bitmap words
+ * and clearing any bits in the last word beyond the last bit.
+ * The length field has absolute priority over the contents of the bitmap.
+ * Canonicalisation differs from normalisation in that leading and trailing
+ * zero terms are significant and preserved.
+ * poly may or may not be WELL-FORMED.
+ */
+ praloc(poly, poly->length);
+}
+
+void
+pnorm(poly_t *poly) {
+ /* Converts poly into a NORMALISED object by removing leading
+ * and trailing zeroes, so that the polynomial starts and ends
+ * with significant terms.
+ * poly may or may not be WELL-FORMED.
+ */
+ unsigned long first;
+
+ /* call pcanon() here so pfirst() and plast() return the correct
+ * results
+ */
+ pcanon(poly);
+ first = pfirst(*poly);
+ if(first)
+ pshift(poly, *poly, 0UL, first, plast(*poly), 0UL);
+ else
+ praloc(poly, plast(*poly));
+}
+
+void
+psnorm(poly_t *poly) {
+ /* Converts poly into a SEMI-NORMALISED object by removing
+ * trailing zeroes, so that the polynomial ends with a
+ * significant term.
+ * poly may or may not be WELL-FORMED.
+ */
+
+ /* call pcanon() here so plast() returns the correct result */
+ pcanon(poly);
+ praloc(poly, plast(*poly));
+}
+
+void
+pchop(poly_t *poly) {
+ /* Normalise poly, then chop off the highest significant term
+ * (produces a SEMI-NORMALISED object). poly becomes a suitable
+ * divisor for pcrc().
+ * poly may or may not be WELL-FORMED.
+ */
+
+ /* call pcanon() here so pfirst() and plast() return correct
+ * results
+ */
+ pcanon(poly);
+ pshift(poly, *poly, 0UL, pfirst(*poly) + 1UL, plast(*poly), 0UL);
+}
+
+void
+pkchop(poly_t *poly) {
+ /* Convert poly from Koopman notation to chopped form (produces
+ * a SEMI-NORMALISED object). poly becomes a suitable divisor
+ * for pcrc().
+ * poly may or may not be WELL-FORMED.
+ */
+ unsigned long first;
+
+ /* call pcanon() here so pfirst() returns the correct result */
+ pcanon(poly);
+ first = pfirst(*poly);
+ if(first >= poly->length) {
+ pfree(poly);
+ return;
+ }
+ pshift(poly, *poly, 0UL, first + 1UL, poly->length, 1UL);
+ piter(poly);
+}
+
+unsigned long
+plen(const poly_t poly) {
+ /* Return length of polynomial.
+ * poly may or may not be WELL-FORMED.
+ */
+ return(poly.length);
+}
+
+int
+pcmp(const poly_t *a, const poly_t *b) {
+ /* Compares poly_t objects for identical sizes and contents.
+ * a and b must be CLEAN.
+ * Defines a total order relation for sorting, etc. although
+ * mathematically, polynomials of equal degree are no greater or
+ * less than one another.
+ */
+ unsigned long iter;
+ bmp_t *aptr, *bptr;
+
+ if(!a || !b) return(!b - !a);
+ if(a->length < b->length) return(-1);
+ if(a->length > b->length) return(1);
+ aptr = a->bitmap;
+ bptr = b->bitmap;
+ for(iter=0UL; iter < a->length; iter += BMP_BIT) {
+ if(*aptr < *bptr)
+ return(-1);
+ if(*aptr++ > *bptr++)
+ return(1);
+ }
+ return(0);
+}
+
+int
+psncmp(const poly_t *a, const poly_t *b) {
+ /* Compares polys for identical effect, i.e. as though the
+ * shorter poly were padded with zeroes to the length of the
+ * longer.
+ * a and b must still be CLEAN, therefore psncmp() is *not*
+ * identical to pcmp() on semi-normalised polys as psnorm()
+ * clears the slack space.
+ */
+ unsigned long length, iter, idx;
+ bmp_t aword, bword;
+ if(!a || !b) return(!b - !a);
+ length = (a->length > b->length) ? a->length : b->length;
+ for(iter = 0UL, idx = 0UL; iter < length; iter += BMP_BIT, ++idx) {
+ aword = (iter < a->length) ? a->bitmap[idx] : BMP_C(0);
+ bword = (iter < b->length) ? b->bitmap[idx] : BMP_C(0);
+ if(aword < bword)
+ return(-1);
+ if(aword > bword)
+ return(1);
+ }
+ return(0);
+}
+
+
+int
+ptst(const poly_t poly) {
+ /* Tests whether a polynomial equals zero. Returns 0 if equal,
+ * a nonzero value otherwise.
+ * poly must be CLEAN.
+ */
+ unsigned long iter;
+ bmp_t *bptr;
+ if(!poly.bitmap) return(0);
+ for(iter = 0UL, bptr = poly.bitmap; iter < poly.length; iter += BMP_BIT)
+ if(*bptr++) return(1);
+ return(0);
+}
+
+unsigned long
+pfirst(const poly_t poly) {
+ /* Returns the index of the first nonzero term in poly. If none
+ * is found, returns the length of poly.
+ * poly must be CLEAN.
+ */
+ unsigned long idx = 0UL, size = SIZE(poly.length);
+ bmp_t accu = BMP_C(0); /* initialiser for Acorn C */
+ unsigned int probe = BMP_SUB, ofs = 0;
+
+ while(idx < size && !(accu = poly.bitmap[idx])) ++idx;
+ if(idx >= size) return(poly.length);
+ while(probe) {
+#ifndef BMP_POF2
+ while((ofs | probe) >= (unsigned int) BMP_BIT) probe >>= 1;
+#endif
+ if(accu >> (ofs | probe)) ofs |= probe;
+ probe >>= 1;
+ }
+
+ return(BMP_BIT - 1UL - ofs + idx * BMP_BIT);
+}
+
+unsigned long
+plast(const poly_t poly) {
+ /* Returns 1 plus the index of the last nonzero term in poly.
+ * If none is found, returns zero.
+ * poly must be CLEAN.
+ */
+ unsigned long idx, size = SIZE(poly.length);
+ bmp_t accu;
+ unsigned int probe = BMP_SUB, ofs = 0;
+
+ if(!poly.length) return(0UL);
+ idx = size - 1UL;
+ while(idx && !(accu = poly.bitmap[idx])) --idx;
+ if(!idx && !(accu = poly.bitmap[idx])) return(0UL);
+ /* now accu == poly.bitmap[idx] and contains last significant term */
+ while(probe) {
+#ifndef BMP_POF2
+ while((ofs | probe) >= (unsigned int) BMP_BIT) probe >>= 1;
+#endif
+ if(accu << (ofs | probe)) ofs |= probe;
+ probe >>= 1;
+ }
+
+ return(idx * BMP_BIT + ofs + 1UL);
+}
+
+poly_t
+psubs(const poly_t src, unsigned long head, unsigned long start, unsigned long end, unsigned long tail) {
+ poly_t dest = PZERO;
+ pshift(&dest, src, head, start, end, tail);
+ return(dest);
+}
+
+void
+pright(poly_t *poly, unsigned long length) {
+ /* Trims or extends poly to length at the left edge, prepending
+ * zeroes if necessary. Analogous to praloc() except the
+ * rightmost terms of poly are preserved.
+ * On entry, poly may or may not be WELL-FORMED.
+ * On exit, poly is CLEAN.
+ */
+
+ if(length > poly->length)
+ pshift(poly, *poly, length - poly->length, 0UL, poly->length, 0UL);
+ else if(length < poly->length)
+ pshift(poly, *poly, 0UL, poly->length - length, poly->length, 0UL);
+ else
+ praloc(poly, poly->length);
+}
+
+void
+pshift(poly_t *dest, const poly_t src, unsigned long head, unsigned long start, unsigned long end, unsigned long tail) {
+ /* copies bits start to end-1 of src to dest, plus the number of leading and trailing zeroes given by head and tail.
+ * end may exceed the length of src in which case more zeroes are appended.
+ * dest may point to src, in which case the poly is edited in place.
+ * On exit, dest is CLEAN.
+ */
+
+ unsigned long length, fulllength, size, fullsize, iter, idx, datidx;
+ /* condition inputs; end, head and tail may be any value */
+ if(end < start) end = start;
+
+ length = end - start + head;
+ fulllength = length + tail;
+ if(fulllength > src.length)
+ praloc(dest, fulllength);
+ else
+ praloc(dest, src.length);
+
+ /* number of words in new poly */
+ size = SIZE(length);
+ fullsize = SIZE(fulllength);
+ /* array index of first word ending up with source material */
+ datidx = IDX(head);
+
+ if(head > start && end > start) {
+ /* shifting right, size > 0 */
+ /* index of the source bit ending up in the LSB of the last word
+ * size * BMP_BIT >= length > head > 0 */
+ iter = size * BMP_BIT - head - 1UL;
+ for(idx = size - 1UL; idx > datidx; iter -= BMP_BIT, --idx)
+ dest->bitmap[idx] = getwrd(src, iter);
+ dest->bitmap[idx] = getwrd(src, iter);
+ /* iter == size * BMP_BIT - head - 1 - BMP_BIT * (size - 1 - datidx)
+ * == BMP_BIT * (size - size + 1 + datidx) - head - 1
+ * == BMP_BIT * (1 + head / BMP_BIT) - head - 1
+ * == BMP_BIT + head - head % BMP_BIT - head - 1
+ * == BMP_BIT - head % BMP_BIT - 1
+ * >= 0
+ */
+ } else if(head <= start) {
+ /* shifting left or copying */
+ /* index of the source bit ending up in the LSB of bitmap[idx] */
+ iter = start - head + BMP_BIT - 1UL;
+ for(idx = datidx; idx < size; iter += BMP_BIT, ++idx)
+ dest->bitmap[idx] = getwrd(src, iter);
+ }
+
+ /* clear head */
+ for(idx = 0UL; idx < datidx; ++idx)
+ dest->bitmap[idx] = BMP_C(0);
+ if(size)
+ dest->bitmap[datidx] &= ~BMP_C(0) >> LOFS(head);
+
+ /* clear tail */
+ if(LOFS(length))
+ dest->bitmap[size - 1UL] &= ~(~BMP_C(0) >> LOFS(length));
+ for(idx = size; idx < fullsize; ++idx)
+ dest->bitmap[idx] = BMP_C(0);
+
+ /* call praloc to shrink poly if required */
+ if(dest->length > fulllength)
+ praloc(dest, fulllength);
+}
+
+void
+ppaste(poly_t *dest, const poly_t src, unsigned long skip, unsigned long seek, unsigned long end, unsigned long fulllength) {
+ /* pastes terms of src, starting from skip, to positions seek to end-1 of dest
+ * then sets length of dest to fulllength (>= end)
+ * to paste n terms of src, give end = seek + n
+ * to truncate dest at end of paste, set fulllength = end
+ * to avoid truncating, set fulllength = plen(*dest)
+ * dest may point to src, in which case the poly is edited in place.
+ * src must be CLEAN in the case that the end is overrun.
+ * On exit, dest is CLEAN.
+ */
+ bmp_t mask;
+ unsigned long seekidx, endidx, iter;
+ int seekofs;
+ if(end < seek) end = seek;
+ if(fulllength < end) fulllength = end;
+
+ /* expand dest if necessary. don't shrink as dest may be src */
+ if(fulllength > dest->length)
+ praloc(dest, fulllength);
+ seekidx = IDX(seek);
+ endidx = IDX(end);
+ seekofs = OFS(seek);
+ /* index of the source bit ending up in the LSB of the first modified word */
+ iter = skip + seekofs;
+ if(seekidx == endidx) {
+ /* paste affects one word (traps end = seek case) */
+ mask = ((BMP_C(1) << seekofs) - (BMP_C(1) << OFS(end))) << 1;
+ dest->bitmap[seekidx] = (dest->bitmap[seekidx] & ~mask) | (getwrd(src, iter) & mask);
+ } else if(seek > skip) {
+ /* shifting right */
+ /* index of the source bit ending up in the LSB of the last modified word */
+ iter += (endidx - seekidx) * BMP_BIT;
+ mask = ~BMP_C(0) >> LOFS(end);
+ dest->bitmap[endidx] = (dest->bitmap[endidx] & mask) | (getwrd(src, iter) & ~mask);
+ for(iter -= BMP_BIT, --endidx; endidx > seekidx; iter -= BMP_BIT, --endidx)
+ dest->bitmap[endidx] = getwrd(src, iter);
+ mask = ~BMP_C(0) >> LOFS(seek);
+ dest->bitmap[endidx] = (dest->bitmap[endidx] & ~mask) | (getwrd(src, iter) & mask);
+ /* iter == skip + seekofs + (endidx - seekidx) * BMP_BIT - BMP_BIT * (endidx - seekidx)
+ * == skip + seekofs + BMP_BIT * (endidx - seekidx - endidx + seekidx)
+ * == skip + seekofs
+ * >= 0
+ */
+ } else {
+ /* shifting left or copying */
+ mask = ~BMP_C(0) >> LOFS(seek);
+ dest->bitmap[seekidx] = (dest->bitmap[seekidx] & ~mask) | (getwrd(src, iter) & mask);
+ for(iter += BMP_BIT, ++seekidx; seekidx < endidx; iter += BMP_BIT, ++seekidx)
+ dest->bitmap[seekidx] = getwrd(src, iter);
+ mask = ~BMP_C(0) >> LOFS(end);
+ dest->bitmap[seekidx] = (dest->bitmap[seekidx] & mask) | (getwrd(src, iter) & ~mask);
+ }
+ /* shrink poly if required */
+ if(dest->length > fulllength)
+ praloc(dest, fulllength);
+}
+
+void
+pdiff(poly_t *dest, const poly_t src, unsigned long ofs) {
+ /* Subtract src from dest (modulo 2) at offset ofs.
+ * In modulo 2 arithmetic, subtraction is equivalent to addition
+ * We include an alias for those who wish to retain the distinction
+ * src and dest must be CLEAN.
+ */
+ psum(dest, src, ofs);
+}
+
+void
+psum(poly_t *dest, const poly_t src, unsigned long ofs) {
+ /* Adds src to dest (modulo 2) at offset ofs.
+ * When ofs == dest->length, catenates src on to dest.
+ * src and dest must be CLEAN.
+ */
+ unsigned long fulllength, idx, iter, end;
+
+ fulllength = ofs + src.length;
+ if(fulllength > dest->length)
+ praloc(dest, fulllength);
+ /* array index of first word in dest to be modified */
+ idx = IDX(ofs);
+ /* index of bit in src to be added to LSB of dest->bitmap[idx] */
+ iter = OFS(ofs);
+ /* stop value for iter */
+ end = BMP_BIT - 1UL + src.length;
+ for(; iter < end; iter += BMP_BIT, ++idx)
+ dest->bitmap[idx] ^= getwrd(src, iter);
+}
+
+void
+prev(poly_t *poly) {
+ /* Reverse or reciprocate a polynomial.
+ * On exit, poly is CLEAN.
+ */
+ unsigned long leftidx = 0UL, rightidx = SIZE(poly->length);
+ unsigned long ofs = LOFS(BMP_BIT - LOFS(poly->length));
+ unsigned long fulllength = poly->length + ofs;
+ bmp_t accu;
+
+ if(ofs)
+ /* removable optimisation */
+ if(poly->length < (unsigned long) BMP_BIT) {
+ *poly->bitmap = rev(*poly->bitmap >> ofs, (int) poly->length) << ofs;
+ return;
+ }
+
+ /* claim remaining bits of last word (as we use public function pshift()) */
+ poly->length = fulllength;
+
+ /* reverse and swap words in the array, leaving it right-justified */
+ while(leftidx < rightidx) {
+ /* rightidx > 0 */
+ accu = rev(poly->bitmap[--rightidx], BMP_BIT);
+ poly->bitmap[rightidx] = rev(poly->bitmap[leftidx], BMP_BIT);
+ poly->bitmap[leftidx++] = accu;
+ }
+ /* shift polynomial to left edge if required */
+ if(ofs)
+ pshift(poly, *poly, 0UL, ofs, fulllength, 0UL);
+}
+
+void
+prevch(poly_t *poly, int bperhx) {
+ /* Reverse each group of bperhx bits in a polynomial.
+ * Does not clean poly.
+ */
+ unsigned long iter = 0, idx, ofs;
+ bmp_t mask, accu;
+
+ if(bperhx < 2 || bperhx > BMP_BIT)
+ return;
+ if(poly->length % bperhx)
+ praloc(poly, bperhx - (poly->length % bperhx) + poly->length);
+ mask = ~BMP_C(0) >> (BMP_BIT - bperhx);
+ for(iter = (unsigned long) (bperhx - 1); iter < poly->length; iter += bperhx) {
+ accu = getwrd(*poly, iter) & mask;
+ accu ^= rev(accu, bperhx);
+ idx = IDX(iter);
+ ofs = OFS(iter);
+ poly->bitmap[idx] ^= accu << ofs;
+ if(ofs + bperhx > (unsigned int) BMP_BIT)
+ /* (BMP_BIT - 1UL - (iter) % BMP_BIT) + bperhx > BMP_BIT
+ * (-1UL - (iter) % BMP_BIT) + bperhx > 0
+ * (- (iter % BMP_BIT)) + bperhx > 1
+ * - (iter % BMP_BIT) > 1 - bperhx
+ * iter % BMP_BIT < bperhx - 1, iter >= bperhx - 1
+ * iter >= BMP_BIT
+ * idx >= 1
+ */
+ poly->bitmap[idx-1] ^= accu >> (BMP_BIT - ofs);
+ }
+}
+
+void
+prcp(poly_t *poly) {
+ /* Reciprocate a chopped polynomial. Use prev() on whole
+ * polynomials.
+ * On exit, poly is SEMI-NORMALISED.
+ */
+ unsigned long first;
+
+ praloc(poly, RNDUP(poly->length));
+ prev(poly);
+ first = pfirst(*poly);
+ if(first >= poly->length) {
+ pfree(poly);
+ return;
+ }
+ pshift(poly, *poly, 0UL, first + 1UL, poly->length, 1UL);
+ piter(poly);
+}
+
+void
+pinv(poly_t *poly) {
+ /* Invert a polynomial, i.e. add 1 (modulo 2) to the coefficient of each term
+ * on exit, poly is CLEAN.
+ */
+ unsigned long idx, size = SIZE(poly->length);
+
+ for(idx = 0UL; idx<size; ++idx)
+ poly->bitmap[idx] = ~poly->bitmap[idx];
+ if(LOFS(poly->length))
+ poly->bitmap[size - 1UL] &= ~(~BMP_C(0) >> LOFS(poly->length));
+}
+
+poly_t
+pmod(const poly_t dividend, const poly_t divisor) {
+ /* Divide dividend by normalised divisor and return the remainder
+ * This function generates a temporary 'chopped' divisor for pcrc()
+ * If calling repeatedly with a constant divisor, produce a chopped copy
+ * with pchop() and call pcrc() directly for higher efficiency.
+ * dividend and divisor must be CLEAN.
+ */
+
+ /* perhaps generate an error if divisor is zero */
+ poly_t subdivisor = psubs(divisor, 0UL, pfirst(divisor) + 1UL, plast(divisor), 0UL);
+ poly_t result = pcrc(dividend, subdivisor, pzero, pzero, 0);
+ pfree(&subdivisor);
+ return(result);
+}
+
+poly_t
+pcrc(const poly_t message, const poly_t divisor, const poly_t init, const poly_t xorout, int flags) {
+ /* Divide message by divisor and return the remainder.
+ * init is added to divisor, highest terms aligned, before
+ * division.
+ * xorout is added to the remainder, highest terms aligned.
+ * If P_MULXN is set in flags, message is multiplied by x^n
+ * (i.e. trailing zeroes equal to the CRC width are appended)
+ * before adding init and division. Set P_MULXN for most CRC
+ * calculations.
+ * All inputs must be CLEAN.
+ * If all inputs are CLEAN, the returned poly_t will be CLEAN.
+ */
+ unsigned long max = 0UL, iter, ofs, resiter;
+ bmp_t probe, rem, dvsr, *rptr, *sptr;
+ const bmp_t *bptr, *eptr;
+ poly_t result = PZERO;
+
+ if(flags & P_MULXN)
+ max = message.length;
+ else if(message.length > divisor.length)
+ max = message.length - divisor.length;
+ bptr=message.bitmap;
+ eptr=message.bitmap+SIZE(message.length);
+ probe=~(~BMP_C(0) >> 1);
+ if(divisor.length <= (unsigned long) BMP_BIT
+ && init.length <= (unsigned long) BMP_BIT) {
+ rem = init.length ? *init.bitmap : BMP_C(0);
+ dvsr = divisor.length ? *divisor.bitmap : BMP_C(0);
+ for(iter = 0UL, ofs = 0UL; iter < max; ++iter, --ofs) {
+ if(!ofs) {
+ ofs = BMP_BIT;
+ rem ^= *bptr++;
+ }
+ if(rem & probe)
+ rem = (rem << 1) ^ dvsr;
+ else
+ rem <<= 1;
+ }
+ if(bptr < eptr)
+ /* max < message.length */
+ rem ^= *bptr >> OFS(BMP_BIT - 1UL + max);
+ if(init.length > max && init.length - max > divisor.length) {
+ palloc(&result, init.length - max);
+ *result.bitmap = rem;
+ } else if(divisor.length) {
+ palloc(&result, divisor.length);
+ *result.bitmap = rem;
+ }
+ } else {
+ /* allocate maximum size plus one word for shifted divisors and one word containing zero.
+ * This also ensures that result[1] exists
+ */
+ palloc(&result, (init.length > divisor.length ? init.length : divisor.length) + (unsigned long) (BMP_BIT << 1));
+ /*if there is content in init, there will be an extra word in result to clear it */
+ psum(&result, init, 0UL);
+ if(max)
+ *result.bitmap ^= *bptr++;
+ for(iter = 0UL, ofs = 0UL; iter < max; ++iter, probe >>= 1) {
+ if(!probe) {
+ probe = ~(~BMP_C(0) >> 1);
+ ofs = 0UL;
+ sptr = rptr = result.bitmap;
+ ++sptr;
+ /* iter < max <= message.length, so bptr is valid
+ * shift result one word to the left, splicing in a message word
+ * and clearing the last active word
+ */
+ *rptr++ = *sptr++ ^ *bptr++;
+ for(resiter = (unsigned long) (BMP_BIT << 1); resiter < result.length; resiter += BMP_BIT)
+ *rptr++ = *sptr++;
+ }
+ ++ofs;
+ if(*result.bitmap & probe)
+ psum(&result, divisor, ofs);
+ }
+ rptr = result.bitmap;
+ ++rptr;
+ while(bptr < eptr)
+ *rptr++ ^= *bptr++;
+ /* 0 <= ofs <= BMP_BIT, location of the first bit of the result */
+ pshift(&result, result, 0UL, ofs, (init.length > max + divisor.length ? init.length - max - divisor.length : 0UL) + divisor.length + ofs, 0UL);
+ }
+ psum(&result, xorout, 0UL);
+ return(result);
+}
+
+int
+piter(poly_t *poly) {
+ /* Replace poly with the 'next' polynomial of equal length.
+ * Returns zero if the next polynomial is all zeroes, a nonzero
+ * value otherwise.
+ * Does not clean poly.
+ */
+ bmp_t *bptr;
+ if(!poly->length) return(0);
+
+ bptr = poly->bitmap + IDX(poly->length - 1UL);
+ *bptr += BMP_C(1) << OFS(poly->length - 1UL);
+ while(bptr != poly->bitmap && !*bptr)
+ ++(*--bptr);
+ return(*bptr != BMP_C(0));
+}
+
+void
+palloc(poly_t *poly, unsigned long length) {
+ /* Replaces poly with a CLEAN object of the specified length,
+ * consisting of all zeroes.
+ * It is safe to call with length = 0, in which case the object
+ * is freed.
+ * poly may or may not be WELL-FORMED.
+ * On exit, poly is CLEAN.
+ */
+ unsigned long size = SIZE(length);
+
+ poly->length = 0UL;
+ free(poly->bitmap);
+ poly->bitmap = NULL;
+ if(!length) return;
+ if(!size)
+ size = IDX(length) + 1UL;
+ poly->bitmap = (bmp_t *) calloc(size, sizeof(bmp_t));
+ if(poly->bitmap) {
+ poly->length = length;
+ } else
+ uerror("cannot allocate memory for poly");
+}
+
+void
+pfree(poly_t *poly) {
+ /* Frees poly's bitmap storage and sets poly equal to the empty
+ * polynomial (PZERO).
+ * poly may or may not be WELL-FORMED.
+ * On exit, poly is CLEAN.
+ */
+
+ /* palloc(poly, 0UL); */
+
+ poly->length = 0UL;
+ free(poly->bitmap);
+ poly->bitmap = NULL;
+}
+
+void
+praloc(poly_t *poly, unsigned long length) {
+ /* Trims or extends poly to length at the right edge, appending
+ * zeroes if necessary.
+ * On entry, poly may or may not be WELL-FORMED.
+ * On exit, poly is CLEAN.
+ */
+ unsigned long oldsize, size = SIZE(length);
+ if(!poly) return;
+ if(!length) {
+ poly->length = 0UL;
+ free(poly->bitmap);
+ poly->bitmap = NULL;
+ return;
+ }
+ if(!size)
+ size = IDX(length) + 1UL;
+ if(!poly->bitmap)
+ poly->length = 0UL;
+ oldsize = SIZE(poly->length);
+ if(oldsize != size)
+ /* reallocate if array pointer is null or array resized */
+ poly->bitmap = (bmp_t *) realloc((void *)poly->bitmap, size * sizeof(bmp_t));
+ if(poly->bitmap) {
+ if(poly->length < length) {
+ /* poly->length >= 0, length > 0, size > 0.
+ * poly expanded. clear old last word and all new words
+ */
+ if(LOFS(poly->length))
+ poly->bitmap[oldsize - 1UL] &= ~(~BMP_C(0) >> LOFS(poly->length));
+ while(oldsize < size)
+ poly->bitmap[oldsize++] = BMP_C(0);
+ } else if(LOFS(length))
+ /* poly->length >= length > 0.
+ * poly shrunk. clear new last word
+ */
+ poly->bitmap[size - 1UL] &= ~(~BMP_C(0) >> LOFS(length));
+ poly->length = length;
+ } else
+ uerror("cannot reallocate memory for poly");
+}
+
+int
+pmpar(const poly_t poly, const poly_t mask) {
+ /* Return even parity of poly masked with mask.
+ * Poly and mask must be CLEAN.
+ */
+ bmp_t res = BMP_C(0);
+ int i = BMP_SUB;
+ const bmp_t *pptr = poly.bitmap, *mptr = mask.bitmap;
+ const bmp_t *const pend = poly.bitmap + SIZE(poly.length);
+ const bmp_t *const mend = mask.bitmap + SIZE(mask.length);
+
+ while(pptr < pend && mptr < mend)
+ res ^= *pptr++ & *mptr++;
+ do
+ res ^= res >> i;
+ while(i >>= 1);
+
+ return((int) (res & BMP_C(1)));
+}
+
+int
+pident(const poly_t a, const poly_t b) {
+ /* Return nonzero if a and b have the same length
+ * and point to the same bitmap.
+ * a and b need not be CLEAN.
+ */
+ return(a.length == b.length && a.bitmap == b.bitmap);
+}
+
+/* Private functions */
+
+static bmp_t
+getwrd(const poly_t poly, unsigned long iter) {
+ /* Fetch unaligned word from poly where LSB of result is
+ * bit iter of the bitmap (counting from zero). If iter exceeds
+ * the length of poly then zeroes are appended as necessary.
+ * Factored from ptostr().
+ * poly must be CLEAN.
+ */
+ bmp_t accu = BMP_C(0);
+ unsigned long idx, size;
+ int ofs;
+
+ idx = IDX(iter);
+ ofs = OFS(iter);
+ size = SIZE(poly.length);
+
+ if(idx < size)
+ accu |= poly.bitmap[idx] >> ofs;
+ if(idx && idx <= size && ofs > 0)
+ accu |= poly.bitmap[idx - 1UL] << (BMP_BIT - ofs);
+ return(accu);
+}
+
+static bmp_t
+rev(bmp_t accu, int bits) {
+ /* Returns the bitmap word argument with the given number of
+ * least significant bits reversed and the rest cleared.
+ */
+ static const unsigned char revtab[256] = {
+ 0x00,0x80,0x40,0xc0,0x20,0xa0,0x60,0xe0,
+ 0x10,0x90,0x50,0xd0,0x30,0xb0,0x70,0xf0,
+ 0x08,0x88,0x48,0xc8,0x28,0xa8,0x68,0xe8,
+ 0x18,0x98,0x58,0xd8,0x38,0xb8,0x78,0xf8,
+ 0x04,0x84,0x44,0xc4,0x24,0xa4,0x64,0xe4,
+ 0x14,0x94,0x54,0xd4,0x34,0xb4,0x74,0xf4,
+ 0x0c,0x8c,0x4c,0xcc,0x2c,0xac,0x6c,0xec,
+ 0x1c,0x9c,0x5c,0xdc,0x3c,0xbc,0x7c,0xfc,
+ 0x02,0x82,0x42,0xc2,0x22,0xa2,0x62,0xe2,
+ 0x12,0x92,0x52,0xd2,0x32,0xb2,0x72,0xf2,
+ 0x0a,0x8a,0x4a,0xca,0x2a,0xaa,0x6a,0xea,
+ 0x1a,0x9a,0x5a,0xda,0x3a,0xba,0x7a,0xfa,
+ 0x06,0x86,0x46,0xc6,0x26,0xa6,0x66,0xe6,
+ 0x16,0x96,0x56,0xd6,0x36,0xb6,0x76,0xf6,
+ 0x0e,0x8e,0x4e,0xce,0x2e,0xae,0x6e,0xee,
+ 0x1e,0x9e,0x5e,0xde,0x3e,0xbe,0x7e,0xfe,
+ 0x01,0x81,0x41,0xc1,0x21,0xa1,0x61,0xe1,
+ 0x11,0x91,0x51,0xd1,0x31,0xb1,0x71,0xf1,
+ 0x09,0x89,0x49,0xc9,0x29,0xa9,0x69,0xe9,
+ 0x19,0x99,0x59,0xd9,0x39,0xb9,0x79,0xf9,
+ 0x05,0x85,0x45,0xc5,0x25,0xa5,0x65,0xe5,
+ 0x15,0x95,0x55,0xd5,0x35,0xb5,0x75,0xf5,
+ 0x0d,0x8d,0x4d,0xcd,0x2d,0xad,0x6d,0xed,
+ 0x1d,0x9d,0x5d,0xdd,0x3d,0xbd,0x7d,0xfd,
+ 0x03,0x83,0x43,0xc3,0x23,0xa3,0x63,0xe3,
+ 0x13,0x93,0x53,0xd3,0x33,0xb3,0x73,0xf3,
+ 0x0b,0x8b,0x4b,0xcb,0x2b,0xab,0x6b,0xeb,
+ 0x1b,0x9b,0x5b,0xdb,0x3b,0xbb,0x7b,0xfb,
+ 0x07,0x87,0x47,0xc7,0x27,0xa7,0x67,0xe7,
+ 0x17,0x97,0x57,0xd7,0x37,0xb7,0x77,0xf7,
+ 0x0f,0x8f,0x4f,0xcf,0x2f,0xaf,0x6f,0xef,
+ 0x1f,0x9f,0x5f,0xdf,0x3f,0xbf,0x7f,0xff
+ };
+ bmp_t result = BMP_C(0);
+ while(bits > 8) {
+ bits -= 8;
+ result = result << 8 | revtab[accu & 0xff];
+ accu >>= 8;
+ }
+ result = result << bits | (bmp_t) (revtab[accu & 0xff] >> (8 - bits));
+ return(result);
+}
+
+static void
+prhex(char **spp, bmp_t bits, int flags, int bperhx) {
+ /* Appends a hexadecimal string representing the bperhx least
+ * significant bits of bits to an external string.
+ * spp points to a character pointer that in turn points to the
+ * end of a hex string being built. prhex() advances this
+ * second pointer by the number of characters written.
+ * The unused MSBs of bits MUST be cleared.
+ * Set P_UPPER in flags to write A-F in uppercase.
+ */
+ static const char hex[] = "0123456789abcdef0123456789ABCDEF";
+ const int upper = (flags & P_UPPER ? 0x10 : 0);
+ while(bperhx > 0) {
+ bperhx -= ((bperhx + 3) & 3) + 1;
+ *(*spp)++ = hex[(bits >> bperhx & BMP_C(0xf)) | upper];
+ }
+}
projects / proxmark3-svn / blobdiff