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proxmark3/client/reveng/poly.c
Philippe Teuwen db4aa08b78 make style
2019-03-28 14:19:41 +01:00

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/* poly.c
* Greg Cook, 23/Feb/2019
*/
/* CRC RevEng: arbitrary-precision CRC calculator and algorithm finder
* Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018,
* 2019 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 <https://www.gnu.org/licenses/>.
*/
/* 2017-11-28: added braces, redundant statement skipped in prev()
* 2016-06-27: pcmp() shortcut returns 0 when pointers identical
* 2015-07-29: discard leading $, &, 0x from argument to strtop()
* 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 = (1 << CHAR_BIT) - 1, 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 = (1 << CHAR_BIT) - 1, c;
const char *s;
poly_t poly = PZERO;
if (bperhx > BMP_BIT || bperhx <= 0 || string == NULL || *string == '\0')
return (poly);
if (~flags & P_DIRECT) {
if (*string == '$' || *string == '&')
++string;
else if (*string == '0'
&& (string[1] == 'x' || string[1] == 'X'))
string += 2;
}
length = (*string != '\0');
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 *) calloc(size, sizeof(char))))
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;
if (aptr == bptr)
return (0);
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.
* src must be CLEAN.
* 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);
}
if (result.bitmap != NULL)
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];
}
}
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