/* poly.c
* Greg Cook, 26/Jul/2016
*/
/* CRC RevEng: arbitrary-precision CRC calculator and algorithm finder
* Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015, 2016 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/>.
*/
/* 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 *) 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;
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.
* 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];
}
}