REM: removed a tab character that Travis CI dislikes

[proxmark3-svn] / client / reveng / poly.c

/* 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];
        }
}