andre@0: /*
andre@0:  *  mplogic.c
andre@0:  *
andre@0:  *  Bitwise logical operations on MPI values
andre@0:  *
andre@0:  * This Source Code Form is subject to the terms of the Mozilla Public
andre@0:  * License, v. 2.0. If a copy of the MPL was not distributed with this
andre@0:  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
andre@0: 
andre@0: #include "mpi-priv.h"
andre@0: #include "mplogic.h"
andre@0: 
andre@0: /* {{{ Lookup table for population count */
andre@0: 
andre@0: static unsigned char bitc[] = {
andre@0:    0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 
andre@0:    1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 
andre@0:    1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 
andre@0:    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 
andre@0:    1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 
andre@0:    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 
andre@0:    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 
andre@0:    3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 
andre@0:    1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 
andre@0:    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 
andre@0:    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 
andre@0:    3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 
andre@0:    2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 
andre@0:    3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 
andre@0:    3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 
andre@0:    4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8
andre@0: };
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /*------------------------------------------------------------------------*/
andre@0: /*
andre@0:   mpl_not(a, b)    - compute b = ~a
andre@0:   mpl_and(a, b, c) - compute c = a & b
andre@0:   mpl_or(a, b, c)  - compute c = a | b
andre@0:   mpl_xor(a, b, c) - compute c = a ^ b
andre@0:  */
andre@0: 
andre@0: /* {{{ mpl_not(a, b) */
andre@0: 
andre@0: mp_err mpl_not(mp_int *a, mp_int *b)
andre@0: {
andre@0:   mp_err   res;
andre@0:   unsigned int      ix;
andre@0: 
andre@0:   ARGCHK(a != NULL && b != NULL, MP_BADARG);
andre@0: 
andre@0:   if((res = mp_copy(a, b)) != MP_OKAY)
andre@0:     return res;
andre@0: 
andre@0:   /* This relies on the fact that the digit type is unsigned */
andre@0:   for(ix = 0; ix < USED(b); ix++) 
andre@0:     DIGIT(b, ix) = ~DIGIT(b, ix);
andre@0: 
andre@0:   s_mp_clamp(b);
andre@0: 
andre@0:   return MP_OKAY;
andre@0: 
andre@0: } /* end mpl_not() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /* {{{ mpl_and(a, b, c) */
andre@0: 
andre@0: mp_err mpl_and(mp_int *a, mp_int *b, mp_int *c)
andre@0: {
andre@0:   mp_int  *which, *other;
andre@0:   mp_err   res;
andre@0:   unsigned int      ix;
andre@0: 
andre@0:   ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
andre@0: 
andre@0:   if(USED(a) <= USED(b)) {
andre@0:     which = a;
andre@0:     other = b;
andre@0:   } else {
andre@0:     which = b;
andre@0:     other = a;
andre@0:   }
andre@0: 
andre@0:   if((res = mp_copy(which, c)) != MP_OKAY)
andre@0:     return res;
andre@0: 
andre@0:   for(ix = 0; ix < USED(which); ix++)
andre@0:     DIGIT(c, ix) &= DIGIT(other, ix);
andre@0: 
andre@0:   s_mp_clamp(c);
andre@0: 
andre@0:   return MP_OKAY;
andre@0: 
andre@0: } /* end mpl_and() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /* {{{ mpl_or(a, b, c) */
andre@0: 
andre@0: mp_err mpl_or(mp_int *a, mp_int *b, mp_int *c)
andre@0: {
andre@0:   mp_int  *which, *other;
andre@0:   mp_err   res;
andre@0:   unsigned int      ix;
andre@0: 
andre@0:   ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
andre@0: 
andre@0:   if(USED(a) >= USED(b)) {
andre@0:     which = a;
andre@0:     other = b;
andre@0:   } else {
andre@0:     which = b;
andre@0:     other = a;
andre@0:   }
andre@0: 
andre@0:   if((res = mp_copy(which, c)) != MP_OKAY)
andre@0:     return res;
andre@0: 
andre@0:   for(ix = 0; ix < USED(which); ix++)
andre@0:     DIGIT(c, ix) |= DIGIT(other, ix);
andre@0: 
andre@0:   return MP_OKAY;
andre@0: 
andre@0: } /* end mpl_or() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /* {{{ mpl_xor(a, b, c) */
andre@0: 
andre@0: mp_err mpl_xor(mp_int *a, mp_int *b, mp_int *c)
andre@0: {
andre@0:   mp_int  *which, *other;
andre@0:   mp_err   res;
andre@0:   unsigned int      ix;
andre@0: 
andre@0:   ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
andre@0: 
andre@0:   if(USED(a) >= USED(b)) {
andre@0:     which = a;
andre@0:     other = b;
andre@0:   } else {
andre@0:     which = b;
andre@0:     other = a;
andre@0:   }
andre@0: 
andre@0:   if((res = mp_copy(which, c)) != MP_OKAY)
andre@0:     return res;
andre@0: 
andre@0:   for(ix = 0; ix < USED(which); ix++)
andre@0:     DIGIT(c, ix) ^= DIGIT(other, ix);
andre@0: 
andre@0:   s_mp_clamp(c);
andre@0: 
andre@0:   return MP_OKAY;
andre@0: 
andre@0: } /* end mpl_xor() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /*------------------------------------------------------------------------*/
andre@0: /*
andre@0:   mpl_rsh(a, b, d)     - b = a >> d
andre@0:   mpl_lsh(a, b, d)     - b = a << d
andre@0:  */
andre@0: 
andre@0: /* {{{ mpl_rsh(a, b, d) */
andre@0: 
andre@0: mp_err mpl_rsh(const mp_int *a, mp_int *b, mp_digit d)
andre@0: {
andre@0:   mp_err   res;
andre@0: 
andre@0:   ARGCHK(a != NULL && b != NULL, MP_BADARG);
andre@0: 
andre@0:   if((res = mp_copy(a, b)) != MP_OKAY)
andre@0:     return res;
andre@0: 
andre@0:   s_mp_div_2d(b, d);
andre@0: 
andre@0:   return MP_OKAY;
andre@0: 
andre@0: } /* end mpl_rsh() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /* {{{ mpl_lsh(a, b, d) */
andre@0: 
andre@0: mp_err mpl_lsh(const mp_int *a, mp_int *b, mp_digit d)
andre@0: {
andre@0:   mp_err   res;
andre@0: 
andre@0:   ARGCHK(a != NULL && b != NULL, MP_BADARG);
andre@0: 
andre@0:   if((res = mp_copy(a, b)) != MP_OKAY)
andre@0:     return res;
andre@0: 
andre@0:   return s_mp_mul_2d(b, d);
andre@0: 
andre@0: } /* end mpl_lsh() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /*------------------------------------------------------------------------*/
andre@0: /*
andre@0:   mpl_num_set(a, num)
andre@0: 
andre@0:   Count the number of set bits in the binary representation of a.
andre@0:   Returns MP_OKAY and sets 'num' to be the number of such bits, if
andre@0:   possible.  If num is NULL, the result is thrown away, but it is
andre@0:   not considered an error.
andre@0: 
andre@0:   mpl_num_clear() does basically the same thing for clear bits.
andre@0:  */
andre@0: 
andre@0: /* {{{ mpl_num_set(a, num) */
andre@0: 
andre@0: mp_err mpl_num_set(mp_int *a, int *num)
andre@0: {
andre@0:   unsigned int   ix;
andre@0:   int            db, nset = 0;
andre@0:   mp_digit       cur;
andre@0:   unsigned char  reg;
andre@0: 
andre@0:   ARGCHK(a != NULL, MP_BADARG);
andre@0: 
andre@0:   for(ix = 0; ix < USED(a); ix++) {
andre@0:     cur = DIGIT(a, ix);
andre@0:     
andre@0:     for(db = 0; db < sizeof(mp_digit); db++) {
andre@0:       reg = (unsigned char)(cur >> (CHAR_BIT * db));
andre@0: 
andre@0:       nset += bitc[reg];
andre@0:     }
andre@0:   }
andre@0: 
andre@0:   if(num)
andre@0:     *num = nset;
andre@0: 
andre@0:   return MP_OKAY;
andre@0: 
andre@0: } /* end mpl_num_set() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /* {{{ mpl_num_clear(a, num) */
andre@0: 
andre@0: mp_err mpl_num_clear(mp_int *a, int *num)
andre@0: {
andre@0:   unsigned int   ix;
andre@0:   int            db, nset = 0;
andre@0:   mp_digit       cur;
andre@0:   unsigned char  reg;
andre@0: 
andre@0:   ARGCHK(a != NULL, MP_BADARG);
andre@0: 
andre@0:   for(ix = 0; ix < USED(a); ix++) {
andre@0:     cur = DIGIT(a, ix);
andre@0:     
andre@0:     for(db = 0; db < sizeof(mp_digit); db++) {
andre@0:       reg = (unsigned char)(cur >> (CHAR_BIT * db));
andre@0: 
andre@0:       nset += bitc[UCHAR_MAX - reg];
andre@0:     }
andre@0:   }
andre@0: 
andre@0:   if(num)
andre@0:     *num = nset;
andre@0: 
andre@0:   return MP_OKAY;
andre@0: 
andre@0: 
andre@0: } /* end mpl_num_clear() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /*------------------------------------------------------------------------*/
andre@0: /*
andre@0:   mpl_parity(a)
andre@0: 
andre@0:   Determines the bitwise parity of the value given.  Returns MP_EVEN
andre@0:   if an even number of digits are set, MP_ODD if an odd number are
andre@0:   set.
andre@0:  */
andre@0: 
andre@0: /* {{{ mpl_parity(a) */
andre@0: 
andre@0: mp_err mpl_parity(mp_int *a)
andre@0: {
andre@0:   unsigned int ix;
andre@0:   int      par = 0;
andre@0:   mp_digit cur;
andre@0: 
andre@0:   ARGCHK(a != NULL, MP_BADARG);
andre@0: 
andre@0:   for(ix = 0; ix < USED(a); ix++) {
andre@0:     int   shft = (sizeof(mp_digit) * CHAR_BIT) / 2;
andre@0: 
andre@0:     cur = DIGIT(a, ix);
andre@0: 
andre@0:     /* Compute parity for current digit */
andre@0:     while(shft != 0) {
andre@0:       cur ^= (cur >> shft);
andre@0:       shft >>= 1;
andre@0:     }
andre@0:     cur &= 1;
andre@0: 
andre@0:     /* XOR with running parity so far   */
andre@0:     par ^= cur;
andre@0:   }
andre@0: 
andre@0:   if(par)
andre@0:     return MP_ODD;
andre@0:   else
andre@0:     return MP_EVEN;
andre@0: 
andre@0: } /* end mpl_parity() */
andre@0: 
andre@0: /* }}} */
andre@0: 
andre@0: /*
andre@0:   mpl_set_bit
andre@0: 
andre@0:   Returns MP_OKAY or some error code.
andre@0:   Grows a if needed to set a bit to 1.
andre@0:  */
andre@0: mp_err mpl_set_bit(mp_int *a, mp_size bitNum, mp_size value)
andre@0: {
andre@0:   mp_size      ix;
andre@0:   mp_err       rv;
andre@0:   mp_digit     mask;
andre@0: 
andre@0:   ARGCHK(a != NULL, MP_BADARG);
andre@0: 
andre@0:   ix = bitNum / MP_DIGIT_BIT;
andre@0:   if (ix + 1 > MP_USED(a)) {
andre@0:     rv = s_mp_pad(a, ix + 1);
andre@0:     if (rv != MP_OKAY)
andre@0:       return rv;
andre@0:   }
andre@0: 
andre@0:   bitNum = bitNum % MP_DIGIT_BIT;
andre@0:   mask = (mp_digit)1 << bitNum;
andre@0:   if (value)
andre@0:     MP_DIGIT(a,ix) |= mask;
andre@0:   else
andre@0:     MP_DIGIT(a,ix) &= ~mask;
andre@0:   s_mp_clamp(a);
andre@0:   return MP_OKAY;
andre@0: }
andre@0: 
andre@0: /*
andre@0:   mpl_get_bit
andre@0: 
andre@0:   returns 0 or 1 or some (negative) error code.
andre@0:  */
andre@0: mp_err mpl_get_bit(const mp_int *a, mp_size bitNum)
andre@0: {
andre@0:   mp_size      bit, ix;
andre@0:   mp_err       rv;
andre@0: 
andre@0:   ARGCHK(a != NULL, MP_BADARG);
andre@0: 
andre@0:   ix = bitNum / MP_DIGIT_BIT;
andre@0:   ARGCHK(ix <= MP_USED(a) - 1, MP_RANGE);
andre@0: 
andre@0:   bit   = bitNum % MP_DIGIT_BIT;
andre@0:   rv = (mp_err)(MP_DIGIT(a, ix) >> bit) & 1;
andre@0:   return rv;
andre@0: }
andre@0: 
andre@0: /*
andre@0:   mpl_get_bits
andre@0:   - Extracts numBits bits from a, where the least significant extracted bit
andre@0:   is bit lsbNum.  Returns a negative value if error occurs.
andre@0:   - Because sign bit is used to indicate error, maximum number of bits to 
andre@0:   be returned is the lesser of (a) the number of bits in an mp_digit, or
andre@0:   (b) one less than the number of bits in an mp_err.
andre@0:   - lsbNum + numbits can be greater than the number of significant bits in
andre@0:   integer a, as long as bit lsbNum is in the high order digit of a.
andre@0:  */
andre@0: mp_err mpl_get_bits(const mp_int *a, mp_size lsbNum, mp_size numBits) 
andre@0: {
andre@0:   mp_size    rshift = (lsbNum % MP_DIGIT_BIT);
andre@0:   mp_size    lsWndx = (lsbNum / MP_DIGIT_BIT);
andre@0:   mp_digit * digit  = MP_DIGITS(a) + lsWndx;
andre@0:   mp_digit   mask   = ((1 << numBits) - 1);
andre@0: 
andre@0:   ARGCHK(numBits < CHAR_BIT * sizeof mask, MP_BADARG);
andre@0:   ARGCHK(MP_HOWMANY(lsbNum, MP_DIGIT_BIT) <= MP_USED(a), MP_RANGE);
andre@0: 
andre@0:   if ((numBits + lsbNum % MP_DIGIT_BIT <= MP_DIGIT_BIT) ||
andre@0:       (lsWndx + 1 >= MP_USED(a))) {
andre@0:     mask &= (digit[0] >> rshift);
andre@0:   } else {
andre@0:     mask &= ((digit[0] >> rshift) | (digit[1] << (MP_DIGIT_BIT - rshift)));
andre@0:   }
andre@0:   return (mp_err)mask;
andre@0: }
andre@0: 
andre@0: /*
andre@0:   mpl_significant_bits
andre@0:   returns number of significnant bits in abs(a).
andre@0:   returns 1 if value is zero.
andre@0:  */
andre@0: mp_err mpl_significant_bits(const mp_int *a)
andre@0: {
andre@0:   mp_err bits 	= 0;
andre@0:   int    ix;
andre@0: 
andre@0:   ARGCHK(a != NULL, MP_BADARG);
andre@0: 
andre@0:   ix = MP_USED(a);
andre@0:   for (ix = MP_USED(a); ix > 0; ) {
andre@0:     mp_digit d;
andre@0:     d = MP_DIGIT(a, --ix);
andre@0:     if (d) {
andre@0:       while (d) {
andre@0: 	++bits;
andre@0: 	d >>= 1;
andre@0:       }
andre@0:       break;
andre@0:     }
andre@0:   }
andre@0:   bits += ix * MP_DIGIT_BIT;
andre@0:   if (!bits)
andre@0:     bits = 1;
andre@0:   return bits;
andre@0: }
andre@0: 
andre@0: /*------------------------------------------------------------------------*/
andre@0: /* HERE THERE BE DRAGONS                                                  */