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/*
* mplogic.c
*
* Bitwise logical operations on MPI values
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
#include "mpi-priv.h"
#include "mplogic.h"
/* {{{ Lookup table for population count */
static unsigned char bitc[] = {
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8
};
/* }}} */
/*------------------------------------------------------------------------*/
/*
mpl_not(a, b) - compute b = ~a
mpl_and(a, b, c) - compute c = a & b
mpl_or(a, b, c) - compute c = a | b
mpl_xor(a, b, c) - compute c = a ^ b
*/
/* {{{ mpl_not(a, b) */
mp_err
mpl_not(mp_int *a, mp_int *b)
{
mp_err res;
unsigned int ix;
ARGCHK(a != NULL && b != NULL, MP_BADARG);
if ((res = mp_copy(a, b)) != MP_OKAY)
return res;
/* This relies on the fact that the digit type is unsigned */
for (ix = 0; ix < USED(b); ix++)
DIGIT(b, ix) = ~DIGIT(b, ix);
s_mp_clamp(b);
return MP_OKAY;
} /* end mpl_not() */
/* }}} */
/* {{{ mpl_and(a, b, c) */
mp_err
mpl_and(mp_int *a, mp_int *b, mp_int *c)
{
mp_int *which, *other;
mp_err res;
unsigned int ix;
ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
if (USED(a) <= USED(b)) {
which = a;
other = b;
} else {
which = b;
other = a;
}
if ((res = mp_copy(which, c)) != MP_OKAY)
return res;
for (ix = 0; ix < USED(which); ix++)
DIGIT(c, ix) &= DIGIT(other, ix);
s_mp_clamp(c);
return MP_OKAY;
} /* end mpl_and() */
/* }}} */
/* {{{ mpl_or(a, b, c) */
mp_err
mpl_or(mp_int *a, mp_int *b, mp_int *c)
{
mp_int *which, *other;
mp_err res;
unsigned int ix;
ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
if (USED(a) >= USED(b)) {
which = a;
other = b;
} else {
which = b;
other = a;
}
if ((res = mp_copy(which, c)) != MP_OKAY)
return res;
for (ix = 0; ix < USED(which); ix++)
DIGIT(c, ix) |= DIGIT(other, ix);
return MP_OKAY;
} /* end mpl_or() */
/* }}} */
/* {{{ mpl_xor(a, b, c) */
mp_err
mpl_xor(mp_int *a, mp_int *b, mp_int *c)
{
mp_int *which, *other;
mp_err res;
unsigned int ix;
ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
if (USED(a) >= USED(b)) {
which = a;
other = b;
} else {
which = b;
other = a;
}
if ((res = mp_copy(which, c)) != MP_OKAY)
return res;
for (ix = 0; ix < USED(which); ix++)
DIGIT(c, ix) ^= DIGIT(other, ix);
s_mp_clamp(c);
return MP_OKAY;
} /* end mpl_xor() */
/* }}} */
/*------------------------------------------------------------------------*/
/*
mpl_rsh(a, b, d) - b = a >> d
mpl_lsh(a, b, d) - b = a << d
*/
/* {{{ mpl_rsh(a, b, d) */
mp_err
mpl_rsh(const mp_int *a, mp_int *b, mp_digit d)
{
mp_err res;
ARGCHK(a != NULL && b != NULL, MP_BADARG);
if ((res = mp_copy(a, b)) != MP_OKAY)
return res;
s_mp_div_2d(b, d);
return MP_OKAY;
} /* end mpl_rsh() */
/* }}} */
/* {{{ mpl_lsh(a, b, d) */
mp_err
mpl_lsh(const mp_int *a, mp_int *b, mp_digit d)
{
mp_err res;
ARGCHK(a != NULL && b != NULL, MP_BADARG);
if ((res = mp_copy(a, b)) != MP_OKAY)
return res;
return s_mp_mul_2d(b, d);
} /* end mpl_lsh() */
/* }}} */
/*------------------------------------------------------------------------*/
/*
mpl_num_set(a, num)
Count the number of set bits in the binary representation of a.
Returns MP_OKAY and sets 'num' to be the number of such bits, if
possible. If num is NULL, the result is thrown away, but it is
not considered an error.
mpl_num_clear() does basically the same thing for clear bits.
*/
/* {{{ mpl_num_set(a, num) */
mp_err
mpl_num_set(mp_int *a, unsigned int *num)
{
unsigned int ix, db, nset = 0;
mp_digit cur;
unsigned char reg;
ARGCHK(a != NULL, MP_BADARG);
for (ix = 0; ix < USED(a); ix++) {
cur = DIGIT(a, ix);
for (db = 0; db < sizeof(mp_digit); db++) {
reg = (unsigned char)(cur >> (CHAR_BIT * db));
nset += bitc[reg];
}
}
if (num)
*num = nset;
return MP_OKAY;
} /* end mpl_num_set() */
/* }}} */
/* {{{ mpl_num_clear(a, num) */
mp_err
mpl_num_clear(mp_int *a, unsigned int *num)
{
unsigned int ix, db, nset = 0;
mp_digit cur;
unsigned char reg;
ARGCHK(a != NULL, MP_BADARG);
for (ix = 0; ix < USED(a); ix++) {
cur = DIGIT(a, ix);
for (db = 0; db < sizeof(mp_digit); db++) {
reg = (unsigned char)(cur >> (CHAR_BIT * db));
nset += bitc[UCHAR_MAX - reg];
}
}
if (num)
*num = nset;
return MP_OKAY;
} /* end mpl_num_clear() */
/* }}} */
/*------------------------------------------------------------------------*/
/*
mpl_parity(a)
Determines the bitwise parity of the value given. Returns MP_EVEN
if an even number of digits are set, MP_ODD if an odd number are
set.
*/
/* {{{ mpl_parity(a) */
mp_err
mpl_parity(mp_int *a)
{
unsigned int ix;
int par = 0;
mp_digit cur;
ARGCHK(a != NULL, MP_BADARG);
for (ix = 0; ix < USED(a); ix++) {
int shft = (sizeof(mp_digit) * CHAR_BIT) / 2;
cur = DIGIT(a, ix);
/* Compute parity for current digit */
while (shft != 0) {
cur ^= (cur >> shft);
shft >>= 1;
}
cur &= 1;
/* XOR with running parity so far */
par ^= cur;
}
if (par)
return MP_ODD;
else
return MP_EVEN;
} /* end mpl_parity() */
/* }}} */
/*
mpl_set_bit
Returns MP_OKAY or some error code.
Grows a if needed to set a bit to 1.
*/
mp_err
mpl_set_bit(mp_int *a, mp_size bitNum, mp_size value)
{
mp_size ix;
mp_err rv;
mp_digit mask;
ARGCHK(a != NULL, MP_BADARG);
ix = bitNum / MP_DIGIT_BIT;
if (ix + 1 > MP_USED(a)) {
rv = s_mp_pad(a, ix + 1);
if (rv != MP_OKAY)
return rv;
}
bitNum = bitNum % MP_DIGIT_BIT;
mask = (mp_digit)1 << bitNum;
if (value)
MP_DIGIT(a, ix) |= mask;
else
MP_DIGIT(a, ix) &= ~mask;
s_mp_clamp(a);
return MP_OKAY;
}
/*
mpl_get_bit
returns 0 or 1 or some (negative) error code.
*/
mp_err
mpl_get_bit(const mp_int *a, mp_size bitNum)
{
mp_size bit, ix;
mp_err rv;
ARGCHK(a != NULL, MP_BADARG);
ix = bitNum / MP_DIGIT_BIT;
ARGCHK(ix <= MP_USED(a) - 1, MP_RANGE);
bit = bitNum % MP_DIGIT_BIT;
rv = (mp_err)(MP_DIGIT(a, ix) >> bit) & 1;
return rv;
}
/*
mpl_get_bits
- Extracts numBits bits from a, where the least significant extracted bit
is bit lsbNum. Returns a negative value if error occurs.
- Because sign bit is used to indicate error, maximum number of bits to
be returned is the lesser of (a) the number of bits in an mp_digit, or
(b) one less than the number of bits in an mp_err.
- lsbNum + numbits can be greater than the number of significant bits in
integer a, as long as bit lsbNum is in the high order digit of a.
*/
mp_err
mpl_get_bits(const mp_int *a, mp_size lsbNum, mp_size numBits)
{
mp_size rshift = (lsbNum % MP_DIGIT_BIT);
mp_size lsWndx = (lsbNum / MP_DIGIT_BIT);
mp_digit *digit = MP_DIGITS(a) + lsWndx;
mp_digit mask = ((1 << numBits) - 1);
ARGCHK(numBits < CHAR_BIT * sizeof mask, MP_BADARG);
ARGCHK(MP_HOWMANY(lsbNum, MP_DIGIT_BIT) <= MP_USED(a), MP_RANGE);
if ((numBits + lsbNum % MP_DIGIT_BIT <= MP_DIGIT_BIT) ||
(lsWndx + 1 >= MP_USED(a))) {
mask &= (digit[0] >> rshift);
} else {
mask &= ((digit[0] >> rshift) | (digit[1] << (MP_DIGIT_BIT - rshift)));
}
return (mp_err)mask;
}
#define LZCNTLOOP(i) \
do { \
x = d >> (i); \
mask = (0 - x); \
mask = (0 - (mask >> (MP_DIGIT_BIT - 1))); \
bits += (i)&mask; \
d ^= (x ^ d) & mask; \
} while (0)
/*
mpl_significant_bits
returns number of significant bits in abs(a).
In other words: floor(lg(abs(a))) + 1.
returns 1 if value is zero.
*/
mp_size
mpl_significant_bits(const mp_int *a)
{
/*
start bits at 1.
lg(0) = 0 => bits = 1 by function semantics.
below does a binary search for the _position_ of the top bit set,
which is floor(lg(abs(a))) for a != 0.
*/
mp_size bits = 1;
int ix;
ARGCHK(a != NULL, MP_BADARG);
for (ix = MP_USED(a); ix > 0;) {
mp_digit d, x, mask;
if ((d = MP_DIGIT(a, --ix)) == 0)
continue;
#if !defined(MP_USE_UINT_DIGIT)
LZCNTLOOP(32);
#endif
LZCNTLOOP(16);
LZCNTLOOP(8);
LZCNTLOOP(4);
LZCNTLOOP(2);
LZCNTLOOP(1);
break;
}
bits += ix * MP_DIGIT_BIT;
return bits;
}
#undef LZCNTLOOP
/*------------------------------------------------------------------------*/
/* HERE THERE BE DRAGONS */