/****************
* Subtract the unsigned integer V from the mpi-integer U and store the
* result in W.
*/
void
gcry_mpi_sub_ui(gcry_mpi_t w, gcry_mpi_t u, unsigned long v )
{
mpi_ptr_t wp, up;
mpi_size_t usize, wsize;
int usign, wsign;
usize = u->nlimbs;
usign = u->sign;
wsign = 0;
/* If not space for W (and possible carry), increase space. */
wsize = usize + 1;
if( w->alloced < wsize )
mpi_resize(w, wsize);
/* These must be after realloc (U may be the same as W). */
up = u->d;
wp = w->d;
if( !usize ) { /* simple */
wp[0] = v;
wsize = v? 1:0;
wsign = 1;
}
else if( usign ) { /* mpi and v are negative */
mpi_limb_t cy;
cy = _gcry_mpih_add_1(wp, up, usize, v);
wp[usize] = cy;
wsize = usize + cy;
}
else { /* The signs are different. Need exact comparison to determine
* which operand to subtract from which. */
if( usize == 1 && up[0] < v ) {
wp[0] = v - up[0];
wsize = 1;
wsign = 1;
}
else {
_gcry_mpih_sub_1(wp, up, usize, v);
/* Size can decrease with at most one limb. */
wsize = usize - (wp[usize-1]==0);
}
}
w->nlimbs = wsize;
w->sign = wsign;
}
void
_gcry_mpih_mul_karatsuba_case( mpi_ptr_t prodp,
mpi_ptr_t up, mpi_size_t usize,
mpi_ptr_t vp, mpi_size_t vsize,
struct karatsuba_ctx *ctx )
{
mpi_limb_t cy;
if( !ctx->tspace || ctx->tspace_size < vsize ) {
if( ctx->tspace )
_gcry_mpi_free_limb_space( ctx->tspace, ctx->tspace_nlimbs );
ctx->tspace_nlimbs = 2 * vsize;
ctx->tspace = mpi_alloc_limb_space (2 * vsize,
(_gcry_is_secure (up)
|| _gcry_is_secure (vp)));
ctx->tspace_size = vsize;
}
MPN_MUL_N_RECURSE( prodp, up, vp, vsize, ctx->tspace );
prodp += vsize;
up += vsize;
usize -= vsize;
if( usize >= vsize ) {
if( !ctx->tp || ctx->tp_size < vsize ) {
if( ctx->tp )
_gcry_mpi_free_limb_space( ctx->tp, ctx->tp_nlimbs );
ctx->tp_nlimbs = 2 * vsize;
ctx->tp = mpi_alloc_limb_space (2 * vsize,
(_gcry_is_secure (up)
|| _gcry_is_secure (vp)));
ctx->tp_size = vsize;
}
do {
MPN_MUL_N_RECURSE( ctx->tp, up, vp, vsize, ctx->tspace );
cy = _gcry_mpih_add_n( prodp, prodp, ctx->tp, vsize );
_gcry_mpih_add_1( prodp + vsize, ctx->tp + vsize, vsize, cy );
prodp += vsize;
up += vsize;
usize -= vsize;
} while( usize >= vsize );
}
if( usize ) {
if( usize < KARATSUBA_THRESHOLD ) {
_gcry_mpih_mul( ctx->tspace, vp, vsize, up, usize );
}
else {
if( !ctx->next ) {
ctx->next = xcalloc( 1, sizeof *ctx );
}
_gcry_mpih_mul_karatsuba_case( ctx->tspace,
vp, vsize,
up, usize,
ctx->next );
}
cy = _gcry_mpih_add_n( prodp, prodp, ctx->tspace, vsize);
_gcry_mpih_add_1( prodp + vsize, ctx->tspace + vsize, usize, cy );
}
}
void
_gcry_mpih_sqr_n( mpi_ptr_t prodp,
mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
{
if( size & 1 ) {
/* The size is odd, and the code below doesn't handle that.
* Multiply the least significant (size - 1) limbs with a recursive
* call, and handle the most significant limb of S1 and S2
* separately.
* A slightly faster way to do this would be to make the Karatsuba
* code below behave as if the size were even, and let it check for
* odd size in the end. I.e., in essence move this code to the end.
* Doing so would save us a recursive call, and potentially make the
* stack grow a lot less.
*/
mpi_size_t esize = size - 1; /* even size */
mpi_limb_t cy_limb;
MPN_SQR_N_RECURSE( prodp, up, esize, tspace );
cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, esize, up[esize] );
prodp[esize + esize] = cy_limb;
cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, size, up[esize] );
prodp[esize + size] = cy_limb;
}
else {
mpi_size_t hsize = size >> 1;
mpi_limb_t cy;
/* Product H. ________________ ________________
* |_____U1 x U1____||____U0 x U0_____|
* Put result in upper part of PROD and pass low part of TSPACE
* as new TSPACE.
*/
MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);
/* Product M. ________________
* |_(U1-U0)(U0-U1)_|
*/
if( _gcry_mpih_cmp( up + hsize, up, hsize) >= 0 )
_gcry_mpih_sub_n( prodp, up + hsize, up, hsize);
else
_gcry_mpih_sub_n (prodp, up, up + hsize, hsize);
/* Read temporary operands from low part of PROD.
* Put result in low part of TSPACE using upper part of TSPACE
* as new TSPACE. */
MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);
/* Add/copy product H */
MPN_COPY(prodp + hsize, prodp + size, hsize);
cy = _gcry_mpih_add_n(prodp + size, prodp + size,
prodp + size + hsize, hsize);
/* Add product M (if NEGFLG M is a negative number). */
cy -= _gcry_mpih_sub_n (prodp + hsize, prodp + hsize, tspace, size);
/* Product L. ________________ ________________
* |________________||____U0 x U0_____|
* Read temporary operands from low part of PROD.
* Put result in low part of TSPACE using upper part of TSPACE
* as new TSPACE. */
MPN_SQR_N_RECURSE (tspace, up, hsize, tspace + size);
/* Add/copy Product L (twice). */
cy += _gcry_mpih_add_n (prodp + hsize, prodp + hsize, tspace, size);
if( cy )
_gcry_mpih_add_1(prodp + hsize + size, prodp + hsize + size,
hsize, cy);
MPN_COPY(prodp, tspace, hsize);
cy = _gcry_mpih_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
if( cy )
_gcry_mpih_add_1 (prodp + size, prodp + size, size, 1);
}
}
static void
mul_n( mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
mpi_size_t size, mpi_ptr_t tspace )
{
if( size & 1 ) {
/* The size is odd, and the code below doesn't handle that.
* Multiply the least significant (size - 1) limbs with a recursive
* call, and handle the most significant limb of S1 and S2
* separately.
* A slightly faster way to do this would be to make the Karatsuba
* code below behave as if the size were even, and let it check for
* odd size in the end. I.e., in essence move this code to the end.
* Doing so would save us a recursive call, and potentially make the
* stack grow a lot less.
*/
mpi_size_t esize = size - 1; /* even size */
mpi_limb_t cy_limb;
MPN_MUL_N_RECURSE( prodp, up, vp, esize, tspace );
cy_limb = _gcry_mpih_addmul_1( prodp + esize, up, esize, vp[esize] );
prodp[esize + esize] = cy_limb;
cy_limb = _gcry_mpih_addmul_1( prodp + esize, vp, size, up[esize] );
prodp[esize + size] = cy_limb;
}
else {
/* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
*
* Split U in two pieces, U1 and U0, such that
* U = U0 + U1*(B**n),
* and V in V1 and V0, such that
* V = V0 + V1*(B**n).
*
* UV is then computed recursively using the identity
*
* 2n n n n
* UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
* 1 1 1 0 0 1 0 0
*
* Where B = 2**BITS_PER_MP_LIMB.
*/
mpi_size_t hsize = size >> 1;
mpi_limb_t cy;
int negflg;
/* Product H. ________________ ________________
* |_____U1 x V1____||____U0 x V0_____|
* Put result in upper part of PROD and pass low part of TSPACE
* as new TSPACE.
*/
MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize, tspace);
/* Product M. ________________
* |_(U1-U0)(V0-V1)_|
*/
if( _gcry_mpih_cmp(up + hsize, up, hsize) >= 0 ) {
_gcry_mpih_sub_n(prodp, up + hsize, up, hsize);
negflg = 0;
}
else {
_gcry_mpih_sub_n(prodp, up, up + hsize, hsize);
negflg = 1;
}
if( _gcry_mpih_cmp(vp + hsize, vp, hsize) >= 0 ) {
_gcry_mpih_sub_n(prodp + hsize, vp + hsize, vp, hsize);
negflg ^= 1;
}
else {
_gcry_mpih_sub_n(prodp + hsize, vp, vp + hsize, hsize);
/* No change of NEGFLG. */
}
/* Read temporary operands from low part of PROD.
* Put result in low part of TSPACE using upper part of TSPACE
* as new TSPACE.
*/
MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize, tspace + size);
/* Add/copy product H. */
MPN_COPY (prodp + hsize, prodp + size, hsize);
cy = _gcry_mpih_add_n( prodp + size, prodp + size,
prodp + size + hsize, hsize);
/* Add product M (if NEGFLG M is a negative number) */
if(negflg)
cy -= _gcry_mpih_sub_n(prodp + hsize, prodp + hsize, tspace, size);
else
cy += _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace, size);
/* Product L. ________________ ________________
* |________________||____U0 x V0_____|
* Read temporary operands from low part of PROD.
* Put result in low part of TSPACE using upper part of TSPACE
* as new TSPACE.
*/
MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);
/* Add/copy Product L (twice) */
cy += _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace, size);
if( cy )
_gcry_mpih_add_1(prodp + hsize + size, prodp + hsize + size, hsize, cy);
MPN_COPY(prodp, tspace, hsize);
cy = _gcry_mpih_add_n(prodp + hsize, prodp + hsize, tspace + hsize, hsize);
if( cy )
_gcry_mpih_add_1(prodp + size, prodp + size, size, 1);
}
}
