void
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 = mpihelp_addmul_1( prodp + esize, up, esize, up[esize] );
prodp[esize + esize] = cy_limb;
cy_limb = mpihelp_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( mpihelp_cmp( up + hsize, up, hsize) >= 0 )
mpihelp_sub_n( prodp, up + hsize, up, hsize);
else
mpihelp_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 = mpihelp_add_n(prodp + size, prodp + size,
prodp + size + hsize, hsize);
/* Add product M (if NEGFLG M is a negative number). */
cy -= mpihelp_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 += mpihelp_add_n (prodp + hsize, prodp + hsize, tspace, size);
if( cy )
mpihelp_add_1(prodp + hsize + size, prodp + hsize + size,
hsize, cy);
MPN_COPY(prodp, tspace, hsize);
cy = mpihelp_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
if( cy )
mpihelp_add_1 (prodp + size, prodp + size, size, 1);
}
}
int mpi_add(MPI w, MPI u, MPI v)
{
mpi_ptr_t wp, up, vp;
mpi_size_t usize, vsize, wsize;
int usign, vsign, wsign;
if (u->nlimbs < v->nlimbs) {
usize = v->nlimbs;
usign = v->sign;
vsize = u->nlimbs;
vsign = u->sign;
wsize = usize + 1;
if (RESIZE_IF_NEEDED(w, wsize) < 0)
return -ENOMEM;
up = v->d;
vp = u->d;
} else {
usize = u->nlimbs;
usign = u->sign;
vsize = v->nlimbs;
vsign = v->sign;
wsize = usize + 1;
if (RESIZE_IF_NEEDED(w, wsize) < 0)
return -ENOMEM;
up = u->d;
vp = v->d;
}
wp = w->d;
wsign = 0;
if (!vsize) {
MPN_COPY(wp, up, usize);
wsize = usize;
wsign = usign;
} else if (usign != vsign) {
if (usize != vsize) {
mpihelp_sub(wp, up, usize, vp, vsize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
wsign = usign;
} else if (mpihelp_cmp(up, vp, usize) < 0) {
mpihelp_sub_n(wp, vp, up, usize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
if (!usign)
wsign = 1;
} else {
mpihelp_sub_n(wp, up, vp, usize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
if (usign)
wsign = 1;
}
} else {
mpi_limb_t cy = mpihelp_add(wp, up, usize, vp, vsize);
wp[usize] = cy;
wsize = usize + cy;
if (usign)
wsign = 1;
}
w->nlimbs = wsize;
w->sign = wsign;
return 0;
}
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 = mpihelp_addmul_1( prodp + esize, up, esize, vp[esize] );
prodp[esize + esize] = cy_limb;
cy_limb = mpihelp_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( mpihelp_cmp(up + hsize, up, hsize) >= 0 ) {
mpihelp_sub_n(prodp, up + hsize, up, hsize);
negflg = 0;
}
else {
mpihelp_sub_n(prodp, up, up + hsize, hsize);
negflg = 1;
}
if( mpihelp_cmp(vp + hsize, vp, hsize) >= 0 ) {
mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize);
negflg ^= 1;
}
else {
mpihelp_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 = mpihelp_add_n( prodp + size, prodp + size,
prodp + size + hsize, hsize);
/* Add product M (if NEGFLG M is a negative number) */
if(negflg)
cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size);
else
cy += mpihelp_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 += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
if( cy )
mpihelp_add_1(prodp + hsize + size, prodp + hsize + size, hsize, cy);
MPN_COPY(prodp, tspace, hsize);
cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize, hsize);
if( cy )
mpihelp_add_1(prodp + size, prodp + size, size, 1);
}
}
void
mpi_add(MPI w, MPI u, MPI v)
{
mpi_ptr_t wp, up, vp;
mpi_size_t usize, vsize, wsize;
int usign, vsign, wsign;
if( u->nlimbs < v->nlimbs ) { /* Swap U and V. */
usize = v->nlimbs;
usign = v->sign;
vsize = u->nlimbs;
vsign = u->sign;
wsize = usize + 1;
RESIZE_IF_NEEDED(w, wsize);
/* These must be after realloc (u or v may be the same as w). */
up = v->d;
vp = u->d;
}
else {
usize = u->nlimbs;
usign = u->sign;
vsize = v->nlimbs;
vsign = v->sign;
wsize = usize + 1;
RESIZE_IF_NEEDED(w, wsize);
/* These must be after realloc (u or v may be the same as w). */
up = u->d;
vp = v->d;
}
wp = w->d;
wsign = 0;
if( !vsize ) { /* simple */
MPN_COPY(wp, up, usize );
wsize = usize;
wsign = usign;
}
else if( usign != vsign ) { /* different sign */
/* This test is right since USIZE >= VSIZE */
if( usize != vsize ) {
mpihelp_sub(wp, up, usize, vp, vsize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
wsign = usign;
}
else if( mpihelp_cmp(up, vp, usize) < 0 ) {
mpihelp_sub_n(wp, vp, up, usize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
if( !usign )
wsign = 1;
}
else {
mpihelp_sub_n(wp, up, vp, usize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
if( usign )
wsign = 1;
}
}
else { /* U and V have same sign. Add them. */
mpi_limb_t cy = mpihelp_add(wp, up, usize, vp, vsize);
wp[usize] = cy;
wsize = usize + cy;
if( usign )
wsign = 1;
}
w->nlimbs = wsize;
w->sign = wsign;
}
