void mpzspv_from_ntt (mpzspv_t x, spv_size_t offset, spv_size_t ntt_size,
spv_size_t monic_pos, mpzspm_t mpzspm)
{
unsigned int i;
spv_size_t log2_ntt_size;
spm_t spm;
spv_t spv;
ASSERT (mpzspv_verify (x, offset, ntt_size, mpzspm));
log2_ntt_size = ceil_log_2 (ntt_size);
for (i = 0; i < mpzspm->sp_num; i++)
{
spm = mpzspm->spm[i];
spv = x[i] + offset;
spv_ntt_gfp_dit (spv, log2_ntt_size, spm);
/* spm->sp - (spm->sp - 1) / ntt_size is the inverse of ntt_size */
spv_mul_sp (spv, spv, spm->sp - (spm->sp - 1) / ntt_size,
ntt_size, spm->sp, spm->mul_c);
if (monic_pos)
spv[monic_pos % ntt_size] = sp_sub (spv[monic_pos % ntt_size],
1, spm->sp);
}
}
void
mpzspv_to_ntt (mpzspv_t x, spv_size_t offset, spv_size_t len,
spv_size_t ntt_size, int monic, mpzspm_t mpzspm)
{
unsigned int i;
spv_size_t j, log2_ntt_size;
spm_t spm;
spv_t spv;
ASSERT (mpzspv_verify (x, offset, len, mpzspm));
ASSERT (mpzspv_verify (x, offset + ntt_size, 0, mpzspm));
log2_ntt_size = ceil_log_2 (ntt_size);
for (i = 0; i < mpzspm->sp_num; i++)
{
spm = mpzspm->spm[i];
spv = x[i] + offset;
if (ntt_size < len)
{
for (j = ntt_size; j < len; j += ntt_size)
spv_add (spv, spv, spv + j, ntt_size, spm->sp);
}
if (ntt_size > len)
spv_set_zero (spv + len, ntt_size - len);
if (monic)
spv[len % ntt_size] = sp_add (spv[len % ntt_size], 1, spm->sp);
spv_ntt_gfp_dif (spv, log2_ntt_size, spm);
}
}
void
mpzspv_mul_by_dct (mpzspv_t dft, const mpzspv_t dct, const spv_size_t len,
const mpzspm_t mpzspm, const int steps)
{
int j;
spv_size_t log2_len = ceil_log_2 (len);
#ifdef _OPENMP
#pragma omp parallel private(j)
{
#pragma omp for
#endif
for (j = 0; j < (int) (mpzspm->sp_num); j++)
{
const spm_t spm = mpzspm->spm[j];
const spv_t spv = dft[j];
unsigned long i, m;
/* Forward DFT of dft[j] */
if ((steps & NTT_MUL_STEP_FFT1) != 0)
spv_ntt_gfp_dif (spv, log2_len, spm);
/* Point-wise product */
if ((steps & NTT_MUL_STEP_MUL) != 0)
{
m = 5UL;
spv[0] = sp_mul (spv[0], dct[j][0], spm->sp, spm->mul_c);
spv[1] = sp_mul (spv[1], dct[j][len / 2UL], spm->sp, spm->mul_c);
for (i = 2UL; i < len; i += 2UL)
{
/* This works, but why? */
if (i + i / 2UL > m)
m = 2UL * m + 1;
spv[i] = sp_mul (spv[i], dct[j][i / 2UL], spm->sp, spm->mul_c);
spv[m - i] = sp_mul (spv[m - i], dct[j][i / 2UL], spm->sp,
spm->mul_c);
}
}
/* Inverse transform of dft[j] */
if ((steps & NTT_MUL_STEP_IFFT) != 0)
{
spv_ntt_gfp_dit (spv, log2_len, spm);
/* Divide by transform length. FIXME: scale the DCT of h instead */
spv_mul_sp (spv, spv, spm->sp - (spm->sp - 1) / len, len,
spm->sp, spm->mul_c);
}
}
#ifdef _OPENMP
}
#endif
}
/*
* malloc - allocates a block with requested size
* (implementation issue: adjust size, extend size)
*
*/
void *malloc(size_t size)
{
size_t asize = 0;
size_t extendsize;
char* bp;
#ifdef TWEAK
int k;
#endif
dbg1("[IN ] : malloc() - malloc(%ld)\n", size);
checkheap();
if (!mm_initialized)
mm_init();
/* Ignore spurious requests */
if (size <= 0)
return NULL;
#ifdef TWEAK
/*
* [Optimization for binary*.rep trace files]
* if requested size is larger than 2^4=16 bytes, and close to power of two
* (when the difference between requested size and its closest larger power of two
* is smaller than one eighth of closest power of two) round up to power of two
*/
k = ceil_log_2(size);
if( k >= 4 && ((1 << k) - size) <= (unsigned)(1 << (k -3))) {
size = 1 << k;
}
dbg1("intermediate size : %ld\n", size);
#endif
#ifdef PUTBUG
if (size <= MINBLKSIZE) {
asize = MINBLKSIZE + WSIZE;
}
else {
asize = DSIZE * ((size + DSIZE-1)/DSIZE);
}
#endif
#ifdef ASIZE1
/* Adjust block size to include overhead and alignment reqs */
/* Block should at least have space for Header, Footer, Pred, Succ Pointers */
if (size <= MINBLKSIZE) {
asize = MINBLKSIZE + WSIZE;
}
else {
asize = DSIZE * ((size + WSIZE + DSIZE-1)/DSIZE);
}
#endif
#ifdef ASIZE2
if (size <= 2*DSIZE+OVERHEAD) {
asize = 2*DSIZE+OVERHEAD+OVERHEAD;
}
else {
/* round up to the nearest order of 16 */
asize = 2*DSIZE * ((size + (OVERHEAD - WSIZE) + 2*DSIZE-1)/(2*DSIZE));
}
#endif
#ifdef ASIZE3
if (size <= DDSIZE){
asize = DDSIZE + DSIZE;
}
else {
asize = DDSIZE*((size + (DSIZE - WSIZE) + (DDSIZE-1)) / DDSIZE);
}
#endif
dbg("malloc: adjusted size %ld, class %ld\n", asize, get_list_num(asize));
/* Search the free list for a fit */
if ((bp = find_fit(asize)) != NULL) {
place(bp, asize);
dbg1("[OUT] : malloc() - found fit\n");
return bp;
}
/* No fit found. Get more memory and place the block */
extendsize = MAX(asize, CHUNKSIZE);
if((bp = extend_heap(extendsize/WSIZE)) == NULL)
return NULL;
place(bp, asize);
dbg1("[OUT] : malloc() - found fit failed, extended the heap\n");
return bp;
}
void
mpzspv_sqr_reciprocal (mpzspv_t dft, const spv_size_t n,
const mpzspm_t mpzspm)
{
const spv_size_t log2_n = ceil_log_2 (n);
const spv_size_t len = ((spv_size_t) 2) << log2_n;
const spv_size_t log2_len = 1 + log2_n;
int j;
ASSERT(mpzspm->max_ntt_size % 3UL == 0UL);
ASSERT(len % 3UL != 0UL);
ASSERT(mpzspm->max_ntt_size % len == 0UL);
#ifdef _OPENMP
#pragma omp parallel
{
#pragma omp for
#endif
for (j = 0; j < (int) (mpzspm->sp_num); j++)
{
const spm_t spm = mpzspm->spm[j];
const spv_t spv = dft[j];
sp_t w1, w2, invlen;
const sp_t sp = spm->sp, mul_c = spm->mul_c;
spv_size_t i;
/* Zero out NTT elements [n .. len-n] */
spv_set_sp (spv + n, (sp_t) 0, len - 2*n + 1);
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
{
printf ("ntt_sqr_reciprocal: NTT vector mod %lu\n", sp);
ntt_print_vec ("ntt_sqr_reciprocal: before weighting:", spv, len);
}
#endif
/* Compute the root for the weight signal, a 3rd primitive root
of unity */
w1 = sp_pow (spm->prim_root, mpzspm->max_ntt_size / 3UL, sp,
mul_c);
/* Compute iw= 1/w */
w2 = sp_pow (spm->inv_prim_root, mpzspm->max_ntt_size / 3UL, sp,
mul_c);
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
printf ("w1 = %lu ,w2 = %lu\n", w1, w2);
#endif
ASSERT(sp_mul(w1, w2, sp, mul_c) == (sp_t) 1);
ASSERT(w1 != (sp_t) 1);
ASSERT(sp_pow (w1, 3UL, sp, mul_c) == (sp_t) 1);
ASSERT(w2 != (sp_t) 1);
ASSERT(sp_pow (w2, 3UL, sp, mul_c) == (sp_t) 1);
/* Fill NTT elements spv[len-n+1 .. len-1] with coefficients and
apply weight signal to spv[i] and spv[l-i] for 0 <= i < n
Use the fact that w^i + w^{-i} = -1 if i != 0 (mod 3). */
for (i = 0; i + 2 < n; i += 3)
{
sp_t t, u;
if (i > 0)
spv[len - i] = spv[i];
t = spv[i + 1];
u = sp_mul (t, w1, sp, mul_c);
spv[i + 1] = u;
spv[len - i - 1] = sp_neg (sp_add (t, u, sp), sp);
t = spv[i + 2];
u = sp_mul (t, w2, sp, mul_c);
spv[i + 2] = u;
spv[len - i - 2] = sp_neg (sp_add (t, u, sp), sp);
}
if (i < n && i > 0)
{
spv[len - i] = spv[i];
}
if (i + 1 < n)
{
sp_t t, u;
t = spv[i + 1];
u = sp_mul (t, w1, sp, mul_c);
spv[i + 1] = u;
spv[len - i - 1] = sp_neg (sp_add (t, u, sp), sp);
}
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
ntt_print_vec ("ntt_sqr_reciprocal: after weighting:", spv, len);
#endif
/* Forward DFT of dft[j] */
spv_ntt_gfp_dif (spv, log2_len, spm);
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
ntt_print_vec ("ntt_sqr_reciprocal: after forward transform:",
spv, len);
#endif
/* Square the transformed vector point-wise */
spv_pwmul (spv, spv, spv, len, sp, mul_c);
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
ntt_print_vec ("ntt_sqr_reciprocal: after point-wise squaring:",
spv, len);
#endif
/* Inverse transform of dft[j] */
spv_ntt_gfp_dit (spv, log2_len, spm);
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
ntt_print_vec ("ntt_sqr_reciprocal: after inverse transform:",
spv, len);
#endif
/* Un-weight and divide by transform length */
invlen = sp - (sp - (sp_t) 1) / len; /* invlen = 1/len (mod sp) */
w1 = sp_mul (invlen, w1, sp, mul_c);
w2 = sp_mul (invlen, w2, sp, mul_c);
for (i = 0; i < 2 * n - 3; i += 3)
{
spv[i] = sp_mul (spv[i], invlen, sp, mul_c);
spv[i + 1] = sp_mul (spv[i + 1], w2, sp, mul_c);
spv[i + 2] = sp_mul (spv[i + 2], w1, sp, mul_c);
}
if (i < 2 * n - 1)
spv[i] = sp_mul (spv[i], invlen, sp, mul_c);
if (i < 2 * n - 2)
spv[i + 1] = sp_mul (spv[i + 1], w2, sp, mul_c);
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
ntt_print_vec ("ntt_sqr_reciprocal: after un-weighting:", spv, len);
#endif
/* Separate the coefficients of R in the wrapped-around product. */
/* Set w1 = cuberoot(1)^l where cuberoot(1) is the same primitive
3rd root of unity we used for the weight signal */
w1 = sp_pow (spm->prim_root, mpzspm->max_ntt_size / 3UL, sp,
mul_c);
w1 = sp_pow (w1, len % 3UL, sp, mul_c);
/* Set w2 = 1/(w1 - 1/w1). Incidentally, w2 = 1/sqrt(-3) */
w2 = sp_inv (w1, sp, mul_c);
w2 = sp_sub (w1, w2, sp);
w2 = sp_inv (w2, sp, mul_c);
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
printf ("For separating: w1 = %lu, w2 = %lu\n", w1, w2);
#endif
for (i = len - (2*n - 2); i <= len / 2; i++)
{
sp_t t, u;
/* spv[i] = s_i + w^{-l} s_{l-i}.
spv[l-i] = s_{l-i} + w^{-l} s_i */
t = sp_mul (spv[i], w1, sp, mul_c); /* t = w^l s_i + s_{l-i} */
t = sp_sub (t, spv[len - i], sp); /* t = w^l s_i + w^{-l} s_i */
t = sp_mul (t, w2, sp, mul_c); /* t = s_1 */
u = sp_sub (spv[i], t, sp); /* u = w^{-l} s_{l-i} */
u = sp_mul (u, w1, sp, mul_c); /* u = s_{l-i} */
spv[i] = t;
spv[len - i] = u;
ASSERT(i < len / 2 || t == u);
}
#ifdef TRACE_ntt_sqr_reciprocal
if (j == 0)
ntt_print_vec ("ntt_sqr_reciprocal: after un-wrapping:", spv, len);
#endif
}
#ifdef _OPENMP
}
#endif
}
void
mpzspv_to_dct1 (mpzspv_t dct, const mpzspv_t spv, const spv_size_t spvlen,
const spv_size_t dctlen, mpzspv_t tmp,
const mpzspm_t mpzspm)
{
const spv_size_t l = 2 * (dctlen - 1); /* Length for the DFT */
const spv_size_t log2_l = ceil_log_2 (l);
int j;
#ifdef _OPENMP
#pragma omp parallel private(j)
{
#pragma omp for
#endif
for (j = 0; j < (int) mpzspm->sp_num; j++)
{
const spm_t spm = mpzspm->spm[j];
spv_size_t i;
/* Make a symmetric copy of spv in tmp. I.e. with spv = [3, 2, 1],
spvlen = 3, dctlen = 5 (hence l = 8), we want
tmp = [3, 2, 1, 0, 0, 0, 1, 2] */
spv_set (tmp[j], spv[j], spvlen);
spv_rev (tmp[j] + l - spvlen + 1, spv[j] + 1, spvlen - 1);
/* Now we have [3, 2, 1, ?, ?, ?, 1, 2]. Fill the ?'s with zeros. */
spv_set_sp (tmp[j] + spvlen, (sp_t) 0, l - 2 * spvlen + 1);
#if 0
printf ("mpzspv_to_dct1: tmp[%d] = [", j);
for (i = 0; i < l; i++)
printf ("%lu, ", tmp[j][i]);
printf ("]\n");
#endif
spv_ntt_gfp_dif (tmp[j], log2_l, spm);
#if 0
printf ("mpzspv_to_dct1: tmp[%d] = [", j);
for (i = 0; i < l; i++)
printf ("%lu, ", tmp[j][i]);
printf ("]\n");
#endif
/* The forward transform is scrambled. We want elements [0 ... l/2]
of the unscrabled data, that is all the coefficients with the most
significant bit in the index (in log2(l) word size) unset, plus the
element at index l/2. By scrambling, these map to the elements with
even index, plus the element at index 1.
The elements with scrambled index 2*i are stored in h[i], the
element with scrambled index 1 is stored in h[params->l] */
#ifdef WANT_ASSERT
/* Test that the coefficients are symmetric (if they were unscrambled)
and that our algorithm for finding identical coefficients in the
scrambled data works */
{
spv_size_t m = 5;
for (i = 2; i < l; i += 2L)
{
/* This works, but why? */
if (i + i / 2L > m)
m = 2L * m + 1L;
ASSERT (tmp[j][i] == tmp[j][m - i]);
#if 0
printf ("mpzspv_to_dct1: DFT[%lu] == DFT[%lu]\n", i, m - i);
#endif
}
}
#endif
/* Copy coefficients to dct buffer */
for (i = 0; i < l / 2; i++)
dct[j][i] = tmp[j][i * 2];
dct[j][l / 2] = tmp[j][1];
}
#ifdef _OPENMP
}
#endif
}
void
mpzspv_mul_ntt (mpzspv_t r, const spv_size_t offsetr,
mpzspv_t x, const spv_size_t offsetx, const spv_size_t lenx,
mpzspv_t y, const spv_size_t offsety, const spv_size_t leny,
const spv_size_t ntt_size, const int monic, const spv_size_t monic_pos,
mpzspm_t mpzspm, const int steps)
{
spv_size_t log2_ntt_size;
int i;
ASSERT (mpzspv_verify (x, offsetx, lenx, mpzspm));
ASSERT (mpzspv_verify (y, offsety, leny, mpzspm));
ASSERT (mpzspv_verify (x, offsetx + ntt_size, 0, mpzspm));
ASSERT (mpzspv_verify (y, offsety + ntt_size, 0, mpzspm));
ASSERT (mpzspv_verify (r, offsetr + ntt_size, 0, mpzspm));
log2_ntt_size = ceil_log_2 (ntt_size);
/* Need parallelization at higher level (e.g., handling a branch of the
product tree in one thread) to make this worthwhile for ECM */
#define MPZSPV_MUL_NTT_OPENMP 0
#if defined(_OPENMP) && MPZSPV_MUL_NTT_OPENMP
#pragma omp parallel if (ntt_size > 16384)
{
#pragma omp for
#endif
for (i = 0; i < (int) mpzspm->sp_num; i++)
{
spv_size_t j;
spm_t spm = mpzspm->spm[i];
spv_t spvr = r[i] + offsetr;
spv_t spvx = x[i] + offsetx;
spv_t spvy = y[i] + offsety;
if ((steps & NTT_MUL_STEP_FFT1) != 0) {
if (ntt_size < lenx)
{
for (j = ntt_size; j < lenx; j += ntt_size)
spv_add (spvx, spvx, spvx + j, ntt_size, spm->sp);
}
if (ntt_size > lenx)
spv_set_zero (spvx + lenx, ntt_size - lenx);
if (monic)
spvx[lenx % ntt_size] = sp_add (spvx[lenx % ntt_size], 1, spm->sp);
spv_ntt_gfp_dif (spvx, log2_ntt_size, spm);
}
if ((steps & NTT_MUL_STEP_FFT2) != 0) {
if (ntt_size < leny)
{
for (j = ntt_size; j < leny; j += ntt_size)
spv_add (spvy, spvy, spvy + j, ntt_size, spm->sp);
}
if (ntt_size > leny)
spv_set_zero (spvy + leny, ntt_size - leny);
if (monic)
spvy[leny % ntt_size] = sp_add (spvy[leny % ntt_size], 1, spm->sp);
spv_ntt_gfp_dif (spvy, log2_ntt_size, spm);
}
if ((steps & NTT_MUL_STEP_MUL) != 0) {
spv_pwmul (spvr, spvx, spvy, ntt_size, spm->sp, spm->mul_c);
}
if ((steps & NTT_MUL_STEP_IFFT) != 0) {
ASSERT (sizeof (mp_limb_t) >= sizeof (sp_t));
spv_ntt_gfp_dit (spvr, log2_ntt_size, spm);
/* spm->sp - (spm->sp - 1) / ntt_size is the inverse of ntt_size */
spv_mul_sp (spvr, spvr, spm->sp - (spm->sp - 1) / ntt_size,
ntt_size, spm->sp, spm->mul_c);
if (monic_pos)
spvr[monic_pos % ntt_size] = sp_sub (spvr[monic_pos % ntt_size],
1, spm->sp);
}
}
#if defined(_OPENMP) && MPZSPV_MUL_NTT_OPENMP
}
#endif
}