int mpn_mulmod_Bexpp1(mp_ptr r, mp_srcptr i1, mp_srcptr i2, mp_size_t limbs, mp_ptr tt)
{
mp_size_t bits = limbs * GMP_LIMB_BITS;
mp_bitcnt_t depth1, depth = 1;
mp_size_t w1, off;
mp_limb_t c = 2 * i1[limbs] + i2[limbs];
if (c & 1)
{
mpn_neg_n(r, i1, limbs + 1);
mpn_normmod_2expp1(r, limbs);
return 0;
} else if (c & 2)
{
mpn_neg_n(r, i2, limbs + 1);
mpn_normmod_2expp1(r, limbs);
return 0;
}
if (limbs <= FFT_MULMOD_2EXPP1_CUTOFF)
{
if(bits)
r[limbs] = mpn_mulmod_2expp1_basecase(r, i1, i2, c, bits, tt);
else
r[limbs] = 0;
return r[limbs];
}
while ((((mp_limb_t)1)<<depth) < bits) depth++;
if (depth < 12) off = mulmod_2expp1_table_n[0];
else off = mulmod_2expp1_table_n[MIN(depth, FFT_N_NUM + 11) - 12];
depth1 = depth/2 - off;
w1 = bits/(((mp_limb_t)1)<<(2*depth1));
mpir_fft_mulmod_2expp1(r, i1, i2, limbs, depth1, w1);
return r[limbs];
}
/*
ret + (xp, n) = (yp, n)*(zp, n) % 2^b + 1
needs (tp, 2n) temp space, everything reduced mod 2^b
inputs, outputs are fully reduced
N.B: 2n is not the same as 2b rounded up to nearest limb!
*/
inline static int
mpn_mulmod_2expp1_internal (mp_ptr xp, mp_srcptr yp, mp_srcptr zp,
mpir_ui b, mp_ptr tp)
{
mp_size_t n, k;
mp_limb_t c;
TMP_DECL;
n = BITS_TO_LIMBS (b);
k = GMP_NUMB_BITS * n - b;
ASSERT(b > 0);
ASSERT(n > 0);
ASSERT_MPN(yp, n);
ASSERT_MPN(zp, n);
ASSERT(!MPN_OVERLAP_P (tp, 2 * n, yp, n));
ASSERT(!MPN_OVERLAP_P (tp, 2 * n, zp, n));
ASSERT(MPN_SAME_OR_SEPARATE_P (xp, tp, n));
ASSERT(MPN_SAME_OR_SEPARATE_P (xp, tp + n, n));
ASSERT(k == 0 || yp[n - 1] >> (GMP_NUMB_BITS - k) == 0);
ASSERT(k == 0 || zp[n - 1] >> (GMP_NUMB_BITS - k) == 0);
#ifndef TUNE_PROGRAM_BUILD
if (k == 0 && n > FFT_MULMOD_2EXPP1_CUTOFF && n == mpir_fft_adjust_limbs(n))
{
mp_bitcnt_t depth1, depth = 1;
mp_size_t w1, off;
mp_ptr tx, ty, tz;
mp_limb_t ret;
TMP_MARK;
tx = TMP_BALLOC_LIMBS(3*n + 3);
ty = tx + n + 1;
tz = ty + n + 1;
MPN_COPY(ty, yp, n);
MPN_COPY(tz, zp, n);
ty[n] = 0;
tz[n] = 0;
while ((((mp_limb_t)1)<<depth) < b) depth++;
if (depth < 12) off = mulmod_2expp1_table_n[0];
else off = mulmod_2expp1_table_n[MIN(depth, FFT_N_NUM + 11) - 12];
depth1 = depth/2 - off;
w1 = b/(((mp_limb_t)1)<<(2*depth1));
mpir_fft_mulmod_2expp1(tx, ty, tz, n, depth1, w1);
MPN_COPY(xp, tx, n);
ret = tx[n];
TMP_FREE;
return ret;
}
#endif
if (yp == zp)
mpn_sqr(tp, yp, n);
else
mpn_mul_n (tp, yp, zp, n);
if (k == 0)
{
c = mpn_sub_n (xp, tp, tp + n, n);
return mpn_add_1 (xp, xp, n, c);
}
c = tp[n - 1];
tp[n - 1] &= GMP_NUMB_MASK >> k;
#if HAVE_NATIVE_mpn_sublsh_nc
c = mpn_sublsh_nc (xp, tp, tp + n, n, k, c);
#else
{
mp_limb_t c1;
c1 = mpn_lshift (tp + n, tp + n, n, k);
tp[n] |= c >> (GMP_NUMB_BITS - k);
c = mpn_sub_n (xp, tp, tp + n, n) + c1;
}
#endif
c = mpn_add_1 (xp, xp, n, c);
xp[n - 1] &= GMP_NUMB_MASK >> k;
return c;
}
int
main(void)
{
mp_bitcnt_t depth, w, depth1, w1;
clock_t start, end;
double elapsed;
double best = 0.0;
mp_size_t best_off, off, best_d, best_w;
gmp_randstate_t state;
printf("/* fft_tuning.h -- autogenerated by tune-fft */\n\n");
printf("#ifndef FFT_TUNING_H\n");
printf("#define FFT_TUNING_H\n\n");
printf("#include \"mpir.h\"\n\n");
printf("#define FFT_TAB \\\n");
fflush(stdout);
gmp_randinit_default(state);
printf(" { "); fflush(stdout);
for (depth = 6; depth <= 10; depth++)
{
printf("{ "); fflush(stdout);
for (w = 1; w <= 2; w++)
{
int iters = 100*((mp_size_t) 1 << (3*(10 - depth)/2)), i;
mp_size_t n = ((mp_limb_t)1<<depth);
mp_bitcnt_t bits1 = (n*w - (depth + 1))/2;
mp_size_t len1 = 2*n;
mp_size_t len2 = 2*n;
mp_bitcnt_t b1 = len1*bits1, b2 = len2*bits1;
mp_size_t n1, n2;
mp_size_t j;
mp_limb_t * i1, *i2, *r1;
n1 = (b1 - 1)/GMP_LIMB_BITS + 1;
n2 = (b2 - 1)/GMP_LIMB_BITS + 1;
i1 = malloc(2*(n1 + n2)*sizeof(mp_limb_t));
i2 = i1 + n1;
r1 = i2 + n2;
mpn_urandomb(i1, state, b1);
mpn_urandomb(i2, state, b2);
best_off = -1;
for (off = 0; off <= 4; off++)
{
start = clock();
for (i = 0; i < iters; i++)
mpn_mul_trunc_sqrt2(r1, i1, n1, i2, n2, depth - off, w*((mp_size_t)1 << (off*2)));
end = clock();
elapsed = ((double) (end - start)) / CLOCKS_PER_SEC;
if (elapsed < best || best_off == -1)
{
best_off = off;
best = elapsed;
}
}
printf("%ld", best_off);
if (w != 2) printf(",");
printf(" "); fflush(stdout);
free(i1);
}
printf("}");
if (depth != 10) printf(",");
printf(" "); fflush(stdout);
}
printf("}\n\n");
best_d = 12;
best_w = 1;
best_off = -1;
printf("#define MULMOD_TAB \\\n");
fflush(stdout);
printf(" { "); fflush(stdout);
for (depth = 12; best_off != 1 ; depth++)
{
for (w = 1; w <= 2; w++)
{
int iters = 100*((mp_size_t) 1 << (3*(18 - depth)/2)), i;
mp_size_t n = ((mp_limb_t)1<<depth);
mp_bitcnt_t bits = n*w;
mp_size_t int_limbs = (bits - 1)/GMP_LIMB_BITS + 1;
mp_size_t j;
mp_limb_t c, * i1, * i2, * r1, * tt;
if (depth <= 21) iters = 32*((mp_size_t) 1 << (21 - depth));
else iters = MAX(32/((mp_size_t) 1 << (depth - 21)), 1);
i1 = malloc(6*(int_limbs+1)*sizeof(mp_limb_t));
i2 = i1 + int_limbs + 1;
r1 = i2 + int_limbs + 1;
tt = r1 + 2*(int_limbs + 1);
mpn_urandomb(i1, state, int_limbs*GMP_LIMB_BITS);
mpn_urandomb(i2, state, int_limbs*GMP_LIMB_BITS);
i1[int_limbs] = 0;
i2[int_limbs] = 0;
depth1 = 1;
while ((((mp_limb_t)1)<<depth1) < bits) depth1++;
depth1 = depth1/2;
w1 = bits/(((mp_limb_t)1)<<(2*depth1));
best_off = -1;
for (off = 0; off <= 4; off++)
{
start = clock();
for (i = 0; i < iters; i++)
mpir_fft_mulmod_2expp1(r1, i1, i2, int_limbs, depth1 - off, w1*((mp_size_t)1 << (off*2)));
end = clock();
elapsed = ((double) (end - start)) / CLOCKS_PER_SEC;
if (best_off == -1 || elapsed < best)
{
best_off = off;
best = elapsed;
}
}
start = clock();
for (i = 0; i < iters; i++)
mpn_mulmod_2expp1_basecase(r1, i1, i2, 0, bits, tt);
end = clock();
elapsed = ((double) (end - start)) / CLOCKS_PER_SEC;
if (elapsed < best)
{
best_d = depth + (w == 2);
best_w = w + 1 - 2*(w == 2);
}
printf("%ld", best_off);
if (w != 2) printf(", "); fflush(stdout);
free(i1);
}
printf(", "); fflush(stdout);
}
printf("1 }\n\n");
printf("#define FFT_N_NUM %ld\n\n", 2*(depth - 12) + 1);
printf("#define FFT_MULMOD_2EXPP1_CUTOFF %ld\n\n", ((mp_limb_t) 1 << best_d)*best_w/(2*GMP_LIMB_BITS));
gmp_randclear(state);
printf("#endif\n");
return 0;
}
