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Faster _fmpz_vec_scalar_divexact_ui #2371

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Faster _fmpz_vec_scalar_divexact_ui #2371

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93a3bbd
Faster _fmpz_vec_scalar_divexact for single-word divisors
fredrik-johansson Jul 18, 2025
57fcdc5
Try to fix _gr_vec_divexact test code
fredrik-johansson Jul 18, 2025
7d6daf2
fmpz_mpoly_scalar_divexact_fmpz
fredrik-johansson Jul 18, 2025
31ccb70
Fix fmpz_mpoly_scalar_divexact_fmpz test
fredrik-johansson Jul 18, 2025
b3990ee
Profiling code; fmpz safety
fredrik-johansson Jul 19, 2025
a11d019
Slightly faster n_binvert
fredrik-johansson Jul 22, 2025
3197a77
Missing underscore
fredrik-johansson Jul 22, 2025
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33 changes: 24 additions & 9 deletions src/fmpz_vec/scalar_divexact.c
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Original file line number Diff line number Diff line change
Expand Up @@ -21,16 +21,15 @@
/* Helper functions that could go in longlong.h, ulong_extras.h
and mpn_extras.h as soon as they find a use elsewhere. */

/* The table is slightly faster but requires GMP internals. */
#define USE BINVERT_TABLE 0

/* Tuned for Zen 3; with assembly code we would not need GMP. */
#define DIVEXACT_1_ODD_GMP_CUTOFF 35
#define DIVEXACT_1_EVEN_GMP_CUTOFF 25

/* The table is slightly faster but requires GMP internals. */
#define USE BINVERT_TABLE 0

#if USE_BINVERT_TABLE
extern const unsigned char __gmp_binvert_limb_table[128];
#endif

/* Invert n mod 2^FLINT_BITS */
static ulong n_binvert(ulong n)
Expand All @@ -39,13 +38,8 @@ static ulong n_binvert(ulong n)

FLINT_ASSERT(n % 2);

#if USE_BINVERT_TABLE
r = __gmp_binvert_limb_table[(n / 2) & 0x7F];
#else
r = (((n + 2) & 4) << 1) ^ n; /* 4 bits */
r = 2 * r - r * r * n; /* 8 bits */
#endif

r = 2 * r - r * r * n; /* 16 bits */
r = 2 * r - r * r * n; /* 32 bits */
#if FLINT_BITS == 64
Expand All @@ -54,6 +48,27 @@ static ulong n_binvert(ulong n)

return r;
}
#else

/* Use Hurchalla's algorithm https://arxiv.org/abs/2204.04342 */
static ulong n_binvert(ulong a)
{
ulong r, y;

r = (3 * a) ^ 2; /* 5 bits */
y = 1 - a * r;
r = r * (1 + y); /* 10 bits */
y *= y;
r = r * (1 + y); /* 20 bits */
y *= y;
r = r * (1 + y); /* 40 bits */
#if FLINT_BITS == 64
y *= y;
r = r * (1 + y); /* 80 bits */
#endif
return r;
}
#endif

FLINT_FORCE_INLINE
ulong n_mulhi(ulong a, ulong b)
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