nmod_vec.h – vectors over integers mod n (word-size n)

Memory management

mp_ptr _nmod_vec_init(slong len)

Returns a vector of the given length. The entries are not necessarily zero.

void _nmod_vec_clear(mp_ptr vec)

Frees the memory used by the given vector.

Random functions

void _nmod_vec_randtest(mp_ptr vec, flint_rand_t state, slong len, nmod_t mod)

Sets vec to a random vector of the given length with entries reduced modulo mod.n.

Basic manipulation and comparison

void _nmod_vec_set(mp_ptr res, mp_srcptr vec, slong len)

Copies len entries from the vector vec to res.

void _nmod_vec_zero(mp_ptr vec, slong len)

Zeros the given vector of the given length.

void _nmod_vec_swap(mp_ptr a, mp_ptr b, slong length)

Swaps the vectors a and b of length \(n\) by actually swapping the entries.

void _nmod_vec_reduce(mp_ptr res, mp_srcptr vec, slong len, nmod_t mod)

Reduces the entries of (vec, len) modulo mod.n and set res to the result.

flint_bitcnt_t _nmod_vec_max_bits(mp_srcptr vec, slong len)

Returns the maximum number of bits of any entry in the vector.

int _nmod_vec_equal(mp_srcptr vec, mp_srcptr vec2, slong len)

Returns~`1` if (vec, len) is equal to (vec2, len), otherwise returns~`0`.

Arithmetic operations

void _nmod_vec_add(mp_ptr res, mp_srcptr vec1, mp_srcptr vec2, slong len, nmod_t mod)

Sets (res, len) to the sum of (vec1, len) and (vec2, len).

void _nmod_vec_sub(mp_ptr res, mp_srcptr vec1, mp_srcptr vec2, slong len, nmod_t mod)

Sets (res, len) to the difference of (vec1, len) and (vec2, len).

void _nmod_vec_neg(mp_ptr res, mp_srcptr vec, slong len, nmod_t mod)

Sets (res, len) to the negation of (vec, len).

void _nmod_vec_scalar_mul_nmod(mp_ptr res, mp_srcptr vec, slong len, mp_limb_t c, nmod_t mod)

Sets (res, len) to (vec, len) multiplied by \(c\). The element \(c\) and all elements of \(vec\) are assumed to be less than \(mod.n\).

void _nmod_vec_scalar_mul_nmod_shoup(mp_ptr res, mp_srcptr vec, slong len, mp_limb_t c, nmod_t mod)

Sets (res, len) to (vec, len) multiplied by \(c\) using n_mulmod_shoup(). \(mod.n\) should be less than \(2^{\mathtt{FLINT\_BITS} - 1}\). \(c\) and all elements of \(vec\) should be less than \(mod.n\).

void _nmod_vec_scalar_addmul_nmod(mp_ptr res, mp_srcptr vec, slong len, mp_limb_t c, nmod_t mod)

Adds (vec, len) times \(c\) to the vector (res, len). The element \(c\) and all elements of \(vec\) are assumed to be less than \(mod.n\).

Dot products

int _nmod_vec_dot_bound_limbs(slong len, nmod_t mod)

Returns the number of limbs (0, 1, 2 or 3) needed to represent the unreduced dot product of two vectors of length len having entries modulo mod.n, assuming that len is nonnegative and that mod.n is nonzero. The computed bound is tight. In other words, this function returns the precise limb size of len times (mod.n - 1) ^ 2.

macro NMOD_VEC_DOT(res, i, len, expr1, expr2, mod, nlimbs)

Effectively performs the computation:

res = 0;
for (i = 0; i < len; i++)
    res += (expr1) * (expr2);

but with the arithmetic performed modulo mod. The nlimbs parameter should be 0, 1, 2 or 3, specifying the number of limbs needed to represent the unreduced result.

mp_limb_t _nmod_vec_dot(mp_srcptr vec1, mp_srcptr vec2, slong len, nmod_t mod, int nlimbs)

Returns the dot product of (vec1, len) and (vec2, len). The nlimbs parameter should be 0, 1, 2 or 3, specifying the number of limbs needed to represent the unreduced result.

mp_limb_t _nmod_vec_dot_rev(mp_srcptr vec1, mp_srcptr vec2, slong len, nmod_t mod, int nlimbs)

The same as _nmod_vec_dot, but reverses vec2.

mp_limb_t _nmod_vec_dot_ptr(mp_srcptr vec1, const mp_ptr *vec2, slong offset, slong len, nmod_t mod, int nlimbs)

Returns the dot product of (vec1, len) and the values at vec2[i][offset]. The nlimbs parameter should be 0, 1, 2 or 3, specifying the number of limbs needed to represent the unreduced result.