nmod_vec.h

Returns an array of len limbs allocated with flint_malloc. The entries are not initialised.

Frees an array allocated with _nmod_vec_init.

Sets the entries of vec to integers chosen uniformly at random in [0, n).

Sets the entries of vec to values of n_randtest reduced modulo n. With probability 1/2 the vector is made sparse. Intended for test code.

Copies the entries of vec to res.

Sets the entries of vec to zero.

Swaps the entries of a and b one by one.

_nmod_vec_equal returns 1 if the two vectors have the same entries and 0 otherwise. _nmod_vec_is_zero returns 1 if every entry is zero and 0 otherwise.

Returns the largest bit length of an entry of vec, or 0 if all entries are zero. The entries need not be reduced.

Sets each entry of res to the corresponding entry of vec reduced modulo n. The entries of vec may be any words.

Prints a header line, then the entries in brackets, each padded to the number of decimal digits of n. _nmod_vec_fprint_pretty returns a positive value on success and a nonpositive value on a write error. Like all functions with a FILE argument, it is declared only if <stdio.h> is included before the FLINT headers.

The same as _nmod_vec_fprint_pretty, writing to stdout and f respectively.

Sets res to the entry-wise sum or difference of vec1 and vec2.

Sets res to the entry-wise negation of vec.

Sets res to c times vec. All require c < n. The first function chooses among the others. _shoup requires n < 2^{\mathtt{FLINT\_BITS} - 1} and _redc requires n odd.

Adds c times vec to res. All require c < n. The first function chooses among the others. _shoup requires n < 2^{\mathtt{FLINT\_BITS} - 1}.

Sets each entry of res to the inverse of the corresponding entry of vec. Raises a FLINT_IMPINV exception if an entry is not invertible. The first three use a single modular inversion. _shoup requires n < 2^{\mathtt{FLINT\_BITS} - 1}. _naive inverts each entry separately. All four allow res to be the same array as vec.

_nmod_vec_dot_params returns parameters for dot products of length at most len modulo n. The others return \sum_{i=0}^{\mathit{len}-1} a_i b_i \bmod n, where a_i is vec1[i] (vec1[i * stride1] for the strided version) and b_i is vec2[i], vec2[len - 1 - i], vec2[i][offset] or vec2[i * stride2] respectively. params must come from _nmod_vec_dot_params with the same modulus and a length at least len.

Returns the number of limbs (0 to 3) of \mathit{len} \, (n - 1)^2, the largest possible unreduced dot product of length len. The second version reads the answer off params, which must have been computed for this len and mod.

Dot product kernel that sums in one limb. Requires the unreduced sum \sum_i a_i b_i to be less than 2^{\mathtt{FLINT\_BITS}}, and on 64-bit machines with AVX2 also n \le 2^{32}.

Dot product kernel for n a power of two: sums in one limb modulo 2^{\mathtt{FLINT\_BITS}}, which n divides. No condition on the length.

Dot product kernel for 64-bit machines that keeps the unreduced sum as h \, 2^{56} + \ell in two words and folds h in with pow2_precomp = 2^{56} \bmod n. Requires n \le 1515531528 and a bound on the length; see splitting at bit 56.

Dot product kernel for n \le 2^{\mathtt{FLINT\_BITS}/2} that adds one-limb products into a two-limb sum. On 64-bit machines with AVX2, _nmod_vec_dot2_half instead splits each product at bit 56, needs pow2_precomp = 2^{56} \bmod n and has a length limit; see splitting each product.

Dot product kernel that adds two-limb products into a two-limb sum. Requires the unreduced sum \sum_i a_i b_i to be less than 2^{2 \mathtt{FLINT\_BITS}}.

Dot product kernel that adds blocks of 8 products in two limbs and the block sums in three limbs. Requires 8 (n - 1)^2 < 2^{2 \mathtt{FLINT\_BITS}}, that is n \le 6521908912666391107 \approx 2^{62.5} on 64-bit machines.

Dot product kernel that adds each product into a three-limb sum. No conditions.

AVX512-IFMA dot product kernel for n \le 2^{52}. Requires the unreduced sum \sum_i a_i b_i to be less than 2^{2 \mathtt{FLINT\_BITS}}. Calls the corresponding _nmod_vec_dot2 function when IFMA is not available or the length is below FLINT_NMOD_VEC_DOT_U52_MIN_LEN.

AVX512-IFMA dot product kernel for any n and any length. Calls the corresponding _nmod_vec_dot3 function when IFMA is not available.

AVX2 or AVX-512 dot product kernel for any n and any length, on 64-bit machines. Calls the corresponding _nmod_vec_dot3 function when AVX2 is not available.

Sets r_i \gets r_i + c \, v_i for 0 \le i < \mathit{len} without reduction, where v_i is vec[i] and r_i is the single limb res[i]. Requires c, v_i < 2^{\mathtt{FLINT\_BITS}/2} and r_i + c v_i < 2^{\mathtt{FLINT\_BITS}}. The AVX2 version is only declared on 64-bit machines with AVX2, where the first function uses it from length 16 on.

Sets r_i \gets r_i + c \, v_i for 0 \le i < \mathit{len} without reduction, where v_i is vec[i] and r_i is the two-limb integer stored least significant limb first at res + 2 i. Requires r_i + c v_i < 2^{2 \mathtt{FLINT\_BITS}}. The _halflimb version also requires c v_i < 2^{\mathtt{FLINT\_BITS}}.

Sets r_i \gets r_i + c \, v_i for 0 \le i < \mathit{len} without reduction, where v_i is vec[i] and r_i is the three-limb integer stored least significant limb first at res + 3 i. Requires r_i + c v_i < 2^{3 \mathtt{FLINT\_BITS}}.