FLINT3.7.0-dev
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vec1d_reduce_to_pm1n, vec4d_reduce_to_pm1n, vec8d_reduce_to_pm1n, vec1d_reduce_to_pm1no, vec4d_reduce_to_pm1no, vec8d_reduce_to_pm1no

Synopsis#include <flint/machine_vectors.h>
vec1d vec1d_reduce_to_pm1n(vec1d a, vec1d n, vec1d ninv)source
vec4d vec4d_reduce_to_pm1n(vec4d a, vec4d n, vec4d ninv)
vec8d vec8d_reduce_to_pm1n(vec8d a, vec8d n, vec8d ninv)
vec1d vec1d_reduce_to_pm1no(vec1d a, vec1d n, vec1d ninv)source
vec4d vec4d_reduce_to_pm1no(vec4d a, vec4d n, vec4d ninv)
vec8d vec8d_reduce_to_pm1no(vec8d a, vec8d n, vec8d ninv)

Returns an integer r=a−qn≡a(modn)r = a - qn \equiv a \pmod n, with qq an approximation of a/na/n rounded to an integer, for an integer ∣a∣<253|a| < 2^{53} and an integer n≥4n \ge 4. The two functions are identical. The result satisfies ∣r∣<n/2+2|r| < n/2 + 2, hence ∣r∣<n|r| < n. On AVX2 the quotient is computed with round_mul, which with the magic constant needs ∣a∣/n≤251|a| / n \le 2^{51}; this is why n≥4n \ge 4 is required. AVX2 and NEON.

Cite this page

The FLINT team, “vec1d_reduce_to_pm1n, vec4d_reduce_to_pm1n, vec8d_reduce_to_pm1n, vec1d_reduce_to_pm1no, vec4d_reduce_to_pm1no, vec8d_reduce_to_pm1no (machine_vectors.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/machine_vectors/vec1d_reduce_to_pm1n.html (generated 2026-11-02).