fft_small_export_mpn_signed_low, fft_small_export_mpn_signed_window
#include <flint/fft_small.h>void fft_small_export_mpn_signed_low(ulong * z, ulong zn, fft_small_op_t X, ulong nslots, const fft_small_plan_t P)sourcevoid fft_small_export_mpn_signed_window(ulong * z, ulong zn, fft_small_op_t X, ulong nslots, ulong lo_limbs, const fft_small_plan_t P)sourceWrite to (z, z_n) the limbs [\mathtt{lo\_limbs}, \mathtt{lo\_limbs} + z_n) of the two's complement value of the signed reconstruction, without resolving the sign; _low is the case lo_limbs = 0, which is the residue modulo B^{z_n} and exact. The value need not fit in the window.
Only the slots that start below limb \mathtt{lo\_limbs} + z_n are read, since carries and borrows only propagate upwards. For lo_limbs > 0 the slots below the first one that can reach limb lo_limbs are dropped as in the truncated export, and the window is within one unit of the exact one. This holds even if those slots hold arbitrary values, as the aliased slots of a cyclic window plan do, because every lifted slot is less than P/2 in absolute value.
The FLINT team, “fft_small_export_mpn_signed_low, fft_small_export_mpn_signed_window (fft_small.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fft_small/fft_small_export_mpn_signed_low.html (generated 2026-10-20).
@misc{flint-doc-fft-small-fft-small-export-mpn-signed-low,
author = {{The FLINT team}},
title = {{fft\_small\_export\_mpn\_signed\_low, fft\_small\_export\_mpn\_signed\_window (fft\_small.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fft_small/fft_small_export_mpn_signed_low.html},
note = {Generated 2026-10-20}
}