FLINT3.7.0-dev
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_mp_real_exp_reduced, _mp_real_sin_cos_reduced

Synopsis#include <flint/mp_real.h>
void _mp_real_exp_reduced(nn_ptr y, ulong * err, nn_srcptr t, slong n, flint_bitcnt_t r, int alg)source
void _mp_real_sin_cos_reduced(nn_ptr ysin, nn_ptr yg, ulong * err, nn_srcptr t, slong n, flint_bitcnt_t r, int alg)source

Evaluate exp⁡(t)\exp(t), respectively sin⁡t\sin t and g=1−cos⁡tg = 1 - \cos t, for a reduced argument (t,n)(t, n) with t<2−rt < 2^{-r}, r≥16r \ge 16 (r≥32r \ge 32 for alg = 1, 2). The exponential is written to n+1n + 1 limbs; the sine and gg are pure fractions written to nn limbs, but both buffers need room for n+1n + 1 limbs. err is the rigorous bound computed at run time, at most 96.

alg selects the method: 0 the tuned choice; 1 the rectangular splitting series (_mp_real_exp_rs, _mp_real_sin_cos_rs); 2 the sinh⁡\sinh series and a square root, resp. the sine series and g=1−1−sin⁡2tg = 1 - \sqrt{1 - \sin^2 t} (half the terms); 3 one bit-burst step, the leading slice of tt by binary splitting and the rest by the series; 4 the full bit-burst algorithm, asymptotically quasi-optimal. The cosine is returned as gg, which keeps the information near the top for the half-angle reconstructions that consume it. Except for the direct series, the arithmetic around the series and the binary splitting is mp_real_t ball arithmetic, so that the bound comes out rigorous. The binary splittings share the transforms of their power tables across the merges (see Power tables with precomputed transforms).

Guides#

Cite this page

The FLINT team, “_mp_real_exp_reduced, _mp_real_sin_cos_reduced (mp_real.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/mp_real/_mp_real_exp_reduced.html (generated 2026-11-02).