gr_ctx_init_dfloat

The element size is $8(n + b)$ bytes, with $b = 1$ for balls and 0 otherwise, and twice that for the complex rings. The real ball ring reports itself as a field, ordered, real, inexact and non-canonical, like gr_ctx_init_real_arb, and the complex ball ring as an algebraically closed field like gr_ctx_init_complex_acb. The precision reported by gr_ctx_get_real_prec is $53n$ bits and cannot be changed.

With DFLOAT_STRONG, the arithmetic operations (add, sub, mul, sqr, div, inv, sqrt, rsqrt, exp, log, sin, cos, sin_cos, atan and the vector operations) canonicalise their results; this makes equal on plain numbers a comparison of values and costs up to 60% on the cheapest operations for $n = 3, 4$. With DFLOAT_FAST (balls only), products bound their rounding errors instead of tracking them exactly when both inputs are exact; this is slightly cheaper but loses exactness ($(2^{60} + 1) \cdot 3$ then gets a radius of about $2^{-46}$).

The rings implement only operations with native code: the arithmetic, the elementary functions documented below and their vector versions. Special functions such as gr_gamma and gr_zeta return GR_UNABLE; use an arb_t ring for them. The constants gr_pi, gr_euler and gr_catalan are table lookups. Conversions with gr_set_other exist between the dfloat rings and from and to arb_t, acb_t, fmpz and fmpq; see Ball semantics, nonfinite values and domains for the rules on nonfinite values and status codes.

@misc{flint-doc-dfloat-gr-ctx-init-dfloat,
  author       = {{The FLINT team}},
  title        = {{gr\_ctx\_init\_dfloat (dfloat.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/dfloat/gr_ctx_init_dfloat.html},
  note         = {Generated 2026-11-02}
}