decimal_ctx_set_prec, decimal_ctx_set_rnd, decimal_ctx_set_rnd_im, decimal_ctx_set_rad_prec, decimal_ctx_set_exp_limits, decimal_ctx_set_flags

In a complex floating-point context, real parts are rounded in the mode set by decimal_ctx_set_rnd, which also resets the mode for imaginary parts, and decimal_ctx_set_rnd_im subsequently changes the mode for imaginary parts alone. The imaginary rounding mode is ignored in the other contexts.

Through the generics interface, gr_ctx_has_real_prec is true and gr_ctx_set_real_prec and gr_ctx_get_real_prec are supported with the precision measured in bits: setting $p$ bits selects $\lceil p \log_{10} 2 \rceil$ digits, and a context with $d$ digits reports $\lfloor d \log_2 10 \rfloor - 1$ bits (directed rounding to $d$ digits has a relative error up to $10^{1-d}$, slightly more than that of $d \log_2 10$ bits). This lets generic algorithms that take a precision in bits (series expansions, linear algebra with adaptive precision) work with decimal contexts. Since they assume radix-2 semantics, their results need not be what they would be for binary types, but they remain correct, since all decimal operations return correctly rounded results or rigorous enclosures.

@misc{flint-doc-decimal-decimal-ctx-set-prec,
  author       = {{The FLINT team}},
  title        = {{decimal\_ctx\_set\_prec, decimal\_ctx\_set\_rnd, decimal\_ctx\_set\_rnd\_im, decimal\_ctx\_set\_rad\_prec, decimal\_ctx\_set\_exp\_limits, decimal\_ctx\_set\_flags (decimal.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/decimal/decimal_ctx_set_prec.html},
  note         = {Generated 2026-11-02}
}