FLINT3.7.0-dev
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decball_pi, decball_exp, decball_expm1, decball_log, decball_log1p, decball_sin, decball_cos, decball_sin_cos, decball_tan, decball_asin, decball_acos, decball_atan, decball_atan2, decball_sinh, decball_cosh, decball_sinh_cosh, decball_tanh, decball_asinh, decball_acosh, decball_atanh, decball_pow

Synopsis#include <flint/decimal.h>
int decball_pi(decball_t res, gr_ctx_t ctx)source
int decball_exp(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_expm1(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_log(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_log1p(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_sin(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_cos(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_sin_cos(decball_t res1, decball_t res2, const decball_t x, gr_ctx_t ctx)source
int decball_tan(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_asin(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_acos(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_atan(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_atan2(decball_t res, const decball_t y, const decball_t x, gr_ctx_t ctx)source
int decball_sinh(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_cosh(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_sinh_cosh(decball_t res1, decball_t res2, const decball_t x, gr_ctx_t ctx)source
int decball_tanh(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_asinh(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_acosh(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_atanh(decball_t res, const decball_t x, gr_ctx_t ctx)source
int decball_pow(decball_t res, const decball_t x, const decball_t y, gr_ctx_t ctx)source

The elementary functions of balls: enclosures of the function values at every point of the input balls, with midpoints rounded to the context precision. The other special functions are available through the generic gr methods.

They are computed by a rigorous roundtrip through arb: the input balls are converted to arb balls, the gr method of the arb ring is evaluated at a precision corresponding to the context precision, and the results are converted back, with the conversion errors added to the radii. A domain error (as \log of a ball containing zero) returns GR_UNABLE, or GR_DOMAIN when the whole ball lies outside the domain.

Guides#

Cite this page

The FLINT team, “decball_pi, decball_exp, decball_expm1, decball_log, decball_log1p, decball_sin, decball_cos, decball_sin_cos, decball_tan, decball_asin, decball_acos, decball_atan, decball_atan2, decball_sinh, decball_cosh, decball_sinh_cosh, decball_tanh, decball_asinh, decball_acosh, decball_atanh, decball_pow (decimal.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/decimal/decball_pi.html (generated 2026-10-20).