decball_set, decball_set_round, decball_set_round2, decball_set_decfloat, decball_set_si, decball_set_ui, decball_set_fmpz, decball_set_fmpq, decball_set_d, decball_set_str, decball_set_fmpz_10exp_fmpz, decball_set_other, decball_set_arb, decball_get_arb, decball_get_fmpz, decball_get_fmpq, decball_get_d, decball_get_mid, decball_get_rad, decball_get_abs_ubound, decball_get_abs_lbound

An arb ball with an infinite or NaN midpoint is not a real number and converts with GR_DOMAIN respectively GR_UNABLE; one with an infinite radius converts to [0 \pm \infty]. Plain decimal literals are parsed exactly (then rounded); any other string goes through the generic expression parser, so "[mid +/- rad]" (the output format), "mid +/- rad", "+/- rad" and arithmetic expressions are accepted, and the same syntax works inside strings for polynomials, matrices and other objects over decimal balls. A radius smaller than 10^{emin} can only be parsed when underflow is allowed in the context. Since inf is not an element of the ring, the printed forms of balls with an infinite radius ("[m +/- inf]", "[+/- inf]") are parsed through set_interval_mid_inf rather than by evaluating inf. Algebraic numbers are converted with decball_set_qqbar, which gives an exact ball for an exactly representable value. The conversions to and from arb are rigorous (the radius accounts for all conversion errors) and handle arbitrarily large exponents by scaling with a power of ten. The conversion from arb is also tight: the midpoint is correctly rounded and the exact rounding error, bounded to the radius precision, is added to the radius, and an exact midpoint that is exactly representable at the context precision gives an exact ball even when its exponent is huge; when scaling in arb is used, the working precision is increased until the scaling error is negligible compared to the radius (unless this would require an unreasonable precision).