Numbers and precision

Inputs

Wherever a number is expected, sdpb-python accepts

Type	Interpretation
int, bool	exact
str	decimal ("1e-30", "0.1") or a fraction ("1/12"); passed to SDPB verbatim
fractions.Fraction	exact, rendered at the working precision
float	by its shortest round-trip decimal: 0.1 means one tenth, not the binary double
mpmath.mpf	exact
anything with a decimal str() (sympy numbers, numpy scalars, Decimal)	via mpmath.mpf(str(value))

The conversion happens in sdpb_python.numbers. Values cross into C++ as decimal strings and are parsed by GMP at the fixed precision.

Outputs

Every number in a Solution, SDPData or SampledMatrix is an mpmath.mpf (matrices are mpmath.matrix). They are created with exactly the solver’s precision (SDPB prints ceil(bits * log10(2)) + 1 digits, which identifies the binary value uniquely), independent of mpmath’s global precision at the time.

mpmath’s global context is left alone. To continue computing at full precision:

import mpmath
mpmath.mp.prec = 768                 # or: with mpmath.workprec(768): ...
gap = abs(solution.primal_objective - solution.dual_objective)

Arithmetic on the results at a lower mpmath.mp.prec silently rounds, as with any mpmath computation.

One precision per process

See Precision. In short: call sdpb_python.set_precision(bits) at the start of a script or notebook; a different precision needs a new process.

GMP rounds the requested precision up to whole limbs, so sdpb_python.precision() and Solution.precision report the value you asked for and the actual bits respectively; the actual value is never smaller.