Rounding Rules for Conversions

As a general rule, all conversions between unrelated types are performed using basic arithmetic operations, therefore conversions are either exact, or follow the same rounding rules as arithmetic for the type in question.

The following table summarises the situation for conversions from native types:

Backend	Rounding Rules
cpp_int	Conversions from integer types are exact if the target has sufficient precision, otherwise they truncate to the first 2^MaxBits bits (modulo arithmetic). Conversions from floating-point types are truncating to the nearest integer.
gmp_int	Conversions are performed by the GMP library except for conversion from `long double` which is truncating.
tom_int	Conversions from floating-point types are truncating, all others are performed by libtommath and are exact.
gmp_float	Conversions are performed by the GMP library except for conversion from `long double` which should be exact provided the target type has as much precision as a `long double`.
mpfr_float	All conversions are performed by the underlying MPFR library.
cpp_dec_float	All conversions are performed using basic arithmetic operations and are truncating.
gmp_rational	See gmp_int
cpp_rational	See cpp_int
tommath_rational	See tom_int