5.16 Internals

A limb means the part of a multi-precision number that fits in a single word. Usually a limb contains 32 or 64 bits. The C data type for a limb is mp_limb_t.

The mpfr_t type is internally defined as a one-element array of a structure, and mpfr_ptr is the C data type representing a pointer to this structure. The mpfr_t type consists of four fields:

• The _mpfr_prec field is used to store the precision of the variable (in bits); this is not less than MPFR_PREC_MIN.
• The _mpfr_sign field is used to store the sign of the variable.
• The _mpfr_exp field stores the exponent. An exponent of 0 means a radix point just above the most significant limb. Non-zero values n are a multiplier 2^n relative to that point. A NaN, an infinity and a zero are indicated by special values of the exponent field.
• Finally, the _mpfr_d field is a pointer to the limbs, least significant limbs stored first. The number of limbs in use is controlled by _mpfr_prec, namely ceil(_mpfr_prec/mp_bits_per_limb). Non-singular (i.e., different from NaN, Infinity or zero) values always have the most significant bit of the most significant limb set to 1. When the precision does not correspond to a whole number of limbs, the excess bits at the low end of the data are zeros.