Malachite for Users of Other Libraries

These pages map the functions of established arithmetic libraries onto their Malachite counterparts, section by section, following the organization of each library’s manual. They are meant to be read in two directions: if you are porting code, look up the function you are using and find what to write instead; if you are wondering what Malachite is still missing, look for the rows marked ✗, which are the ones it is committed to filling in.

GMP

• Integers: the mpz_t type, mapped onto Natural and Integer.
• Rationals: the mpq_t type, mapped onto Rational.

GMP’s floating-point type, mpf_t, will not get a page of its own. GMP’s manual steers new projects toward MPFR, and Malachite’s Float follows MPFR, so the float mapping belongs with the MPFR page.

FLINT

• Integers: the fmpz_t type, mapped onto Natural and Integer.
• Integers mod n: the fmpz_mod.h module, mapped onto the Mod* traits over Natural residues.
• Rationals: the fmpq_t type, mapped onto Rational.
• Gaussian integers: the fmpzi_t type, mapped onto GaussianInteger.
• Integer polynomials: the fmpz_poly_t type, mapped onto IntegerPolynomial. All 48 sections of fmpz_poly.h are mapped.
• Rational polynomials: the fmpq_poly_t type, mapped onto RationalPolynomial. All 32 sections of fmpq_poly.h are mapped.
• Modular polynomials: the fmpz_mod_poly_t type — polynomials over the integers mod \(n\) — mapped onto NaturalPolynomial. All 34 sections of fmpz_mod_poly.h are mapped.
• Word-sized modular polynomials: the nmod_poly_t type — polynomials over the integers mod \(n\), for an \(n\) that fits in a machine word — mapped onto UnsignedPolynomial. All 42 sections of nmod_poly.h are mapped.
• Integer vectors: the fmpz_vec.h module, mapped onto IntegerVector. All 15 sections of fmpz_vec.h are mapped.
• Rational vectors: the fmpq_vec.h module, mapped onto RationalVector. All 8 sections of fmpq_vec.h are mapped.
• Integer vectors mod n: the fmpz_mod_vec.h module, mapped onto NaturalVector with the Mod* traits. All 5 sections of fmpz_mod_vec.h are mapped.
• Word-sized integer vectors mod n: the nmod_vec.h module, mapped onto UnsignedVector with the Mod* traits. All 7 sections of nmod_vec.h are mapped.
• Arithmetic functions: the arith.h module, which computes number-theoretic and combinatorial sequences.

FLINT modules not listed here have no page.

MPFR

• Floats: the mpfr_t type, mapped onto Float.

num

• Integers: num-bigint’s BigUint and BigInt, mapped onto Natural and Integer.
• Rationals: num-rational’s Ratio<T> and BigRational, mapped onto Rational.
• Traits: the num-traits and num-integer trait crates, with num-iter’s ranges, mapped onto malachite-base’s generic vocabulary.

num-complex has no page: Malachite has no complex type for it to map onto.

Azurite

• Naturals: the AzNat type, Azurite’s formally verified multi-limb natural number, mapped onto Natural.
• Integers: the AzInt type, mapped onto Integer.
• Integers modulo a power of 2: the AzZModPow2 k type, mapped onto the mod_power_of_2_* operations of Natural.
• Integers modulo a natural: the AzZMod m type, mapped onto the mod_* operations of Natural.
• Rationals: the AzRat type, mapped onto Rational.
• Floats: the AzFloat type, mapped onto Float.

Azurite’s polynomial and matrix types will get pages as they are mapped.