gmp-d

D-language high-level wrapper for GNU MP (GMP) library that aims to be mostly compatible with std.bigint.BigInt and @safe pure nothrow @nogc except when converting to string.

Basics

• Integers (GMP's mpz_t) are wrapped in gmp.z.MpZ
• Rationals (GMP's mpq_t) are wrapped in gmp.q.MpQ

along with most of their common operations implemented either as member functions, free functions or both.

Sample Usage

MpZ

import gmp.z;

@safe pure nothrow @nogc:

unittest
{
    alias Z = MpZ;
    assert(Z.mersennePrime(15) == 2^^15 - 1);
    const a = 42.Z;
    const b = a.dup; // explicit copying required
}

MpQ

import gmp.q;

@safe pure nothrow @nogc:

unittest
{
    alias Q = MpQ;

    Q x = Q(-4, 6);

    assert(x.numerator == -4);
    assert(x.denominator == 6);

    x.canonicalize();

    assert(x.numerator == -2);
    assert(x.denominator == 3);

    assert(inverse(x) == Q(-3, 2));

    assert(Q(1, 2) + Q(1, 3) == Q(5, 6));
}

Value passing

Value semantics with explicit copying and move

For MpZ, copy construction is disabled by default to prevent inadvertent copying. Instead use f(move(z)) or f(z.move) (from std.algorithm.mutation) to pass by move or f(z.dup) to pass by explicit copy (via MpZ's member function .dup).

Value semantics with copy-on-write a la Phobos’ std.bigint.BigInt

Use Z (CopyableMpZ), for a drop-in-replacement for Phobos’ std.bigint.BigInt. For reference see https://dlang.org/phobos/std_bigint.html#.BigInt.

Mappings to GNU MP C library

Implementation is optimized through

• mapping of GMP's C macros into D inline functions that operate directly on the internal C-representations __mpz_struct and __mpq_struct,

• passing of MpZ-typed parameters as auto ref const in combination with conditional compilation for r-value MpZ passed parameters via __traits(isRef). This enables clever reuse of mpz_t instances when passed to __gmpz-functions. For instance, x + 42.Z can be lowered to

__gmpz_add(rhs._ptr, this._ptr, rhs._ptr);
return move(rhs);

in

opBinary!"+"()(auto ref const MpZ rhs)

Compilation Performance

Compilation is fast; DMD compiles gmp-d in about 0.1 seconds on a modern machine.

Run-time Performance

Wrapper is as light-weight as possible; Some D-functions directly access the internal C-datastructure exposed by the structs and macros in the C-headers of GNU GMP.

Limitations

Note that D's __traits(isRef) currently cannot be used to distinguish l-value from r-value passing of this. This severly limits the possibilities of using C++-style expression templates to realize lazy evaluation in operator overloading. If this limitation were to be fixed (probably via some introspection mechanism other than the trait isRef or non-struct-member operator overloading), this library could implement lowering of expressions such

Z result = base^^exp % modulo

to the builtin

__gmpz_powm(result._ptr, base._ptr, expr._ptr, modulo._ptr)

See the unittests for MpzAddExpr, MpzMulExpr, etc for details on how this currently can be implemented and verified (in ccc-version) with free functions such add and sub.

Future

There are more mpz_t- and mpq_t-functions that should be wrapped but these are good start.