Sdcb.Arithmetic

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Looking for the GMP/MPFR P/Invoke bindings (Sdcb.Arithmetic.Gmp / Sdcb.Arithmetic.Mpfr) that used to live in this repository? They moved to sdcb/Sdcb.Arithmetic.

High-performance, pure managed C# arbitrary-precision arithmetic with GMP/MPFR-class functionality and no native dependencies. It runs anywhere .NET 10 runs (x64, ARM64, AOT), uses AVX-512/AVX2/SSE/NEON where available, and falls back to portable code elsewhere.

Type	Models	Description
BigInt	GMP mpz_t	Immutable arbitrary-precision signed integer
BigRational	GMP mpq_t	Immutable rational, always canonical
Real	MPFR mpfr_t	Correctly-rounded binary floating point: five rounding modes, NaN/±∞/±0, 100+ functions

All three implement .NET generic math (IBinaryInteger<T>, INumber<T>, IBinaryFloatingPointIeee754<T>) and interoperate with System.Numerics.BigInteger.

Install

dotnet add package Sdcb.Arithmetic

Quick start

using Sdcb.Arithmetic;

// Integers (mpz)
BigInt a = BigInt.Parse("123456789012345678901234567890");
BigInt p = BigInt.Pow(2, 521) - 1;                  // Mersenne prime M521
bool prime = p.IsProbablePrime();                   // BPSW + Miller-Rabin
BigInt g = BigInt.Gcd(a, p);
BigInt m = BigInt.ModPow(a, p, BigInt.Pow(10, 30));
Console.WriteLine(p.ToString(16));                  // any base 2..62

// Rationals (mpq), always canonical
BigRational r = new BigRational(1, 3) + new BigRational(1, 6); // 1/2
double d = r.ToDouble();                            // correctly rounded

// Correctly-rounded floating point (mpfr)
Real.DefaultPrecision = 256;                        // bits
Real pi = Real.Pi();
Real y = Real.Sin(Real.Parse("1.5"));
Real z = Real.Exp(y, precision: 512, RealRounding.TowardPositive);
Console.WriteLine(z);                               // round-trip decimal output

Performance

AMD Ryzen 7 5800X (AVX2), .NET 10, operand sizes in 64-bit limbs. Full tables and methodology: docs/performance.md.

Operation	Speedup over BigInteger	Time vs native GMP 6.3 (lower is better)
Multiply	1.9–2.8× (≤ 16 limbs), 3.7–5× (32–2048), 7–28× (4096–65536)	1.3–1.6× (≥ 16 limbs)
Divide 2N/N	2.2–4.3× (16–4096 limbs), 5.9× (16384)	1.5–2.6×
Modular power	4.2–7×	1.3–2.8×
GCD	1.5–5.8×	0.9–1.4×
Add / sub / shift	2.5–11×	1.1–3.1×
Decimal ToString / Parse	up to 16× / 4× (large); ToString 0.9× at ≤ 4 limbs	0.5–1.9× / 0.6–1.4×

Real against native MPFR 4.2 (53–16384 bits, both sides correctly rounded): add/mul 1.3–2.5×, div/sqrt 1.3–3.3×, exp/sin/atan 0.9–1.8×, log/pow 1.6–2.7×.

Every BigInt operation is cross-checked against BigInteger and native GMP, and every Real function bit-for-bit against MPFR in all rounding modes.

Documentation

• Examples: 1,000,000 digits of π, RSA, rounding modes, generic math (also shipped as LINQPad samples in the NuGet package)
• Real: features and functions
• Generic math and conversion semantics
• GMP / MPFR → BigInt / Real API mapping
• Performance
• Design, algorithms and verification
• References

WeChat group

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License

MIT. Sdcb.Arithmetic is an independent C# implementation of published algorithms and contains no GMP or MPFR source code. Native GMP/MPFR are used only as black-box references for testing and benchmarking. See docs/references.md for the literature.