Sdcb.Arithmetic 1.1.0

Sdcb.Arithmetic

English | 中文

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.

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.

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

If the WeChat QR code has expired, join the QQ group .NET骚操作 495782587.

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.