GitHub - lifthrasiir/libbeef: Beeg float library, a Rust port of Fabrice Bellard's libbf · GitHub
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🥩 libbeef
A Rust translation of Fabrice Bellard's libbf —<br>a tiny arbitrary-precision floating-point library. The name stands for "Beeg<br>Float".
Full IEEE 754 semantics: signed zeros, NaN, infinities, configurable exponent<br>width, subnormals, all five rounding modes, all five status flags.
Transcendental functions: exp, log, pow, sin, cos, tan, atan, atan2, asin, acos.
Decimal floating point (BigDecimal) with independent base-10 arithmetic.
no_std compatible (requires alloc).
Pure Rust with zero dependencies.
Quick example
fn main() {<br>let a: Quad = "3.14159265358979323846".parse().unwrap();<br>let b: Quad = "2.71828182845904523536".parse().unwrap();<br>let result = (a * b).sin();<br>println!("{result}");<br>// 0.773942685266708278263054855332479932...<br>}">use libbeef::format::formats;<br>use libbeef::Float;
type Quad = Floatformats::Binary128>;
fn main() {<br>let a: Quad = "3.14159265358979323846".parse().unwrap();<br>let b: Quad = "2.71828182845904523536".parse().unwrap();<br>let result = (a * b).sin();<br>println!("{result}");<br>// 0.773942685266708278263054855332479932...
Float pairs a value with a compile-time format, so * and .sin() use<br>128-bit precision and round-to-nearest-even automatically — no format argument<br>at every call site.
Performance
libbeef implements the same algorithms as the C libbf: NTT-based multiplication,<br>Newton iteration for division/sqrt, and AGM/binary-splitting for<br>transcendentals. The asymptotic complexity is optimal for each operation class:
Operation class<br>Complexity<br>Algorithm
add, sub, cmp<br>O(n)<br>Linear scan
mul<br>O(n log n)<br>Number-theoretic transform
div, sqrt<br>O(M(n))<br>Newton iteration over NTT mul
exp, log, sin, …<br>O(M(n) · log n)<br>AGM / binary splitting
Empirically (full data in docs/benchmark-report.md),<br>libbeef tracks the C libbf's throughput with constant-factor overhead from Rust's<br>bounds checking and allocation model:
op<br>256 bits<br>30 000 bits<br>300 000 bits<br>vs libbf<br>vs rug (GMP/MPFR)
mul<br>6.7<br>84<br>100 ns/limb<br>1.3–2.0×<br>0.9–1.3×
div<br>17.3<br>515<br>659 ns/limb<br>1.1–1.4×<br>2.6–3.5×
sqrt<br>38.3<br>384<br>597 ns/limb<br>1.2–1.3×<br>3.2–4.3×
sin<br>1051<br>— ns/limb<br>0.7× (faster)<br>3.6×
The mul row is the most informative: a quadratic algorithm would show<br>~10× growth per decade of operand size (47 → 469 → 4688 limbs), but libbeef grows<br>4.2× then 1.2× — the O(n log n) NTT envelope, the same shape as the C<br>original. At 300k bits libbeef is ~2× libbf and 1.3× GMP, while being 4× faster<br>than num-bigint's schoolbook/Toom multiplication.
For transcendentals , libbeef matches or beats the C libbf on sin/cos/tan/pow<br>and is within 15% on log/atan. The uniform 3–5× gap to MPFR is algorithmic<br>(MPFR uses different, better algorithms for these functions; the C libbf shows<br>the same gap).
Division and sqrt show a larger constant-factor gap to GMP/MPFR (~3×). This is<br>an inherent property of libbf's Newton-reciprocal approach vs. GMP's tuned<br>divide-and-conquer — the same ratio appears in the C original.
Why libbeef?
1. Pure Rust, no system dependencies. rug/GMP requires a C compiler, system<br>GMP/MPFR libraries, and a build script that probes the host. libbeef is a single<br>cargo add with no build.rs, -lm, nor pkg-config. It builds on any<br>target rustc supports — including WASM, embedded, and cross-compilation — with<br>zero configuration.
2. Small binary footprint. With GMP/MPFR statically linked, a trivial<br>program that multiplies two numbers and computes sin produces:
Library<br>Binary size (stripped)
libbeef<br>482 KiB
num-bigint (integers only, no trig)<br>448 KiB
malachite (integers only, no trig)<br>658 KiB
rug (GMP + MPFR...