Expand description
ARPFloat is an implementation of arbitrary precision
floating point data
structures and utilities. The library can be used to emulate existing
floating point types, such as FP16, FP32 or FP128, and create new
floating-point types that scale to hundreds of digits, and perform very
accurate calculations. The library contains mathematical functions such as
log, exp, sin, cos, tan, and constants such as pi and e
In ARPFloat the rounding mode is a part of the type-system, and this solves
a number of problem that show up when using the global rounding flag that’s
defined in fenv.h.
##no_std The library can be built without the standard library.
Example
use arpfloat::Float;
use arpfloat::FP128;
// Create the number '5' in FP128 format.
let n = Float::from_f64(5.).cast(FP128);
// Use Newton-Raphson to find the square root of 5.
let mut x = n.clone();
for _ in 0..20 {
x += (&n / &x)/2;
}
println!("fp128: {}", x);
println!("fp64: {}", x.as_f64());The program above will print this output:
fp128: 2.2360679774997896964091736687312763
fp64: 2.23606797749979
The library also provides API that exposes rounding modes, and low-level operations.
use arpfloat::FP128;
use arpfloat::RoundingMode::NearestTiesToEven;
use arpfloat::Float;
let x = Float::from_u64(FP128, 1<<53);
let y = Float::from_f64(1000.0).cast(FP128);
let val = Float::mul_with_rm(&x, &y, NearestTiesToEven);View the internal representation of floating point numbers:
use arpfloat::Float;
use arpfloat::FP16;
let fp = Float::from_i64(FP16, 15);
fp.dump(); // Prints FP[+ E=+3 M=11110000000]
let m = fp.get_mantissa();
m.dump(); // Prints 11110000000Control the rounding mode for type conversion:
use arpfloat::{FP16, FP32, RoundingMode, Float};
let x = Float::from_u64(FP32, 2649); // Load an FP32 Value.
let b = x.cast_with_rm(FP16, RoundingMode::Zero); // Convert to FP16.
println!("{}", b); // Prints 2648!Define new float formats and use high-precision transcendental functions:
use arpfloat::{Float, Semantics, RoundingMode};
// Define a new float format with 120 bits of accuracy, and dynamic range
// of 2^10.
let sem = Semantics::new(10, 120, RoundingMode::NearestTiesToEven);
let pi = Float::pi(sem);
let x = Float::exp(&pi);
println!("e^pi = {}", x); // Prints 23.1406926327792....Floating point numbers can be converted to Continued Fractions that approximate the value.
use arpfloat::{Float, FP256, RoundingMode};
let ln = Float::ln2(FP256);
println!("ln(2) = {}", ln);
for i in 1..20 {
let (p,q) = ln.as_fraction(i);
println!("{}/{}", p.as_decimal(), q.as_decimal());
}The program above will print this output:
ln(2) = .6931471805599453094172321214581765680755001343.....
0/1
1/1
2/3
7/10
9/13
61/88
192/277
253/365
445/642
1143/1649
1588/2291
2731/3940
....
Structs
- This is an arbitrary-size unsigned big number implementation. It is used to store the mantissa of the floating point number. The BigInt data structure is backed by
Vec<u64>, and the data is heap-allocated. BigInt implements the basic arithmetic operations such as add, sub, div, mul, etc. - This is the main data structure of this library. It represents an arbitrary-precision floating-point number.
- Controls the semantics of a floating point number with: ‘precision’, that determines the number of bits, ‘exponent’ that controls the dynamic range of the number, and rounding mode that controls how rounding is done after arithmetic operations.
Enums
- Defines the supported rounding modes. See IEEE754-2019 Section 4.3 Rounding-direction attributes.
Constants
- Predefined FP16 float with 5 exponent bits, and 10 mantissa bits.
- Predefined FP32 float with 8 exponent bits, and 23 mantissa bits.
- Predefined FP64 float with 11 exponent bits, and 52 mantissa bits.
- Predefined FP128 float with 15 exponent bits, and 112 mantissa bits.
- Predefined FP256 float with 19 exponent bits, and 236 mantissa bits.