Trait DecimalConstants 

pub trait DecimalConstants: Sized {
    // Required methods
    fn pi() -> Self;
    fn tau() -> Self;
    fn half_pi() -> Self;
    fn quarter_pi() -> Self;
    fn golden() -> Self;
    fn e() -> Self;
    fn deg_per_rad() -> Self;
    fn rad_per_deg() -> Self;
    fn log10_2() -> Self;
    fn pi_with(mode: RoundingMode) -> Self;
    fn tau_with(mode: RoundingMode) -> Self;
    fn half_pi_with(mode: RoundingMode) -> Self;
    fn quarter_pi_with(mode: RoundingMode) -> Self;
    fn golden_with(mode: RoundingMode) -> Self;
    fn e_with(mode: RoundingMode) -> Self;
    fn deg_per_rad_with(mode: RoundingMode) -> Self;
    fn rad_per_deg_with(mode: RoundingMode) -> Self;
    fn log10_2_with(mode: RoundingMode) -> Self;
}

Well-known mathematical constants available on every decimal width (D18 / D38 / D76 / D153 / D307).

Import this trait to call D38s12::pi(), D76::<35>::e(), etc.

All returned values are computed from a raw integer reference at the tier’s maximum storage precision (75 digits for D18/D38 and D76; 153 for D153; 307 for D307) without passing through f64, then rescaled down to the caller’s SCALE with half-to-even rounding. The result is within 0.5 ULP of the canonical decimal expansion at every supported scale on every width.

The one situation where a method does not return a value is when the constant’s magnitude exceeds the type’s storage range at the caller’s SCALE — e.g. D38<38>::pi() would need 3.14 × 10³⁸, which exceeds i128::MAX ≈ 1.7×10³⁸. The method panics with a clear “constant out of storage range” message in that case.

Crossing into f64

to_f64() is itself correctly rounded, but it can only round to the decimal value the type holds — not to the underlying ideal constant. f64 carries ~15.95 decimal digits of mantissa, so any constant produced at SCALE < 15 is intrinsically coarser than the f64 grid: D38<12>::pi().to_f64() lands ~466 ULPs from std::f64::consts::PI, because the 12-digit decimal rounds differently than the closest-f64 to true π. At SCALE ≥ 15 the round-trip is bit-exact for these constants (the decimal value has enough digits to disambiguate the f64 grid).

Practical rule for downstream code that crosses into f64 — CAD bulge-arc tessellation, OpenGL/GLSL, hardware drivers — and uses the f64 value to count, bucket, or seed a fixed-iteration loop: source mathematical constants from std::f64::consts directly at the boundary rather than going through Decimal::pi().to_f64(). Otherwise pick a SCALE of 15 or more so the decimal value can round-trip to the canonical f64.

Required Methods

fn pi() -> Self

Pi (~3.14159265…). One half-turn in radians.

Source: ISO 80000-2 / OEIS A000796. Rescaled per-tier (see the module-level table) to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn tau() -> Self

Tau (~6.28318530…). One full turn in radians.

Defined as 2 * pi. Rescaled per-tier (see the module-level table) to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn half_pi() -> Self

Half-pi (~1.57079632…). One quarter-turn in radians.

Defined as pi / 2. Rescaled per-tier (see the module-level table) to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn quarter_pi() -> Self

Quarter-pi (~0.78539816…). One eighth-turn in radians.

Defined as pi / 4. Rescaled per-tier (see the module-level table) to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn golden() -> Self

The golden ratio (~1.61803398…). Dimensionless.

Defined as (1 + sqrt(5)) / 2. Source: OEIS A001622. Rescaled per-tier (see the module-level table) to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn e() -> Self

Euler’s number (~2.71828182…). Dimensionless.

Source: OEIS A001113. Rescaled per-tier (see the module-level table) to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn deg_per_rad() -> Self

Degrees per radian (~57.29577951…). The factor 180/π: multiply a radian measure by this to convert it to degrees.

Source: the oracle value of 180/π. Sourced per-scale from the constant table to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn rad_per_deg() -> Self

Radians per degree (~0.01745329…). The factor π/180: multiply a degree measure by this to convert it to radians.

Source: the oracle value of π/180. Sourced per-scale from the constant table to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn log10_2() -> Self

Base-10 logarithm of 2 (~0.30103…). The bit-to-digit factor: a value’s decimal-digit count is about bit_length * log10(2), so this scales between binary and decimal magnitudes.

Source: the oracle value of log(2)/log(10). Sourced per-scale from the constant table to the caller’s SCALE via the crate-default rounding mode.

Precision

N/A: constant value, no arithmetic performed.

fn pi_with(mode: RoundingMode) -> Self

pi() under the supplied rounding mode.

fn tau_with(mode: RoundingMode) -> Self

tau() under the supplied rounding mode.

fn half_pi_with(mode: RoundingMode) -> Self

half_pi() under the supplied rounding mode.

fn quarter_pi_with(mode: RoundingMode) -> Self

quarter_pi() under the supplied rounding mode.

fn golden_with(mode: RoundingMode) -> Self

golden() under the supplied rounding mode.

fn e_with(mode: RoundingMode) -> Self

e() under the supplied rounding mode.

fn deg_per_rad_with(mode: RoundingMode) -> Self

deg_per_rad() under the supplied rounding mode.

fn rad_per_deg_with(mode: RoundingMode) -> Self

rad_per_deg() under the supplied rounding mode.

fn log10_2_with(mode: RoundingMode) -> Self

log10_2() under the supplied rounding mode.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors

impl<const N: usize, const SCALE: u32> DecimalConstants for D<Int<N>, SCALE>