decimal-scaled 0.4.2

Const-generic base-10 fixed-point decimals (D9/D18/D38/D76/D153/D307) with integer-only transcendentals correctly rounded to within 0.5 ULP — exact at the type's last representable place. Deterministic across every platform; no_std-friendly.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89

//! Narrow-`GUARD` `sinh_strict` / `cosh_strict` / `tanh_strict` kernel
//! slot for `D307<SCALE>` with `SCALE ∈ 140..=160`.
//!
//! Sibling to [`crate::algos::trig::lookup_d153_s70_82_hyper`]. sinh /
//! cosh / tanh all share the pair `(eˣ, e⁻ˣ)`. The cross-cutting
//! `exp(-v) ≡ 1/exp(v)` identity is already applied at the
//! macro-emitted inherent shells; this slot adds the further win of
//! routing the single remaining `exp_fixed` through the Tang lookup at
//! `GUARD_NARROW = 8`.
//!
//! ## Algorithm
//!
//! ```text
//! ex  = tang_exp_fixed(v_w, w)
//! enx = 1 / ex             (exp(-v) identity)
//! sinh = (ex - enx) / 2
//! cosh = (ex + enx) / 2
//! tanh = (ex - enx) / (ex + enx)
//! ```
//!
//! ## Correctness
//!
//! Error budget at working scale `w = SCALE + 8`:
//!
//! - One `tang_exp_fixed` call: ≤ ~17 LSB-of-w (Tang reduction +
//!   Taylor).
//! - One `1/ex` divide (rounded half-to-even): ≤ 0.5 LSB.
//! - One add / sub: ≤ 1 LSB.
//! - One divide-by-2 (cosh / sinh) or one final divide (tanh): ≤ 0.5
//!   LSB.
//! - Final round-to-storage: ≤ 0.5 LSB.
//!
//! Total ≤ ~20 LSB-of-w = ~20·10⁻⁸ in storage units — many orders of
//! magnitude below half a storage ULP for any `SCALE ≤ 160`.

#![cfg(any(feature = "d307", feature = "wide", feature = "x-wide"))]

use crate::types::widths::wide_trig_d307 as core;
use crate::support::rounding::RoundingMode;
use crate::wide_int::Int1024;

/// Narrow guard for the SCALE 140..=160 hyperbolic slot — matches the
/// sibling Tang exp/ln guard so the per-thread `pow10_w` cache slot
/// is shared.
const GUARD_NARROW: u32 = crate::algos::exp::lookup_d307_s140_160_tang::GUARD_FOR_HYPER;

/// Joint `(ex, enx)` pair shared by sinh / cosh / tanh.
#[inline]
fn ex_enx(v: core::W, w: u32) -> (core::W, core::W) {
    let ex = crate::algos::exp::lookup_d307_s140_160_tang::tang_exp_fixed(v, w);
    let one_w = core::one(w);
    let enx = core::div(one_w, ex, w);
    (ex, enx)
}

/// `sinh_strict` for `D307<SCALE>` with `SCALE ∈ 140..=160`.
#[inline]
#[must_use]
pub(crate) fn sinh_strict<const SCALE: u32>(raw: Int1024, mode: RoundingMode) -> Int1024 {
    let w = SCALE + GUARD_NARROW;
    let v = core::to_work_w(raw, GUARD_NARROW);
    let (ex, enx) = ex_enx(v, w);
    let two = core::lit(2);
    let r = (ex - enx) / two;
    core::round_to_storage_with(r, w, SCALE, mode)
}

/// `cosh_strict` for `D307<SCALE>` with `SCALE ∈ 140..=160`.
#[inline]
#[must_use]
pub(crate) fn cosh_strict<const SCALE: u32>(raw: Int1024, mode: RoundingMode) -> Int1024 {
    let w = SCALE + GUARD_NARROW;
    let v = core::to_work_w(raw, GUARD_NARROW);
    let (ex, enx) = ex_enx(v, w);
    let two = core::lit(2);
    let r = (ex + enx) / two;
    core::round_to_storage_with(r, w, SCALE, mode)
}

/// `tanh_strict` for `D307<SCALE>` with `SCALE ∈ 140..=160`.
#[inline]
#[must_use]
pub(crate) fn tanh_strict<const SCALE: u32>(raw: Int1024, mode: RoundingMode) -> Int1024 {
    let w = SCALE + GUARD_NARROW;
    let v = core::to_work_w(raw, GUARD_NARROW);
    let (ex, enx) = ex_enx(v, w);
    let r = core::div(ex - enx, ex + enx, w);
    core::round_to_storage_with(r, w, SCALE, mode)
}